Effects of the electrical double layer and dispersive tissue properties in a volume conduction model of deep brain stimulation

Fitting the determined impedance in the guinea pig inner ear to randles circuit using square error minimization in the range of 100 Hz to 50 kHz

OBJECTIVE

A number of lumped and distributed parameter models of the inner ear have been proposed in order to improve the vestibular implant stimulation. The models should account for all significant physical phenomena influencing the current propagation: electrical double layer (EDL) and medium polarization. The electrical properties of the medium are reflected in the electrical impedance, therefore the aim of this study was to measure the impedance in the guinea pig inner ear and construct its equivalent circuit.

APPROACH

The electrical impedance was measured from 100 Hz to 50 kHz between a pair of platinum electrodes immersed in saline solution using sinusoidal voltage signals. The Randles circuit was fitted to the measured impedance in the saline solution in order to estimate the EDL parameters (C, W, and R_ct) of the electrode interface in saline. Then, the electrical impedance was measured between all combinations of the electrodes located in semicircular canal ampullae and the vestibular nerve in the guinea pig in vitro. The extended Randles circuit considering the medium polarization (R_i, R_e, C_m) together with EDL parameters (C, R_ct) obtained from the saline solution was fitted to the measured impedance of the guinea pig inner ear. The Warburg element was assumed negligible and was not considered in the guinea pig model.

MAIN RESULTS

For the set-up used, the obtained EDL parameters were: C=27.09*10^-8F, R_ct=18.75 kΩ. The average values of intra-, extracellular resistances, and membrane capacitance were R_i=4.74 kΩ, R_e=45.05 kΩ, C_m=9.69*10^-8F, respectively.

SIGNIFICANCE

The obtained values of the model parameters can serve as a good estimation of the EDL for modelling work. The EDL, together with medium polarization, plays a significant role in the electrical impedance of the guinea pig inner ear, therefore, they should be considered in electrical conductivity models to increase the credibility of the simulations.

Contribution of dielectric dispersions to voltage waveforms arising from electrical stimulation

This study presents an analysis of the effect of incorporating a subset of the complete set of dielectric dispersions in electric field models of implanted electrical stimulation. An analytic volume conductor model was used to determine the voltage waveform at a distance of 5mm from a point current stimulus for 17 different biological tissues. The RMS error of the voltage waveform resulting from the incorporation of a subset of all poles with respect to the voltage waveform resulting from the incorporation of the complete set of dispersive poles was calculated. The stimulus amplitude necessary to elicit action potential propagation in a myelinated mammalian nerve fibre in each of the dispersive models was also determined using a multi-compartment cable axon model. It was found that, for all tissues, removal of dispersions with pole frequencies greater than 1 MHz had a negligible effect on the threshold stimulation amplitude, suggesting that they may be neglected when constructing volume conductor models of electrical stimulation. However, removal of low-frequency dispersions below 1 MHz resulted in greater reductions in the threshold stimulus amplitudes necessary for activation of axons, with errors of up to 86% observed.

Effect of dispersive conductivity and permittivity in volume conductor models of deep brain stimulation

The aim of this study was to examine the effect of dispersive tissue properties on the volume-conducted voltage waveforms and volume of tissue activated during deep brain stimulation. Inhomogeneous finite-element models were developed, incorporating a distributed dispersive electrode-tissue interface and encapsulation tissue of high and low conductivity, under both current-controlled and voltage-controlled stimulation. The models were used to assess the accuracy of capacitive models, where material properties were estimated at a single frequency, with respect to the full dispersive models. The effect of incorporating dispersion in the electrical conductivity and relative permittivity was found to depend on both the applied stimulus and the encapsulation tissue surrounding the electrode. Under current-controlled stimulation, and during voltage-controlled stimulation when the electrode was surrounded by high-resistivity encapsulation tissue, the dispersive material properties of the tissue were found to influence the voltage waveform in the tissue, indicated by RMS errors between the capacitive and dispersive models of 20%-38% at short pulse durations. When the dispersive model was approximated by a capacitive model, the accuracy of estimates of the volume of tissue activated was very sensitive to the frequency at which material properties were estimated. When material properties at 1 kHz were used, the error in the volume of tissue activated by capacitive approximations was reduced to -4.33% and 11.10%, respectively, for current-controlled and voltage-controlled stimulations, with higher errors observed when higher or lower frequencies were used.