A GENERALIZED ACTIVATING FUNCTION FOR PREDICTING VIRTUAL ELECTRODES IN CARDIAC TISSUE

To fully understand the mechanisms of defibrillation, it is critical t o know how a given electrical stimulus causes membrane polarizations i n cardiac tissue. We have extended the concept of the activating funct ion, originally used to describe neuronal stimulation, to derive a new expression that identifies the sources that drive changes in transmem brane potential. Source terms, or virtual electrodes, consist of eithe r second derivatives of extracellular potential weighted by intracellu lar conductivity or extracellular potential gradients weighted by deri vatives of intracellular conductivity. The full response of passive ti ssue can be considered, in simple cases, to be a convolution of this ' 'generalized activating function'' with the impulse response of the ti ssue. Computer simulations of a two-dimensional sheet of passive myoca rdium under steady-state conditions demonstrate that this source term is useful for estimating the effects of applied electrical stimuli. Th e generalized activating function predicts oppositely polarized region s of tissue when unequally anisotropic tissue is point stimulated and a monopolar response when a point stimulus is applied to isotropic tis sue. In the bulk of the myocardium, this new expression is helpful for understanding mechanisms by which virtual electrodes can be produced, such as the hypothetical ''sawtooth'' pattern of polarization, as wel l as polarization owing to regions of depressed conductivity, missing cells or clefts, changes in fiber diameter, or fiber curvature. In com paring solutions obtained with an assumed extracellular potential dist ribution to those with fully coupled intra-and extracellular domains, we find that the former provides a reliable estimate of the total solu tion. Thus the generalized activating function that we have derived pr ovides a useful way of understanding virtual electrode effects in card iac tissue.