Biological tissues dispersivity and power loss density in transcranial magnetic stimulation

Power loss density and energy converted into heat considering dispersive biological tissue was investigated in the framework of transcranial magnetic stimulation (TMS). The solutions were obtained by applying an analytic method of Eaton [1] and a finite-element method (FEM). A commercial available figure-of-8 coil with a biphasic current pulse operates as the source of excitation. The calculations were performed in the frequency domain by using 1000 complex harmonics at different frequencies in order to reconstruct the transient signal in the excitation coil. The displacement current density was taken into account to provide an accurate estimate of the total energy. The human head was modeled as a homogeneous isotropic dispersive volume conductor consisting of grey matter (GM). The dielectric properties of GM were calculated in dependence on the frequency by means of the Cole-Cole model from Gabriel et al. [2]. The induced electric field as well as the current density are compared against those obtained in the non-dispersive case. The results revealed an increased magnitude of the peak value of the current density by 22.3% compared to the non-dispersive case. However, the induced electric field was not influenced by tissues dispersivity. Finally it was shown that the frequency dependent biological tissue affects the time development of the power loss density but has only minor effects on the total energy converted into heat.