Intracellular Biopotentials During Static Extracellular Stimulation

Two properties of the intracellular potentials and electric fields resulting from static extracellular stimulation are obtained for arbitrarily shaped cells. First, the values of intracellular potential are shown to be bounded by the maximum and minimum values of extracellular potential on the surface of the cell. Second, the volume average of the magnitude of intracellular electric field is shown to have an upper bound given by the ratio of the magnitude of the largest extracellular potential difference on the surface of the cell to a generalized length constant λ = [σintraVcell/(σmembAcell)]1/2, where Vcell and Acell are the volume and surface area of the cell, σintra is the intracellular conductivity (reciprocal ohms per centimeter), and σmemb is the membrane conductivity (reciprocal ohms per square centimeter). The use of the upper bound on the volume average of the magnitude of intracellular electric field as an estimate for intracellular isopotentiality is discussed and the use of the generalized length constant for electrically describing arbitrary cells is illustrated for cylindrical- and spheroidal-shaped cells