Statistical Properties Of The Interbeat Interval Cascade In Human Hearts

Statistical properties of interbeat intervals cascade in human hearts are evaluated by considering the joint probability distributionP (Δx2, τ2; Δx1, τ1)for two interbeat incrementsΔx1andΔx2of different time scales τ1and τ2. We present evidence that the conditional probability distributionP (Δx2, τ2| Δx1, τ1)may be described by a Chapman–Kolmogorov equation. The corresponding Kramers–Moyal (KM) coefficients are evaluated. The analysis indicates that while the first and second KM coefficients take on well-defined and significant values, the higher-order coefficients in the KM expansion are small. As a result, the joint probability distributions of the increments in the interbeat intervals are described by a Fokker–Planck equation, with the first two KM coefficients acting as the drift and diffusion coefficients. The method provides a novel technique for distinguishing two classes of subjects, namely, healthy ones and those with congestive heart failure, in terms of the drift and diffusion coefficients which behave differently for two classes of the subjects.