THE DEVELOPMENT OF MATHEMATICAL-MODELS OF THE HEART

Mathematical modelling of cardiac cell activity has developed in rough ly ten-year cycles over the last 30 years, with each major phase of mo delling being focused around particular experimental questions. The fi rst phase (around 1962) was based on the dissection of the K-currents in heart cells into the inward rectifier and delayed current component s. The second phase (1975) was based on identifying separate slow curr ent mechanisms in the plateau and pacemaker ranges of potential and on the discovery of the calcium current in cardiac muscle. The most rece nt phase (starting with the 1985 DiFrancesco-Noble model) was based on the identification of the hyperporarization-activated pacemaker curre nt and on the electrogenicity of sodium-calcium exchange. Although eac h of these developments has depended on advances in experiment method, it is also true that each has also needed to theorize ahead of the ex periment work. There is, therefore, a bi-directional interaction betwe en theory and experiment. Sometimes experimental work leads, sometimes the theoretical work does so. A major use of such models in the case of cardiac cells is their incorporation into integrative studies of ho w large networks of cardiac cells interact to produce normal and abnor mal rhythms. This work has received a major boost from the introductio n of massively parallel computers that provide the required speed and capacity. Already, models of networks of sinus node and atrial cells h ave been constructed.