Predicting clinical physiology: A Markov chain model of heart rate recovery after spontaneous breathing trials in mechanically ventilated patients

Yan Lu, Anton Burykin, Michael W. Deem, Timothy G. Buchman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Analysis of heart rate (HR) dynamics before, during, and after a physiologic stress has clinical importance. For example, the celerity of heart rate recovery (HRR) after a cardiac stress test (eg, treadmill exercise test) has been shown to be an independent predictor of all-cause mortality. Heart rate dynamics are modulated, in part, by the autonomic nervous system. These dynamics are commonly abstracted using metrics of heart rate variability (HRV), which are known to be sensitive to the influence of the autonomic nervous system on HR. The patient-specific modulators of HR should be reflected both in the response to stress as well as in the recovery from stress. We therefore hypothesized that the patient-specific HR response to stress could be used to predict the HRR after the stress. We devised a Markov chain model to predict the poststress HRR dynamics using the parameters (transition matrix) calculated from HR data during the stress. The model correctly predicts the exponential shape of poststress HRR. This model features a simple analytical relationship linking poststress HRR time constant (Toff) with a standard measure of HRV, namely the correlation coefficient of the Poincaré plot (first return map) of the HR recorded during the stress. A corresponding relationship exists between the time constant (Ton) of R-R interval decrease at the onset of stress and the correlation coefficient of the Poincaré plot of prestress R-R intervals. Consequently, the model can be used for the prediction of poststress HRR using the HRV measured during the stress. This direct relationship between the event-to-event microscopic fluctuations (HRV) during the stress and the macroscopic response (HRR) after the stress terminates can be interpreted as an instance of a fluctuation-dissipation relationship. We have thus applied the fluctuation-dissipation theorem to the analysis of heart rate dynamics. The approach is specific neither to cardiac physiology nor to transitions between mechanical and free ventilation as a specific stress. It may therefore have wider applicability to physiologic systems subject to modest stresses.

Original languageEnglish
Pages (from-to)347-361
Number of pages15
JournalJournal of Critical Care
Issue number3
StatePublished - Sep 2009
Externally publishedYes


  • Fluctuation-dissipation theorem
  • Heart rate recovery
  • Heart rate variability
  • Markov chain
  • Mechanical ventilation
  • Physiologic stress
  • Poincaré plot
  • Spontaneous breathing trial


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