Analysis of temporal correlation in heart rate variability through maximum entropy principle in a minimal pairwise glassy model

Abstract

AbstractIn this work we apply statistical mechanics tools to infer cardiac pathologies over a sample of M patients whose heart rate variability has been recorded via 24 h Holter device and that are divided in different classes according to their clinical status (providing a repository of labelled data). Considering the set of inter-beat interval sequences $$\{\mathbf {r}(i) \} = \{ r_1(i), r_2(i), \ldots , \}$$ { r ( i ) } = { r 1 ( i ) , r 2 ( i ) , … , } , with $$i=1,\ldots ,M$$ i = 1 , … , M , we estimate their probability distribution $$P(\mathbf {r})$$ P ( r ) exploiting the maximum entropy principle. By setting constraints on the first and on the second moment we obtain an effective pairwise $$(r_n,r_m)$$ ( r n , r m ) model, whose parameters are shown to depend on the clinical status of the patient. In order to check this framework, we generate synthetic data from our model and we show that their distribution is in excellent agreement with the one obtained from experimental data. Further, our model can be related to a one-dimensional spin-glass with quenched long-range couplings decaying with the spin–spin distance as a power-law. This allows us to speculate that the 1/f noise typical of heart-rate variability may stem from the interplay between the parasympathetic and orthosympathetic systems.