Characterization of Sleep Spindles
Simon Freedman
Illinois Institute of Technology and
W.M. Keck Center for Neurophysics, UCLA
(Dated: September 5, 2011)
Local Field Potential (LFP) measurements from sleep data is important in Neurological studies
because experiments have shown a correlation between sleep and memory consolidation [1]. The
most prominent of the coherent signals within LFP sleep data are spindles, which occur most often
when a person is dozing off, durring Stage 2 of Non-Rapid-Eye-Movement (NREM) sleep [2]. Determining the specific properties of these spindles is essential to developing accurate biological and
physical models to explain the spindles’ presence within the LFP. This paper details a method to
computationally identify sleep spindles, characterizes some of their physical properties, and highlights some significant relationships between these physical properties.
I.
INTRODUCTION
The Keck Center for Neurophysics collects data from
electrodes that are implanted in precise locations on the
hippocampal and neocortex regions of rats’ brains. Each
electrode is approximately 10µm in diameter, and is part
of a group of four called a tetrode. There are 22 tetrodes
on the implant. The electrodes pickup voltages that are
flowing across the brian due to the mass communication
of the neurons within the brain, and relay this information back to a computer in the lab. This signal is referred
to as the Local Field Potential (LFP).
The rat is given a task, so that the lab can measure the
rat’s ability to learn by measuring its ability to perform
the task. The data collected from the rats is labeled ’VR’
(short for Virtual Reality, because the task takes place in
a virtual environment) if it corresponds to when the rat
was performing its task, and ’baseline’ if it is collected
at any other time. The baseline data therefore contains
data from when the rat is sleeping and when the rat is
awake, but not performing the VR task.
This sleep data is important because of the correlation
between sleep and memory consolidation. Memory consolidation is a process wherein the brain transfers certain
new memories that it deems important to a more permanent storage location. The “location” of formation of
newly created memories is thought to be the hippocampus ; however, where the memories are stored more permanently is les clear [4]. Although the mechanism for
this transferral is not well understood, experiments have
shown that this storage mechanism has a positive correlation with sleep. [1]
Specifically, this positive correlation has been found
to occur in hippocampus-dependent spatial-memory [1].
Spatial learning can include remembering a place on the
floor, as well as following a specific path. This means
that experimentally, if a person is given a spatial task,
and in one situation is restrained from sleep and asked to
perform the task again the next day (and somatic symptoms of sleep deprivation are controlled for), and in another situation is allowed to sleep, he is more likely to
perform better on the task in the situation where he was
allowed to sleep than in the situation where he was de-
prived from sleep. Furthermore, experimental data in
various animals shows that the communication between
neurons in the hippocampus that takes place while an
animal is participating in a spatial task is replayed in its
subsequent slow-wave-sleep.
One of the goals of the Mehta lab is to develop a physical and biological model for the process of spatial memory
consolidation. Since, empirically, it is seen that sleep contributes to the hippocampus-dependent spatial-memory,
it is important to consider sleep data when developing a
model.
II.
SLEEP SPINDLES
The lower frequency signal that is contained withing
the LFP of a rat does contain recurring events of coherent oscillations in specific frequency bands, even in sleep.
Determining the physical characteristics of these oscillations can help determine what in the brain is causing
these oscillations, and therefore is integral in developing
a suitable model for whatever process is causing the coherent oscillation.
The easiest to spot of these oscillations are the sleep
spindles. They are recorded as occuring in a 6−20Hz frequency band and have amplitudes that are on the order
of 12 mV . The goal of this project was to develop a suitable method of computationally locating these spindles,
given an LFP sampled at 36kHz as well as determine the
shape and physical characteristics of these spindles. [3]
Most observations seem to conclude that there are actually two different types of sleep spindles, and it is unclear whether both are correlated with memory consolidation, or just one of them. The first is the High Voltage
Spindle (HVS), which is reported to have lower frequencies (7 − 8Hz) and higher amplitude. The second type
is the Low Voltage Spindle, which have higher frequencies (10 − 20Hz), lower amplitudes, and occur primarily
alongside a K-Complex [3]. K-complexes are events that
can occur spontaneously in the second stage of NREM
sleep [5], and appear to be a transition from an up-state
to a down-state [3]; however, due to their many different shapes, they still remain precisely undefined [5]. A
2
second goal of this project was to examine the difference
between these two types of spindles and see how they’re
characteristic propreties compare.
III.
METHODS: SPINDLE AND K-COMPLEX
DETECTION
The following spindle-detection algorithm was adapted
from Johnson et. al, 2010 [3]. The first step in locating
the spindles was to filter the data in the 6 − 20Hz band.
In order to make the data easier to handle computationally, the 36kHz sampled data was initially downsampled
to 800Hz (which is well above the spindle band). Two
filtered signals were constructed. The first signal was the
LFP filtered in the spindle band 6 − 20Hz. The second signal was the LFP filtered in the K-Complex band,
which was 2 − 6Hz. The reason for the LFP filtered in
the K-Complex band was so that one could distinguish
between HVSs and LVSs. All filtering was done with
MATLAB’s 4th order Butterworth filter.
The next step was to find those pieces of the LFP that
were more prominent in these two signals. In order to find
the HVSs, the spindle band filtered LFP was divided into
250ms windows, with a spacing of 25ms between each
window. The variance of the signal was calculated in
each window. This data was referred to as the standard
deviation signal. Each index within the standard deviation signal correponded to one 250ms window from the
original LFP. Those indices that had a variance greater
than two standard deviations above the mean variance,
corresponded to windows that contained High Voltage
Spindles.
Locating the Low Voltage Spindles was performed similarly, with one distinction. In each window, instead of
the variance, the average absolute amplitude was calculated, and those windows with higher than average amplitude of the LFP corresponded to the LVS windows.
In order to find K-complexes, the range of each window
was determined by subtracting the minimum amplitude
in that window from the maximum amplitude, and a corresponding range signal was constructed. The windows
with a range that was greater than two standard deviations above the average of the range signal were determined to be K-Complex windows.
The second step taken to determine which windows
corresponded to High Voltage Spindles, was to make sure
that those windows with high variance also had significantly higher power in the Spindle band than in the KComplex band. This was done by evaluating the average
amplitude within each high-variance window in both the
Spindle filtered signal and in the K-Complex filtered signal. If the average amplitude of the K-Complex filtered
LFP in window i was greater than 80% of the average
power of the Spindle filtered LFP in window i, window i
was disqualified from being a HVS window.
A similar technique was used to ensure that all Low
Voltage Spindles were near a K-complex. If the average
power in the Spindle filtered LFP of window i was greater
than 80% of the average power in the K-Complex filtered
LFP for window i, then window i was deemed ineligible
to contain either a Low Voltage Spindle or a K-complex.
IV.
EXPERIMENT
This algorithm was run on the baseline data of two
different rats, Ozzy and Shamu and comprises three data
sets, labeled Ozzy, Shamu I, and Shamu II. The data analyzed from Ozzy was from one hour of recording off of
one tetrode, while the data collected from Shamu represents two hours of baseline data, on two different days.
For one of these hours (Shamu I), the LFP data was
taken from one tetrode on each of 22 different electrodes.
For the other hour (Shamu II), the LFP data was taken
from one electrode on each of four different tetrodes. The
data was grouped according to the hour of data to which
it corresponds.
The algorithm was able to detect High Voltage Spindles reasonably well, in the sense that what this algorithm determined to be High Voltage Spindles, visually
corresponded to what are called High Voltage Spindles,
and across the data had similar physical characteristics.
Because the thresholds for High Voltage Spindles were
all subjective to the data (the thresholds for HVS windows was set to two standard deviations above the average window variance, so that only 5% of the LFP could
possibly be recognized as HVSs), it is unclear whether
these are the only HVSs in the LFP. The algorithm did
claim to locate windows within the LFP containing KComplexes and Low Voltage Spindles; however, there
were not enough distinct features of these signals to measure, or to label them as representing a coherent signal.
Therefore, only the HVS data is analyzed.
V.
SPINDLE SHAPE
An example of an HVS can be seen in figure 1. This
spindle is composed of 16 cycles, where a cycle refers to
the LFP reaching a maximum voltage and then returning to a minimum voltage. One can immediately notice
FIG. 1: Single High Voltage Spindle. Located using algorithm
described in Section II. Confirmed as a spindle visually.
3
that these oscillations are assymetric. Each cycle of the
spindle seems to rise much faster than it falls. One would
therefore expect that the derivative of the HVS would be
slightly out of phase with the HVS, and that it would
peak during the rise of the HVS, before the HVS itself
peaks.
In plotting consecutive cycles of the spindle on top of
each other (as is done in figure 3) it is therefore advantageous to trigger the signal based on where the derivative
peaks (as seen in figure 2). Experimentally, there appears
to be less jitter on the center cycle when the cycle is triggered at the derivative peak than when it is triggered at
the peak of the LFP during the HVS. The peak of this
derivative is used to measure the width of each spindle
cycle.
FIG. 4: Detailed properties of Spindles
staying approximately 0.10 ± 0.01sec. The amplitude
and sharp slope of each cycle was somewhat consistent
between the two Shamu data sets, staying approximately
0.34mV and 11 − 13mV /sec respectively; however, these
characteristics were not consistent between rats, as the
data in Table I shows for the Ozzy data set.
VII.
FIG. 2: Derivative of the Spindle plotted on top of the Spindle. Peaks of both the LFP and it’s derivative are marked.
FIG. 3: All spindle cycles from the spindle in figure 1 superimposed. Time t = 0 corresponds to the time during the cycle
at which the derivative had its peak.
VI.
RELATIONSHIPS BETWEEN SPINDLE
PROPERTIES
A separate analysis was done by analyzing the cross
correlation between the different spindle properties described, and graphically viewing the relationship by generating a scatter plot comparing the various properties.
This data was not averaged over each spindle, rather every cycle had its own data point.
The strongest correlations occured between the interspindle-cycle-interval and the cycle trough depth (see Appendix A, Figures 9(a), 9(b), and 9(c)). (The trough
depth was defined as the minimum voltage that follows
the peaks of a cycle and precedes the peak of the following cycle.) Similarly there was a strong relationship
between the inter-spindle-cycle-interval and the peak-totrough amplitude (figures 8(a), 8(b), and 8(c)).
The correlation coefficients for each of these data sets
can be seen in Appendix A, Table II. These correlations
suggest that the wider a spindle cycle, the larger its amplitude and the deeper its trough. This is an indication
that whatever biological process is responsible for producing spindles is more complicated than a simple harmonic oscillator, where the amplitude and frequency of
the oscillations are independent. Suitable models for this
behavior are still being researched.
SPINDLE PROPERTIES
The spindle cycle properties that were measured over
each data set are described in Figure 4. These properties
were measured for each cycle in the interval, and then
averaged for each spindle. These averages were then histogramed, as seen in Appendix A, figures 5, 6, and 7.
The averages of these histograms, and their standard deviations, are summarized in Appendix A, Table I.
Thus, between all three data sets, the average interspindle-cycle-interval was the most consistent measure,
VIII.
CONCLUSION
The three-fold difference in spindle cycle amplitude between different rats that is seen in Appendix A, Table I,
as well as the two-fold difference in slope, are preliminary
evidence that the characteristics of spindles are dependent on the rat that they are placed in. This could be a
result of what parts of the brain the electrodes are placed
on, or how deep they are, or even some biological differ-
4
ence between the different rats. Thus, it is important to
have a computational method of spindle detection that
takes the variability of spindle amplitude and slope into
account (such as the method described, which uses a subjective voltage threshold to detect the spindles). Interestingly the degree of correlation between the amplitude
of a spindle cycle, and its width were similar across data
sets, and these preliminary results indicate that this is a
relationship worth examining in more data sets.
That the algorithm described is able to detect the
[1] Stickgold, R. Sleep-dependent memory consolidation. Nature 437, 1272-1278 (2005).
[2] Gennaro, L.D., & Ferrara, M. Sleep Spindles: an overview
Sleep Medicine Reviews 7:5, 423-440 (2003)
[3] Johnson, L.A., Euston, D.R., Tatsuno, M., & McNaughton, B.L. Stored trace reactivation in rat prefrontal
cortex is correlated with down-to-up state fluctuation density. J. Neuroscience 30, 2650-2661 (2010).
[4] Bear MF, Connors BW, Paradiso MA (2001). Neuroscience: Exploring the Brain (2nd ed.). Philadelphia, PA:
Lippincott Williams & Wilkins.
[5] Devuyst, S., Dutoit, T., Stenuit, P., & Kerkhofs, M. (2010)
Automatic K-complexes Detection in Sleep EEG Recordings using Likelihood Thresholds, in International Conference of the IEEE EMBS, Aug 31- Sept 4,2010 Buenos
Aires, Argentina
times at which spindles occur is in itself of interest to
the Keck Center. The location of the spindles can be indicative of different phases of sleep. The lab can quantify
a rats performance in a virtual reality task, and analyze
how this correlates with its sleep spindles– their concentration, their characteristics– in order to teste the relationship between spindles and memory consolidation, as
well as the relationship between different phases of sleep
and memory consolidation.
5
APPENDIX A: ADDITIONAL TABLES AND FIGURES
Ozzy
Shamu I
Shamu II
Peak to Trough Amplitude (mV) 0.601 ± 0.0128 0.338 ± 0.0815 0.345 ± 0.0829
Inter-Spindle-Cycle Interval (sec) 0.0978 ± 0.00953 0.105 ± 0.0134 0.104 ± 0.0139
Sharpest Slope (mV/sec)
33.8 ± 11.9
12.9 ± 7.80
11.5 ± 4.75
TABLE I: Properties of Spindles for the data sets Ozzy, Shamu I, and Shamu II. Each property can be seen graphically in
figure 4. Each table entry represents an average of all average spindle cycles per spindle in the data set, as well as the standard
deviation of those average spindle cycle properties
Correlation Coefficients
Ozzy
Shamu I
Shamu II
Peak to Trough Amplitude - ISCI r
0.242
0.417
0.416
p 4.75 ∗ 10−29 6.51 ∗ 10−67 3.37 ∗ 10−17
Trough Amplitude - ISCI
r
−0.416
−0.460
−0.469
−87
−83
p 1.86 ∗ 10
6.85 ∗ 10
6.03 ∗ 10−22
TABLE II: Correlation Coefficients for the data sets Ozzy, Shamu I, and Shamu II. Spindle cycles in each data set were treated
independently (not averaged per spindle)
6
FIG. 5: Histograms of spindle cycle properties for the Ozzy data set. LFP recorded on 5/25/2011. 154 Spindles detected over
4 LFPs. Each point in each histogram is the average of the cycle property described for one spindle in the data set
7
FIG. 6: Histograms of spindle cycle properties for the Shamu I data set. LFP recorded on 8/2/2011. 209 Spindles detected
over 22 LFPs. Each point in each histogram is the average of the cycle property described for one spindle in the data set
8
FIG. 7: Histograms of spindle cycle properties for the Shamu II data set. LFP recorded on 8/3/2011. 45 Spindles detected
over 4 LFPs. Each point in each histogram is the average of the cycle property described for one spindle in the data set
9
FIG. 8: Scatter Plots comparing the Peak to Trough amplitude of all spindle cycles in the three data sets with their corresponding
spindle cycle widths.
10
FIG. 9: Scatter Plots comparing the Trough amplitude of all spindle cycles in the three data sets with their corresponding
spindle cycle widths.