The Library

Intrinsic dynamics of heart regulatory systems on short timescales : from experiment to modelling

Tools

Khovanov, I. A., Khovanova, N. A., McClintock, P. V. E. and Stefanovska, A.. (2009) Intrinsic dynamics of heart regulatory systems on short timescales : from experiment to modelling. Journal of Statistical Mechanics: Theory and Experiment, Vol.2009 (No.1). Article: P01016. ISSN 1742-5468

Preview

PDF
WRAP_Khovanova_0973918-es-121211-n.khovanova0901.pdf - Accepted Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (383Kb)

Official URL: http://dx.doi.org/10.1088/1742-5468/2009/01/P01016

Abstract

We discuss open problems related to the stochastic modelling of cardiac function. The work is based on an experimental investigation of the dynamics of heart rate variability (HRV) in the absence of respiratory perturbations. We consider first the cardiac control system on short timescales via an analysis of HRV within the framework of a random walk approach. Our experiments show that HRV on timescales of less than a minute takes the form of free diffusion, close to Brownian motion, which can be described as a non-stationary process with stationary increments. Secondly, we consider the inverse problem of modelling the state of the control system so as to reproduce the experimentally observed HRV statistics of. We discuss some simple toy models and identify open problems for the modelling of heart dynamics.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QP Physiology
Divisions:	Faculty of Science > Engineering
Library of Congress Subject Headings (LCSH):	Heart -- Mathematical models, Heart beat -- Mathematical models
Journal or Publication Title:	Journal of Statistical Mechanics: Theory and Experiment
Publisher:	Institute of Physics Publishing Ltd.
ISSN:	1742-5468
Date:	January 2009
Volume:	Vol.2009
Number:	No.1
Number of Pages:	15
Page Range:	Article: P01016
Identification Number:	10.1088/1742-5468/2009/01/P01016
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), Wellcome Trust (London, England)
References:	[1] Ott E 1993 Chaos in Dynamical Systems (Cambridge, UK: Cambridge University Press) [2] Frisch U 1995 Turbulence: The Legacy of A.N. Kolmogorov (Cambridge, UK: Cambridge University Press) [3] Mandelbrot B B 1982 The Fractal Geometry of Nature (W. H. Freeman) [4] Jensen H J 1998 Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems (Cambridge, UK: Cambridge University Press) [5] Kurths J, Voss A, Saparin P, Witt A, Kleiner H J and Wessel N 1995 Chaos 5(1) 88–94 [6] Pincus S M 1991 Proc. Nat. Acad. Sci. 88(6) 2297–2301 [7] Costa M, Goldberger A L and Peng C K 2002 Phys. Rev. Lett. 89(6) 068102 [8] Raab C, Wessel N, Schirdewan A and Kurths J 2006 Phys. Rev. E 73(4) 041907 [9] Kiyono K, Struzik Z R, Aoyagi N, Togo F and Yamamoto Y 2005 Phys. Rev. Lett. 95(5) 058101 [10] Peng C K, Havlin S, Stanley H E and Goldberger A L 1995 Chaos 5(1) 82–87 [11] Hausdorff J M and Peng C K 1996 Phys. Rev. E 54(2) 2154–2157 [12] Pilgram B and Kaplan D T 1999 Amer. J. of Physiol. { Regulatory, Integrative and Comparative Physiol 276(1) R1–R9 [13] Costa M, Goldberger A L and Peng C K 2005 Phys. Rev. Lett. 95 198102 [14] Ivanov P C, Amaral L A N, Goldberger A L, Havlin S, Rosenblum M G, Struzik Z R and Stanley H E 1999 Nature 399(6735) 461–465 [15] Ivanov P C, Amaral L A N, Goldberger A L, Havlin S, M G Rosenblum H E S and Struzik Z R 2001 Chaos 11(3) 641–652 [16] Ivanov P C, Amaral L A N, Goldberger A L and Stanley H E 1998 Europhys. Lett. 43(4) 363–368 [17] Stefanovska A and Braˇciˇc M 1999 Contemporary Phys. 40(1) 31–55 [18] Eckberg D L 2003 J. Physiol. (Lond.) 548(2) 339–352 [19] West B J, Griffin L A, Frederick H J and Moon R E 2005 Resp. Physiol. and Neurobiol. 145(2-3) 219–233 [20] Doessel O, Reumann M, Seemann G and Weiss D 2006 Biomedizinische Technik 51(4) 205–209 [21] Parkes M J 2006 Exper. Physiol. 91(1) 1–15 [22] Malpas S C 2002 Am. J. Physiol.: Heart. Circ. Physiol. 282 H6–H20 [23] Julien C 2006 J. Appl. Physiol. 101(2) 684 [24] Peng C K, Mietus J, Hausdorff J M, Havlin S, Stanley H E and Goldberger A L 1993 Phys. Rev. Lett. 70(9) 1343–1346 [25] Nolan J P 1998 Stat. and Probabil. Lett. 38(2) 187–195 [26] Samorodnitsky G and Taqqu M S 1994 Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance (London, UK: Chapman and Hall) [27] Kolmogorov A N 1940 Doklady Akademii Nauk SSSR 26(1) 6–9 [28] Doob J L 1990 Stochastic Processes (New York: Wiley-Interscience) [29] Yaglom A M 1962 An Introduction to the Theory of Stationary Random Functions (Englewood Cliffs, NJ.: Prentice-Hall) [30] Rytov S M, Kravtsov Y A and Tatarskii V I 1988 Principles of Statistical Radiophysics vol 2: Correlation Theory of Random Processes (Springer-Verlag) [31] Camm A J, Malik M, Bigger J T and et al 1996 Circulation 93(5) 1043–1065 [32] Box G, Jenkins G M and Reinsel G 1994 Time Series Analysis: Forecasting & Control (3rd Edn) (Englewood Cliffs, NJ: Prentice Hall) [33] Nikias C L and Min Shao 1995 Signal Processing with Alpha-stable Distributions and Applications (New York, NY, USA: Wiley-Interscience) [34] Heneghan C and McDarby G 2000 Phys. Rev. E 62(5) 6103–6110 [35] Yulmetyev R, H¨anggi P and Gafarov F 2002 Phys. Rev. E 65(4) 046107 [36] Wilders R 2007 Med. and Biol. Eng. and Comp. 45(2) 189–207 [37] Ponard J G C, Kondratyev A A and Kucera J P 2007 Biophys. J. 92(10) 3734–3752 [38] Dobrzynski H, Li J, Tellez J, Greener I D, Nikolski V P, Wright S E, Parson S H, Jones S A, Lancaster M K, Yamamoto M, Honjo H, Takagishi Y, Kodama I, Efimov I R, Billeter R and Boyett M R 2005 Circulation 111(7) 846–854 [39] Neumann T, Post H, Ganz R E, Walz M K, Skyschally A, Schulz R and Heusch G 2001 Zeitschrift fur Kardiologie 90(7) 484–491 [40] Klabunde R E 2004 Cardiovascular Physiology Concepts (Philadelphia, USA: Lippincott Williams & Wilkins) [41] Armour J A 2004 Amer. J. Physiol. { Regulatory Integrative and Comparative Physiol. 287(2) R262–R271 [42] Fitzhugh R 1961 Biophys. J. 1(6) 445 [43] Morris C and Lecar H 1981 Biophys. J. 35(1) 193–213
URI:	http://wrap.warwick.ac.uk/id/eprint/37161