Three-dimensional finite element solution for biopotentials: erythrocyte in an applied field

The use of the finite-element method in the analysis of bioelectric phenomena is demonstrated. The problem studied is three-dimensional steady current flow around an erythrocyte in an extracellular medium. The finite-element equations for the electrical field problem are derived and mesh generation and the use of a heat-conduction code for analysis are described. Spherical cell geometry, allowing an analytical solution, is also modeled to guide in mesh creation and error estimation for the case of erythrocyte geometry. The results are shown as contour plots of potential on the erythrocyte surface. The maximum transmembrane potential calculated for the erythrocyte is 22% lower than that of the sphere, a significant finding since spherical geometry is often used in studies involving the effect of applied electrical fields on cells.