Abstract
The problem of calculating the potential induced in an electrical syncytium by a point source of current is studied. The interiors of the many interconnected cells are treated as one continuum with resistivity ρ i . The interdigitated extracellular space is treated as a second continuum of resistivity ρ e , occupying the same overall volume, coupled to the first via the resistanceR m and capacitanceC m of the cell membranes. The intra- and extracellular potentials are then solutions to a pair of coupled partial differential equations. The equations are uncoupled, yielding a cable equation for the transmembrane potential and a Poisson equation for a second auxiliary potential. For an unbounded syncytium the potential for a step function source is obtained in terms of error functions. For a spherical syncytium of radiusa, bounded by a membrane with surface resistanceR a, and capacitanceC a, expansions are obtained in spherical harmonics and spherical Bessel functions. For ɛ=ρ ia/R a and β=ρ i /ρ e small, an asymptotic expansion of the potential is developed. The results are compared to earlier results for a spherical cell as well as to microelectrode measurements of the lens of the eye.
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Peskoff, A. Electric potential in three-dimensional electrically syncytial tissues. Bltn Mathcal Biology 41, 163–181 (1979). https://doi.org/10.1007/BF02460876
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DOI: https://doi.org/10.1007/BF02460876