Dynamical Analysis of Heartbeat Interval Time Series After Cardiac Transplantation

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


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.


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.


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Copyright information

© Springer Basel AG 1998

Authors and Affiliations

  • Michael Meyer
    • 1
    • 3
    Email author
  • 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

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