Dynamical Analysis of Heartbeat Interval Time Series After Cardiac Transplantation

  • Michael Meyer
  • C. Marconi
  • G. Ferretti
  • R. Fiocchi
  • F. Mamprin
  • J. E. Skinner
  • P. Cerretelli
Part of the Mathematics and Biosciences in Interaction book series (MBI)

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.

Keywords

Autonomic Nervous System Chaotic Dynamic Cardiac Transplantation Heart Transplant Recipient Brownian Noise 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    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)PubMedCrossRefGoogle Scholar
  2. [2]
    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)CrossRefGoogle Scholar
  3. [3]
    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)PubMedCrossRefGoogle Scholar
  4. [4]
    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)PubMedCrossRefGoogle Scholar
  5. [5]
    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)PubMedCrossRefGoogle Scholar
  6. [6]
    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)PubMedCrossRefGoogle Scholar
  7. [7]
    Goldberger AL, Rigney DR, West BJ: Chaos and fractals in human physiology. Sci. Am. 262, 42–49 (1990)PubMedCrossRefGoogle Scholar
  8. [8]
    Kitney RI, Rompelman O: The Study of Heart-Rate Variability. Oxford University Press, Oxford (1980)Google Scholar
  9. [9]
    Babloyantz A, Desthexhe A: Is the heart a periodic oscillator? Biol Cybern. 58, 203–211 (1988)PubMedCrossRefGoogle Scholar
  10. [10]
    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)CrossRefGoogle Scholar
  11. [11]
    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)PubMedCrossRefGoogle Scholar
  12. [12]
    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)PubMedCrossRefGoogle Scholar
  13. [13]
    Skinner JE, Molnar M, Vybiral T, Mitra M: Application of chaos theory to biology and medicine. Integr. Physiol. Behav. Sci. 27, 39–53 (1992)PubMedCrossRefGoogle Scholar
  14. [14]
    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)PubMedCrossRefGoogle Scholar
  15. [15]
    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)PubMedGoogle Scholar
  16. [16]
    Grassberger P, Procaccia I: Measuring the strangeness of strange attractors. Physica 9D, 189–208)1983)Google Scholar
  17. [17]
    Farmer JD, Ott E, Yorke JA: The dimension of chaotic attractors. Physica D7, 53–180 (1983)Google Scholar
  18. [18]
    Glass L, Malta CP: Chaos in multi-looped negative feedback systems. J. Theor. Biol. 145, 217–223 (1990)PubMedCrossRefGoogle Scholar
  19. [19]
    Liem LB, Dibiase A, Schroeder JS: Arrythmia and clinical electrophysiology of the transplanted human heart. Semn. Thorac. Cardiovasc. Surg. 2, 271–278 (1990)Google Scholar
  20. [20]
    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)PubMedGoogle Scholar
  21. [21]
    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)CrossRefGoogle Scholar
  22. [22]
    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)PubMedCrossRefGoogle Scholar
  23. [23]
    Cerretelli P, Marconi C, Meyer M, Ferretti G, Grassi B: Gas exchange kinetics in heart transplant recipients. Chest 101, 199S-205S (1992)PubMedGoogle Scholar
  24. [24]
    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)Google Scholar
  25. [25]
    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)Google Scholar
  26. [26]
    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)PubMedGoogle Scholar
  27. [27]
    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)PubMedGoogle Scholar
  28. [28]
    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)Google Scholar

Copyright information

© Springer Basel AG 1998

Authors and Affiliations

  • Michael Meyer
    • 1
    • 3
  • C. Marconi
    • 2
  • G. Ferretti
    • 1
  • R. Fiocchi
    • 4
  • F. Mamprin
    • 4
  • J. E. Skinner
    • 5
  • P. Cerretelli
    • 1
    • 2
  1. 1.Département de PhysiologieCMUGenèveSwitzerland
  2. 2.Istituto di Tecnologie Biomediche AvanzateCNRMilanoItaly
  3. 3.Department of PhysiologyMax Planck Institute for experimental MedicineGöttingenGermany
  4. 4.Ospedali RiunitiBergamoItaly
  5. 5.Totts Gap LaboratoriesBangorUSA

Personalised recommendations