Computationally efficient bioelectric field modeling and effects of frequency-dependent tissue capacitance

Standard bioelectric field models assume that the tissue is purely resistive and frequency independent, and that capacitance, induction, and propagation effects can be neglected. However, real tissue properties are frequency dependent, and tissue capacitance can be important for problems involving short stimulation pulses. A straightforward interpolation scheme is introduced here that can account for frequency-dependent effects, while reducing runtime over a direct computation by several orders of magnitude. The exact Helmholtz solution is compared to several approximate field solutions and is used to study neural stimulation. Results show that frequency-independent tissue capacitance always acts to attenuate the stimulation pulse, thereby increasing firing thresholds, while the dispersion effects introduced by frequency-dependent capacitance may decrease firing thresholds.