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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 2, FEBRUARY 2004 Nonlinear Analysis of the Separate Contributions of Autonomic Nervous Systems to Heart Rate Variability Using Principal Dynamic Modes Yuru Zhong, Hengliang Wang, Ki Hwan Ju, Kung-Ming Jan, and Ki H. Chon*, Member, IEEE Abstract—This paper introduces a modified principal dynamic
the occurrence of life-threatening ventricular tachyarrhyth- modes (PDM) method, which is able to separate the dynamics of
mias, whereas augmented vagal tone exerts a protective and sympathetic and parasympathetic nervous activities. The PDM is
antifibrillatory effect Experimental evidence suggests that based on the principle that among all possible choices of expansion
myocardial ischemia, acute myocardial infarction, and chronic bases, there are some that require the minimum number of
basis functions to achieve a given mean-square approximation
heart failure all exhibit signs of autonomic function imbalance of the system output. Such a minimum set of basis functions is
Consistent with autonomic imbalance, patients who have termed PDMs of the nonlinear system. We found that the first
suffered a myocardial infarction have a marked decrease in HRV two dominant PDMs have similar frequency characteristics for
due to a decrease in vagal and an increase in sympathetic neural parasympathetic and sympathetic activities, as reported in the
activities. Power spectral analysis of HRV has been shown to literature. These results are consistent for all nine of our healthy
human subjects using our modified PDM approach. Validation
be useful in risk stratification after myocardial infarction of the purported separation of parasympathetic and sympathetic
Power spectra of human HRV can be divided into three main activities was performed by the application of the autonomic
frequency zones: the power spectral density (PSD) below 0.04 nervous system blocking drugs atropine and propranolol. With
Hz is considered to be very low-frequency (VLF), between 0.04 separate applications of the respective drugs, we found a signifi-
and 0.15 Hz is the low-frequncy (LF), and between 0.15 and 0.5 cant decrease in the amplitude of the waveforms that correspond
to each nervous activity. Furthermore, we observed near complete
Hz is the high-frequncy (HF). The LF is found to be mediated by elimination of these dynamics when both drugs were given to the
both the sympathetic and parasympathetic nervous influences subjects. Comparison of our method to the conventional low-fre-
and the HF is unequivocally believed to be dominated solely quency/high-frequency ratio shows that our proposed approach
by the parasympathetic nervous system The VLF has been provides more accurate assessment of the autonomic nervous
proven to be related to factors other than the autonomic nervous balance. Our nonlinear PDM approach allows a clear separation
system (ANS) (e.g., temperature, hormones, etc.) The ratio of the two autonomic nervous activities, the lack of which has been
the main reason why heart rate variability analysis has not had
of the LF to HF power obtained from spectral analyses has been wide clinical acceptance.
shown to be a good marker of the sympathovagal balance in Index Terms—Autonomic nervous systems, heart rate vari-
assessing HRV For example, a large LF/HF ratio suggests ability, parasympathetic, power spectrum, principal dynamic
predominantly sympathetic control, whereas a small LF/HF ratio indicates predominantly vagal control. However, the LF/HFratio for clinical utility has not gained wide acceptance, mainlybecause it is an approximation of the autonomic balance and does not truly reflect the balance of the two nervous influences.
and parasympathetic influences on the modulation of heart mediated by the sympathetic nervous system, despite the pre- rate. It is through efficient interactions between the parasym- vailing understanding that the LF reflects both the sympathetic pathetic and sympathetic nervous systems that homeostasis of and parasympathetic nervous systems. Another deficiency of the the cardiovascular system is properly maintained. Failure of the LF/HF ratio is that the method is linear and does not properly interactions may lead to sympathetic hyperactivity, promoting account for nonlinear characteristics of the ANS. A plethora ofrecent studies have shown that the physiological mechanisms re- Manuscript received January 27, 2003; revised May 26, 2003. This work was sponsible for heart-rate fluctuations have nonlinear components supported in part by the National Institutes of Health (NIH) through the Center While the LF/HF ratio obtained via the PSD is inaccurate, for Research Resource under Grant RR15217. Asterisk indicates corresponding it shows great promise of being a useful noninvasive marker for Y. Zhong, H. Wang, and K. H. Ju are with the Department of Biomedical determining the state of the ANS, if a new method is developed Engineering, State University of New York at Stony Brook, Stony Brook, NY that can separate the dynamics of the two nervous systems. This 11794-8181 USA.
new method should also account for the nonlinear components K.-M. Jan is with the Department of Cardiology, Columbia University, New York, NY 10027-6902 USA.
of heart rate fluctuations, in order to more accurately represent *K. H. Chon is with the Department of Biomedical Engineering and the nonlinear properties of heart rate dynamics.
the Department of Physiology and Biophysics, HSC T18, Rm. 030, State This paper aims to address the above problem of separating University of New York at Stony Brook, Stony Brook, NY 11794-8181 (e-mail:[email protected]).
the two nervous systems' dynamics by the use of principal Digital Object Identifier 10.1109/TBME.2003.820401 dynamic modes (PDM). The PDM has been shown to be a novel 0018-9294/04$20.00 2004 IEEE IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 2, FEBRUARY 2004 method for characterizing nonlinear physiological systems and then the HR data were normalized to a unit variance. A while reducing higher-order dimensions. The nonlinear PDM total of 300 data points were used for analyses.
method was first introduced and applied in the analysis ofphysiological systems by Marmarelis –The PDMs are calculated using Volterra-Wiener kernels based on expansionof Laguerre polynomials We have modified the PDM The need for the input signal having broad-band character- technique to be used with even a single output signal of HRV istics has been well documented as a prerequisite for a general data, whereas the original PDM required both input and output methodology of nonlinear modeling of dynamic systems using data. Our analyses will reveal that the first two dominant PDMs functional expansion of kernels With recent advances, obtained from the heart rate data of healthy human subjects the strict requirement of input being white is alleviated using correspond to the two autonomic nervous activities. This has the Laguerre expansion of kernels approach However, it is been demonstrated in both time and frequency domains. The still necessary to have the input signal exhibit broad-band char- application of the autonomic nervous blocking agents, propra- acteristics to obtain accurate kernel estimates. The HR data is nolol and atropine, corroborated our finding that the magnitude far from broad-band, however. For example, significant power of the waveforms corresponding to either sympathetic or exists in the VLF of the HR data compared to LF and HF. The parasympathetic nervous activities were significantly reduced.
spectral power bands of interest, the LF and HF, are dwarfed by This technique allows a more in-depth analysis of the ANS and the significantly high spectral power in the VLF band. An ap- offers for the first time a more accurate measure of the balance proach we took to reduce high spectral power in the VLF band between the two autonomic nervous activities. Furthermore, is the method introduced by Tarvainen with the aim of re- the method specifically accounts for the inherent nonlinear ducing VLF power to the level of the LF and HF bands. This dynamics of heart rate control, which the PSD does not.
detrending method is briefly described in the Appendix.
We represent the heart rate data after detrending as HRc. The PDM method requires both the input and output data, but since II. DATA COLLECTION we have only the output signal of HR recordings, we utilize the The data analyzed in this investigation were obtained from following steps to create an input signal. The goal is to create a previously-published study Experimental methods are an input signal that has broad-band characteristics. It is inappro- described in detail in and will be only briefly summarized priate to use white noise data as the input signal even though the here. Data used in this study were collected from nine healthy task was to create a broad-band signal because white noise has male subjects between 19 and 38 years of age and consisted no correlation to the dynamics of heart rate. We used HRc, de- of the simultaneous recordings of surface electrocardiogram layed by one unit, as the input, and undelayed HRc as the output (ECG) and changes in instantaneous lung volume and arterial signal to obtain PDMs. We used the first three PDMs to re- blood pressure. In this study, our analyses were based on only construct the output signal, which was then subtracted from the ECG recordings. The data were collected for 13 min each for original HRc signal to obtain estimation error, labeled HRe. The both supine and upright positions with a minimum of 5 min justification for using the first three PDMs is because they ac- allocated for hemodynamic equilibration between changes in counted for our set threshold value of 90% of the HR dynamics.
body position. The data were collected under three conditions: This created signal, HRe, is considered to be the input signal, 1) control, 2) administration of a single autonomic blocking which has the broad-band characteristics needed for accurate agent, either 0.03 mg/kg of atropine (four of the nine subjects) estimation of PDMs. The obtained input data, HRe, is then nor- or 0.2 mg/kg of propranolol (five of the nine subjects), and 3) malized to a unit variance (HRn). The input signal of HRn and double blockade resulting from the subsequent administration the output signal of HRc are used to calculate the final values of the second blocking agent (all subjects). Selection of which of the PDMs. Note that the PDM is based on the principle that subjects initially received either atropine or propranolol as a among all possible choice of expansion bases, there are some single autonomic blockade agent was random. The interval that require the minimum number of basis functions to achieve between administration of the autonomic agents and data a given mean-square approximation of the system output. The collection was long enough (minimum of 5 min) to allow for methodology of the PDM has been presented before and thus, physiologic equilibration and to prevent transient nonstation- we outline the detailed steps of calculating the PDM in the Ap- arity in each condition. Doses of both atropine and propranolol pendix section for the convenience of the reader were selected to be sufficient for complete blockade of theparasympathetic or sympathetic system Measurements of ECG signals recorded on the frequency-modulated taperecorder were sampled at 360 Hz to allow accurate detection The PDM methodology outlined in the Appendix provided and identification of QRS complexes in the ECG The two PDMs (with time lag , Laguerre coefficient QRS complexes were used to identify beat locations. Once the , and the number of Laguerre functions timing of beats was determined, an instantaneous HR signal correspond to the main frequency-response characteristics of was created at a sampling rate of 4 Hz using the technique the two ANSs, sympathetic and parasympathetic. We obtain described in HR signals were down sampled to 1 Hz fairly consistent waveforms corresponding to parasympathetic after low-pass filtering at 0.5 Hz in order to concentrate on and sympathetic nervous activities for all nine subjects, pro- the frequency bands of interest, which are all below 0.5 Hz.
vided in Figs. 1–4 for the supine position and Figs. 5–8 for the Furthermore, mean and trends were removed from the HR data, upright position. The solid lines represent average waveforms ZHONG et al.: SEPARATE CONTRIBUTIONS OF ANSS TO HRV USING PRINCIPAL DYNAMIC MODES Dynamics of (a) parasympathetic and (b) sympathetic during supine Dynamics of (a) parasympathetic and (b) sympathetic during upright Dynamics of (a) parasympathetic and (b) sympathetic during supine Dynamics of (a) parasympathetic and (b) sympathetic during upright position with application of atropine.
position with application of atropine.
Dynamics of (a) parasympathetic and (b) sympathetic during supine Dynamics of (a) parasympathetic and (b) sympathetic during upright position with application of propranolol.
position with application of propranolol.
Dynamics of (a) parasympathetic and (b) sympathetic during supine Dynamics of (a) parasympathetic and (b) sympathetic during upright position with application of atropine and propranolol.
position with application of atropine and propranolol.
based on nine subjects with dotted lines corresponding to the peak centered at 0.03 Hz. The significance of these two peaks is standard error bounds. Fig. 1(a) and (b) shows frequency re- that many studies have shown that the parasympathetic nervous sponses of the two PDMs obtained during the control condition; system operates both in LF and HF bands. Therefore, this PDM remarkably, they correspond to the dynamics of the parasym- correctly exhibits both the low and high frequencies of the pathetic and sympathetic nervous systems, respectively. The parasympathetic nervous activity. Fig. 1(b) shows prominent dominant peak of Fig. 1(a) is centered at 0.l7 Hz, which is in peaks in the prescribed frequency band of the sympathetic the prescribed frequency range of the parasympathetic nervous nervous system, indeed an exciting finding. Therefore, we con- system. Furthermore, this PDM also shows a prominent second jecture that the two dominant PDMs correspond to sympathetic IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 2, FEBRUARY 2004 and parasympathetic activities. This conjecture, if true, for thefirst time allows separation of the two nervous activities thatare known to interact nonlinearly.
To validate the aforementioned conjecture, we analyzed PDMs of subjects under the influence of propranolol andatropine separately, as well as the application of both drugsto produce a complete blockade of the two nervous activities.
Figs. 2–4 show average frequency response characteristicsof the two PDMs for the application of atropine, propra-nolol, and the combination of atropine and propranolol,respectively. Since the power of HR under the influence ofa drug is different from the HR power of a normal case,we rescaled the PDMs of an abnormal case with: Figs. 2 and 3, we observe similar waveforms to those of Fig. 1in which two PDMs exhibit characteristics corresponding tothe sympathetic and parasympathetic nervous activity. We notethe consistent and significant decrease in the magnitude of thewaveforms with application of the respective ANS blockingdrug. With atropine, which blocks parasympathetic activity, wenote the significant decrease in the amplitude of the PDM thatcorresponds to the parasympathetic activity. Similarly, withpropranolol, which blocks sympathetic activity, we observea significant reduction in the amplitude of the PDM that weconjecture to be the sympathetic activity. With double blockade(both atropine and propranolol), we correctly observe negligibleamplitudes corresponding to the two nervous activities. Thesephenomena are the very effects that atropine and propranololare expected to have on sympathetic and parasympathetic ac-tivities, respectively. Figs. 2–4 further corroborate the viabilityof our conjecture that the two PDMs correspond to the twonervous systems. It should be noted that with the applicationof atropine, we observe some changes in the waveform of thePDM corresponding to sympathetic dynamics. A similar effecton parasympathetic dynamics is also found with the applicationof propranolol. This is expected, since it has been shown thatthese two nervous activities interact in a nonlinear manner. Thechange in the waveform that is not directly targeted by the drugmay be the compensatory effect due to nonlinear interactionsbetween the two mechanisms.
PSD of (a) and (b)control, (c) and (d) application of atropine, (e) and Similar waveforms and characteristics from those of the (f) propranolol, and (g) and (h) atropine and propranolol. For all figures, left andright panels represent supine and upright positions, respectively.
supine position are found for the upright position, as shownin Figs. 5–8. Two dominant PDMs obtained from the controlcondition also correspond to parasympathetic and sympathetic Fig. 9 shows the average spectra obtained from the control and activities, as shown in Fig. 5. As with the supine position, with the application of autonomic blockade drugs. A nonoverlap- we observe a significant decrease in the magnitude values ping Welch periodogram (with Hanning window and a frequency of the PDM corresponding to parasympathetic activity with resolution of 0.015 625 Hz) was used to obtain the spectra.
the application of atropine. Likewise for the PDM waveform Fig. 9(a) and (b) represents supine and upright positions, respec- corresponding to the sympathetic activity with the application tively. The solid and dotted lines represent the mean and standard of propranolol. In addition, we observe the significant reduction error bounds, respectively. A general trend of decreasing power in magnitude of the waveform [Fig. 7(b)] with the application is seen with the application of a single blockade and nearly of propranolol, but it has no significant affect on the PDM complete elimination of the power is seen with application of the that reflects parasympathetic activity, as shown in Fig. 7(a).
double blockade. It is apparent that application of atropine had Finally, we observe a significant reduction in magnitude greater effect on reducing spectral power for all frequencies than of both waveforms in Fig. 8, with the application of both did application of propranolol. Furthermore, atropine, which is atropine and propranolol. These findings further corroborate supposed to block parasympathetic activity, appears to signifi- our conjecture that the two PDMs correspond to sympathetic cantly reduce sympathetic power in the LF range. Therefore, it is and parasympathetic nervous activity.
clear that based on only spectral analysis, it is difficult to examine ZHONG et al.: SEPARATE CONTRIBUTIONS OF ANSS TO HRV USING PRINCIPAL DYNAMIC MODES SYMPATHETIC POWER/PARASYMPATHETIC POWER RATIO OBTAINED WITH PDMS LF POWER/HF POWER RATIO OBTAINED WITH PSD how each drug affected specific nervous activities. To quantita- two more erroneous cases with spectral power decreasing as tively compare the two methods for all nine subjects, we show in the blocking agent is administered from the upright position.
Tables I and II the ratio of sympathetic/parasympathetic activity With the PDM approach, we obtained a single incorrect result obtained by PDMs and the LF/HF ratio obtained by the power (patient 13) as the power decreased from supine control to the spectral analyses, respectively. For the PSD analysis, the LF and administration of atropine. The results obtained by the PDM HF power were obtained in the frequency range of 0.04–0.15 are, therefore, far more accurate than the LF/HF ratio based and 0.15–0.5 Hz, respectively. For the PDM, the ratios were on spectral analysis. The better accuracy was obtained with obtained by integrating the area of the waveforms corresponding the PDM approach because the method is able to separate out to the sympathetic and parasympathetic activities. The LF/HF the dynamics of the two nervous activities, whereas the LF/HF ratio provided three erroneous patterns as the power incorrectly ratio suffers from its assumption that the LF power is solely increased from supine control to supine single blockade and due to sympathetic activity.
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 2, FEBRUARY 2004 MEAN AND STANDARD DEVIATION OF SIGNIFICANT EIGENVALUES V. DISCUSSION AND CONCLUSION PDM method is significant because we have adapted the methodfrom requiring both input and output data to be useful in the case The past two decades of research in HRV have been mainly of having only single output data. In addition, we utilized an ap- based on analysis of the LF/HF ratio, which has been well docu- proach by Tarvainen to reduce significant spectral power mented not to be an accurate approach to assess autonomic ner- in the VLF band, to enable better estimation accuracy with the vous balance While recent nonlinear deterministic methods PDM. The results we have obtained by the modified PDM are have resulted in some promising results it is an unre- physiologically meaningful and potentially exciting. The PDMs solved question whether nonlinear deterministic methods could in the control state, overall, reflect dynamics of the two ANSs.
be meaningfully applied to heart rate data. While the LF/HF For example, with atropine (Figs. 2 and 6), we observe signifi- ratio obtained via the PSD is inaccurate, it shows great promise cant magnitude reduction in dynamics that reflect vagus nervous of being a useful noninvasive marker for determining the state of system and less effect on the dynamics that reflect the sym- the ANS, if a new nonlinear method is developed that can sepa- pathetic nervous system. Similarly, with propranolol (Figs. 3 rate the dynamics of the two nervous systems. Specifically, sym- and 7), significant reduction in the magnitude reflecting sym- pathovagal balance as calculated simply by taking the LF/HF pathetic nervous system is seen while insignificant reduction in ratio of the PSD relies on two major erroneous assumptions: vagus nervous system is observed. While the PDM reflecting that the parasympathetic nervous system dynamics are exhib- the sympathetic nervous activity in the control state appears to ited only in high frequencies, and that ANS control is linear. It include some dynamics of the vagal activities, as notable mag- has been well established that dynamics of the parasympathetic nitude values are seen in high frequencies ( nervous system are not only reflected in high frequencies but immaterial because of the aforementioned verifiable results ob- they are also well represented in low frequencies A recent tained with the application of autonomic blockades. With the report corroborating this statement suggests that the low-fre- PSD, however, it is impossible to delineate dynamics of the two quency component results from an interaction of both the sym- ANSs. For example, atropine appears to indiscriminately block pathetic and parasympathetic nervous systems, and not solely both low and high frequencies, and the effect of atropine is sim- the sympathetic nervous activity Secondly, the LF/HF ratio ilar to the double blockade case. Therefore, with the PSD ap- is based on linear power spectral analysis, which itself is limited proach, only general inferences can be made regarding the bal- because it is widely recognized that control of ANSs involves ance of the two ANSs.
nonlinear interactions. It is through efficient interactions be- Note that magnitudes obtained by the PDM do not corre- tween vagal and sympathetic nervous systems that homeostasis spond directly to the PSD values, as PDMs are based on eigen- of the cardiovascular system is properly maintained. The inter- values. Furthermore, magnitudes between the PDMs that repre- actions are believed to be nonlinear because physiological con- sent sympathetic and parasympathetic nervous systems do not ditions would most likely involve ANS regulation based on dy- correspond in a direct manner since these PDMs are based on namic and simultaneous activity of the vagal and sympathetic different eigenvalues. However, comparison of PDMs that rep- nervous systems in response to physical environmental stress.
resents either vagal or sympathetic nervous activity from the A recent report suggests a quadratic nonlinearity between HRV control state to the application of autonomic blockade is valid and vagal effect rather than a linear relationship If the since PDMs have been normalized by dividing, drug-influenced LF/HF ratio is linear and LF and HF truly reflect sympathetic eigenvalue by the control states eigenvalue.
and parasympathetic nervous activities, respectively, then an au- With a sampling frequency of 1 Hz or a Nyquist frequency tonomic blockade such as atropine should increase the LF/HF of 0.5 Hz, as there is no significant power in the spectrum ratio. Clearly this is not the case, as also evident in our PSD beyond 0.4 Hz, one would expect eigenvalues corresponding plot shown in the second row of Fig. 9; with atropine, we obtain to the first two PDMs to have the greatest values among the significant power reduction in both low and high frequencies.
possible 61 eigenvalues . Indeed, this is the finding, as Therefore, it is not surprising that the LF/HF ratio based on the presented in Table III. For every condition, the ratio between PSD, as shown in Table II, does not truly reflect sympathovagal the sum of the two most significant PDMs and the sum of the rest of the PDMs are calculated. For most cases, the two most We introduced a modification of the PDM approach for the significant PDMs together account for more than 90% of the analysis of autonomic nervous activity. The modification of the total dynamics. Therefore, given the fact that ANSs span most of ZHONG et al.: SEPARATE CONTRIBUTIONS OF ANSS TO HRV USING PRINCIPAL DYNAMIC MODES the frequencies examined, the finding of the two most significant Expansion of the Volterra kernels on a complete basis PDMs reflecting more than 90% of the total dynamics is highly transforms (1) into the multinomial expressions In conclusion, two PDMs have been consistently identified in all nine subjects examined, with each PDM correspondingto the sympathetic or parasympathetic nervous activities. Ourconjecture of the two PDMs reflecting the ANS activities was corroborated by the administration of ANS blocking agents,after which the PDMs were significantly reduced. When bothblocking agents were administered, the PDMs were completely obliterated. This analysis allows accurate and physiologicallymeaningful quantification of the separate contributions of sym- pathetic and parasympathetic activities of HRV.
is the number of Laguerre functions used.
the Laguerre functions calculated with Laguerre coefficient can be constructed with the estimated kernels A. Calculation of PDMS in the following way: The estimation of PDMs using Volterra-Wiener kernels was first introduced in We will briefly describe the steps involved in calculation of PDMs. For further details, the readeris referred to and In discrete time, the general input-output relation of a stable Laguerre functions are chosen as an appropriate orthonormal (finite-memory) nonlinear time-invariant dynamic system is basis because they exhibit exponential decaying properties that given by the discrete-time Volterra series make them suitable for physiological systems modeling. In ad-dition, due to basis function expansion, the estimation accuracyis maintained even with a small data length. We have previouslyshown that a data length of 250 points is sufficient for accuratekernel estimation using Laguerre expansions is a real symmetric square matrix, it can always be decomposed in the following way: eigenvector matrix will always be an orthonormal matrix.
is the output of the system.
the diagonal eigenvalue matrix. We select the significant eigen- is the memory of the system. The Volterra kernels and the corresponding orthonormal eigenvectors describe the dynamics of the system from a define the PDMs of this system.
hierarchy of system nonlinearities.
For each significant eigenvalue , the values of the corre- The kernel values obtained up to a maximum lag sponding eigenvector memory) are combined to form a real symmetric ) define the th PDM square matrix (shown in (2) at the bottom of the page) that can be used to express the second-order Volterra model re- , in a quadratic form The obtained th PDM generates the th mode via convolutionwith the input . The second-order model estimation denotes "transpose" and the is composed of the input -point epoch at each time n and a constant 1 that allows incorporation of the lower order kernel The nonzero values give rise to the contribution of contributions in (3).
linear terms.

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 2, FEBRUARY 2004 B. Detrending Method [18] M. S. Houle and G. E. Billman, "Low-frequency component of heart rate variability spectrum: A poor marker of sympathetic activity," Amer. The detrending method we utilized is based on smoothness J. Physiol., vol. 276, pp. 215–223, 1999.
priors approach and operates like a time-varying FIR filter. The [19] J. J. Goldberger, S. Challapalli, R. Tung, M. A. Parker, and A. H. Kadish, Matlab source code as provided in for applying the de- "Relationship of heart rate variability to parasympathetic effect," Circu-lation, vol. 103, pp. 1977–1983, 2001.
trending method to a signal, Yuru Zhong received the B.E. degree from the
Department of Automation, the University of
Science and Technology of China, Hefei, China, in 2001. Currently, she is a Ph.D. degree student inthe Department of Biomedical Engineering, State The lambda controls the degree of detrend desired. For our anal- University of New York at Stony Brook. Currently, ysis, the value of lambda was adjusted so that the mean power she is a Ph.D. degree student in the Department of of the VLF was close to the mean power of the LF and HF Biomedical Engineering, State University of NewYork at Stony Brook.
without affecting the power in the LF. The value of lambda dif- Her research interests include biomedical signal fered for each subject with the range of values varying from 500 processing and modeling of physiological systems.
Hengliang Wang received the B.S. and M.S. degrees Department of Automa-
[1] "Heart rate variability: Standards of measurement, physiological inter- tion, the University of Science and Technology of China, Hefei, China, in 1997 pretation, and clinical use," in Circulation: Eur. Soc. Cardiol. North and 2000, respectively.
Amer. Soc. Pacing and Electrophysiology, 1996, vol. 93, pp. 1043–1065.
His research interests include biomedical signal processing and medical in- [2] H. V. Huikuri, M. J. Koistinen, S. Yli-Mayry, K. E. Airaksinen, T. Sep- panen, M. J. Ikaheimo, and R. J. Myerburg, "Imparied low-frequencyoscillations of heart rate in patients with prior acute myocardial infarc-tion and life-threatening arrhythmias," Amer. J. Cardiol., vol. 76, pp.
56–60.
Ki Hwan Ju received the M.Sc.E.E. degree in
[3] J. M. Tapanainen, P. E. Thomsen, L. Kober, C. Torp-Pedersen, T. H.
electrical engineering from Yonsei University, Seoul, Makikallo, A. M. Still, K. S. Lindgren, and H. V. Huikuri, "Fractal anal- Korea, in 1984 and the Ph.D. degree from the School ysis of heart rate variability and mortality after an acute myocardial in- of Science and Engineering, Keio University, Tokyo, farction," Amer. J. Cardiol., vol. 90, pp. 347–52, 2002.
Japan, in 1991.
[4] C. Yang and T. Kuo, "Assessment of cardiac sympathetic regulation by He was a Postdoctoral Fellow with the Sports respiratory-related arterial pressure variability in the rat," J. Physiol., Medicine Research Center, Keio University, and a vol. 515, pp. 887–896, 1999.
Research Associate with the University of Tokyo.
[5] A. M. Bianchi, L. T. Mainardi, C. Merloni, S. Chierchia, and S. Cerutti, He was a Visiting Scientist with the City College of "Continuous monitoring of the sympatho-vagal balance through spectral The City University of New York. He is Research analysis," IEEE Eng. Med. Biol., vol. 16, pp. 64–73, Sept./Oct. 1997.
Director of the Institute of Bio-Cybernetics, Tokyo, [6] A. Zaza and F. Lombardi, "Autonomic indexes based on the analysis of and a Research Scientist with the Department of Biomedical Engineering, The heart rate variability: A view from the sinus node," Cardiovasc. Res., State University of New York at Stony Brook. His main areas of interest are vol. 50, pp. 434–442, 2001.
system modeling of intergrative physiology in human and genetic targeted [7] V. Z. Marmarelis, K. H. Chon, and D. J. Marsh, "Nonlinear analysis animal model, and design of medical instruments and biomedical signal of renal auto-regulation in rats using principal dynamic modes," Ann. Biomed. Eng., vol. 27, pp. 23–31, 1999.
[8] V. Z. Marmarelis and M. Orme, "Modeling of neural systems by use of neuronal modes," IEEE Trans. Biomed. Eng., vol. 40, pp. 1149–1158,Nov. 1993.
Kung-Ming Jan, photograph and biography not available at the time of publi-
[9] V. Z. Marmarelis, "Modeling methodology for nonlinear physiological systems," Ann. Biomed. Eng., vol. 25, pp. 239–251, 1997.
, "Identification of nonlinear biological systems using Laguerre ex- pansions of kernels," Ann. Biomed. Eng., vol. 21, pp. 573–589, 1993.
[11] J. P. Saul, R. D. Berger, M. H. Chen, and R. J. Cohen, "Transfer func- tion analysis of autonomic regulation—I: Respiratory sinus arrhythmia," Ki H. Chon (M'96) received the B.S. degree
Amer. J. Physiol., vol. 256, pp. H153–H161, 1989.
in electrical engineering from the University of [12] A. D. Jose and R. R. Taylor, "Autonomic blockade by propranolol and Connecticut, Storrs; the M.S. degree in biomedical atropine to study intrinsic myocardial function in man," J. Clin. Inves- engineering from the University of Iowa, Iowa City; tigat., vol. 48, pp. 2019–2024, 1969.
and the M.S. degree in electrical engineering and [13] R. D. Berger, S. Akselrod, D. Gordon, and R. J. Cohen, "An efficient the Ph.D. degree in biomedical engineering from the algorithm for spectral analysis of heart rate variability," IEEE Trans. University of Southern California, Los Angeles.
Biomed. Eng., vol. BME–33, pp. 900–904, 1986.
He spent three years as a National Institutes [14] N. Wiener, Nonlinear Problems in Random Theory.
of Health (NIH) Postdoctoral Fellow at the Technol Press MIT and Wiley, 1958.
Harvard-MIT Division of Health Science and Tech- [15] K. H. Chon, R. Cohen, and N.-H. Holstein-Rathlou, "Compact and accu- nology, Cambridge, MA, one year as a Research rate linear and nonlinear autoregressive moving average model param- Assistant Professor in the Department of Molecular Pharmacology, Physiology, eter estimation using Laguerre functions," Ann. Biomed. Eng., vol. 25, and Biotechnology at Brown University, Providence, RI, and four years as an pp. 731–738, 1997.
Assistant and Associate Professor in the Department of Electrical Engineering [16] M. Tarvainen, P. Ranta-Aho, and P. Karjalainen, "An advanced at the City College of the City University of New York. Currently, he is an detrending method with application to HRV analysis," IEEE Trans. Associate Professor in the Department of Biomedical Engineering at State Biomed. Eng., vol. 49, pp. 172–175, Feb. 2002.
University of New York at Stony Brook. His current research interests include [17] D. L. Eckberg, "Sympathovagal balance: A critical appraisal," Circula- medical instrumentation, biomedical signal processing, and identification, and tion, vol. 96, pp. 3224–3232, 1997.
modeling of physiological systems.

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