Proceedings of the 29th Annual International
Conference of the IEEE EMBS
Cité Internationale, Lyon, France
August 23-26, 2007.
ThP2A1.19
Arterial Pulse System: Modern Methods For Traditional Indian
Medicine
Aniruddha Joshi, Sharat Chandran, V. K. Jayaraman and B. D. Kulkarni
Abstract— Ayurveda is one of the most comprehensive healing
systems in the world and has classified the body system
according to the theory of Tridosha to overcome ailments.
Diagnosis similar to the traditional pulse-based method requires
a system of clean input signals, and extensive experiments for
obtaining classification features.
In this paper we briefly describe our system of generating
pulse waveforms and use various feature detecting methods to
show that an arterial pulse contains typical physiological properties. The beat-to-beat variability is captured using a complex
B-spline mother wavelet based peak detection algorithm. We
also capture – to our knowledge for the first time – the selfsimilarity in the physiological signal, and quantifiable chaotic
behavior using recurrence plot structures.
Index Terms— pulse-base diagnosis, Peak Detection, Variability, Multifractals, Recurrence Plots.
I. I NTRODUCTION
An individual forward-traveling wavefront, generated by
the heart results in complex patterns of blood flow and
pressure change at different points in the arterial circulation.
More and more noninvasive measurements of physiological
signals, such as ECG, heart sound, wrist pulse waveform,
can be acquired at these locations for the assessment of
physical condition and nonlinear methods have been recently
developed to quantify their dynamics.
Often the pulse waveform is thought to contain less or the
same information as the well explored ECG. An ECG signal
reflects the electrical activity of the heart and bioelectrical
information of body. On the other hand, the convenient,
inexpensive, painless, and noninvasive pulse-based diagnosis
(PBD) extracts – it is often proved by practitioners of
Indian medicine – the imbalances of Tridosha, which in
turn identifies the presence and location of disorders in the
patient’s body [1].
A. This Paper & Our contributions
•
There are various methodologies [2], [3], [4], some
dating to the 1950s, that obtain the arterial pulse.
However, Ayurvedic physicians sense the nadi (or pulse)
by applying varying pressure at pre-defined positions on
wrist. Therefore we designed our system to consist of
three pressure transducers with transmitters, a digitizer
and an interface is connected to a portable computer.
Aniruddha Joshi and Sharat Chandran are with Computer Science
and Engg. Dept., IIT Bombay, Powai, Mumbai, India 400076. email:
ajjoshi,[email protected]
V. K. Jayaraman and B. D. Kulkarni are with Chemical
Engineering
and
Process
Development
Division,
National Chemical Laboratory, Pune, India 411008. email:
vk.jayaraman,[email protected]
1-4244-0788-5/07/$20.00 ©2007 IEEE
Fig. 1.
Our pulse-based diagnosis set-up.
Unlike the other older methods, the data thereby obtained is observed to be without noise. Nominal preprocessing is sufficient to obtain the time series for
further analysis.
• PBD begins with identifying Tridosha in the movement,
rate, rhythm, strength, and quality of the pulse. We compute parameters of the beat-to-beat variability, which are
often more important [5], [6] than the pulse rate, or any
other steady-state parameter.
• We observe that the pulse waveform just like most of the
other physiological signals (e.g., the ECG) contain step
or cusp-like singularities, which are the rapid changes
in the variable values for a very small change in time
[7]. Also, the visual ‘patchiness’ of pulse waveform
suggests that different portions may have different scaling properties. To obtain hidden information about the
singularities, we computed wavelet transform modulus
maxima (WTMM) based multifractal spectrums. No
earlier work has succeeded to show such power law
scaling relationship in the pulse waveform. We also
observed quantifiable chaotic nature in the pulse waveforms from recurrence-plot-based measures.
The rest of the paper is as follows. In Section II, we briefly
describe the system hardware. Section III contains the main
results and we make a few concluding remarks in the last
section.
II. O UR S YSTEM
The nadi or the pulse is sensed by the fingertip at the root
of thumb. What is measured is the tiny pressure exerted by
the artery. Our system uses a similar methodology (Fig. 1). A
set of three pressure transducers (‘Millivolt Output Medium
Pressure Sensor’ with ‘0–4 inch H2O’ of operating Pressure
range, Mouser Electronics, Inc.) is mounted on the wrist to
sense three location pulses, namely vata, pitta and kapha.
The electrical signal proportional to the pressure experienced
by the pressure sensing element is then digitized using the
16-bit multifuction data acquisition card (National Instruments, USA), having an interface with the personal computer.
The data can be obtained for a predetermined length of time
608
(a) Three doshas of a patient
(b) Time-domain features in a
pulse cycle
Fig. 2. A sample pulse waveform in our database. The gray portion for a
single dosha is zoomed on the right.
by using the data acquisition software LabVIEW (National
Instruments, USA). The software controls the digitization
as well. The minimum change in the signal which can be
measured depends solely on the resolution of the digitizer.
Sample waveforms are shown in Fig. 2.
The three different colors are for three different pressure
transducers and the zoomed waveform on the right shows
the number of points per pulse cycle (sampling rate 500 Hz)
and also that the details of the waveform are captured. There
are many important time-domain features in pulse waveform,
similar to the typical P-QRS-T nature of the ECG signal. A
pulse waveform is usually composed of percussion wave (P),
tidal wave (T), valley (V) and dicrotic wave (D) [8]. These
wave-parts should be present in a standard pulse waveform
with definite amplitude and time duration to indicate proper
functioning of the heart and other body organs.
Because the values are so small, the data obtained in this
way can be corrupted due to implicit and explicit electronic
and electrical noise. Proper shielding reduces the noise to
the extent that no digital filtering techniques are required.
(a) Regular behavior of pulse
(b) Non-dying harmonics
(c) Missing secondary peaks in the (d) Waveform looks regular, but
pulse
Fourier spectra contains hidden information
Fig. 3. 100 Fourier coefficients from different pulse time series of length
4096 ms. Each sub-figure indicates specific characteristics of Fourier spectra.
of secondary peaks depending on the health of the patients.
This strength of the spectral harmonics, which accounts for
the morphology of the pulse, can be further used in pulse
detection.
B. Beat-to-beat alterations
A “first order” similarity of the arterial pulse waveform
with the more conventional P-QRS-T nature of ECG signals
are well observed cycles as seen in Fig. 2. A simple desirable
feature in any system would be in identifying the heart
or pulse rate. This is achieved by finding the fundamental
frequency (H1) using the Fourier spectra. As a matter of
verification, we successfully used the well known fact that
the pulse rate reduces as the age increases.
More subtle second order effects are the secondary peaks
within each pulse cycles reflected in the subsequent harmonics H2 through H5 (and sometimes more), also visible in the
figure. Earlier reported [9] cross-correlation coefficient with
these harmonics
k ratio = (H2)2 + (H3)2 + (H4)2 + (H5)2 /H1
Quantifying and modeling the complexity of beat-to-beat
variations, and detecting alterations with disease and aging,
present major challenges in biomedical engineering. Cardiac
inter-beat intervals (that is, heart rate variability (HRV)) have
been analyzed for long to detect, for instance, arrhythmias.
This has not been the case for the pulse waveform; the
belief in Ayurveda is that a similar analysis on pulse reveals
important information
1) Peak Detection: A pre-requisite for capturing such
beat-to-beat variations is to accurately find the start and end
of each beat (pulse cycle). The peak identification algorithm
[10] works on the basis of the maximum rising phase and
does not work accurately on our data. Specifically many
unwanted local maxima also get selected. This is due to
increased details & fine resolution available in our system.
Exploiting the relatively high amplitudes and the steep
slopes in a pulse in a wavelet-based [11] setting is the basis of
our methodology. Our experiments indicate that the mother
wavelet ψ to be used is the complex frequency B-spline
wavelet (fbsp-1-1.5-1),
m √
fb t
f
e2 −1πfc t
sinc
ψ(t) =
b
m
can be used as a important feature for classification.
Ayurveda also treats these secondary peaks as important.
OTHER O BSERVATIONS . In Fig. 3, we provide the first
100 Fourier coefficients of different pulses. We consider only
vata dosha pulse of the left hand here. We observe that the
Fourier spectra vary with respect to the regularity, nature
which has a good temporal localization properties. Here, fb
is a bandwidth parameter, fc is the wavelet central frequency
and m is an integer order parameter. The values we used are
(respectively) 1, 1.5, and 1.
The key to using the wavelet coefficients is the observation
that whenever there is a peak in the pulse waveform, we get a
III. M ETHODS AND R ESULTS
We now enumerate various feature detection methods
applied on the pulse data obtained from our system.
A. Pulse rate and other harmonics
609
(a) 38 cycles, s= 4–800 (b) 7 cycles, s= 4–500 (c) 2 cycles, s= 4–300
Fig. 6.
Fig. 4. The top row provides the input pulse waveform. Subsequent four
rows are thresholded values corresponding to positive & negative values.
We redraw the input again in the last row but also overlay the detected
peaks using our method.
negative and a positive spike in both the real and imaginary
parts. Therefore, we compute the thresholded positive and
negative values at real and imaginary coefficients and select
the common peaks among these four combinations, as shown
in the Fig. 4.
We have applied this algorithm on our database of 79
waveforms from various patients with varying age, disorder.
We achieve 100% accuracy in the peak detection.
2) Variability in angle, box energy: Once the peaks are
successfully detected, other parameters indicated in Fig. 2
are computed, and then variability is studied in the timedomain, the frequency-domain, and using morphology-based
features [12], [6], [5], [13] such as amplitude, energy, angle,
entropy, and velocity. This is important since HRV (and now
variability in pulse) more appropriately emphasizes the fact
that it is the variations between consecutive beats that is
critical, rather than the heart/pulse rate or the average values.
Two examples of this variability is presented in Fig. 5 for 8
patients of different ages and disorders using the data in both
hands. The three rows indicate healthy persons, patients with
stomach problems and muscular pain respectively. Within
each sub-figure the solid, dashed and dotted lines indicate
Self-similarity in arterial pulse.
three age groups ‘below 25’, ‘25 to 50,’ and ‘above 50’
respectively. We observe that the beat-to-beat variations are
different, and thus can be used for classification purposes.
Note that variability analysis requires steady data for longer
duration unlike the 1-minute or so data needed for simple
analysis.
C. Self-similarity and Chaos in Pulse
Fractal forms for, say time series data, consists of subunits
that resemble the structure of the overall object. The pattern
persists for sub-sub-units, and so on. This is reflected for
the arterial pulse as shown in Fig. 6, where we display
the continuous wavelet transform values for different cycle
length and the wavelet scale parameter s.
1) Multifractal Spectra: However, the presence of pathology in the real world, introduces variations such as approximate self-similarity. For example, many physiological signals
like the ECG contain step or cusp-like singularities corresponding to rapid changes in the amplitude for a very small
change in time. Different approaches have been used to show
nonlinear dynamic mechanisms either by describing system
trajectory in the space, by computing fractal dimensions, or
by determining self-similarity properties. However, the study
of multifractal behavior in pulses is under-represented.
We capture the approximate self-similar nature in the
pulse waveform using the multifractal formalism [14]. The
evidence for the power-law scaling relationship in pulse
signals is obtained in our experiments as seen in Fig. 8 which
is obtained using WTMM [15].
O BSERVATIONS . The branching structure of the WTMM
skeleton (figure on the left) indicates the hierarchical organization of the singularities. The spectra have different mean
and range values for various patients, which could be used as
important features in the classification process. In addition,
evidence that heartbeat dynamics exhibit nonlinear properties
indicates the need to study higher order correlations.
2) Quantifying Chaos: The Recurrence Plot (RP) methodology is used to observe the chaotic behavior in the pulse
waveform. Most earlier nonlinear techniques such as fractal
(a) energy in box containing com- (b) angle formed by the rising and
plete pulse cycle
falling edges at main peak
Fig. 5. Variability in two parameters for healthy, stomach problems and
muscular pain patients respectively in three rows. Red lines are for age
group ‘below 25’, Green for ‘25 to 50’ and Blue for ’above 50’ group.
610
Fig. 7.
WTMM branching structure. Fig. 8.
Multifractal spectra of
various pulse waveforms.
has been captured using WTMM-based multifractal spectra,
whereas the chaotic nature has been captured using methods
from recurrence quantification analysis.
The information contained in arterial pulse waveform is
probably under-used. Rigorous machine learning algorithms
could be applied on these waveforms to classify them into
major types of nadis defined in Ayurvedic literature and
we hope to apply this simple to use system for diagnostic
purposes in the near future.
V. ACKNOWLEDGMENTS
(a) Regular Behavior of pulse
(b) Pulse with abnormality after
every two cycles
Fig. 9. Recurrence plots with embedding dimension 5, time delay 8 and
radius 0.3.
dimensions or Lyapunov exponents, suffer from the curse of
dimensionality and require rather long data series. Because
RPs make no such demands, we felt that they could be useful
in the pulse analysis, where the dynamics is changing [16].
The main step of the computation is the N × N matrix:
Ri,j = Θ(i − (xi ) − (xj )),
i, j = 1, . . . , N
where i is a cut-off distance, Θ(x) is the Heaviside function
and the phase space vectors xi s are reconstructed from pulse
time series of length N . Graphically, a dot is placed at
position (i, j), if x(j) is sufficiently close to x(i) as shown
in Fig. 9. As can be seen, RPs can graphically detect hidden
patterns and structural changes in pulse data as also the similarities in patterns across the whole series. Further, Recurrence Quantification analysis [17] provides various features
from RPs such as the longest diagonal line segment (which
is inversely proportional to the largest positive Lyapunov
exponent), percent recurrence, Shannon information entropy
of the line distribution, and trend (slope of line-of-best-fit
through percent recurrence as function of displacement from
the main diagonal). All of these characterize the pulse data
and can be useful for classification. In the two cases shown
in the figure for the normal (& abnormal) pulses, they vary
as 0.062 (& 0.116), 96 (& 179), 3.428 (& 2.330) and -0.059
(& -0.034) respectively.
IV. C ONCLUSION
Historically the tradition of Ayurvedic medicine in India
relies upon information from the pulse for diagnosis. In order
for modern machine learning methods to duplicate the human
task, important features must be computed.
In this paper, we have described briefly our system for
collecting pulse data, and to compute these features. We
have also provided preliminary evidence and observations
that these features cue important and typical properties of
a physiological signal. For instance, we showed that these
attributes vary with disorders, and age groups.
The methods we have employed are varied. The first
harmonic in the Fourier spectra gives the pulse rate. The
beat-to-beat variability in various features such as amplitude, energies, angles, entropies, velocities are captured
using a complex B-spline mother wavelet. The self-similarity
We gratefully acknowledge the financial assistance provided by Department of Science and Technology, New Delhi,
INDIA. We also thank Mr. Anand Kulkarni who helped us
in designing the hardware of our system and Dr. Ashok Bhat
for providing us the domain knowledge of Ayurveda based
pulse-based diagnosis.
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