Towards Automated Comprehension and Alignment of Cardiac Models at the System Invariant Level

The study of cardiac arrhythmias has spurred the development of models across a variety of formulations and scales and designed for different purposes, each with distinct configuration spaces. Nevertheless, these models should be able to exhibit equivalent behavior when their contexts overlap. Configuring models to both support this context equivalence and still exhibit intended behavioral characteristics can be challenging. Due to the complexity of this problem, automation can be desirable. We present a framework aimed at automating the comprehension and alignment of cardiac model behaviors. For model comprehension, we mine a set of properties (invariants) that a model with given configuration will exhibit when executed. Comprehension can be extended to model alignment: we perform comprehension of one model, and then mine a set of configurations for a second, each of which produces invariants aligned to the invariants of the first. The configuration spaces of the two models under study need not be related in any way; rather, the systems are compared by means of the system invariants that they each exhibit. We model system invariants as association rules, a well-studied representation used in the field of data mining. We apply our methodology to two one-dimensional models of cardiac tissue. One model is the well-known differential-equations-based Fenton-Karma model representing the electrophysiology of interconnected cardiac cells, while the other is a timed automaton representation of cardiac tissue designed to enable formal analysis. We demonstrate alignment of the models with respect to activation rates and path conductance. We expect this methodology can be generalized beyond cardiac models.