The term virtual electrode was coined by Seymour Furman to explain the clinical observation of stimulation far from a chronically implanted pacemaker lead.41 Later, this term was adopted by investigators studying both pacing and defibrillation in parallel with a synonymous but more rigorously defined term activating function to designate the "driving force," which drives transmembrane potential in either a depolarizing (positive) or hyperpolarizing (negative) direction following an externally applied electric field. The bidomain equations (1)-(2) can be rewritten in terms of the transmembrane (Vm = ^ — ^e) and extracellular (^e) potentials:
V • ((<Ti + <Te)We) = —Io — V' (¿iVVm), (4)
During diastole, one can neglect the gradient of transmembrane potential in the left-hand side of (5) as well as the total transmembrane current. Therefore, the only source of transmembrane potential changes is the term in the right-hand side of (5), which is known as the generalized activating function:42'43
Quantitative investigation of virtual electrodes and the activating function started with the theoretical predictions of Sepulveda et al.,44 who demonstrated that a unipolar stimulus produces both positive and negative polarization in a two-dimensional syncytium. These positive and negative polarizations are induced by virtual cathodes and virtual anodes, respectively.45 The magnitude and location of positive and negative virtual electrodes depend on both the field configuration (^>e) and tissue structure (ai and ae).43
These findings explained the phenomenon of anodal stimulation, which had eluded investigators for many years. According to classical cable theory, anodal stimulation hyper-polarizes tissue and thus cannot bring about an action potential. However, experimentalists had long observed excitation as a result of anodal stimulation. The virtual electrode theory predicts that virtual anodes are accompanied by virtual cathodes; therefore, action potentials can arise from these regions.
Early theories of predicted efficacy of defibrillation shocks were entirely based on the minimum external voltage gradient (V^e). As evident from the definition of the activating function (6), voltage gradient (V^e), while important, is not the only source of membrane polarization. Tissue structure (ai and ae) may be just as important. Microscopic and macroscopic tissue heterogeneities play an important role by providing the substrate for virtual electrodes during defibrillation shocks. What remains to be determined is the relative contribution of different scales of heterogeneities to defibrillation. Some groups argue that microscopic cell-size heterogeneities play the major role,46 while other groups are convinced that large-scale heterogeneities are more important, because of the averaging effect of small-scale virtual electrodes by electrotonic interaction.47
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