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Effects of prenatal cocaine exposure in quantitative sleep measures in infants

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Effects of prenatal cocaine exposure in quantitative sleep measures in infants

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Content EFFECTS OF PRENATAL COCAINE EXPOSURE ON QUANTITATIVE SLEEP MEASURES IN INFANTS by Frederic Chast A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE (BIOMEDICAL ENGINEERING) August 2002 Copyright 2002 Frederic Chast Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 1416368 UMI UMI Microform 1416368 Copyright 2003 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This thesis, written by k C I - } A £ T under the guidance of his/her Faculty Committee and approved by all its members, has been presented to and accepted by the School of Engineering in partial fulfillm ent of the requirements for the degree of I £cLe' . _ __ _______ Date: ■ _____ Faculty Committee C hairm an Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents List o f Tables..................................................................................................................... iv List o f Figures.................................................................................................................... v Abstract........................................................................................................................... viii I INTRODUCTION...................................................................................................... 1 1.1 Basics of 'EEG....................................................................................................1 1.2 Theory o f sleep studies.......................................................................................2 II PROCESSING OF EEC SIGNALS.......................................................................... 7 II. 1 Origin o f the signals........................................................................................... 7 1 1 . 2 Study o f the delta power.................................................................................... 8 1 1 . 3 Problems encountered with the delta power time series...............................12 II. 4 Power spectral density o f the DPTS............................................................... 13 II. 5 Phase ofthe DPTS...........................................................................................16 III STATISTICAL ANALYSIS OF THE DATA.......................................................20 III. 1 3D representation o f the results......................................................................20 III. 2 Results for the two populations.........................................................25 III. 3 Distribution o f the data: restrictions on using a t-test......................26 III. 4 Basics o f a t-test and Wilcoxon Rank sum test, Matlab implementation... 29 ii Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. Ill 5 Analysis o f the values o f the parameters.......................................................32 III. 6 Comparison between the mean and std o f DPTS for both populations 33 IV OTHER APPROACH: THE HEARTRATE AND EMC....................................37 IV. 1 Study o f the heart rate.....................................................................................37 IV. 2 Study o f the EMC recordings.........................................................................41 IV. 3 Choice o f the standard deviation o f the EMG..................................44 IV. 4 Problems encountered with the EMG signals................................. 4 7 IV. 5 Results for the two populations........................................................ 48 IV. 6 Comparison o f the mean and std o f the SDEMG time signals...................51 V CONCLUSION....................................................................................................... 54 V . 1 Comments on the results.................................................................................54 V.2 Problems encountered.....................................................................................58 V . 3 Other possible areas o f research...................................................................58 VI REFERENCES.................................................................................................... 60 VI.l Articles.............................................................................................................60 VI. 2 Books................................................................................................................61 VII APPENDIX A : EXPOSED PA TIENTS............................................................. 62 VIII APPENDIXB: CONTROL PATIENTS............................................................. 67 iii Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. List of Tables Table 1: results o f the t-test and Wilcoxon test performed on three EEG parameters (area, frequency, maximum) to compare two populations ................. ...30 Table 2: mean values and standard deviations o f the EEG parameters, using both methods.....................................................................................................................32 Table 3: mean and standard deviation o f the original and log o f the DPTS..............35 Table 4: Results o f a t-test comparing the mean and standard deviations o f the DPTS o f both populations................................................................................................36 Table 5: mean values and standard deviations o f the heart rate parameters.............40 Table 6: results o f the t-test and Wilcoxon test performed on three EMG parameters to compare two populations.......................................................................51 Table 7: mean values and standard deviations o f the EMG parameters, using the second method............................................................................................................51 Table 8: Mean and standard deviation o f the SDEMG for both populations.............52 Table 9: Results o f a t-test comparing the mean and standard deviations o f the DPTS o f both populations................................................................................................53 IV Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. List of Figures Figure 1: Illustration o f the principle o f the generation o f an EEG..............................2 Figure 2: location o f the electrodes used to record the EEG, EOG, and EMG........... 2 Figure 3: typical one-minute EEG recording (upper graph) and its Fourier transform............................................................................................................................ 6 Figure 4: delta and theta power o f an all-night EEG signal.......................................11 Figure 5: Fourier transforms ofthe delta power time series o f the same subject.... 14 Figure 6: Night long DPTS............................................................................................ 16 Figure 7: comparison o f two DPTS. The common frequency o f the signal is 0.0005 cycles/min.............................................................................................................18 Figure 8: Comparison o f two DPTS. The common frequency o f the signals is 0.015 cycles/min...............................................................................................................18 Figure 9: comparison o f two DPTS. The common frequency o f the signals is 0.020 cycles/min...............................................................................................................19 Figure 10: EEG recap (1)...............................................................................................22 Figure 11: EEG recap (2)...............................................................................................22 Figure 12: EEG recap (3)...............................................................................................23 Figure 13: EEG recap (4)...............................................................................................23 Figure 14:EEG recap (5)................................................................................................24 Figure 15. EEG recap (6)............................................................................................... 24 Figure 16: 3D visualization o f the EEG parameters.................................................... 25 Figure 17: bar plot o f the EEG parameters..................................................................27 v Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. Figure 18: bar plot o f the decimal log o f EEG parameters......................................... 28 Figure 19: histogram plot o f the mean and standard deviation for the exposed and control population. The data here is the original DPTS...................................... 34 Figure 20: histogram plot o f the mean and standard deviation for the exposed and control population. The data here is the logarithm o f the DPTS........................ 34 Figure 21: three examples o f an all-night heart rate recording sampled at 1 Hz..... 38 Figure 22: Example o f an original heart rate signal and the corresponding corrected signal............................................................................................................... 39 Figure 23: 3D visualization o f the heart rate parameters.......................................... 40 Figure 24: typical 10-minute EMG............................................................................... 43 Figure 25: EMG recap (1).............................................................................................. 44 Figure 26: EMG recap (2).............................................................................................. 45 Figure 27: EMG recap (3)............................................... 45 Figure 28: EMG recap (4).............................................................................................. 46 Figure 29: EMG recap (5).............................................................................................. 46 Figure 30: standard deviation o f an EMG signal versus time.......................................47 Figure 31: 3D visualization o f the EMG parameters....................................................48 Figure 32: bar plot o f the EMG parameters..................................................................49 Figure 33: bar plot o f the decimal log o f all EMG parameters.................................. 50 Figure 34: histogram plot o f the mean and standard deviation o f the EMG for the control and exposed population............................................................................... 52 Figure 35: Idealized evolution o f the sleep stages for the exposed and control population........................................................................................................................ 57 Figure 36: DPTS 1...........................................................................................................63 vi Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. Figure 37: DPTS 2...........................................................................................................63 Figure 38: DPTS 3...........................................................................................................64 Figure 39: Heart rate.......................................................................................................64 Figure 40: SDEMG 1.......................................................................................................65 Figure 41: SDEMG 2.......................................................................................................65 Figure 42: SDEMG 3.......................................................................................................66 Figure 43: DPTS 1...........................................................................................................67 Figure 44: DPTS 2...........................................................................................................68 Figure 45: Heart rate...................................................................................................... 68 Figure 46: SDEMG 1.......................................................................................................69 Figure 47: SDEMG 2.......................................................................................................69 vii Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. Abstract The purpose of the following study is to examine the implication of maternal cocaine exposure during pregnancy on newborn infants. This study focuses mainly on the spectral study of EEGs recorded during sleep. First, the delta waves (1 Hz to 4 Hz) extracted from the EEG for the two groups of subjects (the control group and the group exposed to drugs) are studied; then the periodicity of these waves is analyzed by performing a standard Fourier transform. Three parameters are extracted from the transformed signal and are compared between subjects of the two populations. Secondly, other signals extracted from the polysomnograph such as the heart rate and the EMG, are also considered. The same kind of analysis is performed on these new signals, with the extraction of the same three parameters, in order to refine the spectral characteristics of each group. Even though the results of this study have to be taken with a lot of care due to the small amount of data collected, two results seem to be characteristic of the exposed population: the EEG signal analysis shows that the exposed population has a higher average of delta power, which tends to prove that these infants have deeper quiet sleep stages. Complementary to this result, the EMG signal analysis shows that the same infants have a higher average value of the standard deviation of the EMG, which means that their REM sleep stages are shorter. viii Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. I INTRODUCTION L I Basics o f EEG An EEG, acronym for electroencephalograph, is a recording of voltages from the brain. In special circumstances, the recording can be done directly from the brain surface, but normally electrodes on the scalp are used. The electrodes are placed in a symmetrical pattern. The voltage amplitudes are small, typically in the range of tens of microvolts. They are most likely caused by synchronized activity in very large numbers of synapses in the cerebral cortex. The "center of synchronization" is somewhere deep in the thalamus or brain stem, but the EEG gives only indirect information about those regions. The figure below tries to illustrate how the dendrites of pyramid cells could generate an EEG voltage, if a large group of them are simultaneously excited. The group to the left is not excited at the moment, and the extra cellular excess of positive charge is maximal. The group to the right is depolarized by the synapses, decreasing the charge separation across the membrane. Since the electrodes are extra cellular, it is easy to understand that there will be a voltage between them, the left one being positive. A moment later, the situation might be reversed: 1 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. Figure 1: Illustration of the principle of the generation of an EEG (best resolution available). Electrode Electrode -(+ L2 Theory o f sleep studies The concept of the essential nature of sleep has evolved over the past 35 years from an intuitively appealing but incorrect belief that sleep is simply a state of inactivity which occurs passively when organs became fatigued in order they might rest, to a view of sleep as a complex state which is qualitatively, not just quantitatively, different from wakefulness and which is initiated and maintained by specific mechanisms. Although much progress has been made, the essential nature of sleep remains unresolved. In practice, scientists define sleep by certain physiological measures that are well correlated with sleep. Although these physiological measures derive their value from their correlation with behavioral sleep, they also give information about different kinds or stages of sleep, which are not so apparent in behavioral observations. Three variables are usually used to score sleep stages: 2 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. the EEG (electroencephalogram), EOG (electrooculogram) and EMG (electromyogram), recorded with electrodes placed on different areas of the patient’s head, as shown below: Figure 2: location of the electrodes used to record the EEG, EOG and EMG (best res. available). Electroencephalogram F.EG=Rrain waves Electrooculogram EOG=Eve movement Electromyogram EMG=Muscle tension The spectral study of EEG is a very important source of information to understand the sleep stages. The spectrum of EEG can be divided into five basic spectral bands: - Delta band (1 H z- 4 Hz) - Theta band (4 Hz - 7.5 Hz) Alpha band (7.5 Hz - 12 Hz) - Sigma band (12 H z-1 6 Hz) - Beta band (16 H z-2 5 Hz) It is important to notice that these values might slightly vary with the experimental environment as well as among researchers. These bands are usually related to particular sleep stages, or sleep patterns. 3 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. Wakefulness The EEG alternates between two major patterns during wakefulness. One is low voltage (about 10-30 microvolts) fast (16-25 Hz) activity, often called "activation" or desynchronized pattern. This pattern is most prominent when subjects are alert with their eyes open and they are scanning the visual environment. The other is a sinusoidal 7.5-12 Hz pattern of about 20-40 microvolts (alpha band). Typically, it is most abundant when the subject is relaxed and the eyes are closed. REM (Rapid Eye Movement) may be abundant or scarce, depending on the amount of visual scanning, and the EMG may be high or moderate, depending on the degree of muscle tension. Stage 1 Alpha activity decreases, activation is scarce, and the EEG consists mostly of low voltage, mixed frequency activity, much of it at 4-7.5 Hz (Theta band). REMs are absent, but slow rolling eye movements appear. The EMG is moderate to low. Stage 2 Against a continuing background of low voltage, mixed frequency activity, bursts of distinctive 12-16 Hz (Sigma band) sinusoidal waves called sleep spindles appear in the EEG. Eye movements are rare, and the EMG is low to moderate. Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. Stage 3 High amplitude (>75 pV), slow waves (1-4 Hz, delta band) appear in the EEG; EOG and EMG continue as before. Stage 4 There is a quantitative increase in delta waves so that they come to dominate the EEG tracing. REM The EEG reverts to a low voltage, mixed frequency pattern similar to that of Stage 1. Bursts of prominent rapid eye movements appear. The background EMG is virtually absent, but many small muscle contractions may occur against this low background. It is during this stage that dreams are said to occur. For the most part, the major differences among stages 1, 2, 3, and 4 are in their EEG patterns. Although there are some exceptions, the general physiology of these stages is fairly similar. In contrast, the physiology of REM sleep is so dramatically different from the other four stages that sleep researchers have distinguished two major kinds of sleep: REM sleep and NREM (NonREM) sleep, which is comprised of stages 1, 2, 3, and 4. NREM and REM sleep alternate cyclically through the night. Here is an EEG sample (and its Fourier transform) extracted from an all night EEG recording. This sample is one minute long, and contains 6000 points. 5 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. Figure 3: typical one-minute EEG recording (upper graph) and its Fourier transform (lower graph). The peak located around 2 Hz (delta wave) indicates that, at this time, the subject was probably in the third or fourth stage of sleep. Time (in seconds) 2 3 4 frequency (Hz) 6 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. II PROCESSING OF EEG SIGNALS II. 1 Origin o f the signals The EEG signals that were studied in the following project were provided by the Los Angeles Children’s Hospital. 16 subjects, infants aged of 4 weeks and belonging to two distinct groups, had one or more polysomnographic recordings. The two groups were the following: • The first group comprised children whose mothers had drug experience during the pregnancy. The drugs were “hard” drugs such as cocaine and crack. The infants from the group were labeled “exposed”. • The second group is the reference, children whose mothers were not exposed to any drug during pregnancy. The infants of this group were labeled “control”. The polysomnographic recordings made at the hospital could display several physiological signals. Even though this study focuses on EEGs, other signals such as EMGs and the heart rate will be taken into consideration. The sleep recordings usually lasted a whole night, with an average of about seven hours for all subjects. The EEG signal was recorded at a sampling rate of 100 Hz on two different channels, one for each side of the brain. Hence, to each subject were assigned two different signals of about 2,600,000 points, representing each 0.01 second of sleep. 4 7 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. subjects also participated in an additional all-night study, which was made less than 4 months after the first recording (the subjects were then about 5 months old). The total number of recordings was 40 (16 subjects + 4 additional recordings, 2 channels per recording). The extraction of the signals was made possible with the software “Alice” and the processing with the software “Matlab”. II.2 Study o f the delta power The main focus of the study was the delta band. Indeed, about 75% of the spectral power of all signals was found to be within this band. It is important to notice that since the sampling rate (100 Hz) was greater than twice the maximum frequency studied (4 Hz), the issue of aliasing was not taken into consideration. The way the delta power was assessed for each signal was the following: • The all-night recording was chopped into 30-second periods called epochs. • On each epoch, a spectral analysis was performed. • The power of the delta band was assessed for the epoch. • Finally, these values were displayed versus time for the whole recording. The following Matlab program performed this task: time=input(‘time in seconds=’); fe=input(• sampling frequency (in Hz) ='); 8 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. L=4096; %total number of points in spectrum (including padded points)% df = fe/L; %ffequency resolution in Hz% signal=input( ‘ signal =’); Te=l/fe; N=time*fe; epochs=time/30; t =(l:l:epochs); deltapwr = zeros(epochs,l); totpwr = zeros(epochs,l); freq=(0:df:fe/4)’; Nf=length(ffeq); for i=l:epochs, y = detrend(signal(3000*(i-l)+l:3000*i)); %every “epoch-signal” is detrended (the best line fit is subtracted to the data)% totpwr(i)=std(y)A 2; Pyy = psd(y,L,fe,round(L/3),round(L/6)); Commentary: the previous line Pyy = psd (X,NFFT,fs,WINDOW,NOVERLAP) estimates the Power Spectral Density (PSD) of a discrete-time signal vector X using Welch's averaged, m o d ified periodogram method. X is divided into overlapping sections of X by NOVERLAP samples (here 682 points), each of which is detrended, then windowed by the WINDOW parameter (here a Hanning window over 1365 points), then zero- padded to length NFFT. The squared magnitude of the discrete Fourier transforms of the sections is averaged to fo rm Pxx. 9 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. Pyy = Pyy*totpwr(i)/df/sum(Pyy); %scaling to reflect power% deltapwr(i)=s sum(Pyy(40:164))*df; % delta band: 1 - 4 Hz% thetapwr(i) = sum(Pyy(165:307))*df; %theta band: 4 - 7.5 Hz% alphapwr(i) = sum(Pyy(308:491))*df; %alpha band: 7.5 - 12 Hz% sspwr(i) = sum(Pyy(492:655))*df; %sleep spindles: 12-16 Hz% betapwr(i) = sum(Pyy(656:1024))*df; %beta band: 1 6 -2 5 Hz% end; subplot 411, plot (t,deltapwr, ’r’ ,t,totpwr), subplot 412, plot (t,deltapwr./totpwr), axis ([0 epochs 0 1]) subplot 413, plot (t,thetapwr,’r’,t,totpwr) subplot 414, plot (t,thetapwr’./totpwr),axis ([0 epochs 0 1]) The delta power is obtained by integrating the power spectral density over the range of frequencies that define this band. Here of course, this integration becomes a discrete sum: deltapwr(i)=sum(Pyy(40:164))*df; %deltaband: l- 4 H z % One can notice that the delta power is expressed as a fraction of the total power of the epoch considered. The main problem encountered using this program was that the values of the delta power changed substantially among subjects. To bypass this problem, one of the possibilities was to express the delta power as a percentage of the PSD by replacing the lines: Pyy = Pyy*totpwr(i)/df/sum(Pyy); de ltapwr(i)=sum(Pyy(40:164))*df; by the lines: Pyy = Pyy/df/sum(Pyy); 10 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. deltapwr(i)=sum(Pyy(40:1 64))*df; In this case, the delta power values are all comprised between 0 and 1. As one can see, the last four lines of the program display four graphs: The delta power as a function of time. The normalized delta power as a function of time. The theta power as a function of time. The normalized theta power as a function of time. Here is an example of these graphs displayed after calling this program: Figure 4: delta and theta power of an all-night EEG signal. First graph: delta power (dark) and total power (light and dotted). The y-axis is in (pV )\ Second graph: normalized delta power. The y-axis has no dimension. Third graph: theta power (dark) and total power (light and dotted). The y-axis is in (pV)2. Fourth graph: normalized theta power. The y-axis has no dimension. Note the difference in the y-scale compared to the second graph. 10000- - - X A . i v i jj J i i L ----r .... ■ » ..... " M , i i i 100 200 300 400 500 600 700 800 900 F 0 5 g m , too 2co - ■ ; 300 400 500 600 700 800 900 ltJ ir .iL ' 0 i i ' 100 200 ‘ 300 400 500 600 700, S O D 900 jgffjlil i f ® l i i i i i u j i l i i 100 200 3 0 Q 400 500 600 Trne tn epochs 700 500' m 11 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. On this particular graph, the delta power represents approximately 60 % of the total power, the theta power 5%, the alpha power 1% and the beta power is negligible. The other recordings show very similar results. Regarding the axis, the x-axis is time represented in epochs. Here, the recording lasted 872 epochs (so 26160 seconds, which is approximately 7.5 hours). II.3 Problems encountered with the delta power time series As seen previously, in order to compare the delta power time series (DPTS), the delta power had to be divided, for each epoch, by the total power. In this case, the DPTS has a magnitude comprised between 0 and 1 for each subject. Yet, the signal obtained with this method would turn out to have a low signal-to-noise ratio, and information might also be lost by normalizing all the signals. When going back to the original delta power time series, we see that the problem is actually not so much that the magnitudes of the signals are very different between subjects, but rather that these signals are “skewed”: if a plot of the distribution of values of the delta power versus their occurrence were plotted, one wouldn’t find a normal distribution centered at the mean, and symmetrical about it, which should normally be the case. For many graphs, this problem happened. In order to minimize its effect, the decimal logarithm of the data was taken before computing the power spectrum of the delta power time series. Indeed, what the log transformation does is 12 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. to normalize the frequency distribution of the data. With this change, hopefully, the data would be more compact, and easy to compare between subjects. To summarize, two options were possible: • Normalizing each signal, or • Expressing the delta power time series without normalizing them, but by taking the log of the data. It was impossible to know beforehand which option was the most suitable for the study so each signal was processed using both methods. All the DPTS were saved for each subject, using both methods. The “normalized” method will be referred to as method 1, and the “log” method as method 2. The study of the delta power itself was not the main concern, but rather the way this delta power evolved with time. Was there any noticeable periodicity? And if yes, was this periodicity a trademark of the class of subjects? II. 4 Power spectral density o f the DPTS Here is now the program developed to find the Fourier transform of the delta power time series: fs=2; % sampling frequency = 2 epochs/min % Note frequency scale of spectrum will be in units of minA (-l)% L=200; % total number of points in spectrum (including padded points)% df = fs/L; % frequency resolution in Hz 13 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. y=input(‘signal =’); y = detrend(y); var_y = std(y)A 2; % Variance of y% [Pyy,f] = psd(y,L*2,fs); % Use Welch method with 2*L=400 points, a Hanning window & no segment overlap% Pyy = Pyy*var_y/mean(Pyy); % Scale PSD so that mean value=variance of y% plot (f,Pyy) xlabelf Frequency (cycles/min)’); ylabel(‘ Power spectral density’); Calling this program first prompts the user what signal he wishes to use. It then opens a plot window and displays the plot of the power spectral density versus frequency. Here is an example of two graphs displayed after calling the program on two DPTS (using both methods 1 and 2) of the same subject: Figure 5: Fourier transforms of the delta power time series (DPTS) of the same subject. The upper graph is the Fourier transform of the normalized DPTS, and the lower graph the Fourier transform of the “log” DPTS. X S 0 IB i s 04 008 0 09 0.1 0 12 £ 1 4 0 16 018 0 2 ' - aceen.v. .c-v. -r.; r: o .. -t v a- 0 0G2 DU4 006 QE8 C l 0 12 0,14 0 16 018 0 2 1 : • / ‘ .- ■ ii'C '- i- S /V .i r i . tv - 14 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. Without going deep into the analysis, one can obviously see that both graphs look alike. Each of them has a peak in the frequency that occurs almost at the same frequency for both. The only major noticeable difference is the scale of the y-axis. When using method 1, the amplitude of the DPTS is between 0 and 1, whereas in the second method the DPTS will have a larger scale, usually between 1 and 5. This will be reflected in the amplitude of the power spectrum densities of these functions. The x-axis represents the frequency in cycles/min. Indeed, in the delta power signals, a small time interval (an epoch) represents 30 seconds. If the sampling frequency fs is 2, then the frequency axis is in (30 seconds * 2)'1 or (min)'1 . The graph shown above presents a sharp peak at the frequency of about 0.015 min’1 which means that there is a periodic behavior of 1/0.015 ~ 65 minutes ~ 130 epochs. To understand this example quantitatively, let’s display the plot of the corresponding DPTS of the same subject (figure 6). A periodic behavior is clearly seen on both graphs, and actually more on the second graph than in the first, for which the signal- to-noise ratio is low. Arrows that span over approximately 130 epochs were added to this graph, in order to visualize the periodicities of the signal. The corresponding frequency is 1/(130* 0.5min) = 0.015 min'1 , which is where the peak frequency is on figure 5. 15 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. Figure 6: Night long DPTS. The first graph (upper) has been found using the first “normalized” method. The second graph (lower) corresponds to the same original recording, but was found using the second “log” method. ir 0 8 - S.0.4 0.2 £00 ' S C O 700 800 900 Time fin epochs) •100 200 300 -'400. 3.5 ' 3” 0 100 200 300 400 503' • B O O 700 800 900 Time (m epochs) At this point of the study, one might think that using the second method will be more likely to lead to exploitable results, rather than the first one. Indeed, for most graphs, the noise that appears on the DPTS calculated with the first method “drowns” the data. Yet, the power spectrum of the DPTS doesn’t seem to be too much affected by the noise, so all signals using both methods were kept in order to be later analyzed. II. 5 Phase o f the DPTS A spectral analysis gives information about the frequencies embedded in a time signal. When it is performed, part of the information is lost, especially the one 16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. regarding the phase of the signal. Two signals can have the same spectrum but will look different in a time domain, with a delay in phase for one of them. With sleep studies, it is important to know not only the frequency of the waves, but also when these waves are in a rising or descending phase. When the subject falls asleep, how do these waves “start”? Does it depend on the class of subjects that is studied, control or exposed? To answer these questions, the DPTS of the control group were compared to the DPTS of the exposed group. Of course, the signals must have the same embedded frequencies; otherwise, comparing their phase would be irrelevant. This kind of analysis is more qualitative than quantitative, because the signals studied are not perfect sinusoids: if a signal displays a peak at a certain frequency in its spectrum, it doesn’t mean that its behavior will be perfectly periodic. What was done to compare the two groups with the criterion of the phase was to take two EEG signals from each group (both channels are averaged and the resulting signal is smoothed by taking the moving average over six points, e.g. 3 minutes), with the same value of the peak frequency in their spectrum, and visually assess if they seemed in phase, or if there was a delay, maybe an opposition of phase. Here are three graphs of the DPTS of six subjects (three for each population), chosen here because of their different spectral peak frequency: 0.005, 0.015 and 0.020 cycles/min. In each of these graphs, the upper graph comes from a “control” subject, 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and the lower one from an “exposed” subject. On each graph, there is no significance in terms of the amplitude. Figure 7: comparison of two DPTS. The upper graph comes from a “control” subject, and the lower one from an “exposed” subject. The common frequency of the signals is 0.005 cycles/min. The units on the y-axis are arbitrary. 01 Q 100 200 300 400 ‘ 300 b O C 7 G C • " 800 9 G Q 1 G 0 Q T.r? in apo.'hs Figure 8: Comparison of two DPTS. The common frequency of the signals is 0.015 cycles/min. - G 2 1 D T O O 200 300 400 500 S C O 700 900 -900 1 !.vo in fp'vC.Vj 18 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 9: comparison of two DPTS. The common frequency of the signals is 0.020 cycles/min. — ... -------------- -_i.. 0 ’ 100 200 300 400' B O O 600 ’ 00 900 $00 i.i The rest of the signals, when coupled together, look very similar to the examples chosen above. As one can see, it is difficult to conclude anything from these graphs. In some cases, the pattern of the waves seems to be the same for each of the two subjects, and in others, it is not. The second graph illustrates this paradox very well: in the beginning of the recording, the two signals are in an opposition of phase, whereas the last three waves are obviously synchronized. As a conclusion, the phase of the DPTS of the EEG doesn’t seem to depend on the category of the population. 19 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ill STATISTICAL ANALYSIS OF THE DATA III.l 3D representation o f the results The data processing transformed an all-night EEG recording of about 3,000,000 points, into a 200-point graph representing the power spectral density of the delta power time series. How could this graph be used? Since all the graphs had the same shape (a sharp peak at a low frequency), three parameters were studied: • The peak frequency. • The value of the function at this frequency. • The area under the curve. Regarding this last parameter, the boundaries of integration were chosen so that they would include the peak of every signal. The boundaries selected were 0.005 cycles/minute (lower boundary) and 0.025 cycles/minute (upper boundary). It is important to notice that the frequency resolution was only 0.005 cycles/minute because the sampling frequency was 2 and a number of points in the TFT was 400. In other words, the area under the curve was found by adding the five values of the function at 0.005, 0.010, 0.015, 0.020 and 0.025, and multiplying the result by the frequency resolution of 0.005. Unfortunately, integration with rectangles is not suited for functions that are very sharp, like the ones in this study. This poor 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. resolution was mostly due to the size of the DPTS (about 900 points for all signals) sampled every 2 points (1 point represents 30 seconds) to get a result in cycles per minute. The following short Matlab script performed the task of extracting the three parameters described previously: signal=input('signal='); [value_of_max,ffeq]=max(signal); value_of_max area=sum(signal(2:6)) freq=freq* 1/200-0.005 Then, for each graph, these three parameters were evaluated and plotted on a 3D plot. For each EEG recording, and so for each patient, there are actually two channels, so two recordings. For the same patient, the values obtained for the three parameters of each channel were then averaged. There were usually a lot of similarities of course between these values for the same patient, but in a few cases, the results of only one channel were kept because the other would lead to “unpredicted” values. Here is a quick recap of the data processing and analysis (Figures 10 to 15): 21 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 10: 2 channels of the EEG recording displayed over 5 minutes. Figure 11: each EEG channel is chopped every 30 seconds. <san:» t;f ; - .S 100 :iz) 60 e > -20 -40 -60 -100 •iiiuc sx^on„s 22 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 12: the psd of the 30-second signal is calculated. £ 'J : si i ■ o 1 -o - ! . ■ * l 4 5 5 7 r-ec'ji'i'.* (» > i I !/) Figure 13: the curve is integrated between 1 Hz and 4 Hz. The value obtained, along with other values corresponding to different epochs will be plotted versus time. '3e!t«|rcwf ■ ■ . *n3;:z«3<\ ana ’og; <5 '0 ‘100 2C0 -S C O 400 500 ‘ 600 700 - B O O - time in epochs (1 epoch = 30 seconds) L L £ 8 200 0 0 U 400 , -500 B O O IB ® J U U B 100 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 14: the psd of the DPTS is calculated and plotted versus frequency. P eO of r,Z‘ - ' 0 0.02 0 04 0 06 0 08 01 012 0 14 0.16 Q.tB 0 2 PSD of raw detta-power H i frequency (cycles/min) Figure 15: the peak frequency, value of the maximum and area are plotted in 3D. 0.02 0 01 0 005 0 15 0.2 m m m m m m m s m Frequency of the maxjmurr Maximum gf psd 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. III.2 Results fo r the two populations Here are the two graphs corresponding to methods 1 and 2: Figure 16: 3D visualization of the EEG parameters (upper graph: first method, lower graph: second method). The dark diamonds represent the control population, when the light ones represent the exposed population. •v & ® s tf> c s 3 :6 0 t o O S | 0 4 X. c i n 2 > - O ,f> O V D 3 0 02 0.2 ^ , - - ' ' ' ' : n D f5 o i ^jo.ai maximum of p sd o ‘ "'o 005 frequency of the maximum " -- - 4 4 ' 002 e 0 0!5 4 ^ —- 0.0' maximum o f psd 2 '0005 . frequency of the ri^-cnur": 25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Let’s first notice that, as expected, the scales are not the same depending on the method used. Also, the graph on the left (“normalized”) has 7 control patients and 11 exposed. The one on the right (“log”) has 8 control patients and 10 exposed. This difference can be explained by the following reason: it turned out that the data of two of the patients was not usable with one method but worked better with the other. That’s why one patient appears on the left but not on the right, whereas another one will be in the opposite situation. Finally, one patient had totally unexplainable recordings with either method and his data was simply not kept. Hence the number of data points for each method is 18 starting with a total of 20 recordings. When looking at these two graphs, the impression is that all the points seem scattered and there is no possibility to distinguish between the “control” and “exposed” population, with either method. To quantify this assumption, a t-test was performed with Matlab for each method. III.3 Distribution o f the data: restrictions on using a t-test Before performing the t-test, the distribution of the data has to be examined. Strictly speaking, the t-test does not apply to data that is not normally distributed. Generally, most statistical programs test for normality first before performing t-tests or other parametric tests, but Matlab doesn’t. There are two options if the data is not normally distributed: 26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. • Take the log of the data and then perform the t-test on the converted values, or • Use a “non-parametric” test such as the Wilcoxon Rank Sum test. Here are, in 12 graphs, the values obtained for the three parameters using both methods, represented with a histogram bar plot: Figure 17: bar plot of the parameters (area, frequency, maximum) using both methods. The values are distributed in 10 compartments. In the following lines, “c” stands for “control”, “e” for “exposed” and 1 or 2 is the method chosen. First row, left to right: areacl, areael, areac2, areae2. Second row, left to right: freqcl, freqel, freqc2, freqe2. Third row, left to right: maxcl, maxel, maxcl, maxc2. O f g f ~ _ > I 0.5 1 Q 0.5 1 10 15 0 , 1 0 20 J j l l h 0 0.01 0.02 0 0.01 00 2 0 0.01 0.02 0:01 0.015 . 0:02. a. S I ' g l 2 a , ? r c ■ ’ 0 V jJJ 0 ' 0.2 0.4 0 0.2 0 4 0 0 i n 10 0 10 As one can see, these values are not in general normally distributed. By taking their decimal log, one could expect to reach a more “normal” behavior, but there’s hardly 27 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. any significant difference, when plotting the transformed values, except for a few graphs that look more “bell-curved” as shown below: Figure 18: bar plot of the decimal log of all parameters (area, frequency, maximum) using both methods. The values are distributed in 10 compartments. The negative values on the x-axes are explained by the use of a logarithm on numbers ranging between 0 and 1. First row, left to right: areacl, areael, areac2, areae2. Second row, left to right: freqcl, freqel, freqc2, freqe2. Third row, left to right: maxcl, maxel, maxcl, maxc2. Illl = I p := = = r - C j * T o * = • 0 0 1-' -0 0.5 1 1,5 05 1 1 5 4 4 2 • 2 o < l fl 1 1 n 1 I £ -2 -15-2.5 -2 -15-2.5 -2. - 1 5 -2 . -18 -16 3 1 0 j ii! Given the fact that taking the log of the data didn’t help much, the t-test was performed on the original values of the parameters, knowing that the data was not normally distributed. A Wilcoxon Rank Sum test was also performed, and led to the same results as the t-test. 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 111.4Basics o f a t-test and Wilcoxon Rank sum test, Matlab implementation Even though the t-test and the Wilcoxon Rank sum test are standard techniques and concepts in statistics, here is a quick recap of what they are: the t-test is the most commonly used method to evaluate the differences in means between two groups. For example, the t-test can be used to test for a difference in test scores between a group of patients who were given a drug and a control group who received a placebo. The Wilcoxon test is a nonparametric alternative to t-test for dependant samples. It is designed to test a hypothesis about the location (median) of a population distribution. The significance level reported with a t-test or a Wilcoxon test represents the probability of error involved in accepting the research hypothesis about the existence of a difference. Technically speaking, this is the probability of error associated with rejecting the hypothesis of no difference between the two categories of observations (corresponding to the groups) in the population when, in fact, the hypothesis is true. Matlab has two built-in functions (ttest2 and ranksum) that do all the calculations and return three parameters: • H, which is either 0 or 1. H=0 means: do not reject null hypothesis at significance level of alpha. H=1 means: reject null hypothesis at significance level of alpha (the default value of alpha is 5%). In other words, H=0 if the difference in populations is not significantly different. Otherwise, H=l. • SI, the significance level. It is the probability of observing the given result by 29 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. chance given that the null hypothesis is true. Small values of significance cast doubt on the validity of the null hypothesis. • Cl, the confidence interval. Performing a t-test on, for example, the area in each population, can be made by typing: [H,SI,CI]=ttest2(areac 1 ,areae 1) H = 0 SI = 0.4703 CI = -0.1516 0.3141 H=1 only if the significance level is below 0.05, which is the default value for alpha, the desired significance level. The fact that H=0 means that the two groups cannot be differentiated at a significance level of 5%. Here is a table that shows the results of a t-test and Wilcoxon test on the three parameters area, peak frequency, and value of the peak, at significance level of 5%. Table 1: results of the t-test and Wilcoxon test performed on three parameters (area, frequency, 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. maximum) to compare two populations (control and exposed) at significance level alpha=5%. H (t-test) H (Wilcoxon) Significance level (t-test) Significance level (Wilcoxon) Confidence Interval Areacl, Areael 0 0 0.4703 0.5360 [-0.1516, 0.3141] Freqcl, Freqel 0 0 0.9883 0.9298 [-0.0046, 0.0046] Maxcl, Maxel 0 0 0.9211 0.6590 [-0.1004, 0.0913] Areac2, Areae2 0 0 0.1932 0.1220 [-5.5168, 1.2077] Freqc2, Freqe2 0 0 0.2295 0.3154 [-0.0061, 0.0016] Maxc2, Maxe2 0 0 0.1607 0.0676 [-3.3717, 0.6094] Average Area 0 0 0.3317 0.3290 N/A Average Freq 0 0 0.6089 0.6226 [-0.0053, 0.0031] Average Max 0 0 0.5409 0.3633 N/A As one can see, using all three parameters and both methods, all the values of H are 0. This means that the two populations, “control” and “exposed” cannot be differentiated. With the t-test, the significance levels for the average frequency and average maximum using both methods are respectively 61% and 54%, 10 times more than the required significance level of 5%. Similar results are found with the Wilcoxon test. From the table above, one can see that the second method (“log”) seems to work better than the first one, in a sense that the values of the significance levels are much lower using this second method: Area (19% vs. 47%), Frequency (23% vs. 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 99%), Maximum (16% vs. 92%) for the t-test, and Area (12% vs. 54%), Frequency (32% vs. 93%), Maximum (7% vs. 66%) for the Wilcoxon test. This was expected by just looking at the 3D graphs (figure 10). The one found with the second method seem less scattered than the other one, which is exactly what the previous comparison illustrates. The reason for this discrepancy is probably found when looking at figure 5: taking the log on the raw data seems to increase the SNR, and make periodic behaviors appear clearer. III. 5 Analysis o f the values o f the parameters The following table shows the actual mean values and standard deviations of the parameters. These values need to be compared by pairs of row (Area exposed 1 vs. Area control 1, and so on). When comparing the exposed and control population, it is hard to see general trends. The statistical tests say that no parameter can allow a distinction between the two populations (with a 5% significance level), and the table below confirms this (table 2). One can say that the “maximum” parameter using the second method has a higher value for the exposed group than for the control group, but when using the first method, the same parameter has almost the exact same value. Table 2: mean values and standard deviations of the parameters, using both methods. 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Mean Standard deviation Area exposed 1 0.3709 0.1839 Area control 1 0.4521 0.2547 Area exposed 2 10.6377 3.0098 Area control 2 8.4831 3.3222 Frequency exposed 1 0.0143 0.0044 Frequency control 1 0.0143 0.0039 Frequency exposed 2 0.0172 0.0026 Frequency control 2 0.0150 0.0045 Maximum exposed 1 0.1576 0.0816 Maximum control 1 0.1531 0.0975 Maximum exposed 2 4.6605 2.1263 Maximum control 2 3.2794 1.4784 It seems in conclusion hard to differentiate the two populations by comparing the spectral content of the delta waves of the EEG sleep recordings. III. 6 Comparison between the mean and standard deviations o f the DPTS fo r both populations When a Fourier transform is performed on the DPTS, the signal is detrended. Part of the information is lost in this process: the average and standard deviation of the original DPTS. Yet, both parameters could be a criterion of distinction between the two populations. In each population, the mean and standard deviation of each DPTS was calculated and plotted in a histogram plot shown below. The DPTS that were used were the ones found with the second method, but also the original DPTS. Indeed, it is known that the use of a logarithm on the data will reduce the differences in amplitude. Maybe the original DPTS signals will prove to be very different for the two populations (in terms of mean and standard deviation) and this difference 33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. will be erased by the use of a log. The first method is very unlikely to produce a difference since the data is normalized and reflects a percentage of the total power, which is itself related to the mean of the signal. That’s why the statistical tests were performed both on the original data and the log of this data, which has been frequently used in this study. There were nine signals for the control population and eleven for the exposed population. Here are two histogram plots representing the values taken by the means and standard deviations of the signals (first plot: original signals, second plot: log of the original plots). Figure 19: histogram plot of the mean and standard deviation for the exposed (first row) and control (second row) population. The data here is the original DPTS. 2 0 0 400 6 0 0 8 0 0 Mean (exposed) • ■<r O 1 J f 2m 4 0 0 6 0 0 v /a ? a {cc-.'f "-T: 8 j c g 2 tr u O D !m j too 2 0 0 30 0 . 400 S C O Otaie’ a rc, . 2 0 0 4 0 0 6 0 0 B C G Standard deviation (control) Figure 20: histogram plot of the mean and standard deviation for the exposed (first row) and control (second row) population. The data here is the logarithm of the DPTS. 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ■ » Mi i 3 O i o 1 A u < L , 2.2 2 4 28 0.1 0.2 0 2 04 ,0.S i ^.d-5'c vis- lajio.-. * fc/p-: 3j — Me a - • : control! E h^djTo ds-.yctic-n (cr-nfeo!; As one can see on the histogram plots, taking the log of the data reduces the differences in amplitude and gives a more ’’gaussian” shape to the curves as expected. Here is a table that displays the values of the mean and standard deviation of the original and log of the DPTS: Table 3: mean and standard deviation of the original and log of the DPTS. Mean Standard deviation DPTS control Original 289 149.7 Log 2.27 0.19 DPTS exposed Original 321 164.8 Log 2.33 0.22 Then, in order to compare the mean, and the standard deviation of the DPTS of the 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. exposed population versus the control population, a statistical t-test with a significance level of 5% was performed. Here are the results: Table 4: Results of a t-test comparing the mean and standard deviations of the DPTS of both populations. H Significance level Confidence interval Mean of delta power Control vs. Exposed (original) 0 0.653 [-116.9 181.9] Standard deviation Control vs. Exposed (original) 0 0.868 [-167.3 142.6] Mean of delta power Control vs. Exposed (log) 0 0.567 [-0.256, 0.145] Standard deviation Control vs. Exposed (log) 0 0.884 [-0.062,0.071] Both types of signals and both parameters cannot tell the difference between the two populations: the values of the significance levels are way above 5% (65% and 57% for the mean, 87% and 88% for the standard deviation). This could have been anticipated by just looking at the previous histogram plots. Indeed, the values of the mean and standard deviation don’t seem to differ much between the exposed and control groups. Surprisingly, the values of the significance levels are comparable for the original DPTS and its log. Once again, it might have been possible that the mean of the DPTS signals was higher for one of the populations. This could not have been found in the spectral analysis (with the value of the peak for example) since the signals were detrended before it. 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IV OTHER APPROACH: THE HEART RATE AND EMG Since the results given by the EEGs were not satisfactory, other signals extracted from the polysomnograph would be used to try to tell a difference between the two populations. Two other channels measuring indirectly or directly the electrical activity in other areas of the body were chosen: the heart rate (heart) and the EMG (muscles). I V 1 Study o f the heart rate 20 heart rate recordings were extracted from the polysomnograph. The signals were originally sampled at 1Hz. Here is how the signals were processed: • For each epoch (30 seconds so 30 points), the heart rate is averaged. • The average heart rate for each epoch is plotted versus time. The signal is the equivalent, in the case of the EEG, of the delta power time series. • Then, the power spectral density of the signal is plotted versus frequency. • The same processing as for the EEG is performed, and the area, the peak frequency and the value of the peak are plotted on a 3D graph. Unfortunately, the quality of the original heart rate signals was extremely bad. The majority of recordings had “glitches”, mostly at the end or the beginning of the recordings. Here are a few examples of heart rate recordings as they appear after the extraction: 37 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 21: three examples of an all-night heart rate recording sampled at 1 Hz. 4 * 2 * E C Id----------------1 ------------------1 ------------------!----------------- J------------------1 ------ ■ \ ................... . -4 I I 1 1 ■ ! : , , , . ................... V 0 . - ' 0.5 1 1.5 2 ' 2 5- 4 2 I! it 1 1 , . , , , ™ , , „ i ............ .......X ...__ __1 ....... . • i 0.5 .1 ■ 1 .5 1 iu r.c (;it v.'eom .'O 25 - * 1 Q 4 As one can see, many parts of the recordings are not exploitable due to sudden changes in the value of the heart rate that obviously cannot correspond to any clinical change in the patient. These changes can occur at any time of the recording and are likely due to problems with the positioning of the electrodes on the patient’s chest. It was possible though to “arrange” the signals and manually erase the parts that were not usable: either cut them when they occurred at the beginning or the end of the recording, or replace a part that is not usable by the average between two values of the heart rate, the one right after and the one right before the cut. These changes though turned out to be hard to implement and would, because of their high occurrence, change the frequencies embedded in the signal. 38 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Out of twenty original signals, only eleven could be processed after being manually edited to remove artifacts and out of these eleven signals, just nine of them showed “likely” values of the 3D parameters. Among the nine subjects studied, four belonged to the exposed group, and five to the control group. Here is a graphic example of a signal before and after being arranged (figure 22). As one can see, the original signal is either cropped (at the end) or some of its values are modified and averaged. Figure 22: Example of an original heart rate signal (upper graph) and the corresponding corrected signal. i S - i s o p h f i l time (in seconds) s 10 200 - Q £ 150 sill D S) i i ■ L i 39 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Here is the 3D graph of the parameters obtained with the new heart rate recordings: Figure 23: 3D visualization of the heart rate parameters. The dark diamonds represent the control population, when the light ones represent the exposed population. 5s005. i l i t i i l l o u.«. C l ;U 33—' Q 02 . I q 0 Be o Outs g 0.01 3- ts 0W 5 cf csd 1 1 oa oms 0C1 0.005 f eoi:e-sey of the “-sad.nu The following table displays the average values of the three parameters, and their standard deviation. Table 5: mean values and standard deviations of the heart rate parameters. Mean Standard deviation Area exposed 0.0203 0.0062 Area control 0.0309 0.0077 Frequency exposed 0.0088 0.0065 Frequency control 0.0120 0.0068 Maximum exposed 0.0085 0.0025 Maximum control 0.0106 0.0038 40 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. It’s hard to conclude anything from these values because of the small number of signals. Even when comparing these values to the ones obtained with the EEG, there is no general trend that comes out. No statistical test was performed on the heart rate parameters for the reasons mentioned above, i.e. the small number of signals. In order to have better signals, another approach was possible: use the ECG recordings and measure the RR-intervals (and then infer the heart rate) directly. Once again, the bad quality of the ECG recordings that presented the same type of problems prevented the use of this alternative solution. It was then decided to abandon this approach and focus on the EMG recordings. IV.2 Study o f the EMG recordings An EMG is a recording of electrical activity from the muscular system; in sleep recording, it is synonymous with resting muscle activity or potential. The chin/cheek EMG, along with EEG and EOG, is one of the three basic variables used to score sleep stages and waking. Sleep recording in humans utilizes surface electrodes to measure activity from the sub mental or masseter muscles (a masticatory muscle whose action is closing the jaws). They reflect the changes in resting muscle activity. The chin/cheek EMG is tonically inhibited during REM sleep. One of the channels of the polysomnograph recordings was an EMG channel. Two electrodes are placed on the chin (chin EMG), one right below the lower lip, and one 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. farther down on the chin. These electrodes record the electrical activity of the muscles of this region. The sampling rate for these recordings is 100 Hz. The same approach as for the EEG was used to study the EMG. Here are the steps of the signal processing: • The EMG is chopped every epoch. • For each epoch, the standard deviation of the signal is computed. • This value is plotted versus time along with other values corresponding to other epochs. The signal is equivalent to the DPTS for the EEG and will be referred to as the SDEMG (Standard Deviation of EMG). • The rest is exactly the same as for the EEG: the power spectral density of the logarithm of this signal is found as well as the three parameters area, peak frequency and value of the peak. These values are then plotted on a 3D graph. For that matter, taking the log of the data comes almost as a conclusion of the previous part with the EEG studies, since this method allowed a much better discrimination between the populations. Here is the short Matlab program used to find the standard deviation time series: a=input('signal='); L=lengtb(a); epochs=L/3000; t=[l:epochs]; 42 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. st=zeros( 1,epochs); for i=0: epochs-1, y=[a(3000*i+l :3000*(i+l))]; st(i+l)=std(y,l); end plot(st) Here is an example of a 10-minute EMG recording as well as its SDEMG: Figure 24: the first graph (up) is a typical 10-minute EMG. The second one (middle) represents the standard deviation, computed every epoch, of the first EMG graph. The third graph (down) also represents the standard deviation time series (SDEMG), but this time, for the nightlong recording. The time units on the x-axis are, from top to bottom: seconds, epochs and epochs. •3 C , 2 0 Q C 3 tO O J - < r < 10 1 2 1 4 1 6 1 8 20 T O O 200 3 0 0 400 500 B C 0 T D D 600 900 1 D Q 0 43 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IV J Choice o f the standard deviation o f the EMG The amplitude of the chin EMG provides a rough indication of the subject's muscle tone during sleep. In non-REM (quiet) sleep, this muscle tone is lower than wakefulness, but in REM sleep, muscle tone decreases to levels lower than non- REM sleep. Thus, in general, EMG is used to help with the scoring of REM sleep. The signal measured contains a lot of artifacts, so there's no other information that can be extracted from it, unlike the EEG or ECG. What matters in the EMG is not so much the “baseline” (clearly seen on the recording above), but the way the signal evolves around this baseline. Therefore, the standard deviation is the best parameter to use. Here is a recap of the EMG signals processing (figures 25 to 29): Figure 25: 5-minute long EMG recording. 300 2 5 0 200 • 1 0 0 - 200 2 5 0 ■ : i £ 0 1 0 0 1 5 0 ! im e. (in seconds) 44 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 26: the EMG is chopped every 30 seconds, and the standard deviation is calculated for that epoch. T S 0.25 I 02 I 9 a 01 o L t, w s C L Q S O S o o c=osj- / at" 0 0 02 004 0.06 0 0 B 01 0 1 2 0 1 4 016 0 1 8 0.2 Frequency (cycles/minute) ' ' - 6 4 : D 0 02 0 04 0.06 -0 .0 8 0 .1 0 1 2 - 0 1 4 0 1 6 0 1 B 0 2 0 c;ne x y /c y c.e t,/-[r u ts’ . Figure 27: the value obtained for the standard deviation, along with other values corresponding to different epochs will be plotted versus time (SDEMG). 1 U 0 ' 8 0 70 60 1 0 0 2 0 0 ‘ 300 4 0 0 S C O 600 700 8 0 0 ' 900 1 0 0 0 Time {in epochs) 45 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 28: the power spectral density of the logarithm of the previous signal is plotted versus frequency. 0 .0 6 0 0.02 0.04 0.06 0 0 3 0 .1 0.1 2 014 0 ,1 6 0 1 8 0 2 irrecuenc;' (cyeies/r.*. r.) Figure 29: the three parameters (frequency, area, max) are plotted on a 3D graph. 55 O O -- 0 - 3 5 o ■o frequency of the maximum m ax im u m o f p s d 46 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Contrary to what was done for the EEG signals, the phase here was not studied because the periodicity of the EMG signals is not as obvious as in the case of the EEG. One of the consequences of this non-periodicity is that the spectrum of the standard deviation of the EMG has often a peak at very low frequencies, including zero (the resolution, as for the EEG signals, is limited to 0.005 cycles/min). IV. 4 Problems encountered with the EMG signals The 20 signals obtained when computing the standard deviation of the EMGs were, for some of them, not usable. Some graphs displayed sudden changes in the baseline amplitude, sometimes lasting until the end of the recording, as shown below: Figure 30: The upper graph plots the standard deviation of an EMG signal versus time. The lower graph plots the log of the same standard deviation. Notice around t = 500 epochs an abrupt change in the amplitude, that lasts until the end of the recording. 1 0 0 2 0 0 3 0 0 4 C D ■ ' 5 00 6 G D 703 800 9 0 0 Time (in seonds) I --------- , -------- f ---------- 1 --------- 1 -------- 1 --------- 1 --------- 1 ---------1 --------- r O * ----------- 1 ................». ------------- 1 ------------- 1 ---- 1 -------------- 1 ------------- 1 ------------- u _ ------0 - 5 *o ■ o ' ”O S | I 1 0 0 2 0 0 3 0 0 4 0 0 5 00 6 0 0 7 0 0 800 9 0 0 Time (in secon d s) 47 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In addition to these abrupt changes in the amplitude, one can notice, as it was the case already for the ECG signals, rapid variations of the amplitude that can occur at the beginning or end (see graph above) of the recording. These changes do not correspond to any clinical change in the patient (one might think that they correspond to the time when the patient is still awake or simply awakes), but they are more likely due to technical problems (loose electrodes...). Yet, when these phenomena occur either at the beginning or the end of the recording, they can easily be cropped, and the remaining signal can be processed normally. IV. 5 Results fo r the two populations Here is the 3D graph of the EMG parameters: Figure 31: 3D visualization of the EMG parameters. The dark diamonds represent the control population, and the light ones represent the exposed population. 0D2 G O : 0 005 frequency of the maximum "M m um ,:i psu 48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Here, the points seem to be less scattered than for the EEG. Like the EEG, to confirm or infirm this assumption with a statistical test, the “normality” of the data has to be checked. Here are two tables similar to the ones found with the EEG that show a histogram plot of the three parameters, and a histogram plot of the decimal logarithm of the parameters: Figure 32: bar plot of the parameters (area, frequency, maximum). The values are distributed in 10 compartments. Once again, “c” stands for “control”, “e” for “exposed. First row, left to right: areac, areae. Second row, left to right: freqc, freqe. Third row, left to right: maxc, maxe. « 4 £ Ill c §2 aT Q E 2 3 E 1 2 o 1 1 1 1 0 M I l I I 0,005 0,01 ' 0,015 0.02 4 .------------- ■ ------------- ----------- 0.01 '0.02 0 03 L . 49 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 33: bar plot of the decimal log of all EMG parameters (area, frequency, maximum). The values are distributed in 10 compartments. The absence of a graph for the frequency distribution of the exposed population is explained by the use of a logarithm on frequencies that can be equal to 0. First row, left to right: areac, areae. Second row, left to right: freqc, freqe. Third row, left to right: maxc, maxe. I ti Q I l L _ -.1 In both cases, the data seems “normal” enough to perform a t-test, considering the small amount of data (only 6 control subjects, and 9 exposed subjects) due to problems described previously. A parametric test is also performed, to confirm the t- test. The results are presented in the table below. Once again, the fact that H=0 for all the parameters reflects the inability to discern the two groups at a significance level of 5%. Yet, the frequency brings the best results, since the significance level of both tests performed on this parameter is of 12% (t-test) and 7% (Wilcoxon). 50 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 6: results of the t-test and Wilcoxon test performed on three EMG parameters (area, frequency, maximum) to compare two populations (control and exposed) at significance level alpha=5%. H (t-test) H (Wilcoxon) Significance level (t-test) Significance level (Wilcoxon) Confidence Interval Areae-Areac 0 0 0.376 0.144 [-5.60,2.26] Freqe-Freqc 0 0 0.120 0.066 [-0.012,0.001] Maxc-Maxe 0 0 0.456 0.181 [-2.45,1.17] These results have to be taken with a lot of precaution because the number of patients is very small. As the following table suggests, the average frequency and standard deviation of the exposed group is 0.0061±0.0066 cycles/min, and the average frequency and standard deviation of the control group is 0.0117±0.0052; these distinct values explain the low significance level for this parameter. Table 7: mean values and standard deviations of the EMG parameters, using the second method. Mean Standard deviation Area exposed 2.4430 3.3186 Area control 4.1111 3.6694 Frequency exposed 0.0061 0.0066 Frequency control 0.0117 0.0047 Maximum exposed 1.1364 1.3940 Maximum control 1.7809 1.6070 IV 6 Comparison o f the mean and standard deviation o f the SDEMG time signals Like what was done with the EEG signals, it can be helpful to compare the values of the mean and standard deviation of the SDEMG signals between the two 51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. populations. The mean and standard deviation of each SDEMG was calculated and plotted below. Figure 34: histogram plot of the mean and standard deviation for the control (first row) and exposed (second row) population. Moan of EMG fcontro*' Si.d :A r'VO fcootio:} J O 20 ■ 40 S O 30 0 5- 1 0 1 5 Mean of EMG (exposed) ' Std of EMG (exposed) Here is a table that displays the previous results and shows the mean and standard deviation of the SDEMG for both populations: Table 8: Mean and standard deviation of the SDEMG for both populations. Mean Standard deviation Mean of exposed SDEMG 31.24 14.41 Mean of control SDEMG 20.21 13.14 Standard deviation of exposed SDEMG 9.07 3.04 Standard deviation of control SDEMG 8.80 4.42 52 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In order to see if there was a significant difference between the two populations, a t- test was performed, with a significance level set at 5%. Thp results are shown in the table below: Table 9: Results of a t-test comparing the mean and standard deviations of the DPTS of both populations. H Significance level Confidence interval Mean of SDEMG (Control vs. exposed) 0 0.10 [-24.43, 2.37] Standard deviation of SDEMG (Control vs. exposed) 0 0.88 [-3.91, 3.37] Here again, H=0. Notice though the low value of the significance level that was obtained with the mean of the SDEMG. This low value suggests that the baseline of the EMG will not be the same for the two populations. The mean of the means of the SDEMG time series of the exposed population is 31.2 (standard deviation of 14.4) and only 20.1 for the control population (standard deviation of 13.1). In other words, the muscle tone seems to be lower for the control population than for the exposed population, which tends to indicate a longer period of REM sleep stages for the control infants. 53 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V CONCLUSION V. 1 Comments on the results All the statistical tests that were performed on the many parameters extracted from the EEG, the heart rate or the EMG didn’t allow discrimination between the two populations at a significance level of 5%. a) EEG Fist of all, it seems that the second method (“log”) allows much better results. Indeed, the values of H are comprised between 16% and 23% with this method, as opposed to values ranging from 47% and 98% for the first method (“normalized”). Two reasons can be suggested: • Normalizing the DPTS will erase the differences between the signals since all the values, for both populations, will be comprised between 0 and 1. • Normalizing the data lowered the SNR, which makes it more difficult for the signals to be differentiated. Regarding the parameters extracted from the EEG signals, and focusing only on method 2, the area, the frequency and the maximum parameters are higher for the 54 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. exposed population than for the control population. Let’s not forget that the three parameters were found after detrending the DPTS. Hence, these results should also be compared with the mean of the DPTS. As table 3 suggests it, the exposed population has a higher mean of the delta power than the control population. When combining these two pieces of information, it seems that for the exposed population, the delta waves are more abundant (mean of DPTS), might change faster in time (slightly higher frequency) and with a greater amplitude (maximum) than for the control population. In the theory of sleep studies, delta waves are associated with deep sleep (stages 3 and 4). Therefore, it seems that the exposed infants have deeper quiet sleep. These results should be moderated since table 4 clearly shows that the significance level is high when comparing the mean value of the DPTS of the exposed and control populations. b) Heart rate The fact that only 9 signals were studied for this parameter makes it hard to draw any conclusion. Yet, the values of the three heart rate parameters are all higher for the control population. The only relevant information is that the heart rate seems to vary faster in time for these infants. 55 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. c) EMG Once again here, the three parameters couldn’t differentiate the two populations. The value of H for these three parameters varies between 12% (Frequency) and 45% (Maximum) when using a t-test and 6% (Frequency) to 18% (Maximum) when using a parametric test. The values of all parameters are lower for the exposed population than for the control population. In particular, the frequency parameter is higher for the control population than the exposed population with a difference that is more important than for the frequency parameter extracted with the EEG: • EEG. Control: 0.0143 cycles/min vs. exposed: 0.0172 cycles/min, significance level of 31% with the parametric test. • EMG. Control: 0.011 cycles/min vs. exposed: 0.0061 cycles/min, significance level of 6% with the parametric test. In addition to that, when looking at the value of the mean of the SDEMG in table 8, one can see that it is higher for the exposed population than for the control (exposed: 31.2 vs. control: 20.2). In other words, the standard deviation around the baseline is, overall, higher for the exposed population. A high standard deviation for the EMG means a higher facial muscular activity, which also means less REM sleep. This result comes as a complement of the one obtained with the EEG parameters, when it was found that the exposed population had deeper quiet sleep. 56 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Even though all the previous results should be taken with a lot of precaution due to the problems exposed below, this study seems to show that infants whose mothers have been exposed to drugs tend to have less REM stages and deeper quiet sleep stages than ’’ normal” infants. The following idealized diagram of sleep stages through the night illustrates this result: Figure 35: Idealized evolution of the sleep stages for the exposed (upper graph) and control population (lower graph). The exposed population has less REM sleep, deeper quiet sleep and the oscillations take place at a slower rate than the control population. The units on both axes are arbitrary. REM C . Q . 0.5 CD * o i L L ! Deep sleep 8 5 7 0 5 4 Tune _x Deep Sleep 9 1 0 2 5 1 3 4 T i.. e 57 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V.2 Problems encountered One of the major issues concerned the data itself. The number of signals studied was relatively small with only 16 subjects (and four additional studies). But the main problem regarded the quality of the signals. Some channels, especially the heart rate and the EMG had a poor quality and those signals had to be either rearranged, which would alter the exactness of the results, or simply removed, which lowered the amount of data and thus the strength of the results. Another aspect was the lack of information on the data. Indeed, all exposed patients had mothers who used cocaine/crack during pregnancy, but there was no quantitative information regarding the use of these drugs. It would have been interesting to know the amount of drug used for each patient, and also when these drugs were taken. It matters if the mother used drugs during the first, second or third trimester of the pregnancy because the development of the fetus and its brain are not the same at each trimester. The impact of the drug depends on the time of pregnancy it was taken. V.3 Other possible areas o f research In this project, one of the three major parameters in sleep studies was not taken into account: the EOG. It was mostly a question of time and it could have helped refine 58 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the spectral characteristics of both populations. Another direction could have been followed: it would have been interesting to study the correlation between the signals in general. For example, study the correlation between the DPTS and the SDEMG, and see if these signals varied with the same time pattern. A strong correlation (or a poor one) might have been a marker for one of the populations. The EEG signals could have also been studied from the point of view of correlation. Indeed, for each patient, there were two recordings for each side of the brain, and a low spectral correlation between them for the exposed population might have indicated fewer interhemispheric neuronal connections for these patients. 59 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. VI REFERENCES VI.l Articles J. Dorman, D. Kupfer. Computer analysis of EEG, EOG, and NPT activity during sleep. Int J. Biomedical computing. 1988. Smita Garde, Michael Regalado, Vicki Schechtman, Michael C.K. Khoo. Nonlinear dynamics of heart rate variability in cocaine-exposed neonates during sleep. Am. J. Physiol Heart Circ Physiology 2001. WB. Martin, LC. Johnson, S. Viglione. Pattern recognition of EEG-EOG as a technique for all-night sleep stage scoring. Electroencephalographic clinical Neurophysiology. 1972. Mark Scher, George Dokianakis, Doris Steppe. Computer classification of state in healthy preterm neonates. Sleep 1997. Mark Scher, George Dokianakis, Mingui Sun. Computer classification of sleep in preterm and full-term neonates at similar postconceptional term ages. American Sleep Disorders association 1996. Mark Scher, Gale Richardson, Nancy Day. Effects of prenatal cocaine/crack and other drug exposure on electroencephalo-graphic sleep studies at birth and one year. Pediatrics. Jan. 2000. D. Schramm, B. Scheidt, A. Hubler. Spectral analysis of electroencephalographam during sleep-related apneas in pre-term and term bom infants in the first weeks of life. Clinical Neurophysiology 2000. 60 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. VI.2 Books G. Blanchet, M. Charbit. Numerical signal processing. Ed. Hermes 1998. DJ. Higham, N.J. Higham. Matlab Guide. Ed. SIAM 2000 Leland B. Jackson. Digital filters and signal processing. Ed. KAP 1996. B.P. Lathi. Linear systems and signals. Ed. Berkeley-Cambridge Press 1992. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. VII APPENDIX A: EXPOSED PATIENTS Here are the graphs of the time series signals used in this study. The first appendix contains the graphs of the exposed patients and the second one, the graphs of the control patients. The units and scales used in this appendix are exactly the same as in the second appendix. There are three groups of graphs in each appendix: the DPTS (related to the EEG), heart rate, and SDEMG (related to the EMG). The units vary from group to group: • The x-axis units are always indicated and are the same for the graphs of the same group (the scales are also the same for these graphs). • The y-axis units are the following: - For the DPTS, the scale is logarithmic and the units are in (gV)2. - For the heart rate, the scale is linear and the units are in beats/minute. - For the SDEMG, the scale is logarithmic and the units are in (pV). The name of the patient appears on the y-axis. Some patients’ names appear twice due to multiple sleep recordings. 62 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 36: DPTS 1. ■ v - f - 5 « ti Jut % — s -'n l i l t 4 ■c 0 Ip®# * ~s y 5 ™ £ > - 0 4 o < ? ;; fc 4 I # «i u . 4 0 V 'V f'if/t H t " '~ M s > - ~ 1 * M ,& - ~ t' * W " * 'S S tH lU /r' * u • a " • * '**s^i. if™ '*'"*’ ’ - - jy J jU V ^ k - * * - » j^ “ i,'l*jv<s,^!j^yW >^l ’V 4&i 200 400. B O O 800 ! 0 Q D y : > n e in ep,'-cr,: Figure 37: DPTS 2. 13 0 0 603 eco .200 400 » v V V -w -'V k ,-. V— '“u»* ■ - d ■ ->- JnV w ~" T im # in e p o c h s Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 38: DPTS 3. S T n1 > * T S - «i I f,' c -CL £ G « ; £ W h m * * " - H _ W S J * * * — Jw * -™ 1 0 0 0 V . 200 ‘ 000 !"r.;-j r vjp;*;h* S C O 1 G C 0 Figure 39: Heart rate. C 200 JS •** Tim© in seconds x 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 40: SDEMG 1. e\ j fe b i/> — j. ..-.-.-''U . b } ^ ^ " > k !^ k w j ^ U tw lj KjJ^f ^Jah. r_ ------------j_ - J ___ , _L . 0 100 200 300 400 500 S C O ?0Q 800 900 100D " i n s in e a o c is. Figure 41: SDEMG 2. S00 030 700 800 900 1000 Time ‘i «-,o;:.'; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 42: SDEMG 3. 6 •j LL . Iifi ? ,1 4J-1 fiiU i.r,o - r . -GJ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. VIII APPENDIX B: CONTROL PATIENTS For explanations regarding the units and scales, please refer to the first appendix. Figure 43: DPTS 1. & & c £ o C S 8 T5 4 P- s E p ® 3: r i I I I I I 2co fflo son . eon T im e in e p o c h s t O Q O 67 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 44: DPTS 2. X 4 * - o " I 4 J * v ■ C m s 0,- 3 3 0 - 4 0 0 BO O ' < irre n e p o c h s 800 1 E 0 0 Figure 45: Heart rate. 2 0 0 . r A. .iim jtiU ill I I I L I . too ■■^aiiMu..n.j..u ^ .J i.jiftiJ lililliillM u iiy ^ lik M llillilia W j 0.5 ' • 1 15 ' 2 ' Time in seconds j||jJ 8 i to4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 46: SDEMG 1. fVv^W^ IS£ ' _ j______ t ______1.,___ ..I --- „ ---- 4 ,— ----- ( » . _ J ____ _ L - 0 • 100 - 200. 300 400 , 500 600 700 800 900 1 0 D D Figure 47: SDEMG 2. 0-100 200 3 D Q 403 500 600 ?00 600 900 1000 ■ Time in e p o c h s Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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Creator Chast, Frederic Joseph (author)

Core Title Effects of prenatal cocaine exposure in quantitative sleep measures in infants

School Graduate School

Degree Master of Science

Degree Program Biomedical Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag biology, neuroscience,engineering, biomedical,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Khoo, Michael C.K. (committee chair), [illegible] (committee member), D'Argenio, David (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-303185

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