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1.1 Bioelectric Volume Conductors

A general volume conductor can be defined as a region of volume, , which has conductivity, , and permitivity, , in which resides a source current, , where the V signifies per-unit volume. Solving a volume conductor problem means finding expressions for the electric, , and potential, , fields everywhere within the volume, , and/or on one of the bounded surfaces, . While not unique to biophysics, a property that provides one with significant challenges, is the complexity of the domain, , which is subdivided into several sub-domains, each with different conductivity. In some cases, these inhomogeneous regions are anisotropic (e.g. causing the field to vary with direction).

The bioelectric current sources, , arise from excitable cells undergoing an activation process. Activation of cardiac tissue, for example, can be characterized as the process in which cells undergo rapid depolarization (e.g. when movement of ions across the cell membrane results in inactivation of electrical charges and a drop in potential; see [7,8] for more details). The depolarization process causes a propagation of excitation waves to move through the myocardium (the muscular layer of the heart); these waves in turn produce an extracellular potential field, . This potential field can be characterized by the geometry and conductivity of the volume conductor, and by the distance from, orientation to, and intensity of the source current, .