Improved computer-implemented tools for use in modeling/simulating spatial charge distributions for electrophysiological systems are provided. The improvements are in three areas: (1) the use of solid angles to calculate quantities of free charge and/or bound charge in calculation cells and/or the movement of quantities of free charge across one or more faces of a calculation cell; (2) the use of flattened calculations cells having only two faces with substantial areas as seen from the free charge and/or the bound charge of the electrophysiological system; and (3) the use of at least two spatial charge distributions, specifically, at least one for bound charge and at least one for free charge, so as to include the effects of relative dielectric constants greater than 1.0 for part or all of an electrophysiological system. The three improvements can be used individually or in combinations.