  We discuss open problems related to the stochastic modeling of cardiac
function. The work is based on an experimental investigation of the dynamics of
heart rate variability (HRV) in the absence of respiratory perturbations. We
consider first the cardiac control system on short time scales via an analysis
of HRV within the framework of a random walk approach. Our experiments show
that HRV on timescales of less than a minute takes the form of free diffusion,
close to Brownian motion, which can be described as a non-stationary process
with stationary increments. Secondly, we consider the inverse problem of
modeling the state of the control system so as to reproduce the experimentally
observed HRV statistics of. We discuss some simple toy models and identify open
problems for the modelling of heart dynamics.
