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 (Φm) generated in a spherical cell by a non-uniform extracellular field, as would arise from a point electrode. Φm 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 Φm 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 Φm 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.
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机译：细胞外磁场对细胞的极化作用与神经刺激，心脏起搏和心脏除颤有关。当电极靠近细胞放置时，电场是不均匀的，但是在许多情况下，假定电场是均匀的。我们解析地解决了球形细胞中由点电极引起的非均匀细胞外电场产生的跨膜电压（Φm）。 Φ m 达到其稳态值，其时间常数远小于均匀和非均匀场中的膜时间常数。在非均匀电场下，电池半球中朝向电极的Φ m 的大小大于另一个半球中的Φ m 的大小，而在均匀电场下发生对称极化。均匀场和不均匀场产生的Φ m 的差异的大小随电池与电极之间距离的增加而减小，并且当电极与电池之间的距离大于电池的10倍时，其小于10％直径。对于较小的电极到单元的距离，应考虑由非均匀场产生的特定极化。
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