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A dynamic point process framework for assessing heartbeat dynamics and cardiovascular functions

from Part II - State space methods for clinical data

Published online by Cambridge University Press:  05 October 2015

By
Z. Chen  and
R. Barbieri
Edited by
Zhe Chen
Z. Chen
Affiliation:
New York University
R. Barbieri
Affiliation:
Massachusetts General Hospital
Zhe Chen
Affiliation:
New York University
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Summary

Introduction

Modeling physiological systems by control systems theory, advanced signal processing, and parametric modeling and estimation approaches has been of focal importance in biomedical engineering (Khoo 1999; Marmarelis 2004; Xiao et al. 2005; Porta et al. 2009). In computerized cardiology, various types of data such as the electrocardiogram (ECG), arterial blood pressure (ABP, measured by invasive arterial line catheters or noninvasive finger cuffs), and respiratory effort (RP; e.g., measured by plethysmography or by piezoelectric respiratory belt transducers) are recorded, digitized and saved to a computer to be available for off-line analysis. Modeling autonomic cardiovascular control using mathematical approaches is helpful for understanding and assessing autonomic cardiovascular functions in healthy or pathological subjects (Berntson et al. 1997; Parati et al. 2001; Stauss 2003; Eckberg 2008). Continuous quantification of heartbeat dynamics, as well as their interactions with other cardiovascular measures, have been widely studied in the past decades (Baselli et al. 1988; Saul & Cohen 1994; Chon et al. 1996; Barbieri et al. 2001; Porta et al. 2002).

A central goal in biomedical engineering applied to cardiovascular control is to develop quantitative measures and informative indices that can be extracted from physiological measurements. Assessing and monitoring informative physiological indices is an important task in both clinical practice and laboratory research. Specifically, a major challenge in cardiovascular engineering is to develop statistical models and apply signal processing tools to investigate various cardiovascular-respiratory functions, such as heart rate variability (HRV), respiratory sinus arrhythmia (RSA), and baroreflex sensitivity (BRS). In the literature, numerous methods have been proposed for quantitative HRV analysis (Malpas 2002). Two types of standard methods are widely used, one is time-domain analysis based on heartbeat intervals, the other is frequency-domain analysis (Baselli et al. 1985). In addition, nonlinear system identification methods have also been applied to heartbeat interval analysis (Chon et al. 1996; Christini et al. 1995; Zhang et al. 2004; Xiao et al. 2005). Examples of higher-order characterization for cardiovascular signals include nonlinear autoregressive (AR) models, Volterra–Wiener series expansion, and Volterra–Laguerre models (Korenberg 1991; Marmarelis 1993; Akay 2000).

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Advanced State Space Methods for Neural and Clinical Data , pp. 302 - 329
Publisher: Cambridge University Press
Print publication year: 2015

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References

Akay|M. (2000). Nonlinear Biomedical Signal Processing, Volume II: Dynamic Analysis and Modeling, New York: Wiley-IEEE Press.
Barbieri, R. & Brown, E. N. (2006). Analysis of heartbeat dynamics by point process adaptive filtering. IEEE Transactions on Biomedical Engineering 53(1), 4–12.Google Scholar
Barbieri, R., Matten, E. C., Alabi, A. R. A. & Brown, E. N. (2005). A point-process model of human heartbeat intervals: new definitions of heart rate and heart rate variability. American Journal of Physiology – Heart and Circulatory Physiology 288(1), 424–435.Google Scholar
Barbieri, R., Parati, G. & Saul, J. P. (2001). Closed- versus open-loop assessment of heart rate baroreflex. IEEE Magazine on Engineering in Medicine and Biology 20(2), 33–42.Google Scholar
Baselli, G., Bolis, D., Cerutti, S. & Freschi, C. (1985). Autoregressive modeling and power spectral estimate of R-R interval time series in arrhythmic patients. Computers and Biomedical Research 18(6), 510–530.Google Scholar
Baselli, G., Cerutti, S., Civardi, S., Malliani, A. & Pagani, M. (1988). Cardiovascular variability signals: towards the identification of a closed-loop model of the neural control mechanisms. IEEE Transactions on Biomedical Engineering 35, 1033–1046.Google Scholar
Berntson, G. G., Bigger, J. T., Eckberg, D. L., Grossman, P., Kaufmann, P. G., Malik, M., Nagaraja, H. N., Porges, S. W., Saul, J. P., Stone, P. H. & van der Molen, M. W. (1997). Heart rate variability: origins, methods, and interpretive caveats. Psychophysiology 34, 623–648.Google Scholar
Brown, E. N. (2005). The theory of point processes for neural systems. In C., Chow, B., Gutkin, D., Hansel, C., Meunier & J., Dalibard, eds, Methods and Models in Neurophysics, Amsterdam: Elsevier, pp. 691–726.
Brown, E. N., Ngyuen, D. P., Frank, L. M., Wilson, M. A. & Solo, V. (2001). An analysis of neural receptive field plasticity by point process adaptive filtering. Proceedings of National Academy of Sciences USA 98, 12261–12266.Google Scholar
Chen, Z., Brown, E. N. & Barbieri, R. (2008). A study of probabilistic models for characterizing human heart beat dynamics in autonomic blockade control. In Proceedings of ICASSP'08, pp. 481–484.Google Scholar
Chen, Z., Brown, E. N. & Barbieri, R. (2009a). Assessment of autonomic control and respiratory sinus arrhythmia using point process models of human heart beat dynamics. IEEE Transactions on Biomedical Engineering 56(7), 1791–1802.Google Scholar
Chen, Z., Brown, E. N. & Barbieri, R. (2010b). Characterizing nonlinear heartbeat dynamics within a point process framework. IEEE Transactions on Biomedical Engineering 57(6), 1335–1347.Google Scholar
Chen, Z., Citi, L., Purdon, P., Brown, E.N. & Barbieri, R. (2011b). Instantaneous assessment of autonomic cardiovascular control during general anesthesia. In Proceedings of IEEE Conference on Engineering in Medicine and Biology, pp. 8444–8447.Google Scholar
Chen, Z., Purdon, P. L., Brown, E. N. & Barbieri, R. (2010a). A differential autoregressive modeling approach within a point process framework for non-stationary heartbeat intervals analysis. In Proceedings of IEEE Conference on Engineering in Medicine and Biology, pp. 3567–3570.Google Scholar
Chen, Z., Purdon, P. L., Brown, E.N. & Barbieri, R. (2013). A unified point process probabilistic framework to assess heartbeat dynamics and autonomic cardiovascular control. Frontiers in Computational Physiology and Medicine 3, 1–14.Google Scholar
Chen, Z., Purdon, P. L., Harrell, G., Pierce, E. T., Walsh, J., Brown, E. N. & Barbieri, R. (2011a). Dynamic assessment of baroreflex control of heart rate during induction of propofol anesthesia using a point process method. Annals of Biomedical Engineering 39(1), 260–279.Google Scholar
Chen, Z., Purdon, P. L., Harrell, G., Pierce, E. T., Walsh, J., Salazar, A. F., Tavares, C. L., Brown, E. N. & Barbieri, R. (2009b). Linear and nonlinear quantification of respiratory sinus arrhythmia during propofol general anesthesia. In Proceedings of IEEE Conference on Engineering in Medicine and Biology, pp. 5336–5339.Google Scholar
Chon, K. H., Mukkamala, R., Toska, K., Mullen, T. J., Armoundas, A. A. & Cohen, R. J. (1997). Linear and nonlinear system identification of autonomic heart-rate modulation. IEEE Magazine on Engineering in Medicine and Biology 16, 96–105.Google Scholar
Chon, K. H., Mullen, T. J. & Cohen, R. J. (1996). A dual-input nonlinear system analysis of autonomic modulation of heart rate. IEEE Transactions on Biomedical Engineering 43, 530–540.Google Scholar
Christini, D. J., Bennett, F. M., Lutchen, K. R., Ahmed, H. M., Hausdofi, J. M. & Oriol, N. (1995). Application of linear and nonlinear time series modeling to heart rate dynamics analysis. IEEE Transactions on Biomedical Engineering 42, 411–415.Google Scholar
Costa, M., Goldberger, A. L. & Peng, C.-K. (2002). Multiscale entropy analysis of complex physiologic time seriesh. Physics Review Letters 89, 068102.Google Scholar
Daley, D. J. & Vere-Jones, D. (2007). An Introduction to the Theory of Point Processes: Vol. I, II, New York: Springer.
De Boer, R. W., Karemaker, J. M. & Strackee, J. (1995). Relationships between short-term bloodpressure fluctuations and heart-rate variability in resting subjects: a spectral analysis approach. Medical & Biological Engineering & Computing 23, 352–358.Google Scholar
Eckberg, D. L. (2008). Arterial baroreflexes and cardiovascular modeling. Cardiovascular Engineering 8, 5–13.Google Scholar
Eden, U. T., Frank, L. M., Solo, V. & Brown, E. N. (2004). Dynamic analyses of neural encoding by point process adaptive filtering. Neural Computation 16, 971–998.Google Scholar
Haykin, S. (2001). Adaptive Filter Theory, 4th edn, Englewood Cliffs, NS: Prentice Hall. Hosking, J. R. M. & Wallis, J.R. (1997). Regional Frequency Analysis: An Approach Based on L-moments, Cambridge: Cambridge University Press.
Jo, J. A., Blasi, A., Valladares, E. M., Juarez, R., Baydur, A. & Khoo, M. C. K. (2007). A nonlinear model of cardiac autonomic control in obstructive sleep apnea syndrome. Annals of Biomedical Engineering 35, 1425–1443.Google Scholar
Khoo, M. C. K. (1999). Physiological Control Systems: Analysis, Simulation, and Estimation, New York: Wiley-IEEE Press.
Korenberg, M. J. (1991). Parallel cascade identification and kernel estimation for nonlinear systems. Annals of Biomedical Engineering 19, 429–455.Google Scholar
Lu, S., Ju, K. H. & Chon, K. H. (2001). A new algorithm for linear and nonlinear arma model parameter estimation using affine geometry. IEEE Transactions on Biomedical Engineering 48, 1116–1124.Google Scholar
Malpas, S.C. (2002). Neural influences on cardiovascular variability: possibilities and pitfalls. American Journal of Physiology – Heart and Circulatory Physiology 282, 6–20.Google Scholar
Marmarelis, P. Z. (1993). Identification of nonlinear biological systems using Laguerre expansions of kernels. Annals of Biomedical Engineering 21, 573–589.Google Scholar
Marmarelis, P. Z. (2004). Nonlinear Dynamic Modeling of Physiological Systems, Chichester: Wiley.
Napadow, V., Dhond, R., Conti, G., Makris, N., Brown, E. N. & Barbieri, R. (2008). Brain correlates of autonomic modulation: combining heart rate variability with fMRI. Neuroimage 42(1), 169–177.Google Scholar
Parati, G., DiRienzo, M. & Mancia, G. (2001). Dynamic modulation of baroreflex sensitivity in health and disease. Annals of New York Academy of Science 940, 469–487.Google Scholar
Porta, A., Aletti, F., Vallais, F. & Baselli, G. (2009). Multimodal signal processing for the analysis of cardiovascular variability. Philosophical Transactions on Royal Society, Series A 367, 391–409.Google Scholar
Porta, A., Furlan, R., Rimoldi, O., Pagani, M., Malliani, A. & van de Borne, P. (2002). Quantifying the strength of the linear causal coupling in closed loop interacting cardiovascular variability signals. Biological Cybernetics 86, 241–251.Google Scholar
Ross, S.M. (1997). Introduction to Probability Models, 6th edn, London: Academic Press.
Saul, J. P., Berger, R.D., Albrecht, P., Stein, S. P., Chen, M. H. & Cohen, R. J. (1991). Transfer function analysis of the circulation: unique insights into cardiovascular regulation. American Journal of Physiology – Heart and Circulatory Physiology 261, 1231–1245.Google Scholar
Saul, J. P. & Cohen, R. J. (1994). Respiratory sinus arrhythmia. In M. N., Levy& P. J., Schwartz, eds, Vagal Control of the Heart: Experimental Basis and Clinical Implications, New York: Futura Publishing Inc.
Schetzen, M. (1980). The Volterra and Wiener Theories of Nonlinear Systems, Chichester: Wiley.
Smith, A. C. & Brown, E. N. (2003). Estimating a state-space model from point process observations. Neural Computation 15(5), 965–991.Google Scholar
Stauss, H. M. (2003). Heart rate variability. American Journal of Physiology – Regulatory, Integrative and Comparative Physiology 285, 927–931.Google Scholar
Struzik, Z. R., Hayano, J., Sakata, S., Kwak, S. & Yamamoto, Y. (2003). 1/f scaling in heart rate requires antagonistic autonomic control. Physical Review E 70, 050901.Google Scholar
Tsoulkas, V., Koukoulas, P. & Kalouptsidis, N. (2001). Identification of input output bilinear systems using cumulants. IEEE Transactions on Signal Processing 49, 2753–2761.Google Scholar
Valenza, G., Citi, L. & Barbieri, R. (2014b). Estimation of instantaneous complex dynamics through Lyapunov exponents: a study on heartbeat dynamics. PLoS ONE 9(8), e10562.Google Scholar
Valenza, G., Citi, L., Scilingo, E. P. & Barbieri, R. (2013). Point-process nonlinear models with Laguerre and Volterra expansions: instantaneous assessment of heartbeat dynamics. IEEE Transactions on Signal Processing 61(11), 2914–2926.Google Scholar
Valenza, G., Citi, L., Scilingo, E. P. & Barbieri, R. (2014a). Inhomogeneous point-process entropy: an instantaneous measure of complexity in discrete systems. Physical Review E 89, 052803.Google Scholar
Voss, A., Schulz, S., Schroeder, R., Baumert, M. & Caminal, P. (2009). Methods derived from nonlinear dynamics for analysing heart rate variability. Philosophical Transactions of the Royal Society A 367, 277–296.Google Scholar
Vu, K. M. (2007). The ARIMA and VARIMA Time Series: Their Modelings, Analyses and Applications, Ottawa: AuLac Technologies.
Westwick, D. T. & Kearney, R. E. (2003). Explicit least-squares methods. In Identification of Nonlinear Physiological Systems, Chickester: Wiley, pp. 169–206.
Xiao, X., Mullen, T. J. & Mukkamala, R. (2005). System identification: a multi-signal approach for probing neural cardiovascular regulation. Physiological Measurement 26, R41–R71.Google Scholar
Zhang, Y., Wang, H., Ju, K. H., Jan, K.-M. & Chon, K. H. (2004). Nonlinear analysis of separate contributions of autonomous nervous systems to heart rate variability using principal dynamic modes. IEEE Transactions on Biomedical Engineering 51, 255–262.Google Scholar
Zhao, H., Cupples, W. A., Ju, K. & Chon, K. H. (2007). Time-varying causal coherence function and its application to renal blood pressure and blood flow data. IEEE Transactions on Biomedical Engineering 54, 2142–2150.Google Scholar
Zhao, H., Lu, S., Zou, R., Ju, K. & Chon, K. H. (2005). Estimation of time-varying coherence function using time-varying transfer functionss. Annals of Biomedical Engineering 33, 1582–1594.Google Scholar

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