Abstract
Functional re-innervation of the transplanted human heart by the autonomic nervous system has not yet been demonstrated and lack of autonomic control of the transplanted allograft is reflected by an increased resting heart rate, a sluggish heart rate response to dynamical exercise and a reduced heart rate variability. Recent evidence suggests that a measure of deterministic chaos in the heartbeat interval time series, the point correlation dimension (PD2), is superior to the conventional power spectrum analysis which is based on the assumption of stochastic dynamics and limited by the requirements of stationarity in the data stream. In the PD2 analysis, dimensional changes of the system, i.e. the number of variables involved in the generation of its output (heartbeat interval time series), are determined within small “points” of time (beat-by-beat) irrespective of whether the system is stochastic or deterministic and nonstationary. PD2 was determined from heartbeat interval time series of digitized 40 min electrocardiograms (sampling rate 1200 Hz; supine posture) in 23 heart transplant recipients (HTR; 9 adults, 14 children; 0.07–7.7 yrs after transplantation) and 21 healthy control subjects (CTL; 13 adults, 8 children). PD2 (±SD) averaged 5.4±0.7 (adults) and 5.4±0.6 (children), respectively. The noninteger number of the dimensional estimate suggests that the normal heartbeat exhibits low-dimensional chaotic dynamics. In the HTR group, irrespective of age, PD2 was reduced to ∼1 early after transplantation but would not seem to attain normal control values within the time interval studied in long-term survivors (6–7 yrs). The initial breakdown of nonlinear chaotic dynamics along with the recurrence of low-dimensional deterministic dynamics with time after transplantation would suggest a recovery of cardiac control and heartbeat fluctuations that would be attributable to reorganization of the viable intrinsic cardiac nervous system or re-innervation of the extrinsic autonomic nervous system.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Burke MN, McGinn AL, Homans DC, Christensen BV, Kubo SH, Wilson RF: Evidence for functional sympathetic re-innervation of left ventricle and coronary arteries after orthotopic cardiac transplantation in humans. Circulation 91, 72–78 (1995)
Kaye DM, Ester M, Kingwell B, McPherson G, Esmore D, Jennings G: Functional and neurochemical evidence for partial cardiac sympathetic reinnervation after cardiac transplantation in humans. Circulation 88, 1110–1118 (1995)
Schwaiger M, Hutchins GD, Kolff V, Rosenspire K, Haka MS, Mallette S, Deeb GM, Abrama GD, Wieland D: Evidence for regional catecholamine uptake and storage sites in the transplanted human heart by positron emission tomography. J. Clin. Invest. 87, 1681–1690 (1991)
Wilson RF, Christensen BV, Olivari MT, Simon A, White CW, Laxson DD: Evidence for structural sympathetic re-innervation after orthotopic cardiac transplantation in humans. Circulation 83, 1210–1220 (1991)
Wilson RF, Laxson DD, Christensen BV, McGinn AL, Kubo SH: Regional differences in sympathetic re-innervation after human orthotopic cardiac transplantation. Circulation 88, 165–171 (1993)
Arrowood JA, Goudreau E, Minisi J, Davis AB, Mohanty PK: Evidence against re-innervation of cardiac vagal afferents after human orthotopic cardiac transplantation. Circulation 92, 402–408 (1995)
Goldberger AL, Rigney DR, West BJ: Chaos and fractals in human physiology. Sci. Am. 262, 42–49 (1990)
Kitney RI, Rompelman O: The Study of Heart-Rate Variability. Oxford University Press, Oxford (1980)
Babloyantz A, Desthexhe A: Is the heart a periodic oscillator? Biol Cybern. 58, 203–211 (1988)
Mayer-Kress G, Yates FE, Benton L, Keidel M, Tirsch W, Pöppl SJ, Geist K: Dimensional analysis of nonlinear oscillations in brain, heart, and muscle. Math. Biosci. 90, 155–182 (1988)
Skinner, JE, Carpeggiani C, Landisman CE, Fulton KW: Correlation dimension of heartbeat intervals is reduced in conscious pigs by myocardial ischemia. Circ. Res. 68, 966–976 (1991)
Skinner JE, Pratt CM, Vybiral T: A reduction in the correlation dimension of heartbeat intervals precedes imminent ventricular fibrillation in human subjects. Am. Heart J. 125, 731–743 (1993)
Skinner JE, Molnar M, Vybiral T, Mitra M: Application of chaos theory to biology and medicine. Integr. Physiol. Behav. Sci. 27, 39–53 (1992)
Skinner JE, Molnar M, Tomberg C: The point correlation dimension: performance with nonstationary surrogate data and noise. Integr. Physiol. Behav. Sci. 29, 217–234 (1994)
Elbert T, Ray WJ, Kowalik ZJ, Skinner JE, Graf KE, Birbaumer N: Chaos and physiology: deterministic chaos in excitable cell assemblies. Physiol. Rev. 74, 1–47 (1994)
Grassberger P, Procaccia I: Measuring the strangeness of strange attractors. Physica 9D, 189–208)1983)
Farmer JD, Ott E, Yorke JA: The dimension of chaotic attractors. Physica D7, 53–180 (1983)
Glass L, Malta CP: Chaos in multi-looped negative feedback systems. J. Theor. Biol. 145, 217–223 (1990)
Liem LB, Dibiase A, Schroeder JS: Arrythmia and clinical electrophysiology of the transplanted human heart. Semn. Thorac. Cardiovasc. Surg. 2, 271–278 (1990)
Murphy DA, O’Blenes S, Hanna BD, Armour JA: Functional capacity of nicotine-sensitive canine intrinsic cardiac neurone to modify the heart. Am. J. Physiol. 266 (Regulatory Integrative Comp. Physiol. 35), R1127–R1135 (1994)
Peng C-K, Mietus J, Hausdorff JM, Havlin S, Stanley HE, Goldberger AL: Long-range anticorrelations and non-gausssian behavior of the heartbeat. Phys. Rev. Lett. 70, 1343–1346 (1993)
Peng C-K, Havlin S, Stanley HE, Goldberger AL: Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos 5, 82–87 (1995)
Cerretelli P, Marconi C, Meyer M, Ferretti G, Grassi B: Gas exchange kinetics in heart transplant recipients. Chest 101, 199S-205S (1992)
Hsu DT, Garofano RP, Douglas JM, Michler RE, Quaegebeur JM, Gersony WM, Addonizio LJ: Exercise performance after pediatric heart transplantation. Circulation 88, 238–242 (1993)
Meyer M, Marconi C, Grassi B, Rieu M, Cerretelli P, Cabrol C: Adjustment of cardiac output to step exercise in heart transplant recipients. Applied Cardiopulmonary Pathophysiology 4, 213–223 (1992)
Meyer M, Rahmel A, Marconi C, Grassi B, Cerretelli P, Cabrol C: Adjustment of cardiac output to step exercise in heart transplant recipients. Z. Kardiol. 83: Supp. 3, 103–109 (1994)
Grassi B, Marconi C, Meyer M, Cerretelli P: Gas exchange and cardiovascular kinetics upon different exercise protocols in heart transplant recipients. J. Appl. Physiol. 82, 1952–1962 (1997)
Goldberger AL, West B: Chaos in physiology. In: Chaos in Biological Systems. AV Holden, H Degn, LF Olsen (eds.), Plenum, New York, pp. 1–5 (1987)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Basel AG
About this chapter
Cite this chapter
Meyer, M. et al. (1998). Dynamical Analysis of Heartbeat Interval Time Series After Cardiac Transplantation. In: Losa, G.A., Merlini, D., Nonnenmacher, T.F., Weibel, E.R. (eds) Fractals in Biology and Medicine. Mathematics and Biosciences in Interaction. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8936-0_10
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8936-0_10
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9834-8
Online ISBN: 978-3-0348-8936-0
eBook Packages: Springer Book Archive