Facoltá di Ingegneria dei Sistemi
Dipartimento di Bioingegneria
Dottorato di Ricerca in Bioingegneria
Analysis of Cardio-Respiratory System
during Sleep and in some related
Pathologies
PhD Dissertation:
Martin Oswaldo Mendez Garcia
Advisor:
Professor Anna Maria Bianchi
Tutor:
Professor Sergio Cerutti
Judges:
Professor Thomas Penzel
Professor Pablo Laguna
XIX edition
2004-2007
Pubblication Data:
Analysis of Cardio-Respiratory System during Sleep
and in some related Pathologies
Martin Mendez
Politecnico di Milano
Dipartimento di Bioingegneria
P.zza Leonardo da Vinci 32
20133 Milano
e-mail:[email protected]
Question : What is Sleep?
Maharishi : How can you know sleep when you are
awake? The answer is to go to sleep and nd out what it is.
Question : But I can not it in this way
Maharishi : This question must be raised in sleep
Question : But I cannot raise the question then
Maharishi : So that is sleep .
Sri Kamana Maharishi
Acknowledgements
A Mis padres Raul y Lupe por darme su amor incondicional y sabiduria, a
mis hermanos Esti, Alonso, Carol, Vini y Angel por darme todo apoyo y amor.
I would like to thank to my supervisors Prof. Anna Maria Bianchi and
Prof. Sergio Cerutti. Your insight, advices, patience and good humor have
been invaluable. I would also like to thank Prof. Luca Mainardi, Prof.
Giuseppe Baselli, Prof. Gabriella Signorini and Prof. Penzel for their assistance and encouragement throughout my PhD.
Vorrei ringraziare con tutto il mio cuore a Salvatore Cappadona, Alessia
Fallica, Ezio Preatoni, Umberto Vitale, Elizabetta de Bernardi e Sivia Casarotto
per farmi sentire a casa, darmi la sua amicizia incondizionale, prendere cura
di me in tutto momento e per aprirmi le porte della loro casa. Specialmente
ai genitori di Salvo y Alessia che mi hanno fatto sentire parte di loro.
Tambien agradezco a Enrique y a Naibi por darme su alegria y estar
siempre cerca de mi.
Doy la gracias a Luisa, Terry, Lucia, Bereket y Davide por su gran compagnia y amistad, su gran apoyo y por todos esos momentos que me han
hecho feliz.
Agradezco a Manu, Valentina, Luca, Simona, Mari, Marco, Elena, Michele,
Federico, Katia, Mateo, Diego, Andrea, Alfonso, Soren y todos mi compagneros por hacer unico y alegre el lugar donde he pasado una gran etapa de
mi vida.
ii
A Limberg, Soa y Maria por darme su gran amistad y haberme dado
tanta fuerza y apoyo en los primeros meses de mi llegada en Italia, gracias
de todo Corazon.
A todos mis amigos que siempre han estado cerca de mi y que han hecho
posible realizar mi suegno de vivir en Europa y estudiar mi doctorado, por
ayudarme tanto tanto tanto: Poncho, Marrufo, Robert, Marcos, Enrique,
Angel, Sergio, Gaby, Carla, Valo, Ricardo y Jesus. A mis profesores Jaziri,
Salvador, Ramon, Oscar, Veronica, Joaquin, Emilio, Alfredo, Sonia, Raquel
y Tomas por su gran apoyo para realizar mi doctorado.
Agradezco a la persona que me ha dado todo su amor, mi piccola LENA.
A su familia por hacerme parte de ellos: Giani, Balburga, Marco, Pia, Luca,
Felice y Maia.
A mis peques Lupita, Bubu y Julis por haceme feliz, tambien agradezco
a Julio por darles todo su amor y darme su apoyo.
Quiero dar las gracias a mis dos tesistas y amigos Omar y Davide por
creer en mi y darme su gran amistad.
Por ultimo quiero agradecer a Salvo, Alessia, Ezio, Carla, Valo y Poncho
por estar siempre cerca de mi.
Finalmente quiero agradecer a CONACYT por darme todos los recursos
necesarios para realizar mi doctorado en el extranjero.
Publications
Research submitted and on preparation
1. On Arousal From Sleep, Time-Frequency Analysis (Submitted)
2. Time-Varying Analysis of the Heart Rate Variability in Obstructive
Sleep Apnea Patients (On Preparation).
3. Time-Varying Analysis of the Heart Rate Variability During Sleep (On
Preparation).
Proceedings
1. Anna M. Bianchi, Rita Paradiso, Martin O. Mendez, Gianni Loriga,
Pasquale Scilingo, Sergio Cerutti, Analysis Of Heart Rate And Respiration Variability Signals Obtained Through A Wearable System, International Conference MEDICON 2004X Mediterranean Conference
on Medical and Biological Engineering"Health in the Information Society".
2. MO. Méndez, A. M. Bianchi, S. Cerutti , Non stationary analysis of
heart rate variability during the obstructive sleep apnea, 26th Annual
International Conference of the IEEE Engineering in Medicine and Biology Society, 1-5 Settembre 2004, San Francisco, USA, vol 1 : pp
286- 289.
3. C Mantaras, M. Mendez, V. Patruno, N. Montano, A. M. Bianchi,
S. Cerutti ,Time-Varing Analysis of the Heart Rate Variability during
iv
Arousal from Sleep, 27th Annual International Conference of the IEEEEMBS, September 1-4 (2005), Shangai, China, vol 4 : pp 4427-4429.
4. Mendez M.O., Villantieri O. P., Bianchi A. M., Cerutti S, Sleep Analysis for Wearable Devices Applying Autoregressive Parametric Models,
27th Annual International Conference of the IEEE-EMBS, September
1-4 (2005), Shangai, China, vol 7 : pp 7353-7356.
5. AM Bianchi, OP Villantieri, MO Mendez, V Patruno, S Cerutti, N
Montano , Dierent Eects of CPAP and APAP Therapies on the
Autonomic Nervous System in OSA Patients, Computers in Cardiology,
september 25-28 (2005), Lyon, France.
6. S Puzzuoli, P Marcheschi, AM Bianchi, MO Mendez, D De Rossi,
L Landini, Remote Transmission and Analysis of Signals from Wearable Devices in Sleep Disorders Evaluation, Computers in Cardiology,
september 25-28 (2005), Lyon, France.
7. M. Mendez, O. Villantieri, A. M. Bianchi, N. Montano, V. Patrono,
S. Cerutti. Time-Frequency Analysis of the Heart Rate Variability in
Arousal from Sleep, 3ed European Medical and Biological Engineering
Conference (EMBEC), november 20-25 (2005) Prague, Czech Republic.
8. E Gil, MO Mendez, O Villantieri, J Mateo, JM Vergara, AM Bianchi,
P Laguna, Heart Rate Variability during Pulse Photoplethismography Decreased Amplitude Fluctuations and its correlation with Apneic
Episodes, Computers in Cardiology, september 17-20 (2006), Velencia,
Spain, pp 165-168.
9. MO Mendez, AM Bianchi, OP Villiantieri, S Cerutti,T Penzel, TimeVariant Spectral Analysis of the Heart Rate Variability during Sleep in
Healthy and Obstructive Sleep Apnoea Subjects, Computers in Cardiology, september 17-20 (2006), Velencia, Spain, pp 741-744.
10. Mendez M,. Bianchi A.M, Villantieri O, Cerutti S,Time-varying Analysis of the Heart Rate Variability during REM and Non REM Sleep
v
Stages, 28th Annual International Conference of the IEEE-EMBS,
September 1-4 (2006), NY,USA, 3576-3579.
11. MC Mantaras, MO Mendez, O Villiantieri, N Montano, V Patruno, AM
Bianchi, S Cerutti Non-Parametric and Parametric Time-Frequency
Analysis of HRV during Arousals from Sleep. Computers in Cardiology,
september 17-20 (2006), Velencia, Spain, pp 745-748
12. AM Bianchi, OP Villantieri, MO Mendez, V Patruno, S Cerutti, Signal
Processing and Feature Extraction for Sleep Evaluation in Wearable
Devices, 28th Annual International Conference of the IEEE-EMBS,
September 1-4 (2006), NY,USA,
vi
Contents
1 ABSTRACT
xi
2 INTRODUCTION
1
3 PHYSIOLOGY OF SLEEP
5
3.1
3.2
Overview of Sleep . . . . . . . . . . . . .
Physiologic processes during sleep . . . . .
3.2.1 Central nervous system . . . . . .
3.2.2 Autonomic nervous system (ANS)
3.2.3 Cardiovascular system . . . . . . .
3.2.4 Thermoregulatory process . . . . .
3.2.5 Respiratory system . . . . . . . . .
3.2.6 Biological Clock . . . . . . . . . .
4 SLEEP DISORDERS
4.1
4.2
4.3
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Obstructive Sleep Apnea (OSA) . . . . . . . . . . . . . . . . 25
Arousal from sleep . . . . . . . . . . . . . . . . . . . . . . . 35
Periodic Leg Movements . . . . . . . . . . . . . . . . . . . 36
5 HEART RATE VARIABILITY
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6 MATHEMATICAL APPROACHES
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6.1
6.2
Time-varying autoregressive models . . . . . . . . . . . . . . 48
Time-Frequency Distributions (TFD) . . . . . . . . . . . . . 56
7 PATTERN CLASSIFICATION
7.1
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K-Nearest Neighbor . . . . . . . . . . . . . . . . . . . . . . 64
Contents
7.2
Hidden Markov Models
7.2.1 Evaluation . . .
7.2.2 Decoding . . . .
7.2.3 Learning . . . .
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8 OBJECTIVE
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9 AUTONOMIC NERVOUS SYSTEM DURING SLEEP
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9.1
9.2
9.3
9.4
9.5
9.6
Protocol . . . . . . . . . .
Spectral analysis . . . . . .
Data analysis . . . . . . . .
Results . . . . . . . . . . .
9.4.1 Test series . . . . .
9.4.2 Experimental series
Discussion . . . . . . . . .
Conclusions . . . . . . . .
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10 DETECTION OF THE SLEEP STAGES
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10.1 Database Description . . . . . . . . . . . . . . . . .
10.2 Methods . . . . . . . . . . . . . . . . . . . . . . . .
10.2.1 Selection and Transformation of the Features
10.2.2 Hidden Markov Model . . . . . . . . . . . . .
10.2.3 Classication performance estimation . . . . .
10.3 Results . . . . . . . . . . . . . . . . . . . . . . . . .
10.4 Discussion . . . . . . . . . . . . . . . . . . . . . . .
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11 AROUSAL FROM SLEEP
11.1 Time-Frequency Distributions . . . . . . . .
11.2 Quantitative Analysis of the Time-Frequency
11.2.1 Synthetic Signal . . . . . . . . . . .
11.3 Method Development . . . . . . . . . . . .
11.4 Arousal from Sleep Data . . . . . . . . . .
11.4.1 Protocol . . . . . . . . . . . . . . .
11.4.2 Spectral analysis . . . . . . . . . . .
11.4.3 Data analysis . . . . . . . . . . . .
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Distributions
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ix
Contents
11.5 Application results . . . . . . . . . . . . . . . . . . . . . . . 126
11.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
11.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 134
12 AUTONOMIC NERVOUS SYSTEM DURING OBSTRUCTIVE
137
SLEEP APNEA
12.1
12.2
12.3
12.4
12.5
12.6
Protocol . . . .
Spectral analysis
Data analysis . .
Results . . . . .
Discussion . . .
Conclusions . .
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13 DETECTION OF OBSTRUCTIVE SLEEP APNEA
13.1 Database Description . . . . . . . . . . . . . . . . .
13.2 Methods . . . . . . . . . . . . . . . . . . . . . . . .
13.2.1 RR intervals correction . . . . . . . . . . . .
13.2.2 ECG and Derived Respiratory Signal (DRS) .
13.2.3 Features Sets . . . . . . . . . . . . . . . . .
13.2.4 Selection and Transformation of the Features
13.2.5 Classication performance estimation . . . . .
13.2.6 Post-Processing . . . . . . . . . . . . . . . .
13.3 Results . . . . . . . . . . . . . . . . . . . . . . . . .
13.4 Discussion . . . . . . . . . . . . . . . . . . . . . . .
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14 CONCLUSIONS
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Bibliography
184
Contents
x
1. Abstract
The propose of this study is to improve the understanding of how the different sleep stages during normal condition aect the autonomic nervous
system. Furthermore, this study pretends to describe the temporal evolution
of autonomic nervous system during both arousal from sleep and obstructive
sleep apnoea on a beat-by-beat basis resolution. The behavior of the autonomic nervous system will be evaluated from the heart rate variability due to
their very tie relationships. Most of the researches conducted until date, have
selected discrete stationary segments to evaluate the spectral components
of the heart rate variability by applying Fourier Transform. However, during
sleep and in its relate pathologies, the heart rate variability signal becomes
non-stationary. In order to overcome this problem this work applies suitable
spectral decomposition techniques to study the dynamic relationships of the
involved systems during sleep. In addition, this work focus on the study of
the spectral parameters in order to gain an idea of possible clinical applications for home diagnosis that could benet people all over world. Thus a
rough prior sleep diagnosis could generally avoid expensive and complicated
procedures of sleep evaluation.
The rst study in this thesis deals with the analysis of dynamic of
the Autonomic Nervous System during normal sleep time. Whole night
polysomnography records of 24 normal subjects were used. Dynamic of Autonomic Nervous System for whole sleep time was assessed by extracting the
R-R intervals extracted the Electrocardiogram data. A time-variant autoregressive model was used to obtain the spectral parameters of the Heart Rate
Variability signal. Sleep time was divided in REM-NREM stages. High frequency component presented larger values during NREM sleep than during
1. ABSTRACT
xii
REM sleep. In contrast, low frequency had he oppositive behavior. These
results suggest high participation of the vagal tone and low activation of
sympathetic ow during NREM sleep. Autonomic levels were reverted during REM. Time-variant autoregressive models demonstrated to be ne tool
in evaluating the dynamic changes of the Autonomic Nervous System during
sleep even during non-stationary conditions.
In the second study an algorithm was developed to classify the sleep
stages. Classication was based on the spectral parameters of Heart Rate
Variability signal. The classication goal was localized the time transitions
between NREM and REM sleep. The features for classication were extracted from the Heart Rate Variability by a time-varying autoregressive
model. Hidden Markov Models were used to nd the NREM - REM dynamics from Heart Rate Variability features. The obtained results were :
accuracy = 0.851 , specicity = 0.702 and sensitivity = 0.793. These results suggest that alternative evaluation of the sleep quality could be carried
out by correlated signals of easy acquisition.
In the third study the present work analyzes the time evolution of the
Autonomic Nervous System during arousal from sleep. Seventeen arousal
related to muscular activity and fourteen without muscular activity were
assessed. Arousals were extracted from ve polysomnography recordings
during sleep stage two. Three Time-Frequency Distributions were compared
using synthetic and real arousals. Thereafter, one of the Time-Frequency
Distributions was selected to analyze the time evolution of the Autonomic
Nervous System during arousal events. All tested distributions resulted satisfactory to evaluate Heart Rate Variability even though arousal produces
transitory behavior on it. Smooth Pseudo Wigner-Ville was selected for its
kernel exibility. The high frequency component showed a slight reduction
during arousal episode and increase after that. The low frequency component increased signicantly from the beginning of the arousal and remained
elevated for some seconds after ended the episode. This suggests that the
increment in low frequency is caused by a strong activation of sympathetic
tone more than by a the vagal ow decrement.
xiii
In the fourth study the eects of sleep apnea on the Autonomic Nervous
System were assessed during whole night recordings on normal subjects and
severe pathologic patients. The Heart Rate Variability was computed and
a time-variant autoregressive model was applied to decompose the signal in
its frequency components. Apnea patients showed lower parasympathetic
activity through the dierent sleep stages than normal persons. In addition,
a very low frequency component which appears on pathologic subjects, represents the repetition of apnea events. This very low frequency component
presented higher values during REM sleep than NREM sleep.
The fth study in this thesis was an attempt to develop an algorithm,
based on the spectral indexes of the Electrocardiogram signal, that could be
able to separate between normal and pathologic subjects aected by obstructive apnea, and for pathologic subjects to localize the time spent in apnea.
Spectral parameters of the Heart Rate Variability were calculated by an autoregressive model. Furthermore spectral and time parameters of the Heart
Rate Variability were used as features for classication. K-Nearest Neighbor
algorithm was used to classify apnea-non apnea time. The obtained results
were : accuracy = 0.8555 , specicity = 0.8850 and sensitivity = 0.8390.
These results suggest that it could be feasible and useful to develop a home
apnea pre-diagnosis. However more studies and tests of other classiers are
necessary.
1. ABSTRACT
xiv
2. Introduction
Sleep and wake are governed by complex and inter-related control mechanisms in the body which task consists in maintaining the homeostasis.
Homeostasis mechanisms regulates the internal environment for preserving
a steady state by means of multiple dynamic adjustments. Even though the
human body exhibits equilibrium, its physiological state is not static. Endogenous uctuations are present in the form of circadian rhythms. Therefore metabolic and physiologic variables as heart rate, body temperature and
blood pressure are not always at the same level. However it is possible to
predict their variations over the time. The Central Nervous System (CNS)
preserves the homeostasis in the human body by integrating aerent information and communicating with dierent organs using eerent nervous and
endocrine systems.
For many centuries sleep understanding has been one of the main uncomprehended themes and has attracted the attention of the most diverse
areas of study including philosophy and medicine. Sleep allows important
changes to occur in the body systems, which are essential for maintaining a
health status. The most natural awake-sleep cycle are 16 hours of daytime
and evening activity followed by eight hours of sleep at night. Sleep is a
natural state for resting and is characterized by dierent physical and physiological conditions, such as lower heart rate and arterial pressure, reduction
of responses to external stimuli, decrease in the voluntary movements and
increase of some hormones as melatonin. The sleep-wake cycle is regulated
at a central level by the brain stem and thalamus. Furthermore, external
stimuli such as darkness have a direct inuence in the falling asleep process.
2. INTRODUCTION
2
In the recent decades, sleep has become a major health issue, catching
the attention and extensive consideration by the medical researchers. Consequences of our civilization, such as changes in life style, technology advances
and stressful jobs have produced a reduction on sleep quality, and hence some
pathologies as sleep deprivation appear as major health problems that aect
the daily life of a person. In addition some disturbances such as sleep apnea
or periodic leg movements cause frequent arousals and then sleep fragmentation. Pathological repercussions range from the simple day sleepiness up
to heart failure. Also lower ability of concentration and irritability are some
typical symptoms of sleep deprivation. These eects produce a variety of
problems in the normal daily life of a person and the society around him [Martin SE, 1996]. In addition to social eects, some consequences can be found
at a physiological level, such as changes in blood pressure, heart rate and
temperature. Recent studies demonstrated that a bad quality of sleep is
related to many pathologies [Young et al., 2002] [Martin SE, 1997] [White,
2006], among which it is worth mentioning cardiovascular pathologies, hypertension, insulin resistance and obesity [Spiegel K, 2005].
Sleep behavior is well correlated with some physiological signals recorded
during sleep. Three basic electrophysiological signals (polysomnography) are
recorded from surface electrodes to evaluate wake-sleep alternation and to
classify the dierent sleep stages: EEG, EOG and EMG. Some other signals are added if the sleep study is aimed at the diagnosis of some specic
pathologies (for example, for the diagnosis of the sleep apnea, airow, chest
and abdomen movements, oxygen saturation are added to the set of the
recorded signals).
Polysomnography is the gold standard to evaluate the sleep quality. However, it is a relatively complex and dicult task that requires expertise personnel and specialized hospital infrastructures. These diculties and the
rareness of sleep clinics make sleep analysis to be very expensive. Since sleep
and more specic sleep stages generate changes at a multi-system level, it is
possible to create new alternatives for evaluating sleep quality at home. For
instance, respiration, heart rate, blood pressure and body temperature have
3
a dierent behavior in REM sleep than in NREM sleep. Heart rate presents
an overall reduction during NREM. During REM, heart rate signal shows an
increment in both rate and complexity. Respiration has a low and stable
rate in NREM and is higher and more variable in REM [Bonnet and Arand,
1997] [Trinder J, 2001] [Somers VK, 1995].
As commented previously, most of the physiological variables dier during sleep and wakefulness and the dierent sleep stages. Therefore one might
wonder why physiological sleep is evaluated only from the EEG, EOG, and
EMG, even if other variables have a very tie relationship with sleep stages
and sleep pathologies. In a strict sense, all the variables are correlated and
there is nothing special about the EEG, EOG and EMG. They have been
selected because sleep and sleep stages began to be evaluated and studied
with these measures, and to acquire them no such so sophisticated equipment as the MRI is needed. They can be recorded from surface electrodes
which are non invasive and these measures have large discriminating power.
Combining EEG, EOG and EMG, it is possible to do good classication, separating sleep from wakefulness and individuating the dierent sleep stages.
Although the EEG, EOG, and EMG measures allow a good state of discrimination, there are occasions when states are not clearly dierentiable.
State changes do not occur as simply as light switches. They change more
gradually. This can make dicult to nd a sharp division between states.
Even more vexing is the fact that the dierent processes may change at different rates. For example, during the transition from wakefulness to sleep,
there may be several minutes in which the EEG shows wakefulness, even
though in the subject awareness of the environment is already lost.
Although the discrimination power, among dierent sleep stages and
wake, of heart rate and respiration is not so sharp as the classical measures,
the analysis of their spontaneous oscillations during sleep by signal processing
approaches allow to study and nd an alternative way to evaluate the sleep
state.
2. INTRODUCTION
4
3. Physiology of Sleep
In this chapter an overview of the mechanisms involved in the generation
of sleep and physiological changes during sleep is presented. Much of the discussion in based on a sleep syllabus that is found in http://www.sleephomepages.org/sleepsyllabus.
The section overview of sleep shows a general description of sleep. It describes the behavioral and physiological (based on brain, muscular and ocular
activity) characteristics during sleep (based in the traditional brain, muscular
and ocular activity). Section physiological processes during sleep presents
briey how peripheral systems and variables such as heart rate, autonomic
nervous system, respiration and temperature respond during sleep, according
to the know literature. The following description is based on two general
references [Guyton AC, 2000] [Rhoades RA, 2007].
3.1 Overview of Sleep
During his whole existence the human being presents a Sleep-Wake cycle
which changes during his lifespan. Awake phase is a conscious phase where
there is a full interaction with environment and basic activities for surviving
things such as food, job and home occupy a primary place. On the other
side sleep is an unconscious process where the human being interacts with
his inner world and interaction with real world is basically vanished. Nevertheless, human beings organize their lives around the sleeping process. Sleep
has been thought as a resting process, consequence of the fatigue caused by
wakefulness and daily activities. Sleep is an irresistible necessity [Rechtschaffen, 1998] that when it arrives is so powerful that it is not possible to avoid
it. Sleep is so imperative that one can risks himself by getting a sudden need
of sleep while is driving [Horne and Reyner, 1999], working [Rogers et al.,
3. PHYSIOLOGY OF SLEEP
6
2001] or eating. Consequently, sleep is a vital necessity to our health and
survival.
For Millennia, sleep has been an unresolvable topic of discussion and
many theories have turned around it. The most accepted understanding is
that during sleep the brain turns o. However from the Johannes Berger's
demonstration in 1929 about the dierences in electrical brain activity during
sleep and wakefulness, and later the discovering of REM sleep [Aserinsky E,
1953], have demonstrated that sleep is an active cerebral process. Therefore,
it is not a conceivable thought that the brain needs rest, since sometimes
it is more active during sleep. We can ask ourselves some questions around
this brief introduction: Why do we sleep? What do we do during sleep? and
What is sleep?
Sleep is described by behavioral observations and physiological measures.
We can nd the following behavioral characteristics during sleep: movement reduction, stereotypical postures, reduced response to stimulus and
reversibility.
The physiological denition of sleep is based on electrical measures from
dierent parts of the body. Sleep and each sleep stage have been primary
dened by using three measures [Rechtschaen A, 1968]:
1. the electroencephalogram (EEG) which allows to measure the brain
activity and is recorded from electrodes situated on the head overlying
at cortex level.
2. the electrooculogram (EOG) that is acquired by electrodes placed beside each eye. EOG records eye movements.
3. Electromyogram (EMG) which monitors the muscular activity and is
obtained by electrodes placed under the chin. This has been used since
muscle tone in this area present dramatic changes associated at the
dierent sleep stages.
7
3.1. Overview of Sleep
Figure 3.1: Position of electrodes to acquire EEG, EOG, EMG.
Fig. 3.1 shows the electrode position to acquire these physiological signals.
In wakefulness, we can recognize that the activity is distributed in two
main frequency bands in the EEG. One fast brain activity in the range frequency between 13 and 30 Hz with low voltage (Beta activity). This is often
called activation or desynchronized pattern. The other one is the Alpha activity which is characterized by frequencies between 8 and 12 Hz with high
voltage. Beta activity is presented when the subject is alert and his eyes are
opened. Contrarily, alpha activity is predominant when a subject is relaxed
and his eyes are closed [Guyton AC, 2000].
The EEG shows dierent patterns during sleep. On basis of these patterns the sleep stages have been dened ve sleep stages which are characterized by the following electrophysiological features [Rechtschaen A,
1968]:
• Stage I is known as transition stage, and lasts at least 10 minutes.
During this stage EEG presents a reduction in the frequency brain
3. PHYSIOLOGY OF SLEEP
8
activity at 4-8 Hz (Theta waves) with low voltage. In addition, this
stage shows a low arousal threshold level and a very slow rolling eye
movement.
• Stage II is the predominant sleep stage during the normal sleep time.
The frequency in wave brain activity decreases more and voltage is
mild. Sleep spindles (burst with frequency between 12-14 Hz and
duration between 0.5 to 2 seconds) together with k-complexes (slow
sinusoidal waves with burst of high amplitude) are the main characteristic to dene sleep stage II. EOG appears rarely and EMG is low
to moderate.
• Stages III and IV are called slow wave sleep (SWS), and a high synchronism of the brain activity takes place in these stages. There slow
waves appear, called Delta waves, characterized by high amplitude and
frequency less than 4 Hz. During this sleep stage the highest arousal
threshold is found. This stage is the most important sleep stage for
recovery. EOG and EMG do not change, remaining as in the preceded
stage.
• REM presents a reversion in the EEG signal, high brain activity and low
voltage are observed. EMG is practically suppressed and often small
twitches appear. EOG turns very active due to the fast eyes rolling.
Fig. 3.2 shows the EEG activity during the dierent sleep stages. We can
appreciate how the EEG pattern varies through each sleep stage in amplitude
and frequency. In addition, some special events occur with the sleep stages
such as spindles, k-complexes and sawtooth waves. A particular characteristic of EEG is its amplitude and frequency dynamic from the wakefulness
to REM sleep. EEG amplitude EEG increases at each sleep stage until to
its maximum value in the stage 4 and decreases again during REM sleep.
Contrarily, EEG frequency passes from desynchronized and high frequency
waves in wakefulness to synchronized and low frequency waves in stage 4,
and reverse to desynchronized and high frequency waves in REM sleep.
9
3.1. Overview of Sleep
Figure 3.2: EEG during the different sleep stages
3. PHYSIOLOGY OF SLEEP
10
Sleep stages 1 to 4 present, with some exceptions, a physiology very similar. REM sleep is signicantly dierent to the other sleep stages and sleep
may be subdivided into two major stages: Rapid Eye Movement (REM)
and Non REM (NREM). In summary, REM sleep is a state characterized by
synchronous eye movements, muscle atonia, respiration, and the autonomic
nervous system is accelerated and irregular. In this sleep stage, brain activity reaches high levels similar to wakefulness state. On the contrary, NREM
sleep does not present eye movements and the cardio-respiratory system is
regular and slow. In this stage the muscles are tense and the cortical EEG
presents a pattern completely dierent from REM sleep which is synchronized and slow [Bonnet and Arand, 1997] [Trinder J, 2001].
During sleep the physiological variables have a complex and extremely
organized pattern that follows the REM-NREM sleep cycle. In a young and
healthy subject this cycle has a duration between 90 and 120 minutes. This
sleep cycle is repeated about 3-6 times during the night. However, this sleep
cycle REM-NREM is dynamic and presents a typical evolution in the REM
sleep duration and the sleep stages that constitute NREM sleep. During
the rst REM-NREM cycle SWS occupies most of the cycle, while REM and
stage II have only a presence of few minutes. However, each time that a new
REM-NREM cycle takes place, SWS has a smaller duration and both stage 2
and REM have more participation. In the last REM-NREM cycle REM occupies most of the cycle time and SWS is not present. In clinics and research,
a simple graphical representation of sleep was created in order to compact
and to observe timing, duration and sequence of each sleep stage during the
sleep period [Rechtschaen A, 1968]. This graphical representation is called
Hypnogram and it is illustrated in gure 3.3. Furthermore,this gure illustrates the alternating cycle former described for an overnight sleep of a young
healthy subject. In the gure, black lines corresponds to the REM periods
while the shadow ones to NREM periods. Another important characteristic
in humans is that sleep process always begins with NREM sleep [Pace-Schott
and Hobson, 2002].
The SWS duration depends on the previous waking [Akerstedt T, 1998],
11
3.2. Physiologic processes during sleep
Figure 3.3: REM - NREM sleep cycle
while REM period depends directly on the biological clock, REM tendency
is maximum near to the endogenous minimal temperature [Kavanau, 2002].
In summary, we spend 50 % of our sleep time in sleep stage II , 20 % in
REM sleep and 30 % in the other sleep stages. Guide lines to dene sleep
stages from the polysomnography are found in [Rechtschaen A, 1968].
As already said, behavioral and physiologic processes present changes
that are characteristic for Wake-NREM-REM cycle. These variations show
the participation and coordination of the dierent body systems. However,
physiologic processes also change through the REM-NREM cycle such as eye
movements during REM sleep. REM episodes that occur in the late night
have more eye movements that those of the early night.
3.2 Physiologic processes during sleep
The following subsection gives a deeper idea of the changes in some physiologic processes during sleep. We concentrate our summary on the central
nervous system, autonomic nervous system, respiratory system and cardiovascular system. A description of the main sleep generators located in the
brain is given in subsection Central nervous system. Subsection Autonomic
3. PHYSIOLOGY OF SLEEP
12
nervous system presents how the central nervous system interacts with the
peripheral systems. Description of how the cardiovascular system works
during sleep, is subject of the subsection Cardiovascular system. A brief
description of the thermoregulatory process is commented in Thermoregulatory process. A description of respiration function during wake and sleep is
theme of the subsection Respiratory system. Finally, the central generator
of circadian rhythms is described in Biological Clock.
3.2.1 Central nervous system
The nervous system is the body control centre that coordinates the functions of all systems in the human body. It detects, interprets, and responds
to changes in internal and external conditions to maintain an homeostatic
body regulation. The nervous system integrates information and produces
correct reactions by sending electrical and chemical impulses through nerves
to eector organs such as muscles and glands. The nervous system is constituted by: the central nervous system (CNS)- the brain and spinal cord
-, and the peripheral nervous system (PNS), that performs the connections
with the eectors and receptors.
Sleep-wake cycle and consciousness regulation involve the participation
of the reticular formation, area of cell groups located in the center core of
the brainstem. Reticular formation connects to areas with thalamus and
hypothalamus that also project to the cerebral cortex (ascending reticular
activating system) and to the cerebellum and sensory nerves (descending
reticular activating system), see gure 3.4. During wakefulness, an inhibition of reticular nucleus is observed, while during sleep the reticular nucleus
is active [Jones, 1994] [Stewart et al., 1984] [Evarts EV, 1962]. Reticular
formation plays a major role in the state of arousal. A malfunction produces
lost of consciousness and coma [Hass and Hawkins, 1978] [Obeso et al.,
1980] .
Specic mechanisms located in other brain areas promote NREM sleep
and other mechanisms REM sleep [Gottesmann, 1999]. The rst NREM gen-
13
3.2. Physiologic processes during sleep
Figure 3.4: The brainstem reticular formation and reticular activating system
erator center is located in the basal forebrain areas. Electrical and chemical
stimulation to this area produces NREM sleep. In addition, the nucleus of the
solitary tract seems to be involved in the generation of NREM sleep [McCarley and Massaquoi, 1986] [McCarley et al., 1983]. On the other hand, REM
sleep is produced in a well dened area of the brainstem, the ponds [Steriade
et al., 1984]. Transactional studies observed that the ponds are necessary
and sucient to generated REM sleep. The lateral pontine and medial
medullary reticular areas have cells that are very active during REM sleep
and have little or no activity in NREM sleep [Mitani et al., 1988] [McCarley
et al., 1983]. The same areas are completely quite in waking, even during strong movement. Nevertheless, during some postural changes where
tone reduction of muscles is involved, these cells are active. These areas
are involved in the atonia that characterize REM sleep. Eye movements in
REM sleep are generated by the pontine nucleus with a projection over the
superior calicullus [McCarley and Ito, 1983]. In addition, eye movements
are associated with the PGO (pons, genicule, occipital) waves. The name
PGO waves comes from a typical trajectory followed by pons neurons that
re burst during REM. They excite the thalamus and in turn project to the
3. PHYSIOLOGY OF SLEEP
14
cortex [Pace-Schott and Hobson, 2002].
3.2.2 Autonomic nervous system (ANS)
Autonomic Nervous System has a close relationship with cardiac activity.
This tie relationship allow us to analyze the behavior of ANS from the cardiac activity. In our case, we have a special interest in understanding the
ANS responses during sleep stages and the reaction and participation in
some pathologies and normal physiological events such as obstructive sleep
apnea and arousals from sleep.
The nervous system is divided in two parts: central nervous system CNS
and Peripheral Nervous System (PNS). CNS is the one that receives, processes and decides the best response to the environment changes and our
own desires, in order to maintain the homeostasis and to satisfy our needs.
On the other side, PNS is the one who senses and sends the information
from the peripheral organs, and nally returns back with the decision taken
for the CNS to the eector organs.
At the same time, PNS is subdivided into two parts, the somatic nervous
system (SNS) and the autonomic nervous system (ANS). SNS is known as
the voluntary nervous system, since we can use it in order to react and to
interact consciously with the environment. This system controls voluntarily
and senses skeletal muscle movements.
On the other side, ANS is the involuntary counterpart and maintaining
body homeostasis is its primary function. It is constituted by three kinds of
elements : receptors within viscera, aerent nerves that transmit information to CNS and eerent nerves that transmit the action information back
to the eectors. Smooth muscle, cardiac muscle and glands and all organs
that work unconsciously integrate the ANS. This system works automatically
with any voluntary input. Furthermore, ANS is composed by two eerent
branches: sympathetic and parasympathetic. The sympathetic nerves send
information to eector organs in circumstances of stress such as mental
15
3.2. Physiologic processes during sleep
or physical activity. When sympathetic is activated some changes can occur as increase in blood pressure, heart rate and breath rate. Contrarily,
the parasympathetic nervous system produces a relaxed eect, decrement
in blood pressure, heart rate and breath rate [ADAM, ]. These phenomena
allow us to observe clearly that it is possible to evaluate the function, behavior and condition of the branches of ANS during dierent conditions and
situations, observing only uctuation inside the heart rate or other peripheral
organs.
ANS is located in the spinal cord and Figure 3.5 shows the connection of
the sympathetic and parasympathetic branches of the ANS to the peripheral
organs.
Since ANS, with sympathetic and parasympathetic nervoussystems, controls directly the heart rate, it results very interesting for us to understand
how the two systems interact during sleep. Taking relaxed wakefulness as
reference point to compare ANS changes during sleep, we may observe the
following relations. During NREM sleep, the activity of sympathetic branch
presents slight change, but in principle stay at the same level as wakefulness,
contrarily, activity of parasympathetic nervous system has an increment,
resulting in a HR decrement [Burgess et al., 1997] [Trinder J, 2001]. Therefore, a prevalence in parasympathetic drive over a sympathetic one occurs.
This balance during REM sleep presents a dierent characteristic: both
a high activity increment of sympathetic and parasympathetic drives take
place [Somers et al., 1993a]. However the sympathetic overow presents a
little predominance over the parasympathetic one (see Figure 3.6).
3.2.3 Cardiovascular system
The cardiovascular system, as the other systems, has specic characteristics in Wake-NREM-REM. During the change from relaxed wakefulness to
NREM sleep, the systemic blood pressure exhibits a slight reduction and
less variability [Coote, 1982]. Contrarily in REM sleep, the systemic blood
pressure becomes variable and can have increments as high as 40 mmHg,
3. PHYSIOLOGY OF SLEEP
Figure 3.5:
Autonomic Nervous
http://cti.itc.virginia.edu/ psyc220/
16
System,
extracted
from
17
3.2. Physiologic processes during sleep
Relaxed
Waking
NREM
Sleep
REM
Sleep
Sympathetic
S
S
S
Parasympathetic
P
P
P
Heart rate
70
65
80
Pupil Diameter
O
0
O
Figure 3.6: Autonomic nervous system during sleep. Letter dimension represents the activity.
which with respect to relaxed wakefulness represents rising of 30 % [Parish
and Shepard, 1990]. In addition, a vasodilatation and a vasoconstriction
take place within NREM and REM respectively. However, contrarily to the
classical pattern of physiological variables which are during NREM steady
and reductive, and higher and instable during REM, cardiac output presents
a general reduction during the sleep time with respect to relaxed wakefulness [Miller JC, 1976]. Cerebral blood ow increases only slightly in some
areas during NREM sleep while a higher increment in blood ow occurs in
most of the brain areas during REM sleep [Townsend RE, 1973].
3.2.4 Thermoregulatory process
During NREM sleep the body temperature is regulated at a lower set point
than during wakefulness. Thermoregulation in REM sleep is not persisted,
the body temperature can shift toward the environment temperature. In extreme climates REM sleep is reduced and it is interchanged for NREM sleep,
though normal sleep is fragmented for maintaining the body temperature.
This transition helps to return to a regulated state to continue with the body
temperature regulation [Parmeggiani, 1990].
3. PHYSIOLOGY OF SLEEP
18
3.2.5 Respiratory system
Since one of the major sleep pathologies has respiratory origins, trying to understand the control and function of the respiratory system is an important
issue sleep clinics and in the research eld. This nocturnal noxious event is
called Sleep Apnea (SA). SA is characterized by periods of breath cessation
during sleep time. The origins of this pathology could be both central or
tracheal.
The respiratory system, together with the cardiovascular system, helps
in maintaining the body homeostasis by carrying oxygen demand to the entire body. The respiratory system0 s function is performed by a mechanical
mechanism that takes air with O2 from the environment into the body the
environment air with O2 , and takes out the body air with high CO2 concentration. In addition, gas exchange is achieved in the lungs at alveolar
level by perfusion. The dierent concentrations of partial pressure in CO2
and O2 between blood and lungs allow the perfusion. The respiratory control system is integrated by both involuntary and voluntary controls. This
means, that we can change physical system variables as velocity, duration
and volume of the breaths. Furthermore, an involuntary reex of respiratory
rhythm control is also found in the brain, more specically in the brain stem
and the spinal cord, where an intrinsic respiratory rhythm, the integration of
aerent information coming from central, peripheral sensors and the eerent
information, is transmitted to the eectors organs.
Nervous control of respiratory system
Respiration is an unconscious process. Breathing is cyclic and involves many
muscles that are also used in other functions, such as talking and phonation. Quite breathing is characterized by two main phases : inspiration and
expiration. Inspiration is an active process in which the inspiratory muscles
are in excitation while expiration is a passive process. However expiration
becomes active during conditions such as exercise. Cycle rhythm is mainly
generated by neurons located in the medulla oblongata in the brain. Two
groups of neurons have been related to the respiratory pattern. These groups
19
3.2. Physiologic processes during sleep
gain their names from the respective position in the medulla oblongata. The
dorsal respiratory group (DRG) is active during respiration process while the
ventral respiratory group (VRG) is active in both inspiration and expiration
processes. DRG and VRG have axons projected toward the bulbospinal motor
neuron pools. Lesions in DRG or VDG produce diminution in the respiratory
motion. In addition, other groups of neurons, called the pontine respiratory
group, are found in the pons. Stimulation or lesions in this regions cause
noticeable changes in breathing. Finally, the basic cycle of respiration is
highly modied by several control mechanism, such as soprapontine structures. Multiple control mechanisms and their interaction provide a large
capacity and exibility to the respiratory system at the more diverse conditions. Some simple examples are: anxiousness, exercise, eating and talking.
Until now, we have given a brief idea about respiratory system control mechanisms located in the brainstem and medulla oblongata. In any
feedback control system, it is necessary to describe the eerent and sensor
mechanisms in order to obtain a full scheme of the system. Basically, respiration control is carried out by the integration of information provided by
dierent types of sensors. Most receptors that we can nd in the respiratory
system have a mechanical and chemical nature, responding to gas tension,
blood pH and gas composition of the arterial blood. Nevertheless, the respiration control can also be inuenced by other reex such as arterial blood
pressure and visceral pain.
Reexes from periphery help to regulate the frequency and tidal volume
in the respiratory system. Furthermore, when external agents from the environment arrive to the lungs, this peripheral reexes produce reaction in order
to protect the system. In this rst part, a description of reex associated to
lungs and chess wall is given. Then, the reex associated to the chemical
response will be presented.
Three kinds of pulmonary receptors can be found: slowly adaptive receptors, rapidly adaptive receptors and C bres endings. Aerent bers of
these receptors are predominantly in the vagus nerve. Slowly adaptive recep-
3. PHYSIOLOGY OF SLEEP
20
Figure 3.7: The general locations of the dorsal respiratory group (DRG) and
ventral respiratory group (VRG).
21
3.2. Physiologic processes during sleep
tors (SAR) are situated within conducting airways and are sensory terminals
of myelinated aerent bres. They basically respond to airway stretch and
their usual function is to sense the lung volume. SAR re in proportion
to the applied airway transmural pressure, rapidly adaptive receptors (RAR)
are found in the large airways. The aerent bres that carry the information
acquired by RAR are myelinated. RAR respond to the irritation of airways
by touching or by noxious agents such as dust. RAR re in proportion to
volume change and rate. Finally, the C bre endings are part of the non
myelinated bres. These receptors have a protective role and respond to
lung injury, large ination, acute pulmonary, vascular congestion and some
chemical agents. C bre endings are located adjacent to the alveoli and in
airways. These receptors respond to mechanical events and possibly excite
the medulla since their stimulation changes breathing, produce bronchoconstriction and generate cardiovascular depression. Join, tendon and muscle
spindle are found in the intercostal muscles and they basically advertise the
mechanical eort.
On the other hand, in our body exist chemical mechanisms for regulating
respiration. They drive the central respiratory centers in order to maintain
an adequate exchange of gases (CO2 , pH and O2 ) at a predeterminate physiological level in the blood. The chemoreceptor are located in the carotid and
aortic vases (peripheral chemoreceptors) and in medullary neurons (central
chemoreceptors). Chemoreceptors are strongly linked to the cardiovascular
function by either interacting with the medullary vasomotor center or altering pulmonary stretch receptor activity. Respiratory cessation and circulatory shock increase chemoreceptor activity, enhancing sympathetic outow
to the heart and vasculature via activation of the vasomotor center. Cerebral
ischemia activates central chemoreceptors, which produces a simultaneous
activation of sympathetic and vagal nerves to the cardiovascular system.
Changes in respiration during sleep
Respiration is essential for life and is produced by mechanisms with large exibility and adaptability to maintain the body homeostasis in the most variety
of circumstances. We can considered that sleep results from a withdrawal of
3. PHYSIOLOGY OF SLEEP
22
the wakefulness stimulus that arise from the brainstem reticular formation.
During sleep, respiration presents a general depression. Light sleep is characterized by breath frequency and inspiratory rate reduction, which reects
in some grade the diminution of physical activity. A small increase in PaCO2
is also observed and could be due to a change in the sensitivity of the set
point in the PO2 controller. Breath presents a slow and regular dynamic
during phase 4. On the other side, an irregular respiration takes place during REM sleep. This suggests that the changes in respiration correspond
to an increase on CNS activity, rather than autonomic or metabolic control
systems [Coote, 1982].
Respiratory system responses to hypoxia conditions are reduced during
both slow-wave and REM sleep. Response level during REM and SW sleep
are similar, and the irregular respiration pattern during REM sleep seems to
be unaected by hypoxia [Rhoades RA, 2007].
SW and REM sleep produce a response reduction to airway irritation.
Stimuli that during wakefulness produce coughing, tachypnea (abnormal fast
breathing) and airway constriction, have a great repercussion during sleep
producing apnea and airway occlusion until the stimulus is strong enough to
evoke an arousal from sleep [Rhoades RA, 2007].
Arousal from sleep is dealt within a special section. Arousal have an
important role inside the respiratory system responses because the more important participation of the respiratory sensors produce an arousal in order to
overcome noxious events. Decreasing in PaCO2 is a potent arousal stimulus.
Arousal have an important role in maintaining the homeostasis during sleep.
3.2.6 Biological Clock
Wake-sleep cycle and body temperature, as many other physiological functions, vary throughout timing patterns. Wake-sleep cycle is a circadian process. This means, that the cycle repeats each day. It is thought that the
hypothalamus plays a major role in the regulation of biological rhythms. Cir-
23
3.2. Physiologic processes during sleep
Figure 3.8: The biological circadian clock: suprachiasmatic nucleus.
cadian rhythms are generated by the suprachiasmatic nucleus (SCN) located
in the hypothalamus (see Figure 3.8) [Meijer and Rietveld, 1989] [Lehman
et al., 1987] [Ralph MR and M, 1990] [Schwartz et al., 1986] [Cohen and
Albers, 1991]. The biological clock is endogenous, so changes happen because of mechanisms in the body, and they repeat even in absence of any
time cue [Newman et al., 1992] [Prosser et al., 1989] [Czeisler et al., 1999].
Then wake-sleep cycle is regulated by an endogenous timekeeper called biological clock, which controls the time of each biological function.
However the internal biological clock can be set and reset by external
stimulus. These agents are called zeitbeger [Mistlberger and Rusak, 1994].
Light is the most important zeitbeger due to an important connection with
3. PHYSIOLOGY OF SLEEP
24
the optic nerve [Zordan et al., 2001] [Jewett et al., 1994]. The aerent
retinohypothalamic tract of the optic nerve, begins in the retina and ends in
the SCN. In addition, the SCN controls the activity of the pineal gland (an
endocrine gland) in the posterior of the thalamus [Mistlberger and Rusak,
1994]. The pineal gland releases melatonin which is a hormone that increases sleepiness [Sharma and Chandrashekaran, 2005]. In humans, the
pineal gland begins to secrete melatonin at night about 2-3 hours before we
normally go to bed.
Other two important zeitbegers are the jet lag and shift work. These
disrupt the normal day-nigth pattern and the SNC needs time to reset and
to synchronize with the new light-dark pattern. However while the biological
clock achieves the synchrony harmony with the new wake-sleep cycle, there
is a feeling of malaise and physical distress [Mistlberger and Rusak, 1994].
4. Sleep Disorders
Sleep is a basic life process. When we have a good and sucient sleep time,
we wake up with energy and good mood to develop all ours tasks. Contrarily,
when we do not have a good night, we feel tired, irritable and with somnolence. As a consequence, classical symptoms as low concentration, impaired
memory and bad mood appear. If restorative sleep time was not taken, we
feel a powerful necessity to go to bed and to take a nap. Good sleep quality is disrupted by dierent causes that range from entrainment to job needs.
A variety of sleep pathologies has been documented. For instance, REM
behavior disorder, cataplexy, insomnia, periodic leg movements are some
examples. This study focuses on obstructive sleep apnoea and arousal from
sleep, since those pathologies have large eects on the ANS behavior. Those
pathologies are of large incidence and the function of ANS can be evaluated
from the HRV. Then, it is suitable to develop a rough diagnosis away from
the clinical environment.
4.1 Obstructive Sleep Apnea (OSA)
Obstructive sleep apnea (OSA) is one of the most common pathologies observed in respiratory and sleep clinics. Obstructive sleep apnea is caused
by the closing of the upper airways during sleep [Young et al., 2002]. The
uvula and soft pallet collapses on the back wall of the upper airways. Then
the tongue falls toward the back, collapsing over the back wall of the upper
airway, and consequently no air enters to the lungs [Ayappa and Rapoport,
2003] [Isoni et al., 1993] [Remmers et al., 1978]. A strong eort produced
by the diaphragm, the chest and the abdomen is generated in order to over-
4. SLEEP DISORDERS
26
Figure 4.1: Upper airways during normal sleep, figure adapted from
quitesleep.com
come the obstruction. However, to restore the respiration, generally an
arousal from sleep takes place, reactivating the systems and allowing air to
pass into the lungs [Dingli et al., 2002].
Figures 4.1 and 4.2 show a subject in supine position during sleep. Figure
4.1 presents the subject in normal conditions where the upper airways are
open and the air can ow freely (see circle). Figure 4.2 presents a subject
during an apneic event. Upper airways are completely blocked (see circle).
In addition, obstructive sleep apnea causes a reduction in blood oxygen
saturation (SaO2 ) and an increment in blood carbon dioxide (CO2 ). When
SaO2 drops, the heart starts pumping more blood with each beat. If the
SaO2 continues to drop the heart starts beating faster and faster. As CO2
increases, the brain tries to force the person to breathe. The eort and action of the abdomen and chest also increase. Generally, this action becomes
severe enough to produce an arousal from sleep, and the block is eliminated,
allowing the person to breathe. Then the person goes back to sleep again
and apnea episode happens again. This process can occurs hundreds of
27
4.1. Obstructive Sleep Apnea (OSA)
Figure 4.2: Upper airways during obstructive sleep apnea, figure adapted from
quitesleep.com
times during sleep [Caples et al., 2005].
Not always exists a total upper airway occlusion. Some middle occlusions in the upper airways are sucient to produce a similar behavior in
the physiological variables to OSA; this condition is called hypoapnea. An
event is an obstructive sleep apnea only if no air passes to the lungs with
a duration of at least 10 seconds. In addition, also respiratory thoracic and
abdominal eorts, together with a reduction in SaO2 of around 2-4 %, must
happen in order to dene an apnea as being obstructive. On the other side,
hypopnea is dened only if there is a reduction of ow air at least to 50 % for
10 seconds or longer. Again respiratory eorts are associated and together
with a drop of at least of 4% in the saturation of oxygen in the blood [Atl,
1999]. Figure 4.3 shows two apnea episodes and their repercussion on different physiological variables.
Not only obstructive sleep apnea disrupts sleep. We can nd another
type of apnea, central sleep apnea (Cheyne-Stokes respiration) [Bradley and
4. SLEEP DISORDERS
28
Figure 4.3: Episodes of obstructive sleep apnea and its consequences on physiological variables. Superimposed recordings of the electrooculogram (EOG),
electromyogram (EMG), electrocardiogram (ECG), SNA, REMP, and BP during REM sleep in a patient with OSA. BP during REM, even during lowest
phases (∼ 160/105 mmHg), was higher than in the awake state (∼ 130/75
mmHg). BP surger at the end of the apneic periods reached levels as high as
230/130 mmHg. EOG shows the sharp eye movements characteristic of REM
sleep. Increase in muscle tone (EMG) and cesation of rapid eye movements toward the end of the apneaic period indicates arousal from REM sleep (arrows).
Figure adapted from Somers 1995
29
4.1. Obstructive Sleep Apnea (OSA)
Floras, 2003b]. This is an abnormal respiratory pattern, caused by the failure of the respiratory centers in the brain. In this form of apnea, the upper
airways can be open but the thorax muscles and the diaphragm stop working. This causes a cessation of respiration and reduction in SaO2 in the
blood. This drop in oxygen awakes the sleeper to restore breathing. Apnea
event can be either obstructive and central, or both during the same apnea
period, called mixed apnea. Figure 4.4 shows a representation of air ow
(V), abdominal (A) and thoracic (T) eorts during obstructive, mixed and
central apnea respectively.
Sleep apnea severity is evaluated by dividing the number of apneas during sleep time with the number of sleep hours. The Apnea-Hypopnea Index
(AHI) is normally used in clinics, which is the total number of apneas and
hypopneas per hours of sleep. A normal subject does have sleep apnea
problems when AHI is greater than 15. However for a medical patient which
suers high blood pressure, stroke, daytime sleepiness, ischemic heart disease
(low ow of blood to the heart), insomnia, or mood disorders an AHI higher
than 5 is dened as being a sleep apnea subject [Caples et al., 2005] [Atl,
1999].
Generally, a sleep apnea episode is overcome when a brain activation
(Arousal form sleep) sends information by sympathetic pathways, and respiratory muscles at tracheal level are stimulated to restored respiration [Dingli
et al., 2002]. Sleep apnea repetition and duration seem to be related to sleep
stages. During NREM sleep, duration and repetition of apneas are regular
and constant while during REM sleep they are irregular and random. This
pattern can be observed in gures 4.5 and 4.6
In the last decades, sleep apnea has been widely studied and many consequences are well documented. The most important and possible more
observable consequence is sleep fragmentation, which has in turn its own
consequences. Subjects with bad sleep quality can not concentrate, think,
memorize, and present a strong daily sleepiness [White, 2006] [Somers VK,
1995]. All these eects interrupt the normal personal life, and put in risk
4. SLEEP DISORDERS
30
Figure 4.4: Representation of air flow (V), abdominal (A) and thoracic (T)
efforts during obstructive, mixed and central apnea respectively.
31
4.1. Obstructive Sleep Apnea (OSA)
Figure 4.5: Segment of a polysomnographic record in correspondence of apnea during NREM sleep. Airflow shows that repetition and duration of the
apnea episodes is very regular. During the breathing restore occurs an arousal,
increases the thorax and abdomen efforts, appears a high muscular activity and
increases the heart rate
his/her own life and the persons next to him/her [Young et al., 2002].
Sleep apnea also modies some physiological aspects of the body, of the
most important does are high blood pressure and heart problems. Consecutive stops in the breathing during the night produce stress on the heart
[Naughton, 1998]. Sleep apnea causes a reduction on arterial oxygen saturation and actives the sympathetic system (Fight or Flight) [Pepperell et al.,
2002] . This sends information to blood vessels to constrict and to the heart
to pump harder. As consequence more blood arrive to the brain and muscles
in order to maintain oxygen requirement. However, this causes heart stress
due to the heart forced to pump harder against constricted vessels during
4. SLEEP DISORDERS
32
Figure 4.6: Segment of a polysomnographic record in correspondence of apnea
during REM sleep. Airflow shows that repetition and duration of the apnea
episodes are completely irregular. During breathing restore occurs a series of
events: a strong arousal if the duration of the apnea was large, increases the
thorax and abdomen efforts, appears high muscular activity and increases the
heart rate
night [Caples et al., 2005]. In spite of the apnea happening during the night,
this condition of sympathetic activity continues during wakefulness (see gure 4.7), aecting all the physiological normal conditions [Somers VK, 1995].
This process increases the probability of suering from congestive heart failure and sudden death [Naughton and Bradley, 1998].
In clinics, obstructive sleep apnea is divided in mild, moderate, or severe
categories. This classication helps to determine the therapy. For example,
some treatments that are excellent for mild sleep apnea normally fail for se-
33
4.1. Obstructive Sleep Apnea (OSA)
Figure 4.7: Recordings of sympathetic nerve activity (SNA) during wakefulness in patients with obstructive sleep apnea (OSA) and matched controls
showing high levels of sympathetic nervous activity in patients with sleep apnea. Adapted from Somers 1995
4. SLEEP DISORDERS
34
vere sleep apnea. The gold standard to evaluate the severity level OSA is the
polysomnography. Dierent levels of apnea-hypopnoea index are categorized
as: mild obstructive sleep apnea for 5 − 15 events per hour, moderate obstructive sleep apnea for 1530 events per hour, and severe obstructive sleep
apnea for more than 30 events per hour.
Dierent surgical [Tiner, 1996] [Guilleminault, 1997] [Douglas, 1997]and
not surgical treatments have been developed in order to solve this pathology. Non surgical treatment include: behavioral changes [Caples et al.,
2005], dental appliances [Hans et al., 1997], CPAP (continuous positive airway pressure) [Beninati and Sanders, 2001], and medications. OSA is more
common in obese [Barvaux et al., 2000] people and smokers since there is
a reduction and irritation of the trachea. On this kind of subjects some
behavioral changes could help to reduce apnea episodes during sleep time
and improve sleep quality. Since, the nature of OSA is anatomical to nd a
medication for this problem is not simple.
The most used and probably the best non-surgical treatment to obstructive sleep apnea is CPAP [Collard et al., 1997]. CPAP delivers a determined
air pressure in the nose to hold the airways open during sleep. In this way,
the upper airways do not collapse during sleep. The air delivered by the
CPAP is heated and humidied. Basically, CPAP equipment is a comfortably worn mask. Dierent styles of masks can be found, for instance nasal
masks and full-face masks. In addition, CPAP device is a small box not
larger than a toaster. Furthermore, one of the advantages is its travel portability. Automatic positive airway pressure (APAP) is another device similar
to CPAP [Konermann et al., 1998]. APAP have the lowest possible pressure
level for each position on sleep enough to maintain open the upper airways.
At a given pressure, if a person starts to have an apnea or hypopnoea, APAP
changes and adjusts the pressure higher than necessary until the episodes
have been controlled [Hudgel and Fung, 2000].
35
4.2. Arousal from sleep
4.2 Arousal from sleep
In the last years, Arousal from Sleep (AS) has been one of the most studied
physiologic phenomena, due to its very close relationship with Sleep Fragmentation (SF). SF is a problem associated to several health implications
ranging from simple daytime sleepiness, somnolence and low concentration
to much more severe consequences, such as myocardial infarction, increased
risk of hypertension, cardiac stroke and increased mortality rate, especially
when it is associated with obstructive sleep apnea [Caples et al., 2005]. Furthermore, SF is a common symptom seen in respiratory sleep clinics which is
often caused by repetitive AS as defense to noxious nocturnal stimulus, such
as OSA, and Cheyne-Stokes Respiration [Bonnet and Arand, 1997], [Collard P, 1996], [Davies R, 1997], [Nixon GM, 2002], [Trinder J, 2000].
Arousal from Sleep is classically scored from either the central or occipital derivation of the EEG which is acquired by polysomnography after a
person spends one night in a sleep clinic. An Arousal consists in "an abrupt
shift in EEG frequency, which may include theta, alpha and/or frequencies
greater than 16 Hz but not spindles" [ASDA, 1992], during sleep. Therefore,
an arousal attains certain features, as the duration of the frequency shift,
minimum time that a person must be sleeping before scoring an arousal and
so on. All criteria are dened by the atlas task force of the American sleep
disorders [ASDA, 1992]. Dierent studies have been developed in order to
understand physiologic eects of arousals with and without any pathological event. Other studies have evaluate the arousal consequences on sleep
fragmentation by applying induced arousals at dierent intensities and periodicities [Bonnet, 1989], [Catcheside, 2001], [Davies R, 1993], [Morgan et
al., 1996], [Driscoll DM, 2004], [Sforza et al., 2004]. AS event generates a
typical waveform in the Heart Rate (HR), this pattern consists in an abrupt
increment in HR due to the withdrawal of vagal tone in relation to the start
of AS, immediately followed a few seconds later by a decrement in the HR
and sympathetic activity.
4. SLEEP DISORDERS
36
4.3 Periodic Leg Movements
Periodic leg movement (PLM) is repetitive jerking of the legs during sleep.
It is the only movement disorder that occurs only during sleep. "Periodic"
refers to the fact that the movements are repetitive and rhythmic, occurring
about every 20 − 40 seconds. PLM is also considered a sleep disorder, because the movements often disrupt sleep and lead to daytime sleepiness [Atlas, 1993]. Generally, PLM is also associated with arousal episodes [Atlas,
1993] [Karadeniz et al., 2000b] [Karadeniz et al., 2000a] [Hornyak et al.,
2005] and variation in the HRV [Sforza et al., 2005].
PLM may occur together with other sleep disorders. It is often linked
to the restless legs syndrome, but they are not the same. At least 80 %
of people with restless legs syndrome have PLM, but the reverse is not
true [Garcia-Borreguero et al., 2004] [Hornyak et al., 2006]. Restless legs
syndrome is a condition that involves strange sensations in the legs (and
sometimes arms) during wakefulness and an irresistible urge to move the
limbs to satisfy the sensations.
PLM was rst described in the 1953s and it was called nocturnal myoclonus [SYMONDS, 1953]. PLM movements are not myoclonus, and the
original name is not used today.
PLM can occur at any age. As many sleep disorders, PLM is more common in middle-aged and older people [Bliwise et al., 1988] [Carrier et al.,
2005]. Persistent sleep disruption and daytime sleepiness are not part of
normal aging. Periodic leg movement disorder can be primary or secondary.
Secondary PLM is caused by an underlying medical problem [Salín-Pascual
et al., 1997]. Primary PLM, on the other hand, has no known cause. It has
been linked to abnormalities in regulation of nerves from the brain to the
limbs, but the exact nature of these abnormalities is not known.
Secondary PLM has many dierent causes, including the following:
1. Diabetes mellitus [Hilbert and Mohsenin, 2003].
37
4.3. Periodic Leg Movements
2. Spinal cord injury [Dickel et al., 1994] [Salín-Pascual et al., 1997]Mello1996.
3. Sleep apnea syndrome [Baran et al., 2003].
4. Narcolepsy [Baker et al., 1986].
The most common symptoms noted by people with PLM are not leg movements but poor sleep and daytime sleepiness [Hornyak et al., 2005]. Many
people with PLM are unaware of their leg movements unless their bed partner tells them.
Leg movements involve one or both limbs [Atlas, 1993].
1. Typically the knee, ankle, and big toe join all bend as part of the
movement.
2. The movements vary from slight to strenuous and wild kicking and
thrashing.
3. The movements last about 2 seconds (and thus are much slower than
the leg jerks of myoclonus).
4. The movements are rhythmic and repetitive and occur every 20 − 40
seconds.
In most people with PLM, poor sleep and daytime sleepiness are the
most bothersome symptoms [Hornyak et al., 2005] [Sforza et al., 2002].
Many people do not link their sleep problem with leg movements. Sleep
disturbance has many dierent causes. Polysomnography is the only way to
conrm that you have PLM [Hornyak et al., 2006].
4. SLEEP DISORDERS
38
5. Heart Rate Variability
Sleep is related to variations on physiological variables. Generally, all the
physiological variables such as heart rate, respiration, blood pressure and
temperature, exhibit patterns correlated to the cerebral activations. We
could imagine the entire body as an endogenous system with three possible
states, relaxed Wake-NREM-REM. The combination of physiological variables that, come from dierent subsystems, help us to dene each state.
As commented in the section physiology of sleep, each subsystem presents
patterns that characterize the state, for instance, synchronized cerebral activity during NREM and unsynchronized during REM sleep and wakefulness.
Respiration is regular and slow in NREM while irregular during REM. From
this evidences, we may think that a possible sleep prole could be created
using only peripheral signals of simple acquisition, as is the electrocardiogram. Basically, electrocardiogram recording needs only one lead on the
chess wall close to the heart. Thus in clinical practice electroencephalogram, electrooculogram and electromyogram are used for its sharp changes
among states.
The Electrocardiogram (ECG) is a representation of the cardiac electrical activity during the cardiac cycle. This activity creates well dened wave
forms related to mechanical events on cardiac muscles, showed in gure 5.1.
Figure 5.1 shows the electrical activity acquired by an electrode placed on
the chest surface during a normal cardiac cycle (ECG) while gure 5.1presents
an explanation of how the electrical activity is related to the activity of heart
muscles (extracted from Alexandra holmes's Thesis 2003).
5. HEART RATE VARIABILITY
40
Table 5.1: Relation among the ECG signal and the mechanical and electrical
activity on the heart - part 1
Time interval between the waves T and P
Electrical events
◦ Time after ventricular re-polarization and atrial depolarization.
Mechanical events ◦ Atrial and ventricular diastole, the flow passes from
the veins to ventricles through the atria
P wave - Atrial depolarization
Electrical events
◦ Firing of the Sinoatrial node does not produce sufficient electrical activity to be recorder by the ECG.
Therefore, the first recorder wave, the P wave, occurs when the impluse spreads across the atria.
◦ P wave is a small signal compared with that pertaining to ventricular depolarization (QRS complex) because of the small muscle mass of the atria compared
with the ventricles.
Mechanical events ◦ Atrioventricular valves are open and blood flows
from the atria to the ventricles.
◦ Atria contracts to squeeze blood into the ventricles.
41
Table 5.2: Relation among the ECG signal and the mechanical and electrical
activity on the heart - part 2
PR segment - AV nodal delay
Electrical events
◦ Current flowing in the AV node, but this is too small
to be detected in the ECG.
◦ Actually the PQ segment, but is called the PR segment because R is dominant and Q is sometimes difficult to identify.
Mechanical events ◦ Atrial systole and ventricular diastole
◦ The volume of blood in the ventricle at the end of diastole is known at the end-distolic volume (pre-load)
and no more blood will be added to the ventricle during this cycle.
QRS complex
Electrical events
Mechanical events
◦
◦
◦
◦
ST segment
Electrical events
Mechanical events
◦
◦
◦
◦
◦
Ventricular depolarization.
Ventricular pressure exceeds atrial pressure, and the
atrioventrcular valves are forced shut producing the
first heart sound.
Ventricular systole starts when the ventricles contract.
Atrial commence diastole.
None.
Initially, the ventricles are closed chambers and isovolumetric contraction occurs.
Once ventricular pressure exceeds the atrial pressure
(after-load), the semilunar valves open and blood is
forced into the arteries. This signifies the end of
the isovolumetric contraction period. Each ventricle only empties about half its blood volume during
systole.
The amount of blood remaining in the ventricle at
the end of systole is known as the end-systolic volume, and is equal to the end-diastolic volume minus
the end-systolic volume.
Atria in diastole.
5. HEART RATE VARIABILITY
42
Figure 5.1: cardiac electrical activity, electrocardiogram
Table 5.3: Relation among the ECG signal and the mechanical and electrical
activity on the heart - part 3
T wave
Electrical events
◦ Ventricular repolarization.
Mechanical events ◦ At the end of ventricular systole, and as the ventricles relax, ventricular pressure falls below atrial
pressure and the semilunar valves close. The closing of the valves produces the second heart sound
and signals the onset of ventricular diastole.
◦ Once the ventricular pressure falls below the atrial
pressure, the atrioventricular valves open and the cycle starts again.
43
Heart beat is controlled by the autonomic nervous system via its sympathetic and parasympathetic branches. Cardiac activity is regulated on basis
of information collected by a variety of peripheral receptors, including arterial
baro and chemo receptors located in the bifurcations of the carotid and aortic
bodies. In addition, also mechano and chemo receptors, situated within the
atrial wall, participate in the heart rate control. As a result, ow pressure,
chemical blood composition and stretch on atrial chamber provide continue
information about heart function to the control center located in the brain.
The nucleus of the solitary tract in the medulla receives and integrates all
the information collected by the mechano-chemo peripheral receptors. After
integrating the information, the solitary tract sends back the decision to the
heart. This is a brief description of the feedback mechanism that regulates
the heart function. In other words, the heart function is to pump blood to
all the organs in order to maintain a body homeostasis [Rhoades RA, 2007].
Increase in heart rate, blood pressure, vasoconstriction, etc, is produced by
the sympathetic nervous system, while the parasympathetic nervous system
produces opposite behavior, this means, bradycardia, vasodilatation and so
forth.
Control physiologic systems do not work as light switch (ON-OFF), contrarily they exhibit controls that oscillate around a certain value and seem
to be a proportional control. Thus, we nd that one cardiac cycle is similar
but not identic to another. As a consequence, the distance between cardiac
cycles varies temporally and depends of the physiological conditions. This
physiological variability on the heart rate is called Heart Rate Variability
(HRV). However, as we can observe in gure 5.1, we can select dierent
points in order to measure this variability. From all these points, R peak is
selected because it presents some evident characteristics, such as high frequency content and low noise sensibility. The measurement of the distance
between R intervals is known as tachogram. Figure 5.2 shows this procedure.
From our precedent discussion, we may conceive that mechanical movements of chest wall for the respiration process aects the heart rate, since
baroreceptors are aected by the pressure changes generated during breath-
5. HEART RATE VARIABILITY
Figure 5.2: ECG, tachogram and tachogram spectrum
44
45
ing. In the last decades, the study of beat-by-beat changes in the physiological variables related to cardiovascular function and its correlations with
other systems has become a broad eld of research. Now it is possible to
quantify the relationships between variations in cardiac rhythm and other
cardio-cerebral-respiratory variables by using conventional and advanced approaches of signal processing.
Earlier physiological researches with spectral analysis suggest a strong
correlation between the heart rate and the autonomic nervous system. Wide
band of the spectral components of heart rate includes frequencies from
0.003 Hz until 0.5 Hz. This range is divided in three principal components:
range between 0.003 - 0.04 Hz (Very Low Frequency component, VLF) takes
account of long-term regulation mechanisms, especially during OSA it could
represents apnea repetition, 0.04 - 0.15 Hz (Low Frequency Component, LF)
characterizes sympathetic activation but under certain conditions it could be
inuenced by respiration and consequently by a possible participation of the
vagal nerve. The range between 0.15 - 0.5 Hz (High Frequency Component,
HF) corresponds to parasympathetic ow and is highly synchronous with
respiration [Malliani, 1999b] [Berntson et al., 1997] (see gure 5.2).
Finally, during NREM sleep, heart rate is more regular and lower than
during wakefulness, while in REM sleep heart rate exhibits an increment and
becomes completely irregular. Studying these variations being as function
of the analysis of the HRV behavior is interesting, because the information
extracted exhibits the evolution and behavior of other systems, such as respiratory and ANS in a non invasive way. Furthermore, ECG presents a higher
signal to noise ratio and its acquisition is simply than compared with EEG.
The individual spectral components derived from heart rate variability
signal are not always well dened, since there are dynamical interactions between the various components, particularly those arising from the respiratory
activity (changes in the intrathoracic pressure by mechanics movements) and
blood pressure (baroreex interactions) [DL, 1983]. Most of the studies on
sleep research have used spectral techniques that require some condition
5. HEART RATE VARIABILITY
46
in the signals, particularity "stationarity". In order to maintain this condition, a signal has to maintain its rst and second statistic moments invariant throughout the time [Somers VK, 1993] [Trinder J, 2001] [Burgess HJ,
2004] [Scholz UJ, 1997]. Sleep signals present a variety of steady state
during the night time and the application of these techniques is correct.
However, also physiological signals during sleep present a variety of non linear and non stationary patterns during night time, and advanced spectral
decomposition approaches are required in order to capture the time evolution
of the dynamic interactions.
6. Mathematic Approaches
Physiological signals carry on information about system state. Analysis,
classication and extraction of the main signal characteristics in dierent
physical and physiological conditions are important for understanding and
comprehension of our system. When we acquire physiological signals, they
present a time evolution and some important features may be extracted
to describe their behavior. However, most of the physiological signals also
present an intrinsic pattern that uctuates throughout the time. To study
this uctuation on time domain results a dicult task. In order to resolve
this problem, a series of approaches have been developed. We can nd linear
and non linear methods such as Fourier transform (FT) and recurrence plots
respectively.
Fourier transform models a signal as a linear combination of a set of
orthogonal elementary functions (sinusoids), or described in other words, a
sum of weighted sinusoids. However, the signal to be analyzed by Fourier
transform must obey some statistical characteristics, its mean and variance
must remain constant in time. For this reason, FT does not take care
about the time evolution of the signal since establishes constant uctuations. Physiological signals obey this rule during some such conditions as
resting. Conversely, physiological signals present rapid changes in an innity
of circumstances in order to react fast and maintain the body homeostasis
such as in a simple tilt-rest manoeuver, sit-stand up situations, or in order
to developed changes of state that are necessary to carry on some natural
specic works such as during the dierent sleep stages. Then, it is necessary
to think in other more sophisticated approaches that allow us to evaluate a
time-variant analysis to explore all the evolving characteristic of our signals
6. MATHEMATICAL APPROACHES
48
across time.
This chapter is divided in two sections: Time-Varying Autoregressive
Models (TVAMs) and Time-Frequency Distributions (TFDs). TVAMs generate a signal model as the combination of a weighted linear polynomial and
adapting itself by a prediction of the future output. On the other side, TFD
develops an analysis based on the relation of the signal with itself but shifted,
evaluating the autocorrelation function without the expectation operation.
6.1 Time-varying autoregressive models
Time-varying autoregressive models are powerful approaches that allow us to
generate a model of a phenomena in study. In the biomedical eld, biological
and physiological signals contain important information that can be useful to
understand or to diagnostic the system state. TVAMs are an approach that
generate a explicit mathematical model of a process or a system. Model parameters can be used in signal analysis and pattern recognition. In addition,
it is possible to relate the model parameters to the physical or physiological
aspects of the system in order to acquire a deep understanding.
The ideology of TVAM is based on the lter theory, where the lter
parameters represent the system model. Then we will try to nd the lter
parameters (model of the system) on the bases of an input/output relationship. In this way, if we are able to nd the parameters of the model
at time n we can predict the next system output at time n + τ. A lter
can be classied as linear or non linear. If the output is a linear function of
the observation applied to the lter (system), the lter is said being linear.
Otherwise, the lter is nonlinear. In addition, if the lter parameters remain
unchanged through the time, the lter is non-variant. Otherwise, the lter is time-varying. Any system can be model from the following dierence
equation:
P
y(n) = − ∑ ak y(n − k) +
k=1
Q
∑ bm x(n − m)
m=0
(6.1)
49
6.1. Time-varying autoregressive models
where a0 = 1. x(n) represents the input process while y(n) the output
signal at time n. Parameters bm point out how the present and the past
Q samples of the input are combined linearly to generate the present output. Parameters ak point out how the past output samples are combined to
generate the present output. The second summation of the right side is a
moving average (MA) lter, which is a weighted summation of the present
and Q past input samples. The rst summation of the right side is an autoregressive lter, which is a weighting summation of the past P output
samples. Where P and Q represent the lter order. Finally, we can see the
whole system as a linear combination of MA and AR models or ARMA system. In a dierent landscape, we can see the model as a linear combination
of a FIR and IIR lters. P and Q also represent the observation sample
of the system. In other words, this model shows that the current output
sample may be predicted with a linear combination of the present and some
past input samples and some past output samples. The model is called linear prediction model [Haykin, 1996b] [Rangayyan, 2002] [Bianchi AM, 1993].
Applying z −trans f orm to Equation 6.1, it is easy to obtain the transfer
function of the system:
H(z) = Y (z)/X(z) =
−m
1 + ∑Q
m=0 bm z
1 + ∑Pk=1 ak z−k
(6.2)
Again the ak and bm parameters completely characterize the system. Also
we may factorize the polynomials and obtain a pole-zero model as follows:
−1
1 + ∏Q
m=1 bm (1 − zm z )
H(z) = Y (z)/X(z) =
1 + ∏Pk=1 (1 − pk z−1 )
(6.3)
where zm are the zeros of the system and pk the poles. Now the system
is completely dened by its zeros and poles. It is clear that we can obtain a
direct characterization of the system in the time and the frequency domains.
However when we work with biomedical signals such as heart rate variability, the input of the system that has generated the output sequence is
6. MATHEMATICAL APPROACHES
50
y(n)
z
-1
z
-1
z
- a1
a0 = 1
- a2
-1
- aP
~
y(n)
Σ
Σ
Σ
−
e(n)
Σ
+
Figure 6.1: Signal flow-diagram of the AR model
not observable. Then it is possible to produce a system model on basis of
the output sequence, if we only take the AR system part at time n-1 and
try to predict the output at time n. The prediction (approximation) of the
current output for an all pole system is dened as follows:
P
ỹ(n) = − ∑ ak y(n − k)
(6.4)
k=1
where ỹ(n) denotes the prediction output, then the predicted error is
evaluated as:
P
e(n) = y(n) − ỹ(n) = y(n) + ∑ ak y(n − k)
(6.5)
k=1
Figure 6.1 shows a predictor all pole model.
When the signal to be analyzed is nonstationary as the HRV during sleep
time, it is necessary to develop lter able to adapt its parameter at each new
input sample. An adaptive lter self-adjusts its transfer function in according to the prediction error. Recursive least square (RLS) and least mean
square (LMS) are the more used algorithms to optimize the lter parameters. When we are working with slow process LMS is the better, while when
we deal with non stationary signals RLS is the most adequate algorithm to
51
6.1. Time-varying autoregressive models
update the lter parameters.
We will use matrix notation in order to develop an easier handle for implementation and mathematical description. We can write the lter parameters
as:
a(n) = [a1 (n), a2 (n), a3 (n), ..., aP (n)]T
(6.6)
where the bold-faced character a represents a vector and the superscript
T is vector transposition. The past samples output samples of the AR may
be described in the following manner:
y p (n) = [y(n − 1), y(n − 2), ..., y(n − P)]T
(6.7)
The prediction of the current output may be rewritten:
ỹ(n) = aT (n)y p (n) = yTp (n)a(n) =< y, a >
(6.8)
and the prediction error becomes :
e(n) = y(n) − aT (n)y p (n)
(6.9)
Adaptive process involves a cost function which establishes the algorithm
performance. The objective is to minimize this cost function. It is minimized
in sense of least square at each time n as:
n
CFP (n) =
∑ λn−k |e(n)|2
(6.10)
k=1
where the observation interval is dened between 1 ≤ k ≤ n and λ is the
forgetting factor. λ weights the vector of prediction error giving more importance to the recent error, λn−k always is less than one. Self-adjustment
and forgetting factor are desirable characteristics when we work with non
6. MATHEMATICAL APPROACHES
52
stationary sequences. 1/(1 − λ) represents the memory of the algorithm.
The Wiener-Hopf equation 6.11 is necessary and sucient condition to
minimize the cost function. The normal equation to be solved in the RLS
[Haykin, 1996a] algorithm is:
Φ(n)a(n) = CFP (n)
(6.11)
where a is the optimal lter vector, Φ is the time-average autocorrelation
function weighted (PxP matrix) of the past system outputs:
P
Φ(n) =
∑ λn−k y p (k)yTp (k)
(6.12)
k=1
and
CFP = [CFP , 0 p ]T
(6.13)
where 0 p is an all zero vector of P elements.
Finally a summary of the TVAM based on RLS algorithm to minimize
the the cost function is presented in the following:
Parameters :
• P = lter order
• λ = forgetting factor
• δ = value to initialize P(0)
• where C = Φ(n)−1
Initialization:
• a(n) = 0
53
6.1. Time-varying autoregressive models
• C(0)=δI
• where δI is a P x P identity matrix
• g(n) = correction factor or Kalman gain
Thereafter we only need to compute the following sequence of equations
in order to obtain sample by sample the parameters that characterize out
model [Marple, 1987].
for n = 0ton = Datalength run:
y(n) p = [y(n − 1), y(n − 2), ..., y(n − P)]T
(6.14)
e(n) = y(n) − aT (n)y(n) p
(6.15)
g(n) = C(n − 1)y(n) p {λ + y(n)Tp C(n − 1)y(n)Tp }−1
(6.16)
C(n) = λ−1 C(n − 1) − λ− 1g(n)y(n)Tp C
(6.17)
a(n) = a(n) + e(n)g(n)
(6.18)
Now we can evaluated directly the time evolution of the power spectral
density (PSD) from the time-varying coecients using the next relation:
PSD( f , n) =
T σ2
2
|1 + ∑Pk=1 exp− j2π f kT |
where σ is the variance of the prediction error.
(6.19)
6. MATHEMATICAL APPROACHES
54
So far, we are described the time-varying lter for a single channel.
But as described previously, sleep and its pathologies produce an stable
homeostasis based on the interaction among dierent system. Multichannel
time-varying lters allow us to analyze continuously the mutual interaction
among those systems. We can extend the Equation 6.1 in a multichannel
linear system form S with M variables as follows:

y1 (n) =














 y2 (n) =
S=















∑Pk=1 a11 (k)y1 (n − k)
∑Pk=1 a12 (k)y2 (n − k) + +̇
∑Pk=1 a1M (k)yM (n − k) + e1 (n)
∑Pk=1 a21 (k)y1 (n − k)+
∑Pk=1 a22 (k)y2 (n − k) + +̇
∑Pk=1 a2M (k)yM (n − k) + e2 (n)
yM (n) = ∑Pk=1 aM1 (k)y1 (n − k)+
∑Pk=1 aM2 (k)y2 (n − k) + +̇
∑Pk=1 aMM (k)yM (n − k) + eM (n)
(6.20)
where n represents the time and P is the model order and e is a white
noise (for us it will be the prediction error with zero mean and covariance
V). The model can be described in matrix form as follows:
y(n) =
P
∑ A(k)y(n − k) + e(n)
(6.21)
k=1
Where
¯
¯ a (k) a (k) · · · a (k)
12
1M
¯ 11
¯
¯ a21 (k) a22 (k) · · · a2M (k)
A(k) = ¯¯
..
..
..
..
.
.
.
.
¯
¯
¯ aM1 (k)
···
· · · aMM (k)
¯
¯
¯ y (n) ¯
¯ 1
¯
¯
¯
¯ y2 (n) ¯
y(n) = ¯¯ .. ¯¯
.
¯
¯
¯
¯
¯ yM (n) ¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
(6.22)
(6.23)
55
6.1. Time-varying autoregressive models
¯
¯
¯ e (n) ¯
1
¯
¯
¯
¯
¯ e2 (n) ¯
¯
e(n) = ¯ .. ¯¯
.
¯
¯
¯
¯
¯ eM (n) ¯
(6.24)
we can observe that at specic time n, the model is characterized by:
¯
¯
An = ¯¯ An (1) An (2) · · · An (p) ¯¯
(6.25)
We can update at each time the matrix An in a recursive form according
to :
An+1 = An + Gn e(n + 1)
(6.26)
where e(n + 1) is a Mx1 vector with the prediction errors for all the system output variables, and Gn is the analogous to the Kalman gain vector.
Note that the relation 6.26 in the same that the relation 6.18 for the classical
RLS algorithm, but extended to multichannel case.
For a multichannel AR model the power spectral density in given by
( [Marple, 1987]) :
Pn ( f ) = (An ( f )−1 Vn An ( f ))−H )T
(6.27)
where T is the sampling period, H denotes the Hermitian transpose, V
is the covariance matrix of the multichannel noise input process at time n
(covariance of the prediction error) and A( f ) is given by:
P
An ( f ) = I + ∑ An (k)exp−2πik f T
k=1
where I is the identity matrix.
(6.28)
6. MATHEMATICAL APPROACHES
56
As a result, we obtain the following Hermitian power spectral density
matrix :
¯
¯ P (f) P (f)
12
¯ 11
¯
¯ P21 ( f ) P22 ( f )
Pn ( f ) = ¯¯
..
..
.
.
¯
¯
¯ PM1 ( f )
···
¯
¯
¯
¯
¯
¯
¯
¯
¯
· · · PMM ( f ) ¯
···
···
..
.
P1M ( f )
P2M ( f )
..
.
(6.29)
where the diagonal elements contain the spectra of individual channels
and the o-daigonal elements contain the cross-spectra. Finally, we can
evaluate a measure of the spectral dependence between two channels. This
measure is called complex Coherence and is computed as :
Pi j ( f )
p
γi j ( f )n = p
Pii ( f ) Pj j ( f )
(6.30)
the coherence spectrum between two channels is given by:
¯
¯2
ηi j ( f )n = ¯γi j ( f )n ¯
(6.31)
while the phase spectrum between two channels is given by:
·
Im(ηi j ( f )n )
θi j ( f )n = tan−1
Re(ηi j ( f )n )
¸
(6.32)
6.2 Time-Frequency Distributions (TFD)
This section deals with the non linear counterpart of Time-variant autoregressive models. Time-Frequency Representations (TFRs) help us to characterize a time monodimensional x(t) signal in a time-frequency plane Tx (t, f ).
A TFR allows us to analyze the frequency content of a signal at each time.
TFRs are separated in two basic groups: linear and quadratic TFRs. Inside
to linear TFRs group we can nd the wavelets transform (WT) and the short
57
6.2. Time-Frequency Distributions (TFD)
time Fourier transform (STFT).
WT can be seen like a lter bank, in other words, the analyzed sequence
is ltered or decomposed in its frequency components by a cascade of lters
that are a dichotomy scaled versions of the rst prototype. Compromising
in this approach resides in the selection of the best lter that match the
frequency bands that are typical of HRV.
STFT is based on the Fourier transform of a window that runs through
the signal. As results, we obtain a spectrum that moves together with the
window and we can localize in time, the spectral components of the signal.
This approach suers of the uncertainty principle since frequency resolution
depends of the window length. If the window is large, we obtain a high
frequency resolution but a small time resolution and viceversa.
Finally, Quadratic TFR (QTFR) computes the Fourier Transform of the
Autocorrelation Function at each time without evaluate the Expectation
Operator. In 1942 Eugene Wigner described this approach in the quantum
mechanics context, later in 1948 Ville reformulated it as a TFR, creating the
Wigner-Ville distribution.
QTFRs oer high resolution in both time and frequency. However the
quadratic nature of QTFR generates interference terms that could aect the
interpretation of frequency content of the signal. In order to overcome this
problem have been developed dierent techniques to reduce the interference
terms and to obtain a clearer time-frequency distribution. This work focus
on the QTFRs due to their ability to analyze e fast changes as those present
in the HRV during events as Arousals.
Wigner-Ville distribution is dened as:
WV D(t, f ) =
Z +∞
−∞
τ
τ
x(t − )x∗ (t + )e− jwτ dτ
2
2
(6.33)
6. MATHEMATICAL APPROACHES
58
we can observe that:
τ
τ
x(t − )x∗ (t + ) = x(t)x∗ (t + τ)
2
2
(6.34)
this represents the instantaneous correlation. If we evaluate the autocorrelation function, we remove the time information since the correlation
function is the average of the instantaneous correlation as we can see from
the next equation:
R(τ) =
Z +∞
−∞
τ
τ
x(t − )x∗ (t + ) =
2
2
Z +∞
−∞
x(t)x∗ (t + τ)
(6.35)
From Equation 6.33, it is clear that we obtain an energy distribution of a
signal with high time -frequency resolution. However, due to the quadratic
structure of the transform, when we work with multi-component signals,
the quadratic superposition principle applies for the TFRs. Quadratic superposition principle states (The following mathematic description was taken
from [Hlawatsch F, 1992]):
x(t) = c1 x1 (t) + c2 x2 (t)
(6.36)
⇒
Tx (t, f ) = |c1 |2 Tx1 (t, f )+|c2 |2 Tx2 (t, f )+c1 c∗2 Tx1 x2 (t, f )+c∗1 c2 Tx2 x1 (t, f ) (6.37)
where Tx represents the TFR of the auto-terms while T x1 x2 is the TFR
of the cross-terms (k 6= m). Interference terms have some well dened characteristics. For any pair of signal components ck xk (t) and cm xm (t) exists
one interference term ck c∗m T xk xm (t, f ) + c∗k cm T xk xm (t, f ). For a signal with
N components exists N auto-terms and N(N − 1)/2 interference terms. The
interference terms have a well dened geometry.
Figure 6.2 shows two signal components in the points (t1 , f1 ) and (t2 , f2 )
(auto-terms) and one interference term. Where (t12 , f12 ) is the center of the
59
6.2. Time-Frequency Distributions (TFD)
Direction of oscilation
Signal Term
(t1,f1)
(t12,f12)
1/|τ12|
Interference terms
Signal Term
(t2,f2)
1/|υ12|
Figure 6.2: Geometric distribution of interference terms in the time-frequency
plane, figure taken from htt p : //gdr − isis.org/t f tb/tutorial/ and modified
6. MATHEMATICAL APPROACHES
60
plot and t12 = (t1 + t2 )/2, f12 = ( f1 + f2 )/2; τ12 = t1 − t2 , ϑ12 = f1 − f2 . Interference term is located around the center (t12 , f12 ) and oscillated with an
oscillation period 1/|ϑ12 | with respect to the time and 1/|τ12 | with respect
to the frequency. The frequency of the oscillations is directly proportional
to the distance between the components in the time-frequency plane. The
direction of the oscillations is perpendicular to the line connecting the two
signals.
In other words, the interference term of two mono-component signal is
located at their geometrical midpoint and oscillates perpendicularly to the
line joining the two points interfering, with a frequency proportional to the
distance between these two points. Nevertheless, interference terms also can
occur in mono-component signals as in quadratic chirp.
Interference terms aect the visual readably of the signal energy distribution
on the time-frequency plane. However, these interference terms are required
in order to preserve the good properties of the WVD (marginal properties,
instantaneous frequency and group delay, localization, unitarity). In the past
decades, a number of modications to the WVD were developed in order to
maintain most of the good properties and to reduce the most possible the
interference terms [Choi HI, 1989] [Khadra LM, 1998].
When we work with physiological signals, the basic desirable property in
the TFRs is the time-frequency shift invariance. This property states that
if a signal x(t) is delayed in time or modulated in frequency then its TFR
will be delayed in time and shifted in frequency. We may express this in
mathematic notation as follows:
x̃(t) = x(t − t0 )e j2π f0t = Tx̃ (t, f ) = Tx (t − t0 , f0 )
(6.38)
All shift invariance quadratic time-frequency representation are called
Cohen's class and are derived by ltering the WVD of a signalx(t) with a
2-D lter. Each member of the Cohen's class is unique and is associated
with a signal independent lter called kernel. Cohen's classes generally are
61
6.2. Time-Frequency Distributions (TFD)
dened as:
Z Z
Cx (t, f ) =
τ
τ
φ(t − t 0 , τ)x(t 0 − )x(t 0 + )e−2π f τ dt 0 dτ
2
2
(6.39)
Where φ(t − t 0 , τ) is a function labeled kernel. By choosing dierent kernels, dierent features of the distributions are obtained. There is an innite
number of distributions that can be obtained. However, there is a compromise in the kernel selection. Even if the interference terms are reduced
and readability of energy distribution in the time-frequency plane increase
considerably some of the good properties are lost [Cohen, 1989].
In the past years, some special kernels have been tested to analyze nonstationary biological signals [Hlawatsch F, 1995] [Pola S, 1996] [Karlsson et
al., 2000] [Chan et al., 2001]. Most of them have concluded that any kernel
is the best for all the applications. Materials and methods section for arousal
study shows an analysis of the most used TFRs in the biomedical eld. This
analysis allow us to select the best TFD that help us to analysis the behavior
of the HRV signal during transients periods produced by Arousals from sleep.
6. MATHEMATICAL APPROACHES
62
7. Pattern Classication
Pattern recognition is the process of separating data in classes based on a
series of characteristics that dene each class. Classication is useful for deciding the best response for a specic action. Pattern recognition is a broad
eld with applications on the most diverse areas such as DNA sequence identication, speech recognition and robotics. The pattern recognition process
is formed by some steps :
• Signal Acquisition
• Signal preprocessing or ltering
• Signal processing or feature extraction
• Model designing
• Decision
In the following sections will be analyzed the physiological evolution and
state of the ANS during normal sleep and obstructive sleep apnea. In those
analysis will be put into evidence how obstructive sleep apnea and the different sleep stages produce variations or patterns that characterize each
condition. Thus, it results very interesting to try of developing a model for
classifying the time that a person spends in normal or in apnea sleep.
Model selection depends directly of the features that characterize the
data while decision is close related to the cost that accompanies an erroneous decision.
7. PATTERN CLASSIFICATION
64
In order to reach a reasonable successful classication, it is necessary to
choose the features carefully. The features must give a clear representation
or characterization of the classes to be separated. We are interested in nding a small number of features which give a simple decision region, and a
classier easy to train. Also we want robust features which are insensitive
to noise or other errors. For implementation we want a classier that acts
quickly, and uses few electronic components, memory or precessing steps.
Then we want to nd the best features that represent the dierent classes
simplifying the task of classication.
Classication is usually based on the availability of a set of examples that
have already been classied. This set of examples is labelled the training set
and the resulting learning strategy is characterized as supervised learning.
Learning process can also be unsupervised, it is to say that the system does
not have a priori labelled of examples, and this establishes the classes itself
based on the statistical regularities of the patterns.
Statistical pattern recognition is based on statistical characterizations
of patterns, it assumes that the patterns are generated by a probabilistic
system. A wide range of algorithms can be applied for pattern recognition,
from very simple Bayesian classiers to much more powerful neural networks.
The following is a summary of the pattern recognition techniques used in
this thesis. Much of the description is based on [Duda RO, 2001]. For deeper
understanding of Hidden Markov Model please see the review [Rabiner, 1989]
7.1 K-Nearest Neighbor
K-Nearest Neighbor (KNN) is a non parametric technique of classication,
where it is assumed that we have no a priori parameterized knowledge about
the underlying probability structure (How is assumed in Bayesian classiers).
In other words, it will be base only on information provided by training samples. KNN bypasses probability estimation and goes directly to the decision
functions. Thus, we can use it with arbitrary distributions and without the
65
7.1. K-Nearest Neighbor
assumption that the forms densities are known.
KNN estimates an unknown probability density function assumed that
the probability P that a vector x will fall in a region ℜ is given by :
Z
P=
ℜ
p(x0)d x0
(7.1)
Thus P is an average version of the density function p (x). We can
estimate this smoothed value of p by estimating the probability P. Suppose
that n samples x1 , . . . , xn are drawn independently and identically distributed
in according with the probability law p(x). Clearly, the probability that k of
these n fall in ℜ is given by the binomial law:
Ã
!
n
k
Pk =
Pk (1 − P)n − k
(7.2)
where nk gives the number of combinations of C elements from an ensemble of n, it is called the binomial of N and C, and is computed as:
!
Ã
n
k
=
n!
k!(n − k)!
(7.3)
where n! = 1x2x3x4x . . . xn , and the expected value for k is:
ε[k] = nP
(7.4)
Moreover, this binomial distribution for k peaks is very sharply around
mean, so we expect that the radio k/n will be a very good estimate for
the probability P, and hence for the average density function. This special
estimate is very accurate when n is very large (see Figure 7.1) If we assume
that p(x) is continuous and the region ℜ is so small that p does not vary
appreciably within it, we can write:
Z
P=
ℜ
p(x0)d x0 ' p(x)V
(7.5)
7. PATTERN CLASSIFICATION
66
Figure 7.1: The probability Pk of .nding k patterns in a volume where the space
averaged probability is P as a function of k/n. Each curve is labelled by the total
number of patterns n. For large n, such binomial distributions peak strongly at
k/n = P (here chosen to be 0.7).
where x is a point within ℜ and V is the volume enclosed by ℜ. Combining Equations 7.1, 7.3 and 7.4, we arrive at the following estimation for
p(x):
p(x) '
k/n
V
(7.6)
KNN species kn (number of samples falling in ℜn ) as some function of
n. Here the volume Vn is grown until it encloses kn neighbors of x.
We can estimate the posterior probabilities P(wi |x) from a set of labelled
samples by using the samples to estimate the densities involved. Suppose
that we place a cell of volume V around x and capture k samples, ki of
which turn out to be labelled wi . Then the estimate for the joint probability
p(x, wi ) is:
pn (x, wi ) =
ki /n
V
(7.7)
67
7.2. Hidden Markov Models
and thus a reasonable estimate for P(wi |x) is:
Pn (wi |x) =
pn (x, wi )
c
∑ j=1 pn (x, w j )
=
ki
k
(7.8)
where c is the number of classes. It is to say, to estimate the posterior
probability that wi is the state of nature is merely the fraction of the samples
within the cell that are labelled wi . Consequently for minimum error rate we
select the category most frequently represented within the cell. If there are
enough samples and if the cell is suciently small it can be shown that this
will yield performance approaching the best possible. In general, the larger
the value of k, the greater the probability that wi will be selected.
7.2 Hidden Markov Models
Hidden Markov Models (HMM) have great use in problems that have an
inherent temporality or a recognized pattern in time such as the REM-NREM
cycle. HMMs attempt to model a process where a sequence of events occurs
and an intrinsic pattern exists . A Markov process is a process which moves
from state to state depending only of the previous n states, here a state
could be a sleep stage. This process is called an order n model, where n is
the number of previous states aecting the choice of the present state. The
simplest Markov process is a rst order process, where the choice of state is
made only on the basis of the previous state. Let us to consider a sequence
of states at successive times:
wT = {w(1), w(2), ..., w(T )}
(7.9)
where T denotes the sequence length and w(t) is the state at any time
t . For example we might have a sequence of successive states described as
w6 = w1 , w3 , w2 , w2 , w1 , w3 . It is important to notice that the system can
remain in the same state at dierent steps, and not every state need to be
visited.
7. PATTERN CLASSIFICATION
68
Figure 7.2: The discrete states, wi , in a basic Markov Model are represented
by nodes, and the transition probabilities, ai j , by links.
Our model for the production of any sequence is described by transition
probabilities P(w j (t + 1)|wi (t)) = ai j . That says, that ai j is the time- independent probability of having state w j at step time t + 1 given the state
wi at time t . Fig. 7.2 shows all possible rst order transitions between the
states of the example.
Notices that for a rst order process with M states, there are M 2 transitions between states since it is possible for any state to follow another.
Furthermore, notice that these probabilities do not vary in time, this is an
important (if often unrealistic) assumption. If a rst order discrete time
Markov model, at any step t is in a particular state w(t), the state at step
t + 1 is a random function that depends only on the state at step t and
the transition probabilities. The M 2 transition probabilities may be collected
together in a matrix which is named State Transition Matrix.
Let's suppose we are given a particular model θ, that is the full set
of ai j (State Transition Matrix), and we have a particular sequence wT .
In order to calculate the probability that the model generates the particular sequence we multiply the successive probabilities. For instance, to
nd the probability of the sequence described previously, we would have
69
7.2. Hidden Markov Models
Figure 7.3: The discrete states, W, RN, R, in a basic sleep Markov Model
are represented by nodes, and the transition probabilities, ai j , by links. W
represents wake, NR is NREM sleep and R represents REM sleep
P(wT |θ) = a13 a32 a22 a21 a14 .
For example for a possible WAKE-NREM-REM Markov model which is
shown in the Fig. 7.3, a possible transition probabilities could be as described in Fig. 7.4.
This is, if the sleep stage was W in the past epoch, there is a probability
of 0.3 that it will be W stage now, and 0.6 that it will be NREM and 0.1
that it will be REM. Notice that because the numbers are probabilities, the
sum of the entries for each column is one.
To initialize such a system, we need to state what was the sleep stage (or
probably was) at initial time; we dene this in a vector of initial probabilities,
which will be called πvector.
That is, we know a person is awake rst to go to bed. In summary, we
can dene a rst order Markov model as:
7. PATTERN CLASSIFICATION
70
Figure 7.4: An hypothetic State Transition Matrix for the discrete states of a
Markov Model during sleep. W represents wake, NR is NREM sleep and R
represents REM sleep
• States : Wake, NREM, REM
• πvector : Dening the probability of the system being in each state of
the states at time 0.
• State Transition Matrix : The probability of the sleep stage given the
previous sleep stage.
Note however that we do not have access to direct sleep stages, but we
have all the parameters that we can extract from the physiological systems.
In our particular case, spectral parameters extracted from the heart rate
variability signal will be observable for us. Then we want an algorithm to
classify the sleep stages from the heart rate variability features and be based
under the Markov assumption.
We continue assuming that at every time of sleep, t , the system is in
a state w(t) but now we also assume that it emits some visible symbols
such as the sympathovagal balance levels. Then, the observed sequences of
states is probabilistically related to the hidden process. We can model such
a process using a hidden Markov model where there is a Markov model not
visible and a set of observable symbols which are related somehow to the
hidden states. We can dene a particular sequence of such visible states as
VT = v(1), v(2), ..., v(T ) and thus we might have V6 = v4 , v1 , v1 , v5 , v2 , v3 .
71
7.2. Hidden Markov Models
Finally, we can describe our model as follows: In any state w(t) we have
a probability of emitting a particular visible state vk (t). We denote this
probability P(vk (t)|w j (t)) = b jk . Because we have access only to the visible
states and not to the wi states, such a full model is called hidden Markov
model (Fig. 7.6 ).
The connection between the hidden states and the observable states represent the probability of generating a particular observed state given that the
Markov process is in a particular state.
Thus, we have another matrix termed confusion matrix. This matrix
contains the probabilities of the observable states given a particular hidden
state. For the sleep example the confusion matrix might be given by 7.7
Since we are using probabilities, notice that the sum of each matrix row
is 1. This means that we have the following conditions:
∑ ai j
=
1
f or
all
i
(7.10)
=
1
f or
all
j
(7.11)
j
and
∑ b jk
k
Each probability in the state matrix and in the confusion matrix is time
independent. It is to say, the matrices do not change in time as the system
evolves. In practice, this is one of the most unrealistic assumptions of the
Markov models about real processes.
Once we have given the basic preliminaries about Hidden Markov Models,
we can be able of solving three kinds of problems:
• The evaluation Problem. It supposes that we have an entire HMM,
that is, State Transition Matrix (ai j ), Confusion Matrix (b jk ) and the
7. PATTERN CLASSIFICATION
72
Figure 7.5: Hypothetic start vector for a Markov Model during sleep. W represents wake, NR is NREM sleep and R represents REM sleep
Figure 7.6: Hidden and observable states. The transition between hidden states
in shown in black while emission probabilities in red.
Figure 7.7: Hypothetic Confusion matrix of the sympathovagal balance during
the different sleep stages. sympathovagal balance is evaluated by the classical
Sympathetic/vagal relation. Lbal, Hbal and Ebal mean low, high and equilibrated sympathovagal balance respectively
73
7.2. Hidden Markov Models
vector of initialization πvector. Then we want to know the probability
that a particular sequence of visible states VT was generated by the
model.
• The Decoding problem. In a few words, it is to nd the most
probable sequence of hidden states wT given some observations VT .
• The Learning Problem. This problem deals with calculating the
Markov model (State Transition Matrix (ai j ), Confusion Matrix (b jk ))
that have generated a process. Then, given a set of training observations, known to represent a set of hidden states, to determine the
model parameters.
7.2.1 Evaluation
We can evaluate the probability that a model has generated a sequence VT
of visible states with the following expression:
P(VT ) =
rmax
∑ P(VT |wTr )P(wTr )
(7.12)
r=1
where each r indicates a particular sequence wTr {w(1), w(2), ...w(T )} of
T hidden states. If we have c hidden states, there will be rmax = cT possible terms in the sum of Equation 7.12. This corresponds to all possible
sequences of length T . Equation 7.12 means that in order to compute the
probability that a particular model has generated a sequence of T visible
states VT , we must take each possible sequence of hidden states, calculate
the probability they produce VT , and then add up these probabilities. In
other words, the product of the corresponding transition probabilities ai j of
the hidden states, and the output probabilities b jk of the visible states of
each step.
For the rst-order Markov process the probability for the hidden states
can be reformulated as:
T
P(wTr ) = ∏ P(w(t)|w(t − 1))
t=1
(7.13)
7. PATTERN CLASSIFICATION
74
it is to say, the product of the ai j 's according to the hidden sequence in
evaluation. Since we are assumed that the output probabilities depend only
of the hidden states, we can rewrite the probability of the visible states for
a determined hidden state as:
T
P(VT |wTr ) = ∏ P(v(t)|w(t))
(7.14)
t=1
this means, the product of b jk 's according to the hidden state and the
corresponding visible visible state. Finally we can rewrite Equation 7.12 as:
P(VT ) =
rmax T
∑ ∏ P(v(t)|w(t))P(w(t)|w(t − 1))
(7.15)
r=1 t=1
this equation says, that for a particular sequence of T visible states VT ,
the probability of such sequence is the sum over all rmax possible hidden
states of the conditional probability that the system has made a particular
transition multiplied by the probability that it then emitted the desired visible
state. Notice that these probabilities are captured in the parameters ai j and
b jk .
We can calculate P(VT ) recursively in order to reduce the computation
cost by dening a partial probability α j (t) for each state at each time as:


t = 0 and i 6= initial state
 0
αi (t) =
1
t = 0 and i = initial state


∑ j α(t − 1)ai j b jk v(t) otherwise
(7.16)
where b jk v(t) means the transition probability selected by the visible state
emitted at time t . This means that the only non-zero contribution to the
sum is for the index k which matches with the desired visible state at time
75
7.2. Hidden Markov Models
t . We can implement it in the forward algorithm as follows:
initialize w(1), t = 0, ai j , b jk , visible sequence P(VT ), α(0) = 1
for t ← t + 1
α j ← (t) ∑ j α(t − 1)ai j b jk
until t = T
return P(VT ) ← α0 (T )
(7.17)
end
if we have our πvector we can initialize the partial probabilities α0 ( j) as:
α1 ( j) = πvector( j)b jk
(7.18)
we can also evaluate the partial probabilities in time reversed form. This
is called Backward algorithm, which is dened as:
initialize w(T ), t = T , ai j , b jk , visible sequence P(VT )
for t ← t − 1
β j (t) ← ∑ j β(t + 1)ai j b jk
until t = 1
return P(VT ) ← βi (0)
(7.19)
end
7.2.2 Decoding
When we have a sequence of observable states P(VT ), nding the most probable sequence of hidden states regards to the decoding problem. We can
evaluate the best sequence of hidden states by enumerating every possible
path and calculating the probability of the visible sequence given. However, this procedure is very expensive and is not feasible when we have large
sequences of data. In order to nd a suitable solution we can use the simplest decoding algorithm (Viterbi algorithm), which can be implemented as
7. PATTERN CLASSIFICATION
76
follows:
begin initialize path = [], t = 0
for t ← t + 1
k = 0, α0 = 0
for k ← k + 1
αk (t) ← b jk v(t) ∑i α1 (t − 1)ai j
until k = c
j ← argmax j α j (t)
AppendTo path w j
until T = t
return path
(7.20)
end
In this case, the criterion was to select the state w j which is individually
most likely.
7.2.3 Learning
The goal of the learning in HMM is to adjust the model parameters (State
Transition Matrix (ai j ) and Confusion Matrix (b jk )) from a data-set of training samples. There is not known way to solve for a maximum likelihood
model analytically. But, some interactive procedures, such as Forwardbackward method or gradient techniques for optimization are used. We
are to describe the Forward-backward algorithm since it is a straightforward
technique and the physical meaning of the various parameter estimates can
be easily visualized.
Forward-backward method is an instance of a generalized ExpectationMaximization algorithm. The general approach will be to iteratively update
the weights in order to better explain the observed training sequence.
Previously we dened αi (t) as the probability that is in state wi (t) and
has generated the target sequence up to step t. We can similarly dene βi (t)
77
7.2. Hidden Markov Models
to be the probability that the model is in the state wi (t) and will generate
the remainder of the given target sequence: We can express βi (t) as:


wi (t) 6= sequence' nal state and t = T
 0
βi (t) =
1
wi (t) = sequence' nal state and t = T


∑ j ai j b jk v(t + 1)β j (t + 1) otherwise
(7.21)
Let's imagine that we knew αi (t) up to step T − 1, and we want to
evaluate the probability that the model could generate the last single visible observable state. βi (t) is just the probability that we make a transition to state wi (T ) multiplied by the probability that this hidden state
emitted the correct nal observable symbol. In Equation 7.21 βi (t) will
be either 0 (if wi (T ) in not the nal hidden state) or 1 (if it is). Thus,
βi (T − 1) = ∑ j ai j b jk v(T )βi (T ). Then, after determining βi (T − 1), it is possible to repeat this process, in order to nd βi (T − 2) an so on, in a backward
procedure.
βi (t) αi (t) that we calculate are estimates of the real values, since we do
not know the real value of the transition probabilities ai j and b jk in Equation
7.21. It is possible to improve the values by rst dening the probability of
transition γi j (t) between wi (t − 1) and w j (t) by giving the model generated
that the entire training sequence VT by any path. It is achieved by dening
γi j (t) as follows:
γi j (t) =
αi (t − 1)ai j b jk v(t)β j (t)
P(VT |θ)
(7.22)
where P(VT |θ) is the probability that the model generated a sequence VT
by any path. And γi j (t)is the probability of a transition from state wi (t − 1)
to w j (t) given that the model generate the complete visible sequence VT .
From this we can calculate an improved estimation for ai j . The expected
number of transitions between state wi (t − 1) and w j (t) at any time in the
7. PATTERN CLASSIFICATION
78
sequence is :
T
∑ γi j (t)
(7.23)
t=1
and the expected number of any transition from wi is:
T
∑ ∑ γik (t)
(7.24)
t=1 k
Thus âi j which is the estimate of the probability of a transition from
wi (t) to w j (t) can be evaluated by taking the ratio between the expected
number of transitions from wi (t) to w j (t) and the total expected number of
any transition from wi , thus we have:
T
T
âi j = f rac ∑ γi j (t) ∑ ∑ γik (t)
(7.25)
t=1 k
t=1
in the same manner, we can calculate a better estimation of b̂ jk v(t) by
calculating the ratio between the frequency that any particular symbol vk is
emitted and that for any symbol, this is :
T
T
t=1
t=1
v̂ jk v(t) = f rac ∑ γ jk (t)v(t) ∑ γ jk (t)
(7.26)
Then we start with a rough or arbitrary estimates of ai j and b jk , and
improve those by the repetition of the Equations 7.25 and 7.26, until some
convergence criterion is met. One could be that the change in the estimate
values for the parameters, is suciently small on the following iterations.
8. Objective
In chapters one to six the present understanding of sleep hs been described.
In addition, These sections presented how the sleep stages, respiration and
arousal from sleep aect the ANS and the HRV. The purpose of this thesis
is to further develop an understanding of these subjects with application of
advanced spectral decomposition techniques. These approaches will allow
to put into evidence the evolution of the dynamic relationships of the involved systems during sleep. Possible tool for home sleep evaluation could
be obtained from this study, that it could benet to the general population.
The rst research of this thesis deals with the study of dynamic changes
of the ANS during normal night time sleep. In respect to wakefulness, the
ANS balance was expected to decrease during the whole sleep period. In
addition, during the NREM-REM sleep cycle, the ANS balance was expected
to move toward a vagal preponderance during NREM, and toward a sympathetic inclination during REM.
The second study analyzes the possibility of nding the NREM-REM
dynamic from the autonomic control system behavior during sleep. The hypothesis was that specic characteristics of the sympathovagal balance in
REM and NREM sleep are representative of each sleep stage. We expected
high parasympathetic activity during NREM and high sympathetic activity
during REM.
In the third study the time evolution of the ANS during arousal from
sleep episodes is analyzed. It was hypothesized that a reduction on the
parasympathetic nervous activity takes place on the onset of the arousal,
8. OBJECTIVE
80
and it remains low for the duration of the arousal. Contrarily, it was hypothesized an increment on the sympathetic activity during the arousal period
that continues some seconds after the arousal ended.
In the fourth study the eects of sleep apnea in the ANS on whole night
recordings are assessed on beat-by-beat basis. It was expected a higher
general parasympathetic activity in OSA subjects than in normal subjects.
Furthermore, for OSA patients, it was expected a larger sympathetic activity
during REM thatn during NREM.
The fth study of this thesis is an attempt to develop algorithms able
to separate between normal and pathologic subjects aected by obstructive
apnea. This class separation is based on features extracted only from ECG.
ECG is considered due to its simple signal acquisition and for the impact
that obstructive apnea has on the cardiovascular and respiratory systems,
and in turn on the ECG. Furthermore, for pathologic subjects, the intention
is to localize and calculate the time that a subject spent in apnea. It was
hypothesized that the very low frequency component of the HRV was larger
in the subjects with apnea than in the normal subjects. For apnea subjects,
it was hypothesized that apnea periods have a larger very low frequency
component of the HRV than during no apnea periods. This will be the most
important characteristic to separate normal from apneic subjects.
9. Autonomic Nervous System
during Sleep
The tie relationships between cardiac ANS and sleep architecture have been
demonstrated and are of general understanding. The relationships consist in
a progressive reduction of the cardiac sympathetic activity from wakefulness
to NREM sleep and increases from NREM to REM sleep. Antagonist changes
are present on parasympathetic tone, decreases from NREM to REM [Bonnet and Arand, 1997] [Morgan et al., 1996]. Up to date, most of the studies
have analyzed the HRV data by selecting discrete segments without concerning about gradual changes on the ANS across the REM-NREM sleep
cycles and eliminating all the transitory events produced by some physiologic events such as changes between sleep stages. Only a few studies have
been concerned about of those possible changes [Scholz UJ, 1997] [Trinder J,
2001]. To this regard, during normal sleep condition, it is expected that the
parasympathetic tone is higher in the rst NREM-REM sleep cycle due to
the large duration of the deep sleep. Sympathetic ow is supposed not to be
aected by the sleep cycle. Then, independently of the NREM-REM cycle,
in mean it is expected a dierent behavior of the autonomic balance between
REM and NREM sleep. More work without preselecting the segments of the
HRV signal for analyzing the real time evolution of ANS is required.
The current study was designed to investigate the next points:
• To evaluate the time evolution of the ANS on a beat-by-beat basis
across the sleep stages.
• To re-examine with an alternative mathematic approach that the spec-
9. AUTONOMIC NERVOUS SYSTEM DURING SLEEP
82
tral components of the HRV present dierent behavior between REMNREM sleep.
• To corroborate that the model parameters present characteristics typical for REM and NREM sleep. If it is true, a possible personalized
sleep model could be created.
• To analyze potential features that could be used for a classier to
develop a sleep staging classication.
9.1 Protocol
This study was carried out in collaboration with the San Raaele Hospital in
Milan, Italy. Only healthy subjects with high and moderate sleep eciency
were selected for this study. Clinical analysis and sleep eciency were obtained by expert personal based on the classical clinical practice [Rechtschaffen A, 1968]. Age of the subjects range between 40 and 50 years. Subjects
had a body mass index less than 29 Kg/m2 . The database for this study
was integrated by 24 subjects.
All experiments were conducted at the sleep clinic of the San Rafael
Hospital, Milan, Italy. Experiments were carried out in a special department inside to the sleep clinic. The sleep center has a bathroom and four
bedrooms. The temperature is regulated by mean of an air-conditioner.
Bedrooms are completely dark and windowless.
Sleep evaluation was assessed by polysomnography in the sleep center. This consisted on two central (C3 ,C4 ) and two occipital (O1 -O2 ) EEG
derivations, electrooculogram (EOG, left and right), electromyogram (EMG,
submental), leg movement, airow, thoracic and abdominal eorts, oxygen
saturation and electrocardiogram (ECG). These signals were collected according to the standardized criteria [Rechtschaen A, 1968]. System of
acquisition was an Heritage Digital PSG Grass Telefactor. All data was acquired with 128 Hz as sampling rate.
83
9.2. Spectral analysis
Polysomnographic data was scored each 30 seconds according to the gold
standard criteria established by Rechtschaen and Kales [Rechtschaen A,
1968]. As a result of this procedure, it was obtained the hypnogram (see
chapter 3 Fig. 3.3). For the study were only used the hypnogram and the
ECG signal.
9.2 Spectral analysis
ECG record was extracted from the polysomnography data. R peaks were
detected using a derivative built and tested algorithm. Distances between
consecutive R peaks were evaluated. This procedure gave as result the
tachogram. Some R peaks were misdetected and some ectopic beats were
found in the ECG. Then, ECG and tachogram were plotted together in order
to observe clearly the erroneous beats. Thereafter, time series were searched
for misdetections and ectopic beats. Where a beat or a series of beats were
misdetected, beats were added by hand and the new tachogram recalculated.
If ectopic beats occur, they were corrected and the tachogram recomputed.
The extracted and corrected time series contain information about the
ANS behavior. This information can be obtained by decomposing the time
series in its respective frequency components. Time series present both
steady state periods and segments with rapid changes. Those fast variations
produce non-stationary properties in the signal. The time-variant autoregressive models have appropriate properties for analyzing non-stationary signals
(for more details see 6.1). The time evolution of the HRV spectrum was
directly computed from the obtained time variant autoregressive model parameters. A whole night time variant model was calculated for each subject
on a beat-by-beat basis. Generally, model order selection is base on some criterions. Akaike criterion (AIC) is one of the most used [Marple, 1987]. This
is a goodness measurement for which a model t the data. AIC measures
the trading-o between model complexity and data t. However, during
sleep, the signal is very complex. This complexity is created by the the different behavior of the physiological systems during the dierent sleep stages,
noxious events (apnea), physiological events, k-complexes, arousals, and so
9. AUTONOMIC NERVOUS SYSTEM DURING SLEEP
84
fourth. Then, selection of the best model order is a complex task, and the
use of techniques such as AIC becomes of dicult interpretation. Previous
studies have evaluated HRV signal during dierent conditions with model
orders between eight and twenty. Model orders less that eight under-t the
data, contrarily model orders higher than twenty over-t the data.
In this way, the range of the model order is limited and its selection becomes less hard. Finally, eight coecients as model order were utilized for
the all whole night recordings. Model order selection criteria was the minimum number of coecients that could t the HRV signal in order to simplify
the analysis and to assure only one pole in each spectral band. Recursive
least square algorithm (RLS) was used to estimate autoregressive parameters updating. The forgetting factor (fFactor) 0.98 (window with 50 beats)
across all the subjects records was chosen [Bianchi AM, 1993]. fFactor is
the model memory. It is a window that run each new data giving a larger
weight to the current input and an increasing decay to the old data.
Power spectrum was computed from the estimated time-varying autoregressive parameters for each time series. Power spectrum was obtained
beat-by-beat according to Equation 6.19. Spectral components may be obtained by calculating the power spectral contribution of each pole of the
model in each band or only by subdivided the total spectrum in the specic
bands. The second option is computed faster and it is expected that not
band overlapping do take place. Therefore, from each spectral estimation,
we computed the following time variant spectral indexes of the HRV:
• TP Total Power (0.003 - 0.6 Hz)
• VLF very low frequency component (0.003 - 0.02 Hz)
• LF low frequency component (0.02 - 0.15 Hz)
• HF high frequency component (0.15 - 0.6 Hz)
• LF/HF Low to high frequency components ratio
85
9.3. Data analysis
In addition to the classical spectral indexes, two new indexes were extracted from the model parameters. Taking advantage that it is generated a
model representative for each sleep stage (REM-NREM), and that only one
model pole might fall in each band, the module and phase of the representative pole in the high frequency band were extracted. It was expected, that
the beat-by-beat space evolution of the high frequency pole was characteristic for each sleep stage. From now on, this new parameter will be named
as Sleepy Pole and it is composed by:
• Module Sleepy Pole
• Phase Sleepy Pole
9.3 Data analysis
From the R-peak time series, an average value for HRV was obtained each
30 seconds. The same procedure was carried out for all spectral indexes of
the HRV and phase and module of the sleepy pole. Therefore, there were
selected intervals of data according to the following rules were obtained with
the purpose of comparing the REM and NREM sleep eects on ANS:
• For REM sleep, all average time series were taken two epochs after
the starting of REM stage and before to end the REM stage. In this
way, the eects caused by the physiological transition between sleep
stages and a possible human error were reduced.
• NREM stages were 2, 3 and 4. Only sleep intervals with at least
10 consecutive epochs and with a sequence 2,3 and 4 were selected
together. Transitions from stage 2 to stage 4 were not included in
the study. Sleep transition from light to deep sleep does not produces
an arousal episode, while from deep to light sleep generally produces
an arousal event. When an arousal event occurs strong changes in
the HRV. By selecting in this way our data for statistic analysis, there
were eliminated those hard transition in the HRV, and we can compare
our results with the previous studies. In any case, the autoregressive
9. AUTONOMIC NERVOUS SYSTEM DURING SLEEP
86
model evaluate by-by-beat the the spectral parameters for total sleep
time.
Two groups t-test was performed to evaluate signicant statistic dierences (P<0.05) between REM and NREM sleep stages in each parameter.
9.4 Results
9.4.1 Test series
Simulated signals were generated in order to test the performance of our
time-variant model. The simulated signals consisted in two main frequency
components as those found in the HRV as a reex of the ANS dynamics. The
time series were composed by two sinusoidal functions at dierent amplitudes
and with dierent degrees of added white noise. The next equations describe
the simulated signals:
y1 (n) = sin(2π0.3n1 ) + bsin(2π0.05n1 ) + cw(n1 )
(9.1)
y2 (n) = bsin(2π0.3n2 ) + sin(2π0.05n2 ) + cw(n2 )
(9.2)
yt (n) = [y1 (n), y2 (n)]
(9.3)
where n1 is the time in points from 1 to 300 and n2 from 301 to 800.
b and c are scale factors. Signal was generated with a sampling frequency
equal to 1 Hz. Depending of the forgetting factor and the dynamic of the
signal the RLS algorithm requires 20-150 points to stabilize it [Bianchi AM,
1993] [Blasi et al., 2003]. Fig. 9.1 (A) displays an example of such signals
in which an abrupt change in amplitude of the two components occurs at
the point 300.
87
9.4. Results
A
2
1.5
1
0.5
0
Amplitude
−0.5
−1
−1.5
−2
100
200
300
400
500
600
700
800
Time (sec)
B
C
2
PSD (Hz\s )
Frequency (Hz)
Time (sec)
Figure 9.1: Time-varying spectral analysis of a simulated signal based on two
sinusoidal components plus white noise. A) Simulated noised signal with high
amplitude in the component 0.05 Hz and low one 0.3 Hz component, components present amplitude exchange changes at time = 300. B) Representative
pole position in high and low frequency before (blu) and after (green) to exchange amplitude, C) Time-variant power spectral density (PSD) evaluated
from the model parameters.
9. AUTONOMIC NERVOUS SYSTEM DURING SLEEP
88
Fig. 9.1 (B) shows the localization in the unitary circle of the representative poles - for two frequency ranges (between 0.02 - 0.15 Hz and 0.15
-0.5 Hz) - obtained by the time-varying model. 180 represents 0.5 Hz. The
poles located between 90 and 120 in the unitary circle describe the sinusoidal
component with a frequency of 0.3 Hz, while poles between 0 and 30 belong
to the sinusoidal component with 0.05 Hz. Color blue represents the pole
localization before amplitude change, while green one is after the amplitude
change. We can observe that the pole localization depends directly of the
sinusoidal amplitude (power) with respect to the noise level. It is to say, if
the signal to noise ratio is high the sinusoidal wave is well dened, and the
pole is located very close to the unitary circle. As a results, the spectral
component, which is represented by the pole, is very well dened or concentrated in one determined frequency. On the other hand, if the signal to noise
ratio is low the sinusoidal wave is not well dened, and the pole goes away
from the unitary circle toward the center. This gives a less concentrated
spectral component. It is feasible to think, that the pole may help us to
discriminate between dierent sleep stages if HRV uctuations during REM
and NREM are more or less well dened. Fig. 9.1 (C) shows the temporal
evolution of the power spectral density obtained from the model parameters.
This gure shows how around to the second 300, there is a change in the
power amplitude. This change represents the modication in amplitude of
the sinusoidal components.
The last gure puts into evidence that if the uctuations in the HRV were
characteristic from each sleep stage, then we could be able to distinguish
the dierent sleep stages form the temporal evolution of the ANS. In order
to clarify our curiosity, we analyzed the RR series during REM, sleep stage
2 and 4 from one subject. Fig. 9.2 displays these results. A, C and E
subplots show the RR series of these sleep stages while B, D and F show
their respective temporal evolution for the power spectral components. We
can observe a high power in the high frequency component during sleep
stages 2 and 4. Contrarily, REM sleep shows a lower power amplitude in the
high frequency component and an higher amplitude in the LF component.
The representative poles have dierent distribution in the z-plane between
89
9.4. Results
Table 9.1: Mean and SE of the HRV indexes in function of REM and NREM
sleep stages
Index
RR (s)
LF(s2 )
HF(s2 )
LF/HF
|HFPole|
Ang(HF Pole)
NREM
1.136 ± 0.0247 *
0.1437 ± 0.0689 *
0.3158 ± 0.0829
0.6864 ± 0.3024 *
0.9269 ± 0.0128 *
0.3563 ± 0.0218
Sleep Phase
REM
1.0484 ± 0.0363 *
0.3158 ± 0.0829 *
0.2989 ± 0.1048
1.8681 ± 0.6037 *
0.8484 ± 0.0177 *
0.3467 ± 0.0247
RR = time interval between consecutive R peaks of the Electrocardiogram, LF
= low frequency component, HF = high frequency component, LF/HF low to
high frequency ratio, |HFPole| = module of the higher pole in the HF band,
Ang (HF Pole) = angle of the higher pole in the HF band. * represent significant differences P < 0.05.
REM (green) and stages 2-4 (blue and red). This shows that the ANS
exhibits dierent behavior between REM and NREM sleep and it is feasible
to separate REM and NREM sleep from the spectral parameters.
9.4.2 Experimental series
The result obtained form the spectral analysis of the HRV during sleep time
are presented in the following lines. Sleep time was divided in two classes,
REM and NREM sleep. Dynamic of the ANS across the sleep stages was
evaluated by the spectral components present in HRV. These components
were obtained by a time-varying autoregressive model.
Table 9.1 presents means and standard error of the HRV indexes during REM and NREM sleep for whole night recordings. RR mean intervals
had lower values during REM respect to NREM sleep. This decrement re-
9. AUTONOMIC NERVOUS SYSTEM DURING SLEEP
A
90
B
REM
1.3
2
PSD (Hz/s )
1.1
1
Time (sec)
seconds
1.2
9
0.8
0
100
200
300
400
500
600
Tiempo (sec)
C
D
STAGE 2
Frequency (Hz)
1.4
1.2
PSD (Hz/s2)
Time (sec)
seconds
1.6
1
0.8
0
100
200
300
400
500
600
Tiempo (sec)
F
E
Frequency (Hz)
STAGE 4
1.3
PSD (Hz/s2 )
1.2
Time (sec)
seconds
1.4
1.1
1
0.9
0
100
200
300
400
500
600
700
800
900
90
Tiempo (sec)
1
I
G
120
Frequency (Hz)
60
0.8
1
60
0.6
150
30
0.4
0.8
0.2
180
0
0.6
Poles in High Frequency
0.4
210
GREEN = REM
RED = STAGE 4
BLU = STAGE 2
240
330
300
270
Figure 9.2: Time-varying spectral analysis of RR series in REM, stage 2 and
4 during sleep. A, C and E show the RR series in REM, Stage 2 and 4 during
the sleep time while B, D and F display their respective power spectral density.
Representative pole position for each sleep stage in the z-plane are REM =
green, blue = stage 2 and red = stage 4.
91
9.4. Results
sults statically signicant. As it was expected, LF component in REM sleep
presented higher values than those in NREM sleep, the dierence between
REM and NREM was statistically signicant. HF component had larger levels during NREM sleep than REM sleep. However, the values did not show
signicant dierences how we expected. The symphatovagal balance was
signicantly lower during NREM sleep. Finally, the sleepy pole presented
values closer to the unitary circle during NREM than REM, and these values
were statistically dierent.
Fig. 9.3 depicts the typical time evolution of the sleepy pole, power
spectrum and spectral indexes of the HRV during sleep for a normal subject.
Fig. 9.3 (A) displays the placement of the representative HF pole in REM
(gray x) and NREM (black x) sleep stages. During NREM stage, the HF
poles are concentrated very close to the unitary circle, and these ones go
far from the unitary circle and move toward a lower frequency during REM
sleep. In the gure 180 represents the half of the sampling frequency (mean
of the whole night RR intervals).
Fig. 9.3 (B) shows an example of time evolution of the Power spectral
density. During NREM sleep a frequency component around 0.3 Hz (HF)
is clear. This component exhibits the following characteristics, high concentration and stability. The same spectral component acquires a dierent
behavior during REM sleep, instability and low frequency concentration.
Fig. 9.3 (C) shows the HRV spectral components during the sleep time.
From the top to the bottom RR intervals, LF, HF, LF/HF and module and
frequency of the HF pole during each epoch. Each epoch was computed
according to the hypnogram, this means, each 30 seconds. The RR mean
series exhibits a decrement when REM stage occurs or during the change
from deeper to light sleep stage, such as could be the change from stage 4
to 2. The HF showed similar variations as the RR intervals but not so clear.
The behavior of the LF presented the opposite variations in respect to the
RR intervals with strong changes between REM and NREM. If one observes
the LF/HF ratio, the combination of both frequency components, it reveals
9. AUTONOMIC NERVOUS SYSTEM DURING SLEEP
92
a comprehensible dierence between the REM and NREM sleep stages. The
module of the HF pole shows a characteristic oscillatory pattern. During
REM, this tends to decrease as compared with NREM one. The last subplot
shows the frequency of the HF pole, where an instability of the angle pole
takes place during REM stage and is almost constant in NREM sleep.
9.5 Discussion
This study analyzes the behavior of the Heart Rate Variability during normal
sleep. Time-variant autoregressive model approach was used to obtain the
spectral uctuations of HRV. The extraction of these uctuations allows us
to study the ANS behavior during sleep. ANS behavior was compared between REM and NREM sleep independently of sleep time.
The most important argument on this study regards the application of a
mathematic approach which is able to follow the dynamics of the heart rate
variability across sleep stages. The advantage of the autoregressive models
with respect to the classical ones, such as Fourier Transform analysis, is the
ability for adjusting the model parameters at each new beat along time. We
can visualize this approach as the best linear polynomial that ts a data time
window and runs across the data at each beat. From the polynomial parameters, it is possible to obtain the spectral components at each sample data,
and consequently the analysis of the ANS with the same sampling period. In
addition, this approach does not need an equi-spaced sampling frequency as
those approaches based on the Fourier transform. Time-variant autoregressive models have an elevate computational eciency and a reduced complexity. These characteristics become fundamental when we think about
software or hardware implementation.
Those characteristics make interesting and attractive the application of
time-varying models in the research of the sleep. As it was commented
previously in sections 2 to 4, the variations across the time of consecutive
beats reexed the ability of the heart in adapting at the most diverse circumstances. This characteristic permits us to analyze the intrinsic cardiac
93
9.5. Discussion
control mechanisms (ANS) [Malliani, 1999b]. Not only, it is possible to characterize the cardiac system responses during normal physiological conditions,
also it exhibits patterns that characterize specic pathologies [Bianchi AM,
1990] [Blasi et al., 2003] [Penzel et al., 2003b] [Sforza et al., 2002]. The
HRV seems to be a promising and a non invasive tool for diagnosing and
monitoring the cardiac control mechanisms and the healthy status.
We may relate physiologic mechanisms and the mathematic approach in
four basic steps:
• Control cardiac mechanisms change on a beat by beat basis under
certain physiological levels.
• Those variations are reected as uctuations on the generated beat
series.
• Time-varying models are able to follow sample by sample the dynamic
of a time series.
• Time-varying models could be able to follow beat-by-beat the dynamic
of the ANS in the most diverse conditions.
The application of time-varying models to the HRV signal seems natural
for monitoring physiological cardiac control mechanisms and for diagnosing
health status. However, as any system in the real world, it does exist some
diculties that must be taken in consideration. Heart rate variability or
better for us ANS, reacts depending of the body necessities. Sympathetic
tone increases in conditions of psychological or physiological stress in order
to deliver enough oxygen and nutrients to the organs [Rhoades AR, 2006].
The velocity of reaction depends directly of the own stress, physical condition and physiological limits. When these changes require a fast reaction,
we found transitories on HRV produced mainly by sympathetic activity. On
the other side, parasympathetic ow produces antagonistic changes. However, not necessarily a high participation of one produces a low activation
of the other one. It is surprising how this control is able to maintain in the
best condition the body homeostasis. For example, in a simple rest-stand
9. AUTONOMIC NERVOUS SYSTEM DURING SLEEP
94
or rest-tilt test very rapid changes on HRV can be observed [Mainardi et
al., 2002] [Furlan et al., 2000]. Further, during an arousal from sleep rapid
changes in the HRV are caused by a withdrawal on parasympathetic tone
and an increasing on sympathetic activity [Sforza et al., 2000] [Somers et al.,
1993a]. During normal sleep the changes from SWS to states with higher
cerebral activity such as stage 2 or REM, also rapid changes on HRV are
produced. Not only during normal conditions are generated rapid changes
on HRV, we can also nd sudden reaction of the ANS during pathologies
as obstructive sleep apnea [Somers VK, 1995], central apnea [Somers et al.,
1993b], periodic leg movements [Sforza et al., 2005].
Fluctuations on consecutive beats have been studied in other pathologies
as diabetes [Bianchi AM, 1990], syncope [Mainardi et al., 1997], asthma
[Garrard et al., 1992] [Kazuma et al., 1997] and epilepsy [Yang et al.,
2001] [Tomson et al., 1998] [Evrengül et al., 2005]. Type 2 diabetes is
associates with altered sympatho/vagal balance resulting from a depression
of parasympathetic activity [Bianchi AM, 1990] [Meyer et al., 2004]. Asthma
subjects presents an elevated parasympathetic tone and a reduced sympathetic tone. HRV is a simple non invasive tool to evaluate the ANS that
has been introduced in general anesthesia [Goldberger, 1999] [Fan et al.,
1994]. HRV is used as monitoring index of anesthesia level, since deep anesthesia produce a depression on both parasympathetic and sympathetic tone,
and HRV is very low. When the patient begins the recovery phase, HRV
also begins to increase. Real time monitoring of HRV gives additional information about surgical patient status. The association between HRV and
general cardiac health is supported by many studies that show that exercise
increases ANS tone and that improved physical tness is correlated with increases in HRV [Gulli et al., 2003] [Ishida and Okada, 2001] [Iwane et al.,
2000].
As one can notice, HRV is very sensitive but not specic. Dierent physical, physiological and mental conditions produce similar behavior in HRV.
Besides, the HRV is not characteristic about each condition, HRV is a useful
non invasive tool to evaluate the ANS state. HRV oers a general landscape
95
9.5. Discussion
and it is possible to discriminate between well and bad ANS states. In addition, if we limit the study to a specic situation, HRV oers important
information. HRV could also be combined with other signals in order to obtain a good monitoring and diagnosis. In our rst objective, we limited the
analysis to the status and behavior of the ANS during sleep in normal subjects, and specically to dene dierences between REM and NREM sleep.
Most of previous studies that evaluated ANS behavior during sleep have
applied traditional spectral decomposition techniques, such as Fourier transform or parametric batch analysis. [Scholz UJ, 1997] studied the ANS responses during stationary conditions applying a batch autoregressive model
during standard Valsava manoeuver and orthostatic position and during early
and later REM periods. They found a higher sympathetic activity during later
REM periods. [Busek et al., 2005] analyzed ANS between NREM and REM
sleep, applying Fast Fourier transform to HRV series. They found higher
values on LF, VLF and HF/LF during REM than NREM sleep. These results reect a major sympathetic activation during REM. [Burgess HJ, 2004]
found signicant changes in LF index applying FFT to 2 minutes segments
between REM and NREM. [Trinder J, 2001] studied the eects of the sleep
time in ANS. They concluded that there is an increment in parasympathetic
activity during NREM and a similar behavior of ANS during REM and wakefulness. They carried out the analysis by selecting 2 minutes segments and
applied FFT. In another study [Bonnet and Arand, 1997] arrived to the same
results. They only diered from [Trinder J, 2001] in the length segment selection, ve minutes. Also [Penzel et al., 2003a] studied the HRV during the
dierent sleep stages in segment of ve minutes, they concluded that exist
a general increment of parasympathetic activity during whole sleep. They
clarify the diculty of assuring a stationary condition during sleep in short
time series.
Since spectral components of HRV are directly related to ANS behavior,
the approaches based on spectral analysis result adequate to analyze the
ANS during sleep. However, some studies have presented some approaches
that permit us to obtain a dierent perspective on HRV during sleep. A
9. AUTONOMIC NERVOUS SYSTEM DURING SLEEP
96
well accepted non linear procedure are the Poncairè Plots. This measures
the dynamic of a RR intervals respect to the precedent one. However,
the indexes extracted from this approach are tie correlated to the temporal indexes of HRV [Otzenberger et al., 1998] [Burgess HJ, 2004] [Carrasco
et al., 2001] [Brennan et al., 2001]. They also found and increment on
parasympathetic activity during sleep when compared to wakefulness. Another interesting approach is the Detrend Fluctuation Analysis which gives
a measure of long-range correlation of a time series. [Penzel, 2003] found
that the average scaling index α2 is higher in REM than NREM sleep.
We found statistical dierences in LF between NREM and REM, which is
in agreement with the previous studies previously commented [Somers VK,
1993] [Trinder J, 2001]. This result supports strongly that our approach is
able to describe beat-by-beat the ANS during sleep. However, some discrepancies can be found when we focus on HF component. [Busek et al.,
2005] [Trinder J, 2001] [Scholz UJ, 1997] studies showed a statistical differences between REM-NREM sleep in the HF, result that diers from ours
and other studies [Burgess HJ, 2004] [Penzel, 2003]. These discrepancies
remain unclear and are dicult to discuss. They may be related to source
dierences in the groups of subjects or in the analysis procedure. However,
it is possible to give an explanation based on the model parameters, specially
based on ”sleepypole”. If we observe Fig. 9.2 A, it is clear that HF is lower
during REM sleep, but really it is not lower, it is less concentrated on a
specic frequency. HF presents high dispersion and low concentration. As it
is illustrated by the position on the sleepy pole in the z − plane. The sleepy
pole is more distant from the unitary circle during REM sleep. Thus, the
power is speared on the frequency band. It could be very interesting follows
the time evolution of the sleep pole during REM to possible understand how
the physiological mechanisms evolve in the time.
Besides autoregressive models seem appropriate tools to evaluate the
spectral parameters of the HRV, they present some diculties that it is
necessary to take into consideration in order to obtain their best performance. Time-varying autoregressive models adjust the polynomial model
97
9.5. Discussion
coecients in a minimum square mean sense based on the prediction error.
This procedure assures that we obtain the best model order for each time
series analyzed. In order to obtain the best performance of a time-variant
model it is necessary to select correctly two parameters: model order and
forgetting factor. Dierent criteria have been developed to decide the best
model order. Akaike criterion is one of the most widely used to this purpose.
Akaike criterion is a measure of goodness of how it is tted to a series. This
option is suitable when we work with short time series or with some grade
of complexity. For example, if one wants to analyze sleep stage two, it is
suitable to think in a possible mean model since the statistical properties are
more or less the same. However, if an arousal takes place, a dierent model
order would be necessary. Then, the selection of the model order based on
Akaike criterion results not suitable for sleep analysis if whole night series
must be analyzed on a beat-by-beat basis. Forgetting factor is the second
important parameter, that it is necessary to select. This parameter is related
to the convergence time of the lter and how much are important the past
data. If we select a low forgetting factor, we consider only the present value.
Contrarily, if a high forgetting factor is selected the contribution of the new
data is masked by the past data, since it is given almost the same importance
to the past data. As a consequence, the lter adaptation is very slow.
At this point, some questions could help us to resolve the selection of
both the best model order and forgetting factor. We are interested in founding the values for which we can model or t the sleep time series in all the
dierent circumstances and within the most variable statistical properties.
• What are the minimum and maximum number of coecients necessary
to describe the HRV signal in the most variable conditions?
• How important is the new beat for describe sleep stages?
It is important to take a look to the past, [Scholz UJ, 1997] [Bianchi AM,
1993] [Bianchi AM, 1992] [Cerutti et al., 2001] [Mainardi et al., 1997] [Baselli
et al., 1987] [Blasi et al., 2003] have applied model orders between 8 and
20, and forgetting factors between 0.96 to 0.995. These data oers a most
9. AUTONOMIC NERVOUS SYSTEM DURING SLEEP
98
stretch range to select the parameters. As rst intuition, selecting the higher
model order could be a good option, because we can t the HRV data in any
condition, even if it is very complex. However, a problem emerges: if the signal is very regular or extremely stationary, an over-tting occurs. Situation
not desirable, since data behavior is invented and a no realistic estimation
is obtained. On the other hand, if the lower order is selected, there is a
risk of not modeling the dynamic of the signal. How one can appreciate,
it is dicult to select the parameters. In order to solve this paradigm, we
adopted the following criterion.
• A normal person spends about 50 % of sleep time in stage 2. The
minimum waves that we need to capture are those with frequency 0.02
Hz. this means, that a observation window with at least 50 samples
(beats) is necessary.
• We tested algorithm during all sleep stages, without taking care about
the possible transitories (caused by stage change, arousal, movements,
and so on) changing model order between 8 and 12 coecients and
forgetting factor between 0.975 to 0.992.
We observed that during steady conditions, which occur during NREM
sleep, very often we had over-tting with model order equal to 12. Forgetting
factor lesser that 0.98 gave so much importance to the new entrance beat and
the information contained in the past data is lost . Forgetting factors upper
than 0.9 does not capture the new information. In addition, we thought,
why not force to model to generate one pole for each spectral component
that characterize our physiological system. In other words, two poles for
the continuous component, two for VLF, two for LF and two for HF. Then,
minimal order lter was selected (8 coecients) together with forgetting
factor equal to 0.98.
9.6 Conclusions
The time-varying Autoregressive analysis seems to be a ne tool to assess
the cardiovascular parameters during night recordings. The main advantage
99
9.6. Conclusions
is its ability to adapt at each beat, situation that allow to follow beatby-beat the physiological changes of ANS. The results obtained during the
study capture the real dynamic of the ANS. In addition, this dynamic is in
agreement with the previous studies. During REM as compared with NREM
sleep, LF, RR intervals, LF/HF presented a noticeable increment, while HF
showed a reduction. The pole module of HF component showed to be closer
to the unitary circle during NREM and far during REM.
9. AUTONOMIC NERVOUS SYSTEM DURING SLEEP
100
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Epoch No.
Figure 9.3: Time-varying spectral analysis of RR series during sleep time. A)
Example of pole displacement during REM and NREM sleep stages. Black
x represents NREM while gray x REM sleep stage. 180 in the unity circle
correspond to the half of sampling frequency. B) Dynamic of the spectral
component during sleep time. C) Spectral indexes of the heart rate variability,
from the top to the bottom . RR = time interval between consecutive R peaks of
the Electrocardiogram, LF = low frequency component, HF = high frequency
component, LF/HF = low to high frequency ratio, |HFPole| = module of the
higher pole in the HF band, Ang (HF Pole) = angle of the higher pole in the
HF band. All Indexes are presented as the mean of 30 seconds at each epoch,
which is the time of the hypnogram epoch.
10. Detection of the Sleep Stages
Sleep is natural state for resting. During sleep some changes occur in
the physiological systems. Generally, sleep is evaluated from three basic
electrophysiological signals, Electroencephalogram (EEG), Electrooculogram
(EOG) and Electromyogram (EMG). In addition, some other signals such as
airow and oxygen saturation, are added if the sleep study is aimed at the
diagnosis of some specic pathologies such as sleep apnea. Sleep evaluation is a hard task and is carried out in specialized sleep centers by expert
personnel. Normal sleep has a well dened structure. This structure is
based on specic patterns that EEG, EOG and EMG have during the sleep
time [Rechtschaen A, 1968]. This structure shows a specic time pattern
which formes dierent states. Each sleep state attains a specic behavior of
the electrophysiological signals. Five sleep stages are usually scored during
sleep : Stage 1, Stage 2, Stage 3, Stage 4 and Rapid Eye Movement Stage
(see section 3). Given the particular characteristics of the sleep stages, sleep
can also be divided in two main sleep stages Non Rapid Eye Movement
(NREM) and REM. NREM sleep is formed by the stages 1-4, during these
stages the electrophysiological signals exhibit a regular behavior. Contrarily,
during REM sleep these signals are completely irregular. For instance, EEG
presents wave forms with high frequency and low amplitude during REM,
while during NREM EEG has low frequency and high amplitude levels. Due
to the reduced number of sleep centers, sleep diagnosis is very expensive and
the evaluation of sleep and its related pathologies are underestimated.
In the last decades, the progress in mathematical modelling and the increasing availability of computational resources have initiated the resolution
of problems of high complexity such sleep evaluation. These advances to-
10. DETECTION OF THE SLEEP STAGES
102
gether with the diculty of the manual sleep evaluation and the limited
number of sleep centers, generated important eorts for developing automatic algorithms in order to detect the dierent sleep stages based on EEG
signal [Principe et al., 1989] [Porée et al., 2006] [Flexer et al., 2005].
Sleep presents a cyclical pattern between NREM and REM sleep. This
is repeated several times during the sleep time and has a duration approximately of 90-120 minutes. Sleep cycles also produces specic variations on
other physiological systems of easy measure. These variations are characteristics of the NREM-REM cycle. For instance, we can observe a stable
respiration during NREM sleep and irregular respiration in REM, Heart rate
variability exhibits regular oscillatory patterns in NREM and irregular patterns during REM. Given that HRV presents some interesting characteristics
such as easy acquisition and high signal to noise ratio, it could represent an
alternative signal to evaluate sleep (see chapter 3.2.3).
Beat by beat cardiac system presents uctuations related to the autonomic control function. These uctuations, well known as heart rate variability, describe very close the sympathovagal balance in any circumstance.
Heart rate variability presents oscillation between 0 and 0.5 Hz. Previous
studies have demonstrated that oscillations with frequencies between 0.15
and 0.5 show parasympathetic activation, while those uctuations between
0.04 and 0.15 are characteristic mainly of the sympathetic tone. Further,
those frequencies located in the range 0.003 and 0.04 are related to other
mechanism of long activations such as some variation in the hormone concentrations [Malliani, 1999a].
Based on the results presented in the section 9 and other previous ones
[Scholz UJ, 1997], the evaluation of the NREM - REM cycle from HRV
seems feasible. In order to study such possibility, in this section we propose
the analysis of the sleep classication NREM-REM based on the heart rate
variability signal. This is carried out using the time-varying autoregressive
models to extract the heart rate oscillations that characterize the sleep stages
and the hidden Markov models to classify the dierent sleep stages across
103
10.1. Database Description
the sleep time.
10.1 Database Description
Database was formed by 24 healthy subjects with high and moderate sleep
eciency. Data was collected in the San Raaele Hospital in Milan, Italy,
by specialist personnel. Data analysis and sleep eciency were obtained
by expert personal based on the classical clinical practice [Rechtschaen A,
1968]. The subjects were between 40 and 50 years. Subjects had a body
mass index less than 29 Kg/m2 . System of acquisition was an Heritage
Digital PSG Grass Telefactor. ECG was recorded with 128 Hz as sampling rate. According to standard criteria established by Rechtschaen and
Kales [Rechtschaen A, 1968], sleep stages were scored each 30 seconds
from the polysomnographic data.
The database was divided in two groups, each containing 12 subjects:
training-group and test-group. Each group contains approximately 10800
epochs. The training-set was used to build up and test our algorithm of
classication (HMM). The test-group was used to measure the performance
of the algorithm. Clinical hypnogram was used to quantify the algorithm
performance. For more detailed explication, please see section 9.1.
10.2 Methods
As commented previously, HRV exhibits dierent oscillatory patterns between REM and NREM. Regular oscillations are characteristics of NREM
sleep, while irregular oscillations appear during REM sleep. Based on this
knowledged, we followed the next steps:
1. R peaks were extracted from the ECG record by a derivative built
algorithm.
2. HRV signal was calculated by the dierence between consecutive R
peaks.
10. DETECTION OF THE SLEEP STAGES
104
3. Power spectrum of the HRV time series was estimated by applying a
time-varying autoregressive model.
4. From the total power spectrum, we extracted the dierent frequency
components that describe the function of the autonomic nervous system.
5. From the standard spectral components of the HRV model parameters,
other time series were derived.
6. Standard and derived time series were proposed as candidate features
for sleep classication, which is based on hidden Markov model.
For description of the steps one to ve please see section 9.2. The nal
set of features are shown in Table 10.1.
For all features, the rst and last awake states were eliminated. After,
an automatic arousal searcher was developed. This algorithm searches the
arousal events from the HRV. In order to dene an arousal, a sequence of
consecutive beats must obey the next criteria for each beat at time t :
• beat at time t + 2 must be lesser than %5 from the beat at time t
• beat at time t + 4 must be lesser than %10 from the beat at time t
• beat at time t + 6 must be lesser than %15 from the beat at time t
• At least one beat must be higher than %3 between time t + 6 and
t + 15 with respect to the beat at time t
• if it is true, there is an arousal at time t and jumping 20 beats in order
to search the next arousal.
This procedure is repeated for the total length of the time series.
105
10.2. Methods
Table 10.1: Features extracted from the HRV during sleep. Spectral features
were obtained by a time-varying autoregressive model.
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Feature
RR mean: µ
RR variance: σ2
mod(di f f (σ2 ))
Very Low Frequency: VLF
mod(diff(VLF))
Low Frequency: LF
mod(diff(LF))
High Frequency: HF
mod(diff(HF))
LF/HF
mod(diff(LF/HF))
LF% = LF (σ2 −V LF)
HF% = HF (σ2 −V LF)
Pole in HF (module)
Pole in HF (phase)
Pole in LF (module)
Pole in LF (phase)
10. DETECTION OF THE SLEEP STAGES
106
10.2.1 Selection and Transformation of the Features
Feature Selection is one of the most important steps in pattern recognition.
This procedure involves dierent tasks that simplify the class separation for
the classier. If we select the best features that separate the classes, we
eliminate the features with low informative content, thus the algorithm eciency increase and a better classication is obtained. The most important
task is to prevents the course of dimensionality in estimating the a posterior
distribution for the classication performed.
Dierent procedures can be used in order to select the best set of features for a specic classication. Notice that the features are selected on
the basis of the classication problem. Any feature has information for all
the classication tasks. There are some dierent ways for selecting the best
set of features. The most common is to use those features that by simple
observation give a class separation. In addition, selection can be evaluated
by statistical analysis of the features, based on either statistical dierences
or WRAP methods. WRAP methods consist in selecting the features based
on the classier performance for each group of those. In this work, the test
of Wilconxon/Mann-Whitney was applied to the features in order to nd
those features that are statistically dierent between NREM and REM sleep.
Before applying Wilconxon/Mann-Whitney to select the features, those
were normalized in order to eliminate the subject inter-variability . Normalization transforms a number series in order to attain specic statistical
properties such as limit values, variance, or average. We normalized each
time series to zero mean and unit standard deviation. Therefore for each
time series, the asymmetry and the outlier presence were evaluated through
Fischer coecient and box plot respectively. Selection of the transformation
was decided on base of the asymmetry and outlier characteristics, Table 10.2
shows those results.
After normalization and transformation Wilconxon/Mann-Whitney was
used to the new time series. only the HF features does not show statistical
dierences.
107
10.2. Methods
Table 10.2: Selection of the best transformation based on feature asymmetry
and outliers. For distributions with positive skewness ln(X) was used, while
√
for distribution with negative skewness was applied X
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Feature
µ
σ2
mod(di f f (σ2 ))
VLF
mod(diff(VLF))
LF
mod(diff(LF))
HF
mod(diff(HF))
LF/HF
mod(diff(LF/HF))
LF%
HF%
Pole in HF (module)
Pole in HF (phase)
Pole in LF (module)
Pole in LF (phase)
Strong asymmetry
No
Pos
Pos
Pos
Pos
Pos
Pos
Pos
Pos
Pos
Pos
No
No
Neg
No
Neg
No
Outlier
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
No
No
No
No
No
Transformation
any
ln(X)
ln(X)
ln(X)
ln(X)
ln(X)
ln(X)
ln(X)
ln(X)
ln(X)
ln(X)
any
any
√
X
any
√
X
any
10. DETECTION OF THE SLEEP STAGES
108
10.2.2 Hidden Markov Model
We are trying to recognize the pattern in time of NREM-REM cycle and in
order to do that we will attempt to model the process that could generate
this pattern based only on the visible variables of the HRV signal. In our
case, we will use discrete time steps, discrete states, and we may make
the Markov assumptions. A mathematic approach that allow us to nd the
model behind some observable sequence of data is the hidden Markov model
(HMM). A brief mathematic description of the HMM is presented in section
7.2. The system producing the pattern can be described as a Markov process
consisting of a πvector and a state transition matrix. Our model is a model
containing two sets of states and three sets of probabilities:
• hidden states : the (TRUE) states of a system that may be described
by a Markov process (e.g., Sleep Stages REM and NREM).
• observable states : the states of the process that are `visible' (e.g.,
HF, LF and VLF).
• πvector : contains the probability of the (hidden) model being in a
particular hidden state at time t = 0.
• state transition matrix : holding the probability of a hidden state given
the previous hidden state.
• confusion matrix : containing the probability of observing a particular
observable state given that the hidden model is in a particular hidden
state.
Thus a hidden Markov model is a standard Markov process augmented
by a set of observable states, and some probabilistic relations between them
and the hidden states.
The average each 30 seconds was calculated for all features. In this way,
we have a direct comparison with the clinical hypnogram. Thus, the number of epochs (30 seconds averages) during sleep time represents the chain
length. All epochs, where an arousal was found by our automatic arousal
109
10.3. Results
search algorithm, were considerate as wake state and were not used for the
posterior posterior analysis.
Since the features were normalized, their amplitudes showed similar minimum and maximum values. Amplitude of the features were separated between 100 dierent levels which go from the minimum until the maximum
value. From this procedure we obtained a quantization of the features.
10.2.3 Classication performance estimation
The learning procedure was carried out in the training set. From this set,
the coecients of the confusion matrix and transition matrix for each feature were evaluated. It is to say, we generated one model for each feature.
Thereafter, the classier performance was evaluate by Leave-One-Out crossvalidation technique applying the decoding algorithm. In this way, we found
the best path of states that describe the observation states. In order to
evaluate the performance of the algorithm we calculated the statistical measures of classication accuracy, sensitivity and specicity. The performance
of some features was very low, thus we decide to eliminate those features for
the nal decision. In this way, we have the best set of features for classifying
REM-NREM sleep. The nal state (REM or NREM) was decided by taking
the state with major occurrence at each epoch.
Finally, we classied all recordings of the test-set. In this case, we only
used the decoding algorithm for nding the best path of states that generated the sequence of observation in each subject.
10.3 Results
Classication of the NREM-REM sleep was carried out by applying a timevarying autoregressive model as feature extractor and a hidden Markov model
as classier. Twelve recordings were used to develop and train the classier
and other twelve to test it. The best set of features for classifying NREM-
10. DETECTION OF THE SLEEP STAGES
110
Table 10.3: Classification performance on the training set and test set sets for
a HMM classifier
Features
5
Average of training
set results
Accuracy Sensitivity
0.899
.764
Specificity
.692
Features
5
Average of testing
set results
Accuracy Sensitivity
0.851
0.793
Specificity
0.702
REM sleep were:
1. µ
√
2. V LF
3. mod(di(VLF))
4. Pole in HF (module)
5. Pole in HF (phase)
Table 10.3 shows the performing classication on training-set (leaveone-out cross-validation) and on test-set. The algorithm presents ne performance in the classication NREM and REM sleep from HRV parameters.
Accuracy is more that 85% in both training and test.
Figs 10.1 and 10.2 show the hypnogram (calculated by the physician
based on the standard criteria) and the sleep prole obtained the HMM for
two dierent subjects. In the top, it is shown the gold standard hypnogram
which was evaluated with the standard criteria. Hypnogram was simplied
in Wake, NREM (stages 1 - 4) and REM sleep. On the bottom is presented
the most probability path NREM - REM that the HMM found based on the
111
10.4. Discussion
Figure 10.1: whole night results for one test subject, in the top the Gold Standard and in the bottom sleep profile evaluated by HMM
features. We can observe a high correspondence between the gold standard
and the classication calculated by the algorithm.
10.4 Discussion
This section presented an alternative approach for classifying sleep stages.
This algorithm is based on the patterns that characterize the ANS function
during sleep. This approach oers a new continuous description of the human sleep which is based on probabilistic models. The algorithm is based
on time-varying autoregressive models and Hidden Markov models.
We believe that our approach presents several distinct characteristics.
The most important characteristic is the evaluation of a sleep prole based
only the projection of the central controls toward peripheral systems. This
allow to obtain time signals of easy acquisition such as the surface electrical activity of the heart. We used algorithms that seem to be natural for
evaluating sleep based on the time evolution of the HRV. Time-varying au-
10. DETECTION OF THE SLEEP STAGES
112
Figure 10.2: whole night results for one test subject, in the top the Gold Standard and in the bottom sleep profile evaluated by HMM
toregressive models generate a model in a beat-by-beat basis. This model
presents specic characteristics for REM and NREM sleep. HMM nd the
most probable state based on the feature characteristics and the probability
of passing from one state to another in the successive step. Notice, that
both algorithms generate models of the time series.
Some studies developed automatic classiers obtaining ne results. However, most of the eorts made until now are based on EEG [Todorova et al.,
1997] [Agarwal and Gotman, 2001] [Principe et al., 1989] [Porée et al.,
2006] [Flexer et al., 2005]. When we think in alternative approaches, signals
such as HRV oers ne characteristics for classifying sleep in environments
dierent to the sleep centers, easy acquisition for giving more comfort to
the user and less sensibility to the noise [Redmond and Heneghan, 2006].
In addition, We are not interested in reproducing the standard criteria for
sleep evaluation as most of the studies pretend. We propose an approach to
evaluate the sleep quality based in the harmony of the REM - NREM repetition. Event if our approach does not follow the the gold standard criteria,
this achieves a results that are comparable with the standard.
113
10.4. Discussion
In conclusion, peripheral signals carry important information about sleep
behavior. The projections that central nervous system has over all body are
useful to evaluate some intrinsic mechanisms such as the circadian rhythms
and sleep stages. Application of simple and manageable mathematic approaches, such as time-varying autoregressive models a hidden Markov models to this peripheral signals, approximate nely a sleep prole which is very
similar to the standard one.
10. DETECTION OF THE SLEEP STAGES
114
11. Arousal from Sleep
During constant physiological conditions, HRV signal is stationary, thus application of Fourier Transform (FT) or Autoregressive Batch analysis gives an
adequate spectral decomposition of the signal [Bianchi AM, 1992] [Bianchi AM,
1996] [Mainardi L, 2000]. However, when it is necessary to analyze rapid
changes in the signal (transitions), such as HRV variations during Valsalva
Maneuver, apneas and Arousals from Sleep, these approaches are not the
most suitable, because the signal acquires non-stationary characteristics. In
order to overcome this inconvenient, other techniques such as Short Time
Fourier Transform, Discrete Wavelet Analysis, Time-Varying Analysis and
Quadratic Time-Frequency Distributions (TFDs) have been introduced. A
great amount of works and interesting results on neural control have been
obtained using these mathematic methods on HRV analysis in dierent cardiovascular diseases and sleep disorders [Ramos et al., 2000] [Cerutti et
al., 2001] [Spicuzza et al., 2003] [Novak and Novak, 1993] [Mendez MO,
2003] [Bianchi AM, 1990] . In the following lines we discuss the application
of dierent TFDs in the study of the HRV signal during Arousals from Sleep.
The current study was designed to study the following points:
• To Evaluate the time evolution of the ANS during Arousal from sleep
episodes.
• To analyze the performance during Arousal episodes of the most classical Time-Frequency Distributions applied in the biomedical eld.
• To study the dierent behavior of Arousals from sleep related and not
related to muscular activity.
11. AROUSAL FROM SLEEP
116
This section is divided in three main parts. In Time-Frequency Distributions is presented briey the mathematic description of the dierent TFDs
used during the study. The second part called Quantitative Analysis of the
Time-Frequency Distributions compares the performance of each approach
in synthetic and real signals. Method Development deals with the TimeFrequency analysis of Arousals related and not related to muscular activity.
11.1 Time-Frequency Distributions
Cohen's Class Time-Frequency Distributions of a signal x(t) [BoudeauxBartels GF, 2000] [Cohen, 1989] [Hlawatsch F, 1992] have a special characteristic of being time and frequency shift invariant. All TFDs that obey
this property are dened by the equation described in 6.39. In the section
Mathematic Approaches was commented that changing the function labeled
kernel φ(t, τ) dierent TFRs can be obtained. We focus the study on the
most common TFRs used to analyze HRV signal, Smooth Pseudo WignerVille Distribution (SPWVD) and Choi-Williams Distribution (CWD). In the
next subsections, TFD's are described in function to their respective kernel.
Smooth Pseudo Wigner-Ville Distribution
t
t
(11.1)
φ(t, τ) = ϕ(t)η( )η∗ (− )
2
2
This distribution was introduced by Martin W. and Flandrin P. in 1985
[Martin W, 1985]. It is characterized by independent smoothing functions in
time and in frequency. The smoothing in time is produced by ϕ(t) window
while η( 2t )η∗ (− 2t ) window originate a smoothing in frequency.
Choi-Williams Distribution
r
φ(t, τ) =
2
σ 1 − σ ( t )2
e 4 τ
4π τ
(11.2)
Introduced by Choi and Williams in 1989 [Choi HI, 1989]. The scaling
factor σ determines the cross-terms suppression (they are generated by the
117 11.2. Quantitative Analysis of the Time-Frequency Distributions
quadratic nature of the Time-Frequency Distributions), time and frequency
resolution and concentration of auto-terms. High value of σ gives a good
denition of auto-terms and low cross-terms suppression, while low values
of σ reduces cross-terms and spread out the auto-terms.
Born-Jordan Distribution
(
φ(t, τ) =
¯t ¯
¯ ¯<
¯τ¯
0 ¯ τt ¯ >
1
τ
1
2
1
2
(11.3)
This distribution has some attractive properties since it associates mixed
products of time and frequency [Cohen, 1966]. The distribution had been
used as base for creating other distributions, or used for evaluating new
distributions proposed in [Khadra LM, 1998] [Jeong J, 1992] [Stankovic L,
1996].
11.2 Quantitative Analysis of the Time-Frequency
Distributions
11.2.1 Synthetic Signal
In the previous paragraphs the denitions of the SPWVD, CWD and BJD
were presented, now it is illustrated an analysis of these approaches by using a
synthetic bi-component signal formed by a sinusoid and a Gaussian function.
Synthetic signal structure is as follows:
(
f (x) =
sin 2 f π
1 ≤ n ≤ 512
j0.05
gaus · e
192 ≤ n ≤ 319
where f = 0.25 Hz.
Frequency values for each component were assigned in function to those
typically found in HRV signal. The analysis of the TFDs is limited to a simple
synthetic signal whose constitution allows us to assess, in a truthful way the
11. AROUSAL FROM SLEEP
118
ability of the dierent TFDs in analyzing physiological conditions such as AS.
The sampling frequency of the synthetic signal was 4 Hz with a duration of 512 samples. The TFD parameters were chosen on the basis of the
recommendations and experimental results reported in previous studies for
SPWV : the smooth time window is Hamming, 21 samples; smooth frequency window is Hamming 129 samples. Finally, we used CWD with a
xed σ = 1 according to [Pola S, 1996]. Three frequency bands, C: (0.05
- 0.1 Hz); B: (0.2 - 0.3 Hz) and A: (0.35 - 0.45 Hz) across all time were
created in order to have a clear indication of the amplitude evolution of the
cross-terms and auto-terms in the frequency ranges of interest. These bands
show the cross-term attenuation and negative components generated due to
the quadratic nature of the approach. Each band and the total frequency
range (0-0.5 Hz) were integrated across the frequency axis with the intention
of comparing the theoretical time evolution of instantaneous power of the
signal and the one obtained through the TFD. The results of the TFDs are
shown by means of an image, the energy distribution is plotted in a gray
scale of 256 values. In a second step, we applied the Hilbert Transformation
to the real signal, eliminating the negative frequencies in the time-frequency
domain, in order to evaluate how much the cross-terms are reduced and the
mathematical properties of the TFDs are retained.
11.3 Method Development
Time evolution of the PSD of the synthetic signal is shown in gure 11.1.
This signal is formed by a sinusoid and a Gaussian function, and the timefrequency distribution enhances the typical components that are found during
an arousal event. All the TFDs are able to disjoin clearly the components
of the signal without problems in distinguishing each component. However, BJD shows a greater number of cross-terms coming from the negative
frequencies between signal components in the positive frequencies. Again
this cross-terms found in BJD help to retain all its desirable properties as
marginals. The three TFDs have practically an analogous ability in eliminating the cross-terms that occur between the two components and tracking
119
11.4. Arousal from Sleep Data
accurately the frequency changes along the time.
Figure 11.2 shows the behaviour of the TFDs for the synthetic signal,
presented in the former plot, after applying the Hilbert transformation in
order to obtain an analytic signal. One can observe from this gure that
SPWVD does not show perceptible visual changes in the energy distribution
when an analytic or real signal is used. On the contrary, when a real signal is
converted into an analytic one by the Hilbert transformation, the CWD and
BJD present very noticeable visual changes in their graphical representation
of the energy content. In addition, the cross-terms are almost completely
removed and the marginal property is not retained since those are not able
to follow time by time the instantaneous power of the signal (see row three).
Then at this point, we can say that the three TFDs have the same performance when an analytic signal is analysed. If we compare the row 2 in gures
11.1 and 11.2, power in the band B shows a clear increment when an analytic
signal is analyzed, this means that the auto-terms are more concentrated in
the time-frequency plane and the cross-terms reduced.
11.4 Arousal from Sleep Data
11.4.1 Protocol
This study was carried out in cooperation to Santa Martha and Sacco Hospitals in Milan, Italy. Subjects that participate in the study were Obese and
healthy. These subjects refereed for suspecting of obstructive sleep apnea. In
the study was included ve whole night polysomnography recordings. Subjects age was between 40 and 60 years. They presented 36 ± 2Kg/m2 as
Body Mass Index.
All experiments were conducted at the sleep clinic of the Santa Martha
Hospital in Milan, Italy. Experiments were carried out in a special department
inside to the sleep clinic. The center has a bathroom and various bedrooms.
The temperature is regulated by mean of an air-conditioner. Bedrooms are
completely dark and windowless.
11. AROUSAL FROM SLEEP
120
SPWVD
A
Frequency (Hz)
0.4
BJD
0.4 A
0.4 A
0.3
0.3
B
0.2
C
0.1
0.3
B
0.2
0.2
0.1 C
0.1 C
0
0
0
600
600
600
500
500
C
400
s(t) 2
CWD
500
C
400
300
300
200
B
100
C
400
300
200
B
200
B
100
B
100
A
A
A
0
0
1000
1000
1000
500
500
500
0
0
0
s(t) 2
0
−500
−500
0
100
200
300
Sample
400
500
−500
0
100
200
300
Sample
400
500
0
100
200
300
Sample
400
500
Figure 11.1: Time-Frequency analysis of the synthetic signal. The first
row shows the time evolution of the PSDs of the signal obtained by three
Time-Frequency representations, Smooth Pseudo Wigner-Ville Distribution
(SPWVD), Choi-Williams Distribution (CWD) and Born-Jordan Distribution
(BJD). The second row depicts the instantaneous power for A (dashed line),
B (black line) and C (gray line) frequency bands. The third row presents the
instantaneous power for the whole frequency axis, gray line represents the
theoretical instantaneous power while black line is the one obtained after integrating the PSD respect to the frequency axis.
121
11.4. Arousal from Sleep Data
Frequency (Hz)
SPWVD
0.4 A
0.4 A
0.3
0.3
B
0.4 A
0.3
B
B
0.2
0.2
0.1 C
0.1 C
0.1 C
0
0
0
600
B
400
s(t) 2
BJD
0.2
600
C
600
B
400
200
A
C
A
A
0
−200
−200
−200
2000
2000
2000
1500
1500
1500
1000
1000
1000
500
500
500
0
0
0
−500
−500
−500
−1000
0
100
200
300
Sample
400
500
C
200
0
−1000
B
400
200
0
s(t) 2
CWD
−1000
0
100
200
300
Sample
400
500
0
100
200
300
Sample
400
500
Figure 11.2: Time-Frequency analysis of a synthetic signal, after the Hilbert
transformation. The first row shows the time evolution of the PSD of the signal
obtained by three Time-Frequency representations, Smooth Pseudo WignerVille Distribution (SPWVD), Choi-Williams Distribution (CWD) and BornJordan Distribution (BJD). The second row depicts the instantaneous power
for A (dashed line), B (black line) and C (gray line) frequency bands. The
third row present the instantaneous power for the whole frequency axis, gray
line represents the theoretical instantaneous power while black line is the one
obtained after integrating the PSD respect to the frequency axis.
11. AROUSAL FROM SLEEP
122
On based to the clinic standards, sleep evaluation was assessed by polysomnogram in sleep center. Each polysomnogrphy record consisted on two central
(C3 , C4 ) and two occipital (O1 , O2 ) EEG, electrooculogram (EOG, left and
right), electromyogram (EMG, submental), leg movement, airow, toraxic
and abdominal eorts, oxygen saturation and electrocardiogram (ECG). All
signals were acquire according to standardized criteria [Rechtschaen A,
1968]. System of acquisition was a Heritage Digital PSG Grass Telefactor.
The system acquisition was set to 100 Hz as sampling rate for the signal
recording.
Sleep stages were scored in epochs of 30 seconds according to the gold
standard criteria established by Rechtschaen and Kales [Rechtschaen A,
1968]. The hypnogram was created and synchronized with the sleep time.
Only ECG, EEG, submental activation and hypnogram were required for the
study. Arousals were identied from EEG C4/A1 channel during stage 2 as
dened in [ASDA, 1992].
The arousals were detected by an algorithm described in the next lines
and then checked by expert clinical personal. We restrain arousal denition
into a closed and limited group of arousals, which are characterized by frequency Beta shift higher than a threshold and duration between 3 and 6
seconds. The arousals were detected as follows:
• EEG channel was ltered by a low-pass lter with cut frequency of
30 Hz. - Four lters, with 0-4 Hz, 4-8 Hz, 8-13 Hz and 13-30 Hz as
pass band, were used to separate delta, theta, alpha and beta cerebral
activity components respectively.
• Beta and theta components were squared and smoothed with a moving
average lter (100 points).
• From smoothed beta rhythm only events higher than a threshold (200
% higher than the previous ten seconds) value and with a time duration
between 3 and 6 seconds were taken as arousal
123
11.4. Arousal from Sleep Data
• Arousal were classied in two groups, 1) EEG shift frequency and
2) EEG shift frequency with chin activity. Figure 11.3 depicts an
example of an arousal episode, the rst (A) without and the second
(B) accompanied by EMG chin activity . From the top to the bottom,
RR intervals, EEG signal, Beta rectied cerebral rhythm, Chin activity
and Theta cerebral rhythm. One can appreciate a decrement in the
RR intervals, an increment in the modied beta activity and peaks in
EMG at the same time period.
• A new arousal is identied at least 40 seconds after the end to the
previous one. - Arousals close at least 120 seconds to a sleep stage
change were not considered.
• Rectied Beta rhythm allows to nd some possible arousals. after to
this process, expert clinical personal revised the entrant arousals.
Fourteen arousal without muscular activity and seventeen with muscular activity were selected free of noise and distant of any pathologic event
(OSA or PLM). Therefore, the RR intervals were searched and detected
from ECG channel by a derivative algorithm. Due to the low sampling
frequency a better detection of R peaks was obtained by a parabolic interpolation [Bianchi AM, 1993]. RR time series were veried and manually
corrected where misdetections occurred and when extra-systoles happened
the corresponding portion of the signal was discarded and a mean beat was
created. RR minimum value localized inside the Arousal episode interval
(corresponding to the Beta increment) was taken as synchronization point,
only 30 seconds before and 60 seconds afterwards to the synchronization
point were used in the analysis.
11.4.2 Spectral analysis
Resulting RR sequences were re-sampled at 2 Hz by cubic spline interpolation and detrended for subtracting the mean value. Therefore, to each
RR sequence was applied Hilbert Transform in order to obtain an analytic
signal. After that, SPWVD was used to obtain the evolution of RR power at
dierent frequencies and times. We decided to use this distribution on the
11. AROUSAL FROM SLEEP
124
B)
A)
RR (sec)
1.2
1.2
1
1
0.8
0.8
200
200
EEG (µV) 0
0
−200
−200
50
50
Beta (µV)
0
0
200
200
Chin (µV) 0
0
−200
−200
400
400
Tetha (µV) 200
200
0
0
20
40
60
Time (sec)
80
100
0
0
20
40
60
80
100
Time (sec)
Figure 11.3: Example of an arousal episode, the first (A) without and the second (B) accompanied by EMG activity. From the top to the bottom, RR intervals, EEG signal, Beta rectified rhythm (see protocol section), Chin activity
and theta cerebral rhythm.
125
11.4. Arousal from Sleep Data
basis of a comparative analysis on synthetic signals which is also presented
in the result session. Then, the time evolution of the classical heart rate
variability indexes was computed:
• Total power, from 0.005 to 0.5 Hz (PT)
• Very low frequency power, from 0.005 to 0.04 Hz (VLF)
• Low frequency power, from 0.04 to 0.15 Hz (LF)
• High frequency power, from 0.15 to 0.5 Hz (HF)
• Low to high frequency ratio (LF/HF)
All spectral powers were evaluated in absolute units. The representation and spectral indexes were obtained using the absolute values of the
distribution.
11.4.3 Data analysis
Segments of 90 seconds of data and spectral indexes were analyzed. These
were synchronized with the occurrence of the minimum RR value that took
place during the EEG shift beta component (Arousal). Then, an ensemble
average was obtained for each spectral index, RR intervals and smoothed
Beta activity. Each sequence was normalized as the percentage of change
respect to the mean of the rst 20 seconds of each sequence. All the indexes
values were given as mean ± standard error. In addition all the indexes were
divided in four phases dened as: "0" : average of ve beats, ten seconds
before RR minimum value; "1" : average of three beats around RR minimum
value; "2" : average of four beats after 5 seconds of RR minimum value and
"3" : average of ten beats after 15 seconds of RR minimum value. These
intervals and points were selected taking key points that could characterize
the arousal episode in the RR intervals. One way ANOVA for repeated
measures was performed to compare the indexes in the time respect to the
reference value. Bonferroni's post-hoc analyses were performed to estimate
signicant dierences ( p < 0.05). Two group t-test was used to compare
stage by stage data and spectral indexes between groups (arousal with chin
activity and arousal without chin activity).
11. AROUSAL FROM SLEEP
126
11.5 Application results
Figure 11.4 depicts the energy distribution of the RR intervals (as real and
analytic form) during an AS using SPWVD, CWD and BJD. In the second
column (real signal) all TFDs disjoin perfectly the spectral components of
the RR intervals but BJD shows greater auto-term concentration and higher
frequency localization. Cross-terms spread across the frequency axis are
present in CWD and BJD. The behaviour of the TFDs, after applying the
Hilbert transform to the RR sequences was similar (see column one), but
small residuals of spread cross-terms are visible in CWD and BJD. Finally,
on the bases of these previous results, we decided to use the SPWVD for
the analysis of the RR sequences.
Figure 11.5 displays mean and SE of time course of the spectral indexes
of HRV for seventeen AS with (black symbols) and fourteen without (gray
symbols) chin activity. The values are represented as the percentage change
with respect to a baseline. The gure shows around 20 seconds rst and
after to the RR minimum value in order to observe the whole evolution of
arousal eect on HRV indexes. RR intervals present the classical behavior in
both circumstances, a decrement which reaches its minimum value around
seven seconds after the initial increment in the cerebral Beta activity, after
that it begins a recovery phase over-passing the baseline and returning to
the baseline 15 seconds later. RR intervals for arousals accompanied with
chin activity showed signicant lower values respect to baseline in the time
interval between 14 and 22 seconds, while RR for arousals without chin activity only from 18 until 19 seconds. The second subplot shows the time
evolution of rectied beta activity, with both groups presenting virtually the
same characteristics in amplitude and duration. Signicant dierences from
baseline are found within the 15-to-22 seconds time frame. HF component, in both cases, has a decrement immediately when an arousal happens,
however a large decrement is observed with EMG activity appears, then a
constant increment which arrives at the maximum value close to the nal of
the arousal. No signicant dierences were found in any situation. LF component, in both cases, presents a strong increment arriving at its maximum
127
11.5. Application results
SPWVD (analytic signal)
SPWVD (real signal)
0.4
Freq (Hz)
Freq (Hz)
0.4
0.3
0.2
0.1
0.3
0.2
0.1
0
0
CWD (analytic signal)
CWD (real signal)
0.4
Freq (Hz)
Freq (Hz)
0.4
0.3
0.2
0.1
0.3
0.2
0.1
0
0
BJD (analytic signal)
BJD (real signal)
0.4
Freq (Hz)
Freq (Hz)
0.4
0.3
0.2
0.1
0.3
0.2
0.1
0
0
RR intervals
RR intervals
1.5
s(t)
s(t)
1.5
1
0.5
1
0.5
0
10
20
30
40
50
Time (sec)
60
70
80
90
0
10
20
30
40
50
Time (sec)
60
70
80
90
Figure 11.4: Energy distribution of RR intervals during an Arousal from sleep
obtained with SPWVD, CWD and BJD. RR intervals were analyzed as a real
and analytic (after Hilbert transformation) sequences.
11. AROUSAL FROM SLEEP
128
close to the same time in which the RR value is minimum and going back to
the baseline value 25 seconds later; values are higher when chin activity is
present. Signicant dierences respect to baseline are detectable within the
15-to-26 seconds and the 19-to-22 seconds, when chin and not-chin activity
is present respectively, after the increment in beta activity. VLF component
and LF/HF ratio showed an analogous performance as the LF component.
Comparison of spectral indexes between arousals with and without chin
activity in some specic periods (periods selection is dened in methodology
section), is showed in Figure 11.6. Values are given as mean SE and they
are calculated as the percentage change respect to the average of 20 beats,
30 seconds before the RR minimum. Patterns in both cases are the same.
RR intervals show a decrement in phase 1 respect to the baseline. Then
a rise occurs during phase 2 and nally it goes back to the same value of
the baseline. Only signicant dierences between the dierent classes of
arousals are found in phase 1. HF component is characterized by a decrease
in phase 1 followed by a rise during phase 2 and a return to the basal values
during phase 3. Not signicant dierences are found between arousals. LF,
VLF and LF/HF ratio show an increase during phase 1 which value remain
similar in phase 2. Finally in phase 3 these go back to the baseline values.
Statistical dierences were present in VLF, LF and LF / HF ratio during
phase 2 between both types of arousals.
11.6 Discussion
This study compared dierent Time-Frequency Distributions, Smoothed Pseudo
Wigner-Ville, Choi-Williams and Born-Jordan Distributions, using synthetic
and real sequences of data. Furthermore, a time-frequency analysis of the
Heart Rate Variability during spontaneous arousal from sleep in obese subjects was carried on applying SPWVD in NREM Sleep stage 2. Arousals
were divided in two groups: a) Arousals accompanied by chin activity (UCL
denition) and [Smurra et al., 2001] b) Arousals without chin activity (ASDA
denition) [ASDA, 1992].
Our main observations were: from a methodological point of view, SP-
11.6. Discussion
∆ RR (%)
129
5
0
−5
−10
−15
∗∗
°
∆ Beta (%)
5
° ° ° °° ° °°
15
20
10
400
∗
∗
∗∗
°
200
°°
25
30
35
40
∗∗
∗
° °°
∆ LF (%)
∆ HF (%)
0
5
10
15
20
25
30
35
40
5
10
15
20
25
30
35
40
30
35
40
25
30
35
40
20
25
Time (sec)
30
35
40
20
0
−20
−40
1000
° °°°°
° ° ∗∗∗
∗ °°
°°
°
500
0
∆ VLF(%)
5
10
15
20
25
600
°°°° °°°
°°
∗∗∗∗∗∗∗
°°
400
200
0
∆ LF/HF (%)
5
10
15
20
1500
1000
°
500
°
°°°°° °
∗∗ ∗ °
0
5
10
15
Figure 11.5: Subject average time evolution of indexes of the heart rate variability, form the top to the bottom, RR intervals, cerebral Beta activity, HF
(High frequency component), LF (Low frequency component), VLF (Very low
frequency component) and LF/HF (Low to high frequency ratio). Values are
mean SE. Gray symbols , arousal without chin movement, * indicates significant difference time points (p < 0.05 vs baseline). Black symbols, arousal
with chin movement, indicates significant difference time points (p < 0.05 vs
baseline).
11. AROUSAL FROM SLEEP
130
RR (%)
0
−5
−10
*
HF (%)
20
0
−20
LF (%)
1000
*
500
0
VLF (%)
800
600
400
*
200
LF/HF (%)
0
1500
1000
*
500
0
0
1
2
3
Phase
Figure 11.6: Subject average time evolution of indexes of the heart rate variability, from the top to the bottom, RR intervals, cerebral Beta activity, HF
(High frequency component), LF (Low frequency component), VLF (Very low
frequency component) and LF/HF (Low to high frequency ratio). Values are
mean SE. Gray symbols , arousal without chin movement, * indicates significant difference time points (p < 0.05 vs baseline). Black symbols, arousal
with chin movement, indicates significant difference time points (p < 0.05 vs
baseline).
131
11.6. Discussion
WVD, CWD and BJD showed characteristics suitable for analyzing the time
evolution of the HRV spectral indexes during a real arousal from sleep. Even
though the clearest energy representation was obtained when SPWVD is
used, the other two distributions also allowed distinguish in a comprehensible way the energy content at each time of an arousal. More important,
if a Hilbert Transform is applied to a time sequence, CWD and BJD do
not retain their marginal properties and show both a similar time-frequency
representation and a smoothed instantaneous power as SPWVD. From the
application point of view, Arousal from Sleep accompanied and not accompanied with chin activity presented similar time evolution in the RR intervals and spectral indexes, however when a chin activity took place a higher
sympato-vagal activation is observed. SPWVD displayed a cleaner timefrequency representation than BJD and CWD. Its smooth windows are able
to eliminate almost completely cross-terms, but not to follow time by time
the real value of instantaneous power of the signal, as shown in gure 2,
column one; the real instantaneous power of the signal oscillates (gray line)
while the one calculated from the distribution does not present oscillations
(black line). Nevertheless, SPWVD tracks the varying frequency components with a great time resolution, as it can be noticed in gure 2. Even
though, CWD and BJD did not displayed clear time frequency energy distribution, the auto-terms were completely identiable with a great time and
frequency resolution. BJD presented the greatest quantity of cross-terms,
but how is reported in literature and is observed in Fig.2, BJD is able to follow, at each time instant, the exact power of the signal. When an analytic
signal is examined, basically the three TFDs showed the same performance
in visual representation as well as in instantaneous power. Therefore, it is
almost indierent to use any of these distributions in such condition. This
observation suggests that the major quantity of cross-terms are generated
between the negative and positive frequencies at the same time. Our study
shows in a simple and practical way the eect of the analytic signal in order to minimize cross-terms when a multi-component signal is analyzed, a
rigorous and interesting mathematical description is found in the papers presented by Schreier and Boashash [Schreier PJ, 2003] [Schreier PJ, 2003] .
As a nal point, when spectral components of the HRV are studied in the
11. AROUSAL FROM SLEEP
132
time-frequency plane, there is no necessity to know the exact value of the
energy at one point, while it is more important to detect the changes in the
frequency components of the signal, therefore, SPWVD could be a good
option for the dynamical evaluation of the ANS. However, BJD and CWD
showed to be ne tools such as SPWVD to analyze HRV during transient
events. Some works have made comparative studies between the SPWV,
CWD and others distributions, remarking that the best analysis approach
depends on the self features of the signal under study [Pola S, 1996] [Chan
et al., 2001] [Hlawatsch F, 1995].
Arousals maybe be physiologically linked to dierent sleep disturbances
such as periodic leg movements, restless leg syndrome, sleep apnea. Physiological arousal main function might has to do with an alerting reaction, activating bodily systems such as the cardio-respiratory one, in order to maintain
a body homeostasis. In addition, the nature of spontaneous arousal could be
seen as a vigilance system monitoring the external environment. However,
due to the very close relation with sleep pathologies arousal from sleep is
seen as an indicator of sleep fragmentation, and its quantication gives a
clinical index of sleep quality [Halász et al., 2004].
Arousal responds dierently for the specic causes of activation, and
some other cerebral waves such as k-complexes and spindles seem to participate as primary form of arousal. For instance, some studies have found an
increment in delta power during the breathing restore in OSA patients [Berry
et al., 1998]. Then a hierarchy arousal response could be found and depends
of the eerent information arrived to the central nervous system. K-complex,
D- activations and arousal produce a dierent reaction level of the autonomic
nervous system which is adequate to overcome a noxious event. K-complex
produces a mild autonomic activation while arousals generates very strong
autonomic reaction [Sforza et al., 2000]. In this way, an arousal with EMG
activation suggests a greater vigilance state or a powerful response than ones
without EMG activation.
Characteristic changes in heart rate have been reported previously in
133
11.6. Discussion
dierent physiological and pathological conditions. In conditions were repetitive arousals occur as Cycle Alternating Pattern (CAP) [Ferini-Strambi et
al., 2000] or Periodic Leg Movement [Sforza et al., 2005] a VLF component
appears, reecting the inuence of arousal repetition in symphato-vagal balance. A single arousal produces a large increment in the LF component
which is also reected in the sympatho-vagal balance. This increment suggests a major activation in the sympathetic activity in order to reactivate
some mechanisms of either defense o alertness. Time-frequency approaches
allow to evaluate the time evolution of the sympatho-vagal balance with high
time and frequency resolution. Time and frequency resolutions are dened
in the kernel parameters. In SPWVD, length of the independent smoothing
windows (kernel) dene the resolution. Length selection of these windows
depends directly of the signal characteristics in analysis. Appropriate selection of length windows allows to obtain a good time-frequency representation
and the extraction of the most important information of interest. If a large
frequency smoothing window is selected, cross-terms are reduced but a risk
of not seeing the dierent frequencies could happen due to low frequency
resolution, contrarily a short frequency smoothing window increases the resolution, reduces the ability to eliminate cross-terms and consequently a not
clear time-frequency representation may be obtained.
Only a few studies in literature have so far addressed the issue of using time-frequency approaches to analyze the HRV during arousal episodes.
From the time or frequency domain, our results are in agreement with the
previous studies [Bonnet and Arand, 1997] [Bonnet, 1989] [Morgan et al.,
1996] [Berry et al., 1998] [Halász et al., 2004]. Contrarily, there are a little discrepancies with Blasi et. al. [Blasi et al., 2003] when it is analyzed
the time evolution of the spectral parameters. LF time activation and the
time during which spectral indexes remain altered after arousal event show
some discrepancies These disagreements could be produced by both subject
characteristics and arousal type. They considered evoked arousals while we
analyzed only the spontaneous ones; this suggest that acoustic click could be
responsible of the LF lag response since this process involves the activation
and participation of sensory systems. Induced arousals suggest a dierent
11. AROUSAL FROM SLEEP
134
behavior in the ANS response; in fact, Sforza et. al. [Sforza et al., 2005]
documented a dierent autonomic response in correspondence of dierent
EEG events. On the other hand, Smurra et. al. [Smurra et al., 2001]compared the feasibility of the visual scoring of the AS using ASDA and UCL
denitions, from the EEG and electromyography activity during NREM sleep.
They found that the arousal scored with the two methods were comparable
in terms of concurrence and reprodicibility,. Vice versa, a clear dierence
between the two denitions is found when arousal is considered in terms of
eects on HRV. The results suggest that arousals accompanied with chin
activity (UCL denition) presented a statistical higher autonomic response
during the phase of maximum tachycardia and a similar time evolution (see
Figure 5). Finally, the RR intervals obtained with our protocol showed the
typical pattern of tachy-bradycardia when an arousal episode happens, alone
or together with chin activity. In addition, signicant dierences found between dierent groups of arousals suggest that a major activation in the
autonomic sympathetic activity take place when an external repercussion
also occurs.
This study is limited to a small and specic sample of subjects (obese),
and a deeper study is necessary in normal and a larger group of subjects.
Furthermore, the selection of arousals was reserved at sub-denition from
the ASDA report. An extension of our protocol is necessary in order to include other denitions of arousals [Halász et al., 2004] [Sforza et al., 2000].
Additionally, a future work could be the analysis of Arousals using the timefrequency approaches in a bivariate form in order to obtain maximum information through dierent signals as respiration and heart rate during an
arousal event.
11.7 Conclusions
SPWVD, BJD and CWD demonstrated to be ne tools to evaluate the parameters of the HRV even during transient episodes as arousals. SPWVD
oers a simple computation and clear representation of the energy distribution of the arousal time by time although its time and frequency resolution is
135
11.7. Conclusions
smaller that BJD and CWD. When an analytic signal is used in the evaluation, it is indierent to use any distribution since their energy representations
are extremely similar. Besides BJD loses the excellent properties when an
analytic signal is used, this distribution presents a major time-frequency resolution than the other ones. Arousals accompanied with chin activity present
a higher sympathetic activity than arousal without chin activity in sleep
stage 2. Even if it is present a greater sympathetic activity, the duration of
the tachy-bradycardia and recovery time were similar. Finally, these results
suggest that arousal accompanied by an external body manifestation (chin
activity) produces a stronger stress than only cortical arousals.
11. AROUSAL FROM SLEEP
136
12. Autonomic Nervous System
during Obstructive Sleep Apnea
Obstructive sleep apnea (OSA) is a common respiratory disorder characterized by repetitive punctuations or reductions of respiration during sleep. This
illness is a prevalent problem with major health implications ranging from
sleepiness to serious cardiac arrhythmias [Javaheri et al., 1998] [Javaheri,
2006] [Leung and Bradley, 2001] [Alchanatis et al., 2002]. OSA is also associated with increase risks of hypertension, myocardial infarction, heart stroke
and mortality rates [Bradley and Floras, 2003a] [Young et al., 2002] [White,
2006].
OSA is diagnosed if at least 10 apneic events per hour during sleep
occur [of Sleep Medicine Task Force, 1999]. Possibly this event happens
hundreds of times when someone sleep. The pathologic mechanisms that
accompany this disorder elicits a distinctive heart rate rhythm of bradytachycardia [Guilleminault et al., 1984]. The physiological basis of the
rhythm are such that during obstructive events, inspiratory eorts are made
against an occluded upper airway, similar to those performed during the
Mueller maneuver (inspiration against a closed glottis). This produces vagal
stimulation and consequently bradycardia. The good respiration is maintained by the activation of the upper airways muscles which are not activated through the disorder. A negative intrathoracic pressure results from
the inspiratory eorts of the diaphragm contractions together. This is accompanied by a drop of the oxygen saturation in the blood. This provokes
an amplication in the diaphragm eorts and adjuncts to the low oxygen,
it is produced a central activation (arousal) [Bonsignore et al., 1997]. The
12. AUTONOMIC NERVOUS SYSTEM DURING OBSTRUCTIVE
SLEEP APNEA
138
arousal restores the breath with the activation of the respiratory innervations
by increasing sympathetic discharge [Halász et al., 2004]. Then, it produces
a tachycardia and opens the upper airways just for a while permitting a only
few breathes . The sleep is interrupted by the arousal without waking the
patient. Nevertheless, the person doesn't have a restful sleep [Remmers et
al., 1978].
Diagnosis of OSA is usually performed by polysomnography procedure in
a sleep laboratory. This consists in measuring and recording several signals
such as airow, thoracic eorts and oxygen saturation [of Sleep Medicine
Task Force, 1999]. These signals are used to evaluate the pathology [Young
et al., 2002]. Polysomnography is an expensive and time consuming procedure with important resources invested in patients with mild-to-moderate
disease . Furthermore, the laboratory environment often disturbs or interferes with the patient's sleep, and so, it can aect the diagnosis.
Sleep apnea generates a typical pattern tachy-bradycardia on heart rate
variability [Guilleminault et al., 1984]. This pattern change depend on the
sleep stage. During NREM sleep, there is a regular apnea repetition, while in
REM sleep, apnea repetition is highly irregular [Penzel et al., 2003a]. Apnea
reduces the complexity on the HRV signal, here complexity is thought as
randomness [Goldberger, 2006]. Based on the HRV pattern produced by
apnea, some mathematical approaches have been used in order to develop a
possible alternative diagnosis [Roche F, 2003] [Hilton et al., 1999] [de Chazal
et al., 2003] [Zywietz et al., 2004]. For example, one symptom that helps to
diagnosis sleep apnea is that a subjects with sleep apnea presents diurnal hypertension. This seems to be produced by an alteration of some neural and
humoral mechanisms [Narkiewicz and Somers, 2003]. A combination of non
invasive information of easy handle could help in performing a pre-diagnosis.
So far, most of the studies have used time indexes, Fourier transform and
wavelets to analyze the behavior of the ANS based on HRV during apnea.
Time-varying autoregressive models are an alternative powerful mathematic
approach for assessing temporal series as HRV. This permit us to analyze at
139
12.1. Protocol
each sample the spectral characteristics of a time series. As a consequence,
it is possible to evaluate on a beat-by-beat basis the spectral parameters of
the HRV and to obtain an assessment of the dynamic ANS during apnea
conditions.
This study was created to assess :
a) The behavior of the spectral parameters of the HRV in normal subjects and in patients with severe obstructive sleep apnea.
b) To compare the behavior of the ANS during dierent sleep stages, in
normal and pathologic (obstructive apnea) sleep.
c) To test the suitability of the time-varying autoregressive models to
the analysis of sleep apnea on whole nigh recording.
12.1 Protocol
This study was carried out in collaboration with the Philipps Hospital in
Marburg, Germany. A total of ten recordings were used for this study. From
these recordings, ve subjects had severe obstructive sleep apnea and ve
were healthy subjects. The group with apnea had in average apnea hypoapnea index (AHI) equal to 71 ± 9, with age range between 50 ± 5 years,
and weight between 100 ± 20 Kg. The normal group presented an AHI of
zero, the age range was between 38 ± 6 years and weight of 75 ± 10 Kg.
Recordings were made at the sleep clinic of the Philipps Hospital. Data
were collected in a special center in the sleep clinic. The center has bathrooms and various bedrooms. The temperature is regulated by mean of an
air-conditioner. Bedrooms for sleep diagnosis are completely dark.
As required for sleep studies, signals were collected according to standardized criteria [of Sleep Medicine Task Force, 1999] [Rechtschaen A,
1968]. Evaluation was assessed by polysomnography in the sleep center.
12. AUTONOMIC NERVOUS SYSTEM DURING OBSTRUCTIVE
SLEEP APNEA
140
This consisted on two central (C3 ,C4 ) and two occipital (O1 ,O2 ) EEG signals,
electrooculogram (EOG, left and right), electromyogram (EMG, submental),
leg movement, airow, toraxic and abdominal eorts, oxygen saturation and
electrocardiogram (ECG). Acquisition system was a polygraph (Schwarzer
polygraph, Neurocard, Munchen, Germany). Sampling rate for ECG was
200 Hz. Stage 1, 2, 3, 4 and REM sleep stages were scored each 30 seconds
according to the standard criteria Rechtschaen and Kales [Rechtschaen A,
1968] by expert technicians. Only the hypnogram and ECG signal were used
in the study.
ECG (lead II) signal was extracted from polysomnography data. Thereafter, R peaks were searched and the RR intervals computed. ECG and
tachogram were plotted together in order to identify misdetection beats.
Ectopic beats and misdetection were corrected by visual inspection. After
that all the corrections were made, the new tachogram was recalculated.
12.2 Spectral analysis
Average was calculated for all the indexes on time windows of 30 seconds.
Eight coecients were selected for the model. The recursive least square
algorithm (RLS) was used to estimate autoregressive parameters updating.
The forgetting factor selected for the entire sleep time was 0.98 (time window with 50 beats). The same order lter and forgetting factor was used
for all recordings, independently of normal or apnea cases.
From the estimate time-varying autoregressive parameters the power
spectrum was computed for each time series. In order to assess the behavior
of the ANS, each spectra was divided in the following classical indexes :
a) VLF component (0.005 - 0.04)
b) LF component (0.04 - 0.15 Hz)
141
12.3. Data analysis
c) HF component (0.15 - 0.6 Hz)
d) low to high frequency components ratio (LF/HF)
All spectral indexes were normalized by the total power.
12.3 Data analysis
Average was calculated for all the indices on time windows of 30 seconds.
Wake, Light (stage 2), Deep (stage 3-4), and REM sleep stages were used
in statistical analysis. Repeated Measures Anova (Bonferroni's post-hoc
analyzes) were performed to estimate signicant statistic dierences (P <
0.05), for normal subjects through the dierent sleep stages, while Anova
One Way was applied to the pathologic subjects since some recordings did
not have deep sleep. Two samples t-test was employed in order to compared
statistically (P < 0.05) the dierent sleep stages between groups.
12.4 Results
Overnight recordings coming from ve healthy and ve pathologic subjects
with severe obstructive sleep apnoea were analyzed. Fig. 12.1 shows the
power spectra density (PSD) of the HRV uctuations in healthy and apnea
subjects during REM and NREM sleep. PSD was obtained by a time-varying
autoregressive model with order eight and forgetting factor 0.98. In the right
side, PSD during NREM sleep is illustrated. In the top, it is shown the PSD
for a normal subject. We observe a clear component in frequencies around
0.3 Hz, while in the other areas there is no spectral components. In the
bottom right side, it is illustrated the PSD during NREM for a subject with
OSA. A spectral component lower than 0.1 Hz appears. Nevertheless, it is
clear a high concentration but with low intensity in the frequencies around
0.3 Hz. On the left side of the plot, it is presented the PSD of the same
healthy and apneic subjects but during REM sleep. In the top, if we compare
respect to the NREM sleep in the healthy subject, we can appreciate that
some components in the VLF appears while seems that frequencies around
12. AUTONOMIC NERVOUS SYSTEM DURING OBSTRUCTIVE
SLEEP APNEA
142
0.3 are vanished. PSD during REM in apnea conditions is presented in the
bottom part of the left side. Respect to the NREM with apnea, it is notorious an increment in the VLF and practically a lost in frequencies around
0.3 Hz. Finally, when REM with apnea is contrasted with normal REM, only
the dimension on the PSD change.
Table 12.1 presents the mean and standard error of the HRV indexes
used in the study. Firstly, we compare REM with the others sleep stages
for each group. Signicant dierences are shown by a gray box. In normal
subjects, the RR intervals presented higher values in light and deep sleep
than REM and wake, being signicant only in light respect to REM. VLFn
was lower during deep, light and wake than REM (P>0.5). LFn and LF/HF
presented a smaller value during deep and light than wake and REM. The
signicant dierence was found respect to REM and deep sleep stage. HFn
presented a large level (P>0.5) during deep sleep.
Statistic analysis of REM sleep respect to NREM and wakefulness during
apneic conditions are shown in the right side of the table 12.1. VLFn demonstrated statistic dierence between light-deep and REM. LFn had higher values in light sleep than all sleep stages, and it was signicantly dierent from
REM. HFn resulted to be higher during REM sleep with respect to the other
stages. However, only statistic dierences were found in deep sleep. Besides
the LF/HF ratio was higher in REM sleep no signicant dierences were
found with the other sleep stages.
Finally, in the following lines are presented the results obtained from the
statistic analysis for each sleep stage between healthy and apneic subjects.
Table 12.1 shows the signicant dierence with ∗. Most of the spectral indexes presented statistic dierence in the sleep stages between both groups.
VLFn, LFn and LF/HF were higher in OSA subjects than normal subjects
while HFn presented lower values.
Fig. 12.2 depicts the typical time evolution of the spectral parameters of
the HRV obtained by a time-varying autoregressive model for a normal and
143
12.4. Results
0.5
0.5
0
0
0.2
0.2
Frequency
0.4
0.4
Time (sec)
Time (sec)
0.5
0.5
0
0
0.2
0.2
0.4
0.4
Time (sec)
Time (sec)
Figure 12.1: Power spectral density of the HRV during REM and NREM sleep.
The spectra were evaluated by a Time-varying autoregressive model. In the
right side is shown the PSD during NREM in normal and apnea condition.
The left side presents the PSD during REM sleep in the same conditions
12. AUTONOMIC NERVOUS SYSTEM DURING OBSTRUCTIVE
SLEEP APNEA
144
VLFn
RR (s)
0.428 ± 0.01
0.367 ± 0.03
0.97 ± 0.05
Wake
0.327 ± 0.03
0.503 ± 0.45
0.169 ± 0.02
1.008 ± 0.06
Light
1.399 ± 0.36
0.494 ± 0.03
0.393 ± 0.02
0.111 ± 0.02
0.986 ± 0.06
3.347 ± 0.54
0.241 ± 0.04
0.499 ± 0.02
0.259 ± 0.04
0.942 ± 0.05
Rem
20.33 ± 7.81∗
0.102 ± 0.01∗
0.515 ± 0.01∗
0.382 ± 0.01
0.875 ± 0.02
Wake
10.39 ± 1.43∗
0.095 ± 0.03∗
0.637 ± 0.01∗
0.267 ± 0.01∗
0.949 ± 0.03
6.097 ± 2.45∗
0.186 ± 0.03∗
0.583 ± 0.02∗
0.230 ± 0.01∗
0.899 ± 0.04
14.06 ± 1.17∗
0.515 ± 0.00∗
0.521 ± 0.41
0.428 ± 0.04∗
0.975 ± 0.03
Obstructive Sleep Apnea
Light
Deep
Rem
Table 12.1: Mean and Standard Error of the spectral indexes of Heart Rate Variability during the different Sleep Stages
in both normal and pathologic subjects
LFn
0.203 ± 0.03
2.802 ± 0.66
Index
HFn
5.020 ± 1.05
Normal
Deep
LF/HF
RR = time interval between consecutive R peaks of the Electrocardiogram, LFn = low frequency component,
HFn = high frequency component, LF/HF low to high frequency ratio. * represents significant difference
between corresponding sleep stages of the groups. The gray color denotes the statistic difference between
REM and the other sleep stages for each group. P < 0.05.
145
12.5. Discussion
a pathologic subject. From the top to the bottom, there are plotted hypnogram, RR intervals, VLFn, LFn, HFn and LF/HF. First column presents
indexes for the healthy subject while column two for the apneic patient.
All the spectral indexes were normalized with respect to the total power.
In normal subject, RR intervals elicit large and fast changes when REM or
Wake stages are present, and a stable behavior during NREM sleep. VLFn
component presented large oscillation during REM and Wake, and reduced
level when NREM sleep stage occurs. In the third row, it is depicted the LFn
component, which shows low levels when deep sleep took place. Thereafter,
HFn component presented the maximum value during deep sleep and levels
very close to zero during REM and Wake. Finally the HF/LF ratio showed
a temporal evolution similar to LFn.
When apnea occurs all the cardio-respiratory and hemodynamic behaviours of the human body are altered, then a dierent temporal evolution of the classical spectral indexes through overnight are changed. From
the second column in Figure 12.2, it is appreciable that in terms of sleep,
hypnogram is relatively normal in spite of the subject never arrives to the
deep sleep. RR intervals present a performance very close to a normal subject
but with large oscillations in all the sleep stages. Mainly during REM these
oscillations presented enormous changes. Again VLFn component shows
higher levels in REM than during NREM while the LFn component presents
opposite changes. The main dierence with the normal subjects is the very
low levels in the HFn.
12.5 Discussion
A whole night spectral analysis of the HRV in ve normal and ve patients
with severe obstructive sleep apnoea recordings was carried out. A simple
time-varying autoregressive approach was applied in order to obtain the classical spectral indexes of the HRV.
Our results about HRV during apnea are in agreement with the previ-
12. AUTONOMIC NERVOUS SYSTEM DURING OBSTRUCTIVE
SLEEP APNEA
146
Figure 12.2: . Time evolution of spectral indexes of the Heart Rate Variability in healthy and severe obstructive apnoea subjects. The time-variant spectra
was obtained by an autoregressive model. From the top to the bottom: Hypnogram, RR intervals, VLFn (very low frequency), LFn (low frequency), HFn
(High frequency) and LF/HF (low to high ratio). All the spectral indexes were
normalised by the mean of the whole record of each index.
ous ones [Wiklund et al., 2000] [Penzel et al., 2003a]. A decrease in the HF
component activity during all sleep stages was observed. They conclude that
subjects with sleep apnea present an autonomic disfunction, represented by
low levels in HF and high levels in LF, even during wakefulness.
Changes of the ANS during normal sleep have previously been documented by a series of studies [Penzel et al., 2003a] [Busek et al., 2005]
[Trinder J, 2001] [Scholz UJ, 1997] [Burgess HJ, 2004]. They have described an increment on LF activity from wakefulness to NREM sleep and
increase to the same wakefulness levels during REM sleep. This nding is
conrmed in this study. As it was discussed in chapter 9, some studies
showed discrepancies in the HF activity between REM and NREM. For a
discussion about that, please see the discission presented in the chapter 9.
In addition, this situation conrms the model that during REM sleep LF and
147
12.5. Discussion
HF activity are similar, it is like having the accelerator and break together
in a car.
These descriptions conrm that time-varying autoregressive model approach has a high performance and is robust to assess the dynamic of the
ANS during sleep in any situation, stationary or transitory. Therefore, it is
possible to eliminate the necessity of preselect stationary segments. Other
mathematic approaches as wavelets [Zywietz et al., 2004] [Roche et al.,
2003] and time-frequency distributions also oer great time and frequency
resolution and eliminate the necessity of stationarity, too.
It is important to comment the power that could represent the autoregressive models, since it could be possible a) to evaluate with some accuracy
the sleep stages, b) to determine if the subject suer of sleep fragmentation and nally c) to give a good approximation of the periods in apnoea
and periods in normal respiration. The computational eciency is also an
attractive feature.
How it was argued in the experiment 9, this methodology could be critical in concerning to the model order and forgetting factor. We commented
that previous studies of HRV used a model order in the range between 8-16.
Those studies based their decision on special test criteria such as Akaike
criterion. It is well known, that HRV acquires dierent statistic characteristics across the dierent sleep stages, movements, apneas, arousal and the
innity of the various physiologic and pathologic events. All these episodes
make very dicult dening the best model order, and the selection is taken
in base to others necessities. The computation time is one of the more important factors. A second point is the trade-o between under-tting and
over tting the data. For a complex signal a higher model order able to t
the signal is required. However, in signals with low complexity, the minimum
order is the best. When the model order is higher than the optimum one,
there is over-tting and negative power is found in the spectrum. Therefore,
in this special problem the minimum order gives us excellent results. It ts
correctly when the complexity of the signal is low or mild and reaches a good
12. AUTONOMIC NERVOUS SYSTEM DURING OBSTRUCTIVE
SLEEP APNEA
148
tting when the complexity increase.
The next section studies the possibility of implementing an approach of
pattern recognition in order to try of detecting the time that a subject spend
in apnea during the sleep time.
12.6 Conclusions
In conclusion time-variant parametric models oer ne characteristic in the
spectral decomposition of the Heart Rate Variability signal in dierent circumstances. Furthermore, although the VLFn and LFn presented similar
time evolution in normal as well as pathologic subjects, the mechanism involved works in a dierent way. Autoregressive models plus an adequate
pattern recognition could oer an easy way and an economic approach in
order to detect sleep stages and obstructive sleep apnea diagnosis.
13. Detection of Obstructive
Sleep Apnea
Sleep apnea (SA) is a common sleep disorder characterized by repetitive
cessations of breathing during sleep time. In clinics, SA is classied in three
classes: obstructive, central and mixed. Obstructive apnea consists in an
interruption in the airow to the lungs caused by an occlusion at the upper
airways level. Central apnea is produced by a malfunction of the central
respiratory drive, this means, that all the respiratory muscles stop and no air
enters to the lungs. Finally, mixed apnea is a combination of both central
and obstructive. Mixed apnea is generated rstly by a failure in the respiratory drives that also produces a collapse in the upper airways. Independently
of the type of sleep apnea, an apnea event typically is accompanied by a
reduction in the blood oxygen and arousal events that allow restore the respiration. An apneic event generates well dened oscillations in the heart
rate, produced by dierent causes that are related to the apnea class. During obstructive sleep apnea, respiratory muscles do not stop working, and
mechanical eorts are generated in order to overcome the occlusion. If these
eorts are not sucient, oxygen in the blood begins to decrease, muscle efforts increase by the hypoxia, until an arousal takes place to reactivate all
the systems and restore the respiration. Obstructive sleep apnea is very common in the population with a prevalence between 2% and 4% and is generally
related to aging and obesity. Sleep apnea generates a typical tachycardiabradycardia pattern on the heart rate. It is originated by a withdrawal of the
vagal tone and a strong activation of the sympathetic ow during an apnea
episode. When apnea is ended, a great vagal stimulation happens producing
bradycardia.
13. DETECTION OF OBSTRUCTIVE SLEEP APNEA
150
Severe sleep apnea could have hundreds of respiratory events during sleep
with serious health and social consequences, ranging from simple sleepiness
until heart failure. Sleepiness is caused by the low sleep quality provoked
by a disrupted sleep, while heart failure is consequence of dierent eects
produced by both alteration of physiologic control levels and sleep disrupted
consequences. Some eects that accompany daily the apnea patient are hypertension, irritability, bad mood, impaired memory and low concentration.
Sleep apnea diagnosis requires dierent signals that generally are obtained by the polysomnography procedure. The diagnosis is based on some
physiological measures such as oxygen saturation, airow reduction or cessation , eorts of respiratory muscles and at least one night in a specialized
clinic. Due to the limited number of sleep centers and specialized personal,
diagnosing sleep apnea becomes no accessible to the population and this
pathology is underestimated. Sleep apnea is divided in two levels, moderate
and severe. The level depends directly on the number of apneas or hypoapneas occurring during sleep time. An hypoapnea is dened as a partial
occlusion in the upper airways and it produces similar physiological changes
as those of the obstructive apnea.
Sleep apnea diagnosis is expensive since requires dedicated personal, infrastructure and special systems. These diculties generate the necessity of
investing eorts in order to obtain a simpler and reliable sleep apnea diagnosis based on the sleep apnea projections onto peripheral systems of easier
measurement such as heart rate and pulse oximetry.
In the past decade, some researches have focused on this concept, and
many studies have been presented using a variety of signal processing and
pattern recognition techniques. Some studies used features extracted from
the ECG as RR intervals, R amplitude, T duration, R area and peripheral
tonometry [Penzel et al., 2002a] [Penzel et al., 2002b] [de Chazal et al.,
2003]. Dierent mathematic approaches have been applied to HRV in order
to obtain spectral component that characterize apnea episodes, for example
151
13.1. Database Description
Fourier transform [de Chazal et al., 2003] [de Chazal et al., 2004], spectrogram [Jarvis MR, 2000] and wavelets [Hilton et al., 1999] [Roche et al.,
2003]. In addition, dierent techniques of classication have been used to
distinguish between normal sleep and apneic sleep [Penzel et al., 2002b].
Important results were obtained by those studies that achieved good
classication between normal respiration time and apneic time. Important
results were obtained during a competition in year 2000 conducted by the
organizers of Computer in Cardiology conference. This competition was focused on an apnea screening based on ECG [Penzel et al., 2002b].
Motivated for the results of the competition and following very close the
established criteria, we decided to test a time-variant feature extraction algorithm and some classiers to detect sleep apnea. This section is dedicated
to study a reliable sleep apnea diagnosis based only in measures of supercial
electrical activity of the heart.
13.1 Database Description
Database was downloaded from the web-page www.physione.net. This database
was used during the annual Computers in Cardiology Challenge celebrated in
year 2000 [Penzel T, 2000] [Penzel et al., 2002b]. It consists of 70 ECG whole
night recordings with a duration close to eight hours. Data were collected by
the Philipps University in Marburg, Germany. Standard ECG recordings were
acquired with a sampling frequency of 100 Hz and with resolution of 16 bits.
In order to acquire a standard ECG, electrode position was modied lead V2.
Apnea scoring was carried out based on the standard criterion [Sleep Atlas, 1999] by expert personal. Standard apnea scoring was changed on a
temporal scoring with a minute-by-minute resolution. A minute was dened
as apnea if at least one apnea or hypo-apnea episode happens. Otherwise,
that minute was dened as normal breathing. This procedure was used for
the total sleep time for each subject.
13. DETECTION OF OBSTRUCTIVE SLEEP APNEA
152
Recordings presented only obstructive sleep apnea pathology. The subjects were separated into three groups: Apnea group (class A), Borderline
group (class B) and Normal group (class C). Recordings with 5 minutes with
apnea or less belonged to class C. Twenty recordings met this criterion. The
group was composed by six males and ve females. Age ranged between 27
and 42 years (mean: 33). Subjects of Class A showed at least 100 minutes
of sleep disorder. Forty recordings satised this condition. They presented
between 100 and 534 minutes of apnea. Fifteen men and one woman entered this class. They were 50 years as mean (29-63 years). Finally, class
B was formed by ten recordings with 10 to 96 minutes of apnea. Four men
and one woman fullled this criterion. The average age was 46 years (39-53
years). The database was of 32 subjects ( 25 men and 7 female). The
total Subjects age ranged between 27 and 63 years (48 ± 10.8 years) with
weights between 53 and 135 Kg (86.3±22.2 Kg). The data were selected for
previous studies [Penzel T, 2000]. Each subject participated with dierent
number of recordings, 22 subjects contributed with two recordings each, two
subjects with three recordings each and four subjects with four recordings
each.
The database is divided in two groups each containing 35 subjects:
release-group and withheld-group. Each group contains 20 apnea, 5 borderline and 10 normal subjects. The total time was balanced between groups,
release-group had 17045 minutes while withheld-group had 17268 minutes.
From the release-group we selected 25 subjects randomly. This set was used
to develop and to test our algorithm of classication (KNN). From the second group, withheld-group, 50 recordings selected randomly were used to
measure the performance of our algorithm. The algorithm performance was
measured by comparing the apneogram calculated by the classier with the
apneaogram given in the web-page.
13.2 Methods
Based on previous knowledge about physiological eects that OSA has on
ECG signal (section 12), we derived signals as QRS area [Travaglini A, 1998]
153
13.2. Methods
and RR intervals [Hilton et al., 1999] [Penzel et al., 2003a] [Roche et al.,
1999]. From the top to the bottom Fig. shows the power spectra of RR intervals, power spectra of the R peak amplitude, hypnogram and apneogram. We
can appreciate that during normal respiration (color blue in the apneogram)
there is high power in the frequency around 0.3 Hz while in frequencies lower
than .1 Hz there is not power. Contrarily, during apnea periods even if there
is a high power around 0.3 Hz, high power levels appear in frequencies lower
than 0.1 Hz. In addition, if we observe the apnea periods between REM
and NREM sleep, the frequency component around 0.3 Hz is more concentrated during NREM than during REM sleep. From these time series, a
set of features were extracted and used for a supervised pattern recognition
algorithm. R area is a measure correlated to respiration. However, a good
estimation of respiration from R area needs specic ECG derivations. RR
intervals show characteristic oscillations (brady-tachycardia) during an apnea event, this pattern produces a very low frequency in the signal spectrum
that could help to identify an apnea event. In addition, when there are some
apneas consecutively, they produce a low frequency that characterizes apnea
repetition. Time and Spectral parameters extracted from RR intervals and
R area by a time-varying autoregressive model were used as input for the
classier. Classier performance was optimized from the ECG release-group.
13.2.1 RR intervals correction
Database has the QRS complex points for each recording. An automatic
algorithm searched the R peaks into ECG signal corresponding to each QRS
point. Resulting series were plotted with the respective ECG for manual
correction misdetected beats. After correction, the RR time series were
computed. However, after the visual inspection and correction, some RR
intervals presented unreasonable physiological distances. In order to correct
those intervals, it was developed the following procedure. A RR mean each
10 beats was calculated by a mean lter. Two limit bands with respect to
the RR mean were generated. All RR intervals superior to 30 % and inferior
to 20 % with respect the RR mean at each beat were searched. RR intervals
that attained this condition were changed by the mean RR value at that
13. DETECTION OF OBSTRUCTIVE SLEEP APNEA
154
Figure 13.1: Time-varying spectral analysis of a patient with severe sleep apnea during sleep time. From the top to the bottom: power spectra of the RR
intervals, power spectra of the R peak amplitude, hypnogram and apneogram.
In power spectra, blue color represent 0 while red maximum value. For the
apneogram, blue color is normal respiration and red color is apnea.
time.
13.2.2 ECG and Derived Respiratory Signal (DRS)
Previous studies have analyzed the QRS variation during both normal respiration and respiratory manoeuver such as Valsalva [Travaglini A, 1998].
They reported variations on the QRS area with frequency close to the mechanical movements produced by the respiration. The changes are generated
by the relative distance between the electrode located on chest surface and
the heart, and by the changes in the thoracic impedance produced for ination and deation of lungs. In addition, to this information, changes in the
155
13.2. Methods
HRV (variations between consecutive R peaks produced by changes in the
aortic receptors) also inuence the ventricular contraction, as consequence
there is a variation in the QRS area. In order to obtain a reliable estimation
of respiration, the baseline was subtracted from the original ECG. Baseline
was calculated by a median lter of 200 ms width. From the resulting ECG,
the minimum value was searched 100 ms before and after to the maximum
R peak value. Then, the area was calculated inside the region enclosed
between those points.
13.2.3 Features Sets
Preprocessing (RR detection and Derived respiratory Signal (DRS) evaluation) gave two time series with physical and physiological information about
ANS and respiratory system. Based on those time series, it is possible to
extract characteristics that could be of physiological and clinical interest.
In addition, these characteristics are potential features to be considered for
classication.
Two new time series were obtained from the relation between RR intervals and DRS. At each time tn (where n is time at each beat), it was
created a vector in the cartesian plane, here x-axis represents the RR value
and y-axis is the area value normalized with total series variance. One time
series represents the module of the vector (SeriesMod) and second series is
the vector phase (SeriesPha). Not time was invested on these time series,
we expected variations that could booster apnea non apnea events. Finally,
the Features considered for classication are the following :
• Mean and variance of RR intervals.
• Mean and variance of the dierence between consecutive RR intervals.
• Mean and variance of DRS.
• Mean and variance of the dierence between consecutive DRS.
13. DETECTION OF OBSTRUCTIVE SLEEP APNEA
156
For RR intervals were obtained the spectral parameters from a timevarying autoregressive lter at each beat. The lter order was set to 8
and forgetting factor 0.98. Representative poles (pole closer to the unitary
circle ) in the frequency range between 0.15-0.5 Hz (SleepyHFpole) and
0.003-0.07 (SleepyVLFpole) were extracted at each beat. The same lter
was used to obtain the Power Spectral Density (PSD) for SeriesMod and
SeriesPha. Classical bands of spectral indexes of the HRV were selected to
extract the information from the PDSs obtained. VLF = 0.003-0.04 Hz, LF
= 0.04 - 0.15 Hz, HF = 0.15-0.5 Hz. This signal processing procedure gives
the next features:
• Mean and variance of SleepyHFpole module.
• Mean and variance of the dierence between consecutive SleepyHFpole
module.
• Mean and variance of SleepyHFpole phase.
• Mean and variance of the dierence between consecutive SleepyHFpole
phase.
• Mean and variance of SleepyVLFpole module.
• Mean and variance of the dierence between consecutive SleepyVLFpole module.
• Mean and variance of SleepyVLFpole phase.
• Mean and variance of the dierence between consecutive SleepyVLFpole phase.
• Mean and variance of HF SeriesMod.
• Mean and variance of the dierence between consecutive HF SeriesMod.
• Mean and variance of LF SeriesMod.
157
13.2. Methods
• Mean and variance of the dierence between consecutive LF SeriesMod.
• Mean and variance of VLF SeriesMod.
• Mean and variance of the dierence between consecutive VLF SeriesMod.
• Mean and variance of HF SeriesPha.
• Mean and variance of the dierence between consecutive HF SeriesPha.
• Mean and variance of LF SeriesPha.
• Mean and variance of the dierence between consecutive LF SeriesPha.
• Mean and variance of VLF SeriesPha.
• Mean and variance of the dierence between consecutive VLF SeriesPha.
PSD for RR intervals and DRS, and the interrelation between them were
obtained by a bivariate time-varying autoregressive model at each beat. The
total spectrum at each beat was separated in the classical spectral indexes
of HRV for the resulting PSD. Further, coherence was evaluated in order
to obtain the frequency interrelation between both time series. Features
extracted from this process were:
• Mean and variance of HF RR intervals.
• Mean and variance of the dierence between consecutive HF RR intervals.
• Mean and variance of LF RR intervals.
• Mean and variance of the dierence between consecutive LF RR intervals.
• Mean and variance of VLF RR intervals.
13. DETECTION OF OBSTRUCTIVE SLEEP APNEA
158
• Mean and variance of the dierence between consecutive VLF RR
intervals.
• Mean and variance of HF DRS.
• Mean and variance of the dierence between consecutive HF DRS.
• Mean and variance of LF DRS.
• Mean and variance of the dierence between consecutive LF DRS.
• Mean and variance of VLF DRS.
• Mean and variance of the dierence between consecutive VLF DRS.
• Mean and variance of HF coherence.
• Mean and variance of the dierence between consecutive HF coherence.
• Mean and variance of VLF coherence.
• Mean and variance of the dierence between consecutive VLF coherence.
when we deal with physiological series, it is important to normalize our
time series in order to eliminate the inter subject variability. It is produced
by the personal physiological limits and conditions. In this way, some inconsistences are eliminated and it is assured that noise caused by the diversity
of subjects is reduced or damped. Normalization procedure is a mathematical procedure that transforms a series number from one value domain into
another domain, in such a way the output vector features attain statistical
properties such as certain limit values, variance, or even desire average. In
the normalization, an input vector (time series) x is converted into a normalized output vector xn . That is to say, each element xi of the input vector
is converted into an element xin of the output vector:
xin = ϕ(xi ) xi Belongsx
xn = ϕ(x)
(13.1)
(13.2)
159
13.2. Methods
ϕ stands for the normalization function. This function can be implemented in various ways, depending on what type of value domain the transformed vector should occupy and what types of classical properties it should
exhibit. The most frequently used normalization are:
• Normalization into an interval.
• Normalization to zero mean.
• Normalization to zero mean and unit standard deviation.
• Normalization to sum 1.
• Normalization to Euclidean norm 1.
The transformation is not only dependent on the values in x, but also
on the statistical properties of x such as value domain limits, variance and
mean value.
We applied two normalization to the data. Features coming from RR intervals, and DRS were normalized to zero mean and unit standard deviation.
HF, LF and LF were normalized in two dierent ways. The rst normalization was into zero mean and unit standard deviation and the second one as
total power percent. For Coherence and sleepy pole no normalization were
applied since these values range between 0 and 1. A total of 144 features
was extracted.
13.2.4 Selection and Transformation of the Features
Selection of the best features for separating classes is a fundamental task in
pattern recognition. This procedure prevents the course of dimensionality in
estimating the posterior distribution for the classication performed. Feature selection can be addressed in dierent ways. It can be evaluated from
the statistical analysis of the features (based on statistical dierences) or by
WRAP methods. WRAP methods consist in selecting the features based on
13. DETECTION OF OBSTRUCTIVE SLEEP APNEA
160
the classier performance for each group of their. The WRAP method was
applied in this work to obtain the best group of features for classication
using KNN accuracy as evaluation measure.
Feature selection consists in taking those features in which the PDF
of the classes are much better separated. Another important issue is the
decision boundary. it is to say, which kind of error we prefer to do, since
each erroneous decision has a cost. Is it better underestimate the apnea or
overestimated it?. In this rst step, we selected features able to nd apnea.
Then it is possible that a overestimation of apnea will occur.
We followed the next procedure to obtain the best group of features and
the best K. First, K was set to 15. Then, the WRAP was then used to nd
the best parameters for classifying apnea events. Thereafter, we selected
the rst feature given by the WRAP method and an interactive algorithm
was created in order to obtain the classier performance at dierent K's.
Fig 13.2 shows the curves of performance at each K. We observe how the
performance of the classier rises until k = 27. Finally, after selecting the
best K, WRAP method was used as search algorithm for selecting the nal
best group of features. Figure 13.3 shows the results obtained by the WRAP
method in selecting the best feature group for apnea classication.
13.2.5 Classication performance estimation
Classier performance has been estimated in two ways. First, Leave-OneOut cross-validation technique was used to evaluate classier performance in
the release-group. Second, we classied all recordings of the withheld-group
and the overall and individual statistical measures of classication accuracy,
sensitivity and specicity were calculated. Specicity gives idea about the
percentage of normal events correctly classied. Sensitivity represents the
percentage of apnea events classied and accuracy is a measure of the total
events correctly classied normal and pathologic.
161
13.2. Methods
Performance (%)
0.9
0.85
0.8
0.75
0.7
0.65
0
10
20
30
40
50
60
70
k
Figure 13.2: Classifier performance with one feature at different K’s, dot is
specificity, ∗ represents accuracy and + is sensitivity. Arrow shows K selected
for classification
Performance (%)
0.9
0.88
0.86
0.84
0.82
0.8
0
5
10
Number of Features
15
20
Figure 13.3: Classifier performance during feature selection , o is specificity,
∗ represents accuracy and + is precision.
13. DETECTION OF OBSTRUCTIVE SLEEP APNEA
162
13.2.6 Post-Processing
Generally, when dealing with time series, the output of a classier can
be post-processed to eliminate spurious misclassication events. Spurious
events are produced when the values of the features are located in the proximity of the decision boundary or just by outliers. In order to produce an
automatic post processing procedure, a median window running across the
classication sequences for each recording was used. This procedure booster
our classication performance. Dierent windows were tested in order to
boost the classication and to adapt our classier to data. A mean window
of 7 minutes gave the best results.
13.3 Results
Out of the 25 subjects for training procedure, we took ten normal, ten apnea
subjects and 2 borderline for training. Thereafter we selected randomly 2343
minutes of normal respiration and 2023 minutes with apnea. In this way, we
assured a balanced database for training our classier.
The best set of features with the best smoothing window were used to
classify apnea and no apnea events on the training set. The best set of
features in order of importance were:
1. Percentage of very low frequency in RR intervals
2. Coherence in very low frequency
3. Very low frequency derived from the RR intervals and Area of the R
peak
4. Variance of low frequency in RR intervals.
Power spectral components made up the majority of our features. Table
13.1 shows the performing classication on the release-set (leave-one-out
cross-validation) and on the withheld-set.
Finally, we measured the number of minutes that each subject spent in
apnea during sleep time for the withheld set. Figure 13.4 shows the results
obtained automatically by the classier. A threshold of 50 apneas per night
163
13.4. Discussion
Table 13.1: Classification performance on the release and withheld sets for a
KNN classifier
Features
4
Average of training
set results
Accuracy Sensitivity Specificity
0.8636
0.8934
0.8337
Average of testing
set results
Features
Accuracy Sensitivity Specificity
4
0.8555
0.8390
0.8850
All results using the release and withheld sets, 25
subjects for creating the balance training set and
25 subjects were used for testing the classifier
or approximately 6 min/h allows a total separation of the subjects classied
as normal and those classied as apnea. Furthermore, most of the borderline
subjects were enclosed between 50 and 110 apneas per night.
13.4 Discussion
In this work we studied the possibility of recognizing obstructive sleep apnea based on beat-by-beat features in ECG recordings. It was explored the
application of time-varying autoregressive models and KNN linear classier.
The objective was to classify minute-by-minute the probability of being in
apnea or not. In addition based on the number of minutes spent in apnea,
it is possible to give a possible sleep apnea severity estimate.
Our classication algorithm presents some advantages with respect to
other previously presented in literature. Autoregressive models are able to
evaluate beat-by-beat the spectral components of a time series even during
non stationary conditions. Other techniques as FFT require stationarity in
13. DETECTION OF OBSTRUCTIVE SLEEP APNEA
164
Minutes per night in apnea
500
Apnea
Borderline
Normal
400
300
200
100
0
0
5
10
15
20
25
Recording
Figure 13.4: Class separation based on minutes per night calculated by the
KNN classifier processing 4 features for 25 recording of the withheld set. Note
that applying a threshold of 50 minutes per night apnea and normal classes are
separated.
order to obtain a good estimation of the spectral components that are found
in a time series. Autoregressive models present a high time-frequency resolution, this is an important characteristic when dealing with signals such
as HRV. In addition, evaluation of spectral parameters by autoregressive
models has a very low computational cost, thus the extraction of spectral
features is easy. The high time resolution (beat-by-beat) allow us to obtain
both a possible real time apnea system detection or at dierent resolutions
as higher as a beat duration. Furthermore, KNN classier is easy implement
and it is able to nd a proper trade-o between a complex decision boundary
or a simple one. This approach is very ecient with a low amount of data
if the training set is representative of the classes to be separated.
Power spectral features extracted by the autoregressive models represent
the most robust features to evaluate apnea condition. Specially the spectral
component in very low frequency which denes the rhythm of apnea-normal
respiration. This frequency is very regular during NREM sleep since apnea repetition is periodic. During REM sleep apnea repetition becomes
predictable periodic together with the duration of one apnea and the subsequent. Besides the non regularity of apnea repetition, a high power in the
165
13.4. Discussion
very low frequency remains in REM sleep. Since our algorithm is based on
this component, isolate apneas are dicult to detect. Other physiological
and pathological events during sleep, such as Cyclic Alternating Pattern and
Periodic Leg Movements, could produce error during apnea detection. This
error is produced by the intrinsic characteristic of HRV, higher sensibility
and lower specicity. Future research will evaluate the features extracted by
the autoregressive model with other classiers such as Neural Networks, and
will assess possible improvements using dierent time resolutions such as 30s.
Our algorithm sightly overestimate apnea, this could be reduced by the
extraction of other features with dierent nature, as those obtained with
non-linear approaches, for instance measurements of time series complexity.
Other interesting algorithms to classify sleep apnea based on ECG signals
have been proposed during the Computer in Cardiology competition celebrated during the conference in the year 2000. In conclusion time-variant
models oer ne characteristic in the spectral decomposition for extracting
spectral features from Heart Rate Variability during apnea conditions.
13. DETECTION OF OBSTRUCTIVE SLEEP APNEA
166
14. Conclusions
The research presented in this thesis addresses the analysis of the autonomic
nervous system during sleep and in some related pathologies in order to evaluate alternative approaches for assessing sleep quality. Several mathematic
techniques toward the analysis of this problem have been used.
Born-Jordan, Choi-Williams and Smooth Pseudo Wigner-Ville TimeFrequency Distributions resulted ne tools to evaluated the dynamic behavior of the autonomic nervous system during arousal from sleep. These
approaches capture with high time-frequency resolution the changes of the
sympatovagal balanced even in short segments and non stationary conditions.
During arousal episode a strong activation of sympathetic nervous produced
the tachycardia. Therefore, after the end of the episode an increase in
parasympathetic activity occurs and a return back of the sympathetic activity to normal levels produces the bradycardia. If a real heart rate sequence of
an arousal episode is transformed in analytic signal the results showed that
those Time-Frequency distributions give almost the same results.
The time-varying autoregressive model, proposed to analyze the dynamic
behavior of the autonomic nervous systems during normal and apneic sleep,
eliminates the limitations of stationarity that are necessary in the classical
approaches such as Fourier Transform. As a consequences, it is not necessary to select segments for analyzing the heart rate series during sleep. In
normal sleep, it was observed high activity of sympathetic nervous system
during REM sleep, while during NREM sleep parasympathetic activity was
higher. Hidden Markov models presented suitable characteristics to classify
REM and NREM sleep from the changes in the sympathovagal balance dur-
14. CONCLUSIONS
168
ing normal sleep. In apneic sleep, a component in very low frequency was
predominant, this spectral component represents the apnea period. During
apneic sleep, the increase in sympathetic activation produced higher sympathovalagal balance with respect to the normal sleep. Finally, based on the
sympathovagal balance, K-Nearest Neighbor presented a suitable classication between normal and apneaic sleep.
The research in this thesis introduces several interesting practical problems. In particular, the evaluation of sleep from peripheral signals of easy
acquisition for home diagnosis. A direction for future research is to analyze other characteristics of the ECG that could complement the features
extracted from heart rate variability signal and give more robust and specic sleep evaluation. Another direction of this research is the application
of non linear techniques to heart rate variability, this will allow to capture
features that explain the problem from other points of view. This could give
additional information that could oer more robust decision about the sleep
quality. Finally, the application of other classiers with dierent philosophy
could help in improving classication.
It is suitable to evaluate sleep from alternative measures of easy acquisition. This thesis presents potential improvements inside sleep research and
possible sleep pre-diagnosis could be addressed. The algorithms presented
in this thesis present low computational cost and easy software implementation. Thus, those algorithms could be integrated in wearable devices. In
this way, the cost for sleep evaluation could be reduced and people from all
the world could enjoy of this aid.
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