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.

中文翻译：

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短期内心脏调节系统的内在动力学：从实验到建模

我们讨论与心脏功能随机建模相关的开放性问题。这项工作基于在没有呼吸扰动的情况下对心率变异性 (HRV) 的动态进行的实验研究。我们首先通过随机游走方法框架内的 HRV 分析来考虑短时间尺度上的心脏控制系统。我们的实验表明，不到一分钟的时间尺度上的 HRV 采取自由扩散的形式，接近布朗运动，可以将其描述为具有平稳增量的非平稳过程。其次，我们考虑对控制系统的状态进行建模的逆问题，以便重现实验观察到的 HRV 统计数据。我们讨论了一些简单的玩具模型，并确定了心脏动力学建模的开放问题。