Wavelet Coherence Reveals Entrainment of Heart Rate Variability Among People Involved in Group Activities

Transcription

1 Wavelet Coherence Reveals Entrainment of Heart Rate Variability Among People Involved in Group Activities Joshal Daftari, Giorgio Quer and Ramesh Rao Calit2 and Department of Electrical and Computer Engineering, University of California, San Diego La Jolla, CA 9293, USA Abstract The study of group dynamics is of primary importance in psychology and medicine because group dynamics affects the state of each member in a group. We study the RR interval time series, a heart rate measure, for a group of individuals involved in Kundalini meditation sessions. We analyze individual signals and study the wavelet coherence among the heart rate variability of different individuals. For specific activities, we found a high degree of coherence among all the people in the group. We also propose a novel method to detect temporally varying connections among the individuals based on the coherence of their heart rate. I. INTRODUCTION AND RELATED WORK Group dynamics is the study of interactions among two or more people connected by some form of social relationship []. In athletics and team sports, the dynamics of the group can dramatically influence the outcome and the well-being of the players [2]. Similar phenomena manifest themselves in guided group meditation or prayer activities. Because of this connection, the study of group dynamics is relevant in the fields of psychology, sociology, communication studies, and medicine; there are many significant examples of how a group can influence the well-being of the individual [3]. Group dynamics are also highly pertinent to understanding animal interactions, see e.g., [4], where the authors have systematically analyzed the relationships between group states and the dynamics of individual elements in a community of baboons. There is however, still a need to quantify the effects of group dynamics on each member of the group. Relatively inexpensive sensors and wireless technologies are now available to sense and store information about movement, blood pressure, temperature, heart rate, body composition, and many other physiological parameters of an individual, (see [5] and references therein). Indeed, there are already many people that wear one or more of these devices to track daily activities and/or modify their lifestyle and diet in order to improve their health. However, it is often difficult to properly interpret the data and extract the relevant information, in part because many proprietary algorithms used in conjunction with these devices are poorly documented. Among the many physiological signals that can be tracked, the RR interval time series is particularly valuable and easy to measure. It is defined as the time interval between successive peaks seen on an electrocardiogram (ECG). Specifically, it refers to the R peaks of the QRS complex, which is the combination of three of the graphical deflections observed on an ECG as a result of ventricular contractions. By analyzing the RR signal, we can calculate the variation in the beat-to-beat interval, the heart rate variability (HRV). The fact that HRV can be easily derived makes it a promising candidate for the study of human physiological response. It has become a noninvasive tool for accessing the activities of the autonomous nervous system. Much study has been conducted using HRV to signify cardiovascular mortality and reduced cardiac activity [6]. We develop a novel approach to exploit HRV as an indicator of the synchronicity and one s state of well-being. HRV is regulated by the opposite influence of the sympathetic and the parasympathetic branches of the autonomic nervous system, i.e., the predominance of the former tends to decrease the variation in successive RR intervals, while the predominance of the latter tends to increase it. The HRV is generally analyzed in the frequency domain, and the frequencies of interest are divided into three major bands, see [6]: the very low frequency (, in the range.3.4 Hz), the low frequency (, in the range.4.5 Hz), and the high frequency (, in the range.5.4 Hz). As an example, a high component of the HRV around the frequency f, in the time interval between t and t, means that there is a significant periodicity in the RR time series in that time interval, with period approximately equal to /f. Different physiological phenomenon can be inferred from fluctuations in the RR time series [7]. The most important are () respiratory sinus arrhythmia due to breathing, at and, (2) Mayer waves of blood pressure, at a frequency of about. Hz, and (3) oscillations at the, which may reflect factors related to long-term fluctuations in the thermoregulatory system or regulation of blood pressure and water balance. However, the physiological basis for fluctuations is still under study [6]. Many signal processing methods have been proposed to distinguish among the causes of HRV and to extract relevant information. A natural choice to study a non-stationary signal in the frequency domain is the use of wavelet analysis, as proposed in [8]. In this paper, we analyze the RR interval signals from a group of people performing the same activities together, in order to detect if there is any entrainment (adjusting of internal rhythm to synchronize with an external cycle) among them. The goal is to check and quantify how shared activity might induce shared physiological states. These shared states may have a strong influence on the group goals, as well as on the physiological state of each member of the group. We collected the signals from a group of practitioners participating in Kundalini yoga meditation sessions, while wearing a heart rate monitor. Kundalini Yoga consists of movements and meditations which target the whole body. These yoga meditation

2 techniques were conducted by D. Shannahoff-Khalsa, and are detailed in [9], where their therapeutic value for treating various health conditions is described. After the data collection, we examined the spectral distribution of the RR series using the Welch method [], proposing a simple technique to monitor the evolution in time of the signal spectrum. Then we analyzed the degree of coupling between two practitioners with standard wavelet transformation and wavelet coherence []. Finally, we present a new measure of the entrainment among a group of practitioners, defining the wavelet coherence among a set of N > 2 signals. To the best of our knowledge, the study of such a coupling has been done only between two physiological parameters [2] but never for signals from two different individuals or, as in our case, for a group of people. We also propose a graphical representation of connections within the group, derived from the coherence signal. The main contributions of this paper are: the collection of RR interval data from a group of people performing a coordinated group activity; the joint processing and analysis of RR interval time series from two or more people; the proposal of a novel measure of coherence among a set of N > 2 signals, and the exploitation of this technique to analyze the data collected; the graphical results that underline the entrainment in HRV during certain activities among the people, and the proposed time varying entrainment network structure among them. The rest of the paper is organized as follows. In Section II we provide mathematical preliminaries and introduce the concept of coherence among N > 2 signals. Then in Section III we present the experimental setup. In Section IV we analyze the RR interval time series of each individual and show the results of this analysis. In Section V we present the joint analysis of the RR interval data among the yoga practitioners and show the corresponding results. Section VI concludes the paper. II. MATHEMATICAL BACKGROUND In this section we describe the Welch method [] and the wavelet coherence method [3] that will be used in this paper to analyze the RR signals captured during the yoga activities and study the common patterns of the RR signals among the people involved in the yoga activity. We assume a time series x, whose elements are x (k), with k =,...,K. The analysis of the frequency components of x cannot be done through a standard Fourier transformation of the signal, since the signal is non-stationary. In this case, the standard Fourier transformation gives only global information about the signal, while it tells us nothing about the characteristics of the signal at a specific time. We start by defining a simple extension of Welch s method to work with non-stationary signals. A. Welch s method The Welch method [] is a technique used to estimate the power of a signal as a function of frequency; it is effective in reducing noise compared to other standard methods. In In Section IV-A we describe how this time series is obtained from the irregularly sampled RR signal. order to get the spectral estimate of the time series x, we divide the signal into M equally spaced segments of length L, x (:L),x (D+:D+L),...,x (MD+:MD+L), where D is the shift between each segment. With the notation x (p:q), with p q integers, we refer to the segment with elements x (p),x (p+),...,x (q). In order to have overlapping segments, i.e., to include in the analysis all the points of the time series, it is necessary that: K L M = +, () D where is the ceiling function. In the standard Welch method, for each segment x (md+:md+l), we calculate the modified periodogram as: L 2 w (l) x (md+l) e j2π f L l l= P x (md+:md+l) =, (2) L w (l) 2 where w is a Hamming window, whose elements are w (),w (2),...,w (L), and 2πf/L is the discrete angular frequency, with f =,...,L. From the modified periodograms, we can estimate the power spectral density of the signal x by averaging over all the segments, i.e., ˆP x = M M m= l= P x (md+:md+l). (3) This method is very useful to analyze and represent graphically the spectral power at different frequencies, but it provides only global information about the signal. Since we deal with nonstationary signals, we propose a simple modification of the method to give instantaneous representation of the spectral power of the signal. Instead of applying the Welch method to the entire signal, we consider a segment of length N < K starting with element x (n), i.e., x n = x (n:n+n ). (4) We define M 2 = N L D +, and we apply Eq. (2) to the new signal x n, obtaining the modified periodogram. Then we apply Eq. (3), i.e., P x (md+:md+l) n ˆP xn = M 2 M 2 m= P x (md+:md+l) n. (5) In this way we can calculate the spectral power characteristics of a specific segment of the signal, and we can evaluate how these characteristics change in time as a function of n. B. The Continuous Wavelet Transform: CWT The Welch method is very useful in analyzing the characteristics of a signal, as well as the evolution of such characteristics in time. In this section, we are interested in capturing with more detail any common frequency pattern among a set of two or more signals. We advocate the use of the Continuous Wavelet Transform (CWT) for a time series x, see e.g., [3], whose elements are defined as: W (k,s) x = K i= x (i) Ψ ( i k s ), (6)

3 where Ψ( ) is the scaled, translated and normalized version of the discrete basis function, which in our case is a Morlet wavelet [4], and is the complex conjugate. s is the wavelet scale, which is proportional to the period [3]. The CWT gives us a valid tool to analyze the time evolution of the spectral components of our time series. C. The Cross Wavelet Transform: XWT In order to compare two time series, and in particular the time evolution of their spectral components, we use the Cross Wavelet Transform (XWT) that gives us information about the distribution of the cross power between the two signals in the frequency domain and how this distribution evolves in time. The XWT between the time series x and y, named W xy, is defined element by element as: W (k,s) xy = W (k,s) x ( W (k,s) y ). (7) The absolute value of the XWT, W xy, is called the cross wavelet power, while the phase of the XWT, W xy is the relative phase between the time series x and y. D. Pairwise Wavelet Coherence The wavelet coherence is a function that quantifies the degree of coherence at a specific time and frequency between a couple of time series x and y. This function is defined as [], [5]: C (k,s) xy = ( S W xy (k,s) ) 2 ( W (k,s) S 2) ( W (k,s) 2), (8) S x where S( ) is a smoothing function in time, k, and in scale, s, composed of two discrete convolutions, i.e., S(f (a,b)) = g(b b ) h(a a,b)f(a,b )da db, (9) where the integral is a Haar integral among functions defined in a discrete domain, see e.g., [6]. The two components of the smoothing function are: g(b) = c rect(.6b), () where c is a constant, rect(b) = for b.5, rect(b) = otherwise, and h(a,b) = e a2 2b 2. () E. N Signal Wavelet Coherence In this section, we extend the definition of wavelet coherence in order to jointly compare a set of N signals in time and frequency and to recognize if there exists any frequency pattern common to all of them. We propose a measure of the N signals coherence that maintains the commutative property of the pairwise coherence, and that it is limited between and, i.e., C z (k,s),...,z N = ( N N 2) N h= i=h+ y C (k,s) z h z i. (2) To the best of our knowledge, we did not find in the literature any measure of the wavelet coherence among a set of N > 2 signals. III. EXPERIMENTAL SETUP In this section we present the activities performed in the yoga sessions and the devices used to collect the RR interval data from each person involved. We conducted the experiment over five yoga sessions, obtaining similar results. We present here only two of them, named (Y) and (Y2), which included similar activities, in order to present a fair comparison. A. Yoga session: activities We consider seven practitioners, six males and one female, referred as S,S 2,...,S 7, with ages that range from 23 to 55 years, performing Kundalini yoga meditation techniques as described in [9], for a period of approximately 9 minutes per session. Kundalini yoga involves movements, chanting and meditation coordinated and guided by a professional instructor. Between two successive activities, there is a relaxation period during which the group members could speak with the instructor and among each other. The activities performed in the two yoga sessions under consideration are: A All the practitioners, led by the instructor, chant together the words Ong Namo Guru Dev Namo, sitting with a straight spine. The chant involves two cycles of breathing, each at a period of seconds, with a duration of approximately 5 minutes. A2 Each practitioner inhales deeply, pulling the chest forward, then exhales, relaxing the spine. The movements and the breathing frequency are not coordinated among the practitioners. The duration of this activity is approximately 2 minutes. A3 Each practitioner raises his/her shoulders while inhaling, and lowers them while exhaling. The pace varies on an individual basis and the movements are not synchronized. The duration of this activity is approximately 2 minutes. A4 Each practitioner meditates while pressing the right thumb firmly against the bridge of the nose. There is no chanting involved. The breathing is not coordinated among the group. The duration of this activity is approximately 3.5 minutes. A5 Each practitioner is performing specific gestures involving repetitive movements with their hands and fingers. The duration of this meditation is approximately minutes. A6 All the practitioners chant together the words Ek Ong Kar, while they are seated and relaxed. The chant consists of three repeated phases of coordinated breathing, with a period of.5 seconds. The duration of this activity varies between and 22 minutes. A7 All the practitioners chant together the words Ek Ong Kar Sat Gurprasad. The breathing cycle among all of them is coordinated with a period of about 4 seconds and the activity lasts for minutes. B. Heart rate monitor devices Each practitioner wears a heart rate monitor device during the whole duration of the Kundalini yoga session. The device is a POLAR Team 2 Pro system, which is composed of a chest strap, a sensor, and a transmitter. Each sensor is synchronized to a common internal clock time. The signal is recorded in the form of RR intervals, i.e., the time between two consecutive R peaks, as described in Section I. This signal is recorded each time a new peak occurs, so by construction it is unevenly sampled. The signals are collected off-line using the POLAR Team 2 software on a central server, together with the

4 corresponding absolute time. The collected data is available online on the website of our HealthWare research group [7]..9 A A2 A3 A4 A5 A6 A7 IV. HEART SIGNAL ANALYSIS In this section we present the analysis of the RR interval time series for the three authors of the paper, i.e., subjects S, S 2, and S 3, while involved in a yoga session (Y). We exploit the signal processing tools described in Section II. The task is to analyze the distribution of this signal in the frequency domain, discriminating the spectral power into the three ranges of interest introduced in Section I, i.e.,,, and. First, we preprocess the RR signal, in order to remove the artifacts introduced by the sensor and to obtain a signal with a constant sampling period. Then we analyze this signal using the Welch method. Fi(n) Figure Time(sec) F i (n) with i {,, } for S during yoga session (Y). A. Preprocessing of RR interval time series The preprocessing of the RR signal consists of two steps. In the former (a), we remove the artifacts introduced by the sensor, and in the latter (b), we transform the signal into a RR signal sampled at a frequency of 4 Hz. To perform (a), we apply the algorithm suggested in [8], which is briefly described in Table I.. Initialize x (). F (n) A A2 A3 A4 A5 A6 A7 S S2 S3 For every i =,...,K. Consider the neighborhood of x (i), i.e., U(x (i) ) = {x (h) s.t. i h p}. 2. Take the median ũ of U(x (i) ). 3. Evaluate the two conditions: x (i) ũ ũ ǫ, x (i) x (i ) x (i ) ǫ. 4. If any of these two conditions is not verified, we detect an artifact and remove the point x (i). Table I ALGORITHM TO DETECT ARTIFACTS FROM RR INTERVAL TIME-SERIES. We use p = 2 and ǫ =.2, as specified in [8]. We obtain a new signal, which for simplicity of notation we call x, free from artifacts but still unevenly sampled. Then (b) we apply the spline interpolation to obtain an evenly sampled signal with a sampling period of.25 seconds, which is a standard sampling period for analyzing this kind of signal, according to the standards suggested in [6]. B. Power Estimate using Welch s method We analyze the RR interval signal x, obtained after the preprocessing by exploiting the Welch s method and its extension proposed in Section II-A. We are interested in evaluating the spectral power in the three frequency ranges of interest for this signal, i.e., the very low frequency (, in the range R =.3.4 Hz), the low frequency (, in the range Figure Time(sec) F (n) for three practitioners during yoga session (Y). R =.4.5 Hz), and the high frequency (, in the range R =.5.4 Hz). The spectral power is calculated for the three ranges of interest, i {,, }, as a function of n: T i (n) = ˆPxn, (3) R i where ˆP xn is calculated as a function of time n using Eq. (5), and where we have N = 2, L = 256, and D = 28. In Fig. we represent the fraction of spectral power in the three ranges, i.e., F i (n) = T i (n) T (n)+t (n)+t (n). (4) The vertical dotted lines divide the time into the different activities performed during the yoga session, described in Section III-A. Note that for the activities A, A6, and A7 we have a predominance of the components for subject S. In Fig. 2 we represent F (n), which corresponds to the fraction of spectral power with respect to the three ranges of interest for the three subjects involved. We note that the behavior of F (n) is similar for all the subjects, with a predominance of the components during the activities A, A6, and A7. This evidence gives us a motivation to further analyze the degree of entrainment among the subjects involved in the experiment, exploiting the wavelet tools.

5 A V. G ROUP E NTRAINMENT A2 A3 A4 A5 A6 A7 A. Entrainment network In order to give a graphical representation of the degree of entrainment among N 2 practitioners involved in a specific activity, we define the quantity of entrainment among these people as: R R (k,s) Cx,...,xN e(a, R, {x,..., xn }) = R RA R, (5) R A where A is the time interval considered, R is the frequency range, and x,..., xn are the RR signals corresponding to (k,s) the N people involved. Cx,...,xN is calculated according to Eq. (2). Given this definition, we can also calculate a new measure, namely the entrainment level, between each Period (sec) Time (sec) Figure 3. Wavelet coherence of RR interval signal between S and S2 during yoga session (Y). A A2 A3 A4 A5 A6 A Period (sec) Time (sec) Figure 4. Wavelet coherence of RR interval signal for a group of three practitioners during yoga session (Y). combination of two people involved in the yoga activity, and in particular, we can discriminate between a strong and a weak entrainment level between two people involved in the same activity. We consider as a base level the average quantity of entrainment during all the intervals in which the people are not involved in any yoga activity, say B. We calculate the entrainment level for the selected activity A, and for each pair of people Si and Sj, as the ratio: E(A, R, {xi, xj }) = e(a, R, {xi, xj }). e(b, R, {x,..., xn }) (6) In Fig. 6 we represent the entrainment level between each pair of people in yoga session (Y2), during activity A6, considering the range of frequency R. We draw a thick A A2 A3 A4 A6 A Period (sec) In this section 2 we calculate the wavelet coherence described in Section II to represent the synchronicity between two or more RR signals, as a function of time and frequency. In other words, we aim to detect if there is a similar periodicity in the variation of the RR signal between two or more subjects involved in the same yoga activities. We use the MATLAB code available in [9] that we opportunely modified for our analysis. In Fig. 3 we represent the wavelet coherence between subject S and subject S2 during the different activities of yoga session (Y) 3, computed using Eq. (8). We divide the time into activities and frequencies into,, and as mentioned in Section I. We found it remarkable that using the simple devices described in Section III-B we are able to capture the coherence of the heart signal between the two subjects, as a function of frequency and time. This entrainment is very clear for the activities A and A6 at the, and also for activity A7 at the. This is mostly due to the fact that these three activities involved a coordinated breathing pattern with a determined breathing period, which is reflected in the heart signal at the corresponding frequency. In Fig. 4 we represent the wavelet coherence among the subjects S, S2, and S3, using the definition in Eq. (2). From this figure, it becomes evident that there is a high degree of entrainment among all the subjects, for activity A and A6 with a period of about 2 seconds, and for activity A7 with a period of about 4 seconds. In Fig. 5 we show the results of wavelet coherence for the yoga session (Y2), among subjects S, S4,..., S7. We found that also in this case we have a high degree of coherence for activity A and A6 at the and for activity A7 at the, similar to the results in Fig. 4. We note that there is also an important component at the between the activities A2 and A3. The origin of this clear entrainment among all the people in the group at is not clear. It may be due to the fact that practitioners alternate between energydemanding activities and short relaxing periods between the activities, which correspond to a decrease and an increase of the RR intervals, respectively. This can be the reason of this periodicity at the, but further experiments are needed to address the actual cause of this behavior Time (sec) 2 The figures in this section are best viewed in color. each figure in this section, the signal below the continuous line is not significant, since under that line the border effects cannot be neglected [2]. 3 In Figure 5. Wavelet coherence of RR interval signal for a group of five practitioners during yoga session (Y2).

6 Figure 6. Entrainment network for activity A6, in the frequency range R. A thick line, a thin line, and the absence of a line between a pair of people correspond respectively to strong, medium, and weak entrainment level. Figure 7. Entrainment network for activity A7, in the frequency range R. A thick line, a thin line, and the absence of a line between a pair of people correspond respectively to strong, medium, and weak entrainment level. line between subject S i and S j if E(A,R,{x i,x j }) > 2, a thin line if E(A,R,{x i,x j }) [.5,2] and no line if E(A,R,{x i,x j }) <.5. From the figure, we see that subjects S 4, S 5, and S 7 are the most entangled. This can be due to the fact that they are more engaged in the activity than the others. Finally, in Fig. 7, we represent the entrainment level during activity A7, considering the range of frequency R. It is interesting to see that subjects 7 is not connected to anybody in this case. Indeed, as verified a posteriori interviewing S 7, the subject was not focused during activity A7, and left the group straight at the end of that activity. These results can be reproduced using the code that is available on our HealthWare website [7]. This online platform is a novel effort to collect physiological data from different sensors, analyze this data by means of open algorithms and resources, and archive this data with the chosen level of privacy. VI. CONCLUSIONS In this paper we studied the RR interval time series of heart rate signals of people performing group activities. We analyzed these signals through a Welch transformation for nonstationary signals and through wavelet coherence, proposing a measure of the coherence among more than two signals. We showed that for certain activities all the members in the group reach a state of coherence, and we proposed a method to quantify this level of coupling among the group members. This is just an initial step to the goal of quantifying, with the help of wireless devices and centralized signal processing, how people interact in a group and how the group can influence the wellbeing of an individual. In addition, we developed tools to query the HRV time series data to find specific patterns of interest. These techniques are ready to be applied for the analysis of a set of time series to recognize any pattern common to all the time series. For example, it can be applied in a wireless sensor network to recognize an occurrence detected by many sensors. ACKNOWLEDGMENTS The authors thank Maureen C. Curran for editorial assistance and California Institute for Telecommunication and Technology (Calit2) for providing the environment for the experiments. REFERENCES [] D. Forsyth, Group Dynamics. Wadsworth/Cengage, 2. [2] D. Lusher, G. Robins, and P. 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