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A point-process model of human heartbeat intervals: new definitions of heart rate and heart rate variability

Neuroscience Statistics Research Laboratory, Department of Anesthesia and Critical Care, Massachusetts General Hospital, and Division of Health Sciences and Technology, Harvard Medical School/Massachusetts Institute of Technology, Boston, Massachusetts

Submitted 23 May 2003 ; accepted in final form 12 September 2004

Heart rate is a vital sign, whereas heart rate variability is an important quantitative measure of cardiovascular regulation by the autonomic nervous system. Although the design of algorithms to compute heart rate and assess heart rate variability is an active area of research, none of the approaches considers the natural point-process structure of human heartbeats, and none gives instantaneous estimates of heart rate variability. We model the stochastic structure of heartbeat intervals as a history-dependent inverse Gaussian process and derive from it an explicit probability density that gives new definitions of heart rate and heart rate variability: instantaneous R-R interval and heart rate standard deviations. We estimate the time-varying parameters of the inverse Gaussian model by local maximum likelihood and assess model goodness-of-fit by Kolmogorov-Smirnov tests based on the time-rescaling theorem. We illustrate our new definitions in an analysis of human heartbeat intervals from 10 healthy subjects undergoing a tilt-table experiment. Although several studies have identified deterministic, nonlinear dynamical features in human heartbeat intervals, our analysis shows that a highly accurate description of these series at rest and in extreme physiological conditions may be given by an elementary, physiologically based, stochastic model.

tilt table; inverse Gaussian; time-rescaling theorem; Kolmogorov-Smirnov test; autonomic regulation