Simplified parametric models of the dielectric properties of brain and muscle tissue during electrical stimulation

Parametric models are commonly used to describe the dispersive dielectric properties of biological tissues. While distinct regions of dispersion have been identified, the relative contribution of each during electrical stimulation is unknown. This study quantified the contribution of individual poles in parametric models of brain and muscle dielectric properties during electrical stimulation. The effect on the extracellular voltage waveform and threshold current for nerve stimulation of selectively removing subsets of poles from Cole-Cole and Debye models was examined. Errors were introduced when dispersions below 100 kHz were removed in both brain and muscle tissue. Poles below 1 kHz influenced the amplitude of the extracellular voltage waveform and the predicted minimum stimulation current. Poles between 1 kHz and 100 kHz influenced the waveform shape, with a minor effect on stimulus amplitude. The results confirm that low frequency dispersion in conductivity and permittivity can fundamentally influence the electric field and neural response during stimulation and provide insight into the relative contribution of the different dispersive regimes. Furthermore, they provide justification for for simplifying parametric models of dielectric properties through the removal of high frequency poles above 100 kHz which could improve the efficiency of time-domain solvers for simulations involving time-varying or aperiodic stimuli as may be required for certain closed-loop stimulation paradigms.