THEORETICAL CARDIOLOGY: FROM MATHEMATICAL TO QUALITATIVE MODELS

Abstract

A central concern in simulation studies is the adequation, or inadequation, of a designed model with respect to its intended goal. Models of cardiac electrical activity may differ in complexity, level of description and representation. Depending on the events to be be simulated, analytical, cellular automatas and qualitative models can be used. Their advantages and shortcomings can be put forth by comparing the space and time complexities, and if factors clinically relevant for studying arrhythmias and ischemias are taken into account in the respective models. In this paper, the factors under scrutiny are those characterizing impulse formation and conduction. If and how they are represented and computed constitutes a means of comparison between the models. The simplifying assumptions built into each can thus be put forth. Through illustrative examples, we then show that qualitative models can assume the explanatory and a predictive role usually devolved to numerical models. Such models can be used as a primer to quantification in a multi-stage process. A possibly useful development would be to integrate the analytical, cellular and qualitative models within a single computational framework. Central to this task is qualification. All piece of knowledge that is implicit in the mathematical or procedural representations has to be made explicit. Semantic links can thereafter be established between the models. This knowledge could be the starting point of a system emulating the reasoning of a theoretician working at different levels of detail. Its role would be to help researchers select, instantiate and interpret results of their most detailed cellular automata and/or analytical models.