We discuss open problems related to the stochastic modeling of cardiacfunction. The work is based on an experimental investigation of the dynamics ofheart rate variability (HRV) in the absence of respiratory perturbations. Weconsider first the cardiac control system on short time scales via an analysisof HRV within the framework of a random walk approach. Our experiments showthat 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 processwith stationary increments. Secondly, we consider the inverse problem ofmodeling the state of the control system so as to reproduce the experimentallyobserved HRV statistics of. We discuss some simple toy models and identify openproblems for the modelling of heart dynamics.
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