Modeling of cardiac rhythms. A signal-processing perspective

The authors describe their perspective on the modeling of cardiac rhythms as a component of cardiac arrhythmia signal-processing algorithms. They emphasize that these models are for a specific end purpose and that the aspects of cardiac behavior that are captured by the models are only those relevant for the development of the signal-processing algorithms. The approach is to use statistics to describe ranges of cardiac behavior that share some common feature with respect to the purpose of the signal processing. The statistical approach has the advantage that, coupled with a statistical performance criterion, it specifies an optimal signal-processing algorithm. These optimal algorithms are often computationally intractable, however, especially for real-time use in instruments. Approximations are therefore crucial. The mathematical form of the model is then important since, even if two forms generate identical statistics, the approximations that are natural in different forms can be quite different. Two different mathematical formulations are described--stochastic Petri nets and interacting Markov chains--and the different types of approximately optimal signal-processing algorithms that are natural in these two frameworks are discussed.