Mixing dynamics of heart rate variability

The theoretical Erlang distribution of the k -fold Poincaré return time of a mixing dynamical system is a very good fit of the experimental RR histograms of normal subjects. From this perspective, a heartbeat is emitted when the state of the attractor has returned k consecutive times to some finite region of the phase space of an abstract dynamical system that generates the RR sequence. The higher frequency, k times that of normal heartbeats is hypothesized to be related to the synchronization of the array of pacemaker cells in the SA node. For arrhythmia patients, the RR histogram deviates from the Erlang distribution, significantly to the point that it is bimodal. In this case, the distribution can be fitted with the weighted average of an Erlang and another distribution, revealing that the heart in arrhythmia cases operates near the boundary between a mixing attractor and a more complicated one.