Polarization of a spherical cell in a non-uniform electric field: transient response and comparison with polarization in a uniform field

Polarization of cells by extracellular fields is relevant to neural stimulation, cardiac pacing, and cardiac defibrillation. When electrodes are positioned close to cells the electric field is non-uniform, but in many cases has been assumed to be uniform. We solved analytically for the transmembrane voltage (φ_m) generated in a spherical cell by a non-uniform extracellular field, as would arise from a point electrode. φ_m reached its steady state value with a time constant much less than the membrane time constant in both uniform and non-uniform fields. The magnitude of φ_m in the hemisphere of the cell toward the electrode was larger than in the other hemisphere under the non-uniform field, while symmetric polarization occurred under the uniform field. The magnitude of the differences in φ_m generated by the uniform and nonuniform fields decreased as the distance between the cell and electrode increased, and was less than 10% for electrode to cell distances greater than 10 times the cell diameter. The specific polarization generated by a non-uniform field should be considered for small electrode to cell distances.