Analysis of bipolar external excitation of spherical tissue by spatially opposed current source and sink points

The recently increasing role in medical imaging that electrophysiology plays has spurned the need for its quantitative analysis at all scales-ions, cells, tissues, organs, etc.; so, here is presented a model of nerve tissue in a spherical volume excited by a point current source at one pole and a point current sink at the opposite pole. The sphere of tissue is described as an isotropic bidomain, consisting of the intra- and extra-cellular regions and the membrane that separates them, and is immersed in an infinite isotropic conductive bath. The system of coupled differential equations is solved by redefining the domains to be in terms of a monodomain and a membrane. The solution takes the form of an infinite sum of the product of certain transcendental functions. The study concludes with a numeric example in which the boundary conditions are shown to be satisfied, validating this analysis, paving the way for more sophisticated models of excitable tissue.