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.