Point-process nonlinear models with laguerre and volterra expansions: Instantaneous assessment of heartbeat dynamics

IEEE Transactions on Signal Processing

Volumn 61, Issue 11, 2013, Pages 2914-2926

  Valenza, Gaetano ^a,b,c   Citi, Luca ^a   Scilingo, Enzo Pasquale ^c   Barbieri, Riccardo ^b  

^a MASSACHUSETTS GENERAL HOSPITAL   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c UNIVERSITY OF PISA   (Italy)

Author keywords

Bispectrum; heart rate variability (HRV); high order statistics; Laguerre expansion; nonlinear analysis; point process; trispectrum; Wiener Volterra model

Indexed keywords

BISPECTRUM; HEART RATE VARIABILITY; HIGH ORDER STATISTICS; LAGUERRE EXPANSION; POINT PROCESS; TRISPECTRUM;

CARDIOVASCULAR SYSTEM; EXPANSION; NONLINEAR SYSTEMS; SIGNAL PROCESSING;

NONLINEAR ANALYSIS;

EID: 84877889692     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2013.2253775     Document Type: Article

References (90)

1. Task, Force, of the European Society of Cardiology, the North American Society of Pacing, and Electrophysiology, "Heart rate variability: Standards of measurement, physiological interpretation and clinical use.," Circulation, vol. 93, no. 5, pp. 1043-65, 1996.
2. U. R. Acharya, K. P. Joseph,N.Kannathal, C. Lim, and J. Suri, "Heart rate variability: A review," Med. Biolog. Eng. Comput., vol. 44, no. 12, pp. 1031-1051, 2006. (Pubitemid 47090818)
3. F. Atyabi, M. Livari, K. Kaviani, and M. Tabar, "Two statistical methods for resolving healthy individuals and those with congestive heart failure based on extended self-similarity and a recursive method," J. Biolog. Phys., vol. 32, no. 6, pp. 489-495, 2006. (Pubitemid 46872925)
4. L. Glass, "Introduction to controversial topics in nonlinear science: Is the normal heart rate chaotic?," Chaos: Interdiciplinary J. Nonlinear Sci., vol. 19, no. 2, p. 028501, 2009.
5. "Synchronization and rhythmic processes in physiology," Nature, vol. 410, no. 6825, pp. 277-284, 2001.
6. A. Goldberger, C. Peng, and L. Lipsitz, "What is physiologic complexity and how does it change with aging and disease?," Neurobiol. Aging, vol. 23, no. 1, pp. 23-26, 2002. (Pubitemid 34066531)
7. C. Poon and C. Merrill, "Decrease of cardiac chaos in congestive heart failure," Nature, vol. 389, no. 6650, pp. 492-495, 1997. (Pubitemid 27435323)
8. M. Tulppo, A. Kiviniemi, A. Hautala, M. Kallio, T. Seppanen, T. Makikallio, and H. Huikuri, "Physiological background of the loss of fractal heart rate dynamics," Circulation, vol. 112, no. 3, p. 314, 2005.
9. G. Wu, N. Arzeno, L. Shen, D. Tang, D. Zheng, N. Zhao, D. Eckberg, and C. Poon, "Chaotic signatures of heart rate variability and its power spectrum in health, aging and heart failure," PLoS One, vol. 4, no. 2, p. e4323, 2009.
10. O. Stiedl and M. Meyer, "Fractal dynamics in circadian cardiac time series of corticotropin-releasing factor receptor subtype-2 deficient mice," J. Math. Biol., vol. 47, no. 2, pp. 169-197, 2003. (Pubitemid 41246266)
11. K. Sunagawa, T. Kawada, and T. Nakahara, "Dynamic nonlinear vagosympathetic interaction in regulating heart rate," Heart Vessels, vol. 13, no. 4, pp. 157-174, 1998. (Pubitemid 29322458)
12. K. Chon, T. Mullen, and R. Cohen, "A dual-input nonlinear system analysis of autonomic modulation of heart rate," IEEE Trans. Biomed. Eng., vol. 43, no. 5, pp. 530-544, 1996. (Pubitemid 26131474)
13. D. Christini, F. Bennett, K. Lutchen, H. Ahmed, J. Hausdorff, and N. Oriol, "Application of linear and nonlinear time series modeling to heart rate dynamics analysis," IEEE Trans. Biomed. Eng., vol. 42, no. 4, pp. 411-415, 1995.
14. T. Makikallio, J. Tapanainen, M. Tulppo, and H. Huikuri, "Clinical applicability of heart rate variability analysis by methods based on nonlinear dynamics," Cardiac Electrophys. Rev., vol. 6, no. 3, pp. 250-255, 2002. (Pubitemid 35276934)
15. L. Faes, G. Nollo, and K. Chon, "Assessment of granger causality by nonlinear model identification: Application to short-term cardiovascular variability," Ann. Biomed. Eng., vol. 36, no. 3, pp. 381-395, 2008.
16. A. Fowler andM.McGuinness, "A delay recruitment model of the cardiovascular control system," J.Math. Biol., vol. 51, no. 5, pp. 508-526, 2005. (Pubitemid 41625888)
17. A. Porta, S. Guzzetti, R. Furlan, T. Gnecchi-Ruscone, N.Montano, and A. Malliani, "Complexity and nonlinearity in short-term heart period variability: Comparison of methods based on local nonlinear prediction," IEEE Trans. Biomed. Eng., vol. 54, no. 1, pp. 94-106, 2007. (Pubitemid 46127142)
18. J. Jo, A. Blasi, E. Valladares, R. Juarez, A. Baydur, and M. Khoo, "A nonlinear model of cardiac autonomic control in obstructive sleep apnea syndrome," Ann. Biomed. Eng., vol. 35, no. 8, pp. 1425-1443, 2007. (Pubitemid 47115172)
19. R.Barbieri, E.Matten,A.Alabi, andE. Brown, "Apoint-processmodel of human heartbeat intervals: New definitions of heart rate and heart rate variability," Amer. J. Physiol.-Heart Circ. Phys., vol. 288, no. 1, p. H424, 2005.
20. R. Barbieri and E. Brown, "Analysis of heartbeat dynamics by point process adaptive filtering," IEEE Trans. Biomed. Eng., vol. 53, no. 1, pp. 4-12, 2006. (Pubitemid 43074786)
21. Z.Chen, E. Brown, andR.Barbieri, "Assessment of autonomic control and respiratory sinus arrhythmia using point process models of human heart beat dynamics," IEEE Trans. Biomed. Eng., vol. 56, no. 7, pp. 1791-1802, 2009.
22. Z. Chen, E. Brown, and R. Barbieri, "Characterizing nonlinear heartbeat dynamics within a point process framework," IEEE Trans. Biomed. Eng., vol. 57, no. 6, pp. 1335-1347, 2010.
23. Y. Ogata, "Space-time point-process models for earthquake occurrences," Ann. Inst. Statist. Math., vol. 50, no. 2, pp. 379-402, 1998. (Pubitemid 128487986)
24. A. Horváth and M. Telek, "A markovian point process exhibiting multifractal behaviour and its application to traffic modeling," in Proc. 4th Int. Conf.Matrix-AnalyticMethods in Stoch. Models, Singapore, 2002, pp. 183-208.
25. R. Barbieri, L. Frank, D. Nguyen,M. Quirk, V. Solo, M. Wilson, and E. Brown, "Dynamic analyses of information encoding in neural ensembles," Neural Computat., vol. 16, no. 2, pp. 277-307, 2004. (Pubitemid 38085366)
26. Y. Wang, A. Paiva, J. Principe, and J. Sanchez, "Sequential Monte Carlo point-process estimation of kinematics from neural spiking activity for brain-machine interfaces," Neural Computat., vol. 21, no. 10, pp. 2894-2930, 2009.
27. R. Barbieri, M. Quirk, L. Frank, M.Wilson, and E. Brown, "Construction and analysis of non-Poisson stimulus-response models of neural spiking activity," J. Neurosci. Methods, vol. 105, no. 1, pp. 25-37, 2001. (Pubitemid 32106917)
28. M. Akay, Nonlinear Biomedical Signal Processing Vol. II: Dynamic Analysis and Modeling. Hoboken, NJ, USA: Wiley-IEEE , 2000.
29. M. Korenberg and L. Paarmann, "Orthogonal approaches to time-series analysis and system identification," IEEE Signal Process. Mag., vol. 8, no. 3, pp. 29-43, 1991. (Pubitemid 21690720)
30. M. Korenberg, "Parallel cascade identification and kernel estimation for nonlinear systems," Ann. Biomed. Eng., vol. 19, no. 4, pp. 429-455, 1991.
31. V. Marmarelis, "Identification of nonlinear biological system using Laguerre expansions of kernels," Ann. Biomed. Eng., vol. 21, pp. 573-589, 1993. (Pubitemid 24026377)
32. V. Marmarelis and T. Berger, "General methodology for nonlinear modeling of neural systems with Poisson point-process inputs," Math. Biosci., vol. 196, no. 1, pp. 1-13, 2005. (Pubitemid 40982022)
33. N. Wiener, "Nonlinear problems in random theory," in Nonlinear Problems in Random Theory, N. Wiener, Ed. Cambridge, MA, USA: The MIT Press, 1966, vol. 1, p. 142, Aug. 1966 (Paper), ISBN 0-262-73012-X..
34. A.Watanabe and L. Stark, "Kernel method for nonlinear analysis: Identification of a biological control system," Math. Biosci., vol. 27, no. 1-2, pp. 99-108, 1975.
35. H. Ogura, "Estimation of wiener kernels of a nonlinear system and a fast algorithm using digital Laguerre filters," in Proc. 15th NIBBConf., Okazaki, Japan, 1985, pp. 14-62.
36. D. Song, R. Chan, V. Marmarelis, R. Hampson, S. Deadwyler, and T. Berger, "Nonlinear dynamic modeling of spike train transformations for Hippocampal-cortical prostheses," IEEE Trans. Biomed. Eng., vol. 54, no. 6, pp. 1053-1066, 2007. (Pubitemid 46815130)
37. D. Song, R. Chan, V. Marmarelis, R. Hampson, S. Deadwyler, and T. Berger, "Nonlinear modeling of neural population dynamics for Hippocampal prostheses," Neural Netw., vol. 22, no. 9, pp. 1340-1351, 2009.
38. V. Marmarelis, Nonlinear Dynamic Modeling of Physiological Systems. Hoboken, NJ, USA: Wiley-IEEE, 2004.
39. V. Marmarelis, D. Shin, D. Song, R. Hampson, S. Deadwyler, and T. Berger, "Nonlinear modeling of dynamic interactions within neuronal ensembles using principal dynamic modes," J. Computat. Neurosci., pp. 1-15, 2012.
40. C.Nikias and J.Mendel, "Signal processingwith higher-order spectra," IEEE Signal Process. Mag., vol. 10, no. 3, pp. 10-37, 1993.
41. C. Nikias, Higher-Order Spectra Analysis: A Nonlinear Signal Processing Framework. Englewood Cliffs,NJ,USA: PTR Prentice-Hall, 1993.
42. A. Agogino and K. Goebel,Mill Dataset, BEST Lab, UC Berkeley, CA, USA, and Prognostics Data Repository, NASA Ames [Online]. Available: http://ti.arc.nasa.gov/tech/dash/pcoe/prognostic-data-repository/
43. M. C. Teich, D. H. Johnson, A. R. Kumar, and R. G. Turcott, "Rate fluctuations and fractional power-law noise recorded from cells in the lower auditory pathway of the cat," Hearing Res., vol. 46, pp. 41-52, 1990. (Pubitemid 20203600)
44. R. Taylor et al., Old Faithful Eruptions for 2011, Geyser Observation and Study Association (GOSA), Yellowstone National Park [Online]. Available: http://www.gosa.org/geyser.aspx?pGeyserNo=OLDFAITHFUL
45. J. Hausdorff et al., "Gait in aging and disease database," Online at Physionet Database [Online]. Available: http://physionet.org/ physiobank/ database/gaitdb/
46. J. Mendel, "Tutorial on higher-order statistics (spectra) in signal processing and system theory: Theoretical results and some applications," Proc. IEEE, vol. 79, pp. 278-305, 1991.
47. C. Nikias, Higher-Order Spectral Analysis: A Nonlinear Signal Processing Framework. Englewood Cliffs,NJ,USA: PTR Prentice-Hall, 1993.
48. M. Schetzen, The Volterra and Wiener Theories of Nonlinear Systems, rev. ed. Malabar, FL, USA: Kreiger, 2006.
49. C. Granger and R. Joyeux, "An introduction to long-memory time series models and fractional differencing," J. Time Ser. Anal., vol. 1, no. 1, pp. 15-29, 1980.
50. Z. Chen, P. Purdon, E. Brown, and R. Barbieri, "A differential autoregressive modeling approach within a point process framework for non-stationary heartbeat intervals analysis," in Proc. IEEE Eng. Med. Biol. Conf. (EMBC), 2010, pp. 3567-3570, IEEE.
51. C. Loader, Local Regression and Likelihood. NewYork, NY, USA: Springer-Verlag, 1999.
52. R. Tibshirani and T. Hastie, "Local likelihood estimation," J. Amer. Stat. Assoc., pp. 559-567, 1987.
53. E. Brown, R. Barbieri, U. Eden, and L. Frank, "Likelihood methods for neural spike train data analysis," Comput. Neurosci.: A Comprehens. Approach, pp. 253-286, 2003.
54. D.Westwick and R. Kearney, Explicit Least-SquaresMethods, in Identification of Nonlinear Physiological Systems. Hoboken, NJ, USA: Wiley-IEEE, 2003, vol. 7.
55. S. Billings, "Identification of nonlinear system-A survey," Proc. IEEE, vol. 127, pp. 272-285, 1980.
56. J. Le Caillec and R. Garello, "Nonlinear system identification using autoregressive quadratic models," Signal Process., vol. 81, no. 2, pp. 357-379, 2001. (Pubitemid 32196404)
57. P. Koukoulas and N. Kalouptsidis, "Nonlinear system identification using Gaussian inputs," IEEE Trans. Signal Process., vol. 43, no. 8, pp. 1831-1841, 1995.
58. Z. Chen, P. Purdon, G. Harrell, E. Pierce, J. Walsh, E. Brown, and R. Barbieri, "Dynamic assessment of baroreflex control of heart rate during induction of propofol anesthesia using a point process method," Ann. Biomed. Eng., pp. 1-17, 2011.
59. P. Huber, B. Kleiner, T. Gasser, and G. Dumermuth, "Statistical methods for investigating phase relations in stationary stochastic processes," IEEE Trans. Audio Electroacoust., vol. 19, no. 1, pp. 78-86, 1971.
60. C. Nikias and M. Raghuveer, "Bispectrum estimation: A digital signal processing framework," Proc. IEEE, vol. 75, no. 7, pp. 869-891, 1987. (Pubitemid 17651268)
61. J. Nichols, C. Olson, J. Michalowicz, and F. Bucholtz, "The bispectrum and bicoherence for quadratically nonlinear systems subject to non- Gaussian inputs," IEEE Trans. Signal Process., vol. 57, no. 10, pp. 3879-3890, 2009.
62. D. Brillinger, "An introduction to polyspectra," Ann. Math. Statist., pp. 1351-1374, 1965.
63. J. Caillec and R. Garello, "Asymptotic bias and variance of conventional bispectrum estimates for 2-D signals," Multidimens. Syst. Signal Process., vol. 16, no. 1, pp. 49-84, 2005. (Pubitemid 40329463)
64. A. Barnett and R. Wolff, "A time-domain test for some types of nonlinearity," IEEE Trans. Signal Process., vol. 53, no. 1, pp. 26-33, 2005. (Pubitemid 40085330)
65. D. Brillinger and M. Rosenblatt, "Asymptotic theory of estimates of kth-order spectra," Proc. Natl. Acad. Sci. U. S. A., vol. 57, no. 2, p. 206, 1967.
66. V. Chandran and S. Elgar, "Pattern recognition using invariants defined from higher order spectra-one dimensional inputs," IEEE Trans. Signal Process., vol. 41, no. 1, p. 205, 1993.
67. T. Ng, S. Chang, and Q. Sun, "Blind detection of photomontage using higher order statistics," in Proc. Int. Symp. Circuits Syst., 2004, vol. 5, pp. V-688, IEEE.
68. K. Chua, V. Chandran, U. Acharya, and C. Lim, "Application of higher order statistics/spectra in biomedical signals-A review," Med. Eng. Phys., vol. 32, no. 7, pp. 679-689, 2010.
69. S. Zhou, J. Gan, and F. Sepulveda, "Classifying mental tasks based on features of higher-order statistics from EEG signals in brain-computer interface," Inf. Sci., vol. 178, no. 6, pp. 1629-1640, 2008.
70. S. Akselrod, "Components of heart rate variability: Basic studies," Heart Rate Variab., pp. 147-163, 1995.
71. A. Malliani, "Association of heart rate variability components with physiological regulatory mechanisms," Heart Rate Variabil., pp. 173-188, 1995.
72. S. Malpas, "Neural influences on cardiovascular variability: Possibilities and pitfalls," Amer. J. Physiol.-Heart Circ. Phys., vol. 282, no. 1, p. H6, 2002.
73. M. Ursino and E. Magosso, "Role of short-term cardiovascular regulation in heart period variability: A modeling study," Amer. J. Physiol. -Heart Circ. Phys., vol. 284, no. 4, p. H1479, 2003.
74. D. Brillinger, "The identification of polynomial systems by means of higher order spectra 1," J. Sound Vibr., vol. 12, no. 3, pp. 301-313, 1970.
75. M. Priestley, "Spectral analysis and time series," 1981.
76. O. Rössler, "An equation for continuous chaos," Phys. Lett. A, vol. 57, no. 5, pp. 397-398, 1976.
77. T. Heldt, M. B. Oefinger,M. Hoshiyama, and R. G. Mark, "Circulatory response to passive and active changes in posture," Comput. Cardiol., vol. 30, pp. 263-266, 2003.
78. T. Heldt, E. B. Shim, R. D. Kamm, and R. G. Mark, "Computational modeling of cardiovascular response to orthostatic stress," J. Appl. Physiol., vol. 92, no. 3, pp. 1239-1254, Mar. 2002. (Pubitemid 34670985)
79. A. Porta, E. Tobaldini, S. Guzzetti, R. Furlan, N. Montano, and T. Gnecchi-Ruscone, "Assessment of cardiac autonomic modulation during graded head-up tilt by symbolic analysis of heart rate variability," Amer. J. Physiol.-Heart Circ. Phys., vol. 293, no. 1, pp. H702-H708, 2007. (Pubitemid 47105132)
80. A. Goldberger, L. Amaral, L. Glass, J. Hausdorff, P. Ivanov, R. Mark, J. Mietus, G. Moody, C. Peng, and H. Stanley, "Physiobank, physiotoolkit, and physionet: Components of a new research resource for complex physiologic signals," Circulation, vol. 101, no. 23, p. e215, 2000.
81. C. Peng, S. Havlin, H. Stanley, and A. Goldberger, "Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series," Chaos, vol. 5, no. 1, p. 82, 1995.
82. F. Wilcoxon, "Individual comparisons by ranking methods," Biometr. Bull., vol. 1, no. 6, pp. 80-83, 1945.
83. S. Mason and N. Graham, "Areas beneath the relative operating characteristics (ROC) and relative operating levels (ROL) curves: Statistical significance and interpretation," Quart. J. Royal Meteorolog. Soc., vol. 128, no. 584, pp. 2145-2166, 2002. (Pubitemid 34995960)
84. Y. Fusheng, H. Bo, and T. Qingyu, "Approximate entropy and its application in biosignal analysis," Nonlin. Biomed. Signal Process., p. 72, 2000.
85. J. Richman and J. Moorman, "Physiological time-series analysis using approximate entropy and sample entropy," Amer. J. Physiol.-Heart Circ. Phys., vol. 278, no. 6, p. H2039, 2000.
86. P. Schwartz and G. De Ferrari, "Sympathetic-parasympathetic interaction in health and disease: Abnormalities and relevance in heart failure," Heart Failure Rev., pp. 1-7, 2010.
87. R. Thuraisingham and G. Gottwald, "On multiscale entropy analysis for physiological data," Phys. A, Statist. Mechan. Appl., vol. 366, pp. 323-332, 2006.
88. M. Costa, A. Goldberger, and C. Peng, "Multiscale entropy analysis of complex physiologic time series," Phys. Rev. Lett., vol. 89, no. 6, p. 68102, 2002.
89. S. Pincus, "Approximate entropy as a measure of system complexity," Proc. Natl. Acad. Sci. U.S.A., vol. 88, no. 6, p. 2297, 1991.
90. L. Citi, G. Valenza, and R. Barbieri, "Instantaneous estimation of highorder nonlinear heartbeat dynamics by Lyapunov exponents," in Proc. IEEE Eng. Med. Bio. Conf. (EMBC), 2012, pp. 13-16.