Electric potential in three-dimensional electrically syncytial tissues

✍ Scribed by A. Peskoff

• Publisher: Springer
• Year: 1979
• Tongue: English
• Weight: 854 KB
• Volume: 41
• Category: Article
• ISSN: 1522-9602
• DOI: 10.1016/s0092-8240(79)80031-2

✦ Synopsis

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 Pi. The interdigitated extracellular space is treated as a second continuum of resistivity Pc, occupying the same overall volume, coupled to the first via the resistance R m and capacitance C 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 syneytium the potential for a step function source is obtained in terms of error functions. For a spherical syncytium of radius a, bounded by a membrane with surface resistance Ra, and capacitance Ca, expansions are obtained in spherical harmonics and spherical Bessel functions. For =p~a/R, and ~=Pi/Pe 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.