Recent experimental measurements demonstrated that the transmembrane potential induced in cardiac muscle by defibrillation-strength shocks has a complex spatial pattern that cannot be explained with traditional core- conductor based models. To fill this gap in theoretical understanding, this project will develop a model of shock-induced transmembrane potential that is applicable specifically to strong electric fields. The model will test the hypotheses that under strong fields, transmembrane potential should be viewed not as arising from a single mechanism hut as a joint effect of many, and that it contains a significant contribution from the active response of the membrane.
The Specific Aims of the proposed work are: (1) Derive a unified model that includes all mechanisms contributing to the shock-induced transmembrane potential. (2) For each mechanism, establish the rules that govern its behavior and determine its sensitivity to experimental conditions. (3) Modify a model of the membrane dynamics to be applicable to strong fields by incorporating the active response caused by the polarization of individual cells. (4) Combine the models developed in Specific Aims 1 and 3 to form a fully excitable, unified model that is applicable to the myocardium under strong electric fields. (5) Verify this model by comparing its predictions with direct measurements of shock-induced transmembrane potential. The unified model will describe the response of the myocardium on the tissue level. To assure its consistency with the cellular-level behavior, the model will be derived from cellular-level differential equations using a formal homogenization method. The rules governing separate mechanisms will be expressed as differential equations extracted analytically from the unified model. The model of cardiac dynamics for strong electric fields will follow a Hodgkin-Huxley formalism, but instead of describing the physiological state of a space-clamped membrane, the governing equations will contain macroscopic state variables that describe the overall physiological state of entire clusters of cells. Rate coefficients will be determined from computer simulations involving realistic models of cardiac membrane. The model will be verified by performing detailed computer simulations of experimental conditions under which the shock- induced transmembrane potential was measured and by comparing the results. This research will provide analytical tools to predict passive and active response of the heart to defibrillation-strength shocks which will lead to better understanding of the mechanism of defibrillation, to improvements in therapy, and to reduced mortality from sudden cardiac death.
