The Effect of Variation in Permittivity of Different Tissues on Induced Electric Field in the Brain during Transcranial Magnetic Stimulation

Estimation of electric field in the brain during Transcranial Magnetic Stimulation (TMS) requires knowledge of the electric property of brain tissue. Grey and white matters have unusually high relative permittivities of $\sim$ 10$^{6}$ at low frequencies. However, relative permittivity of cerebrospinal fluid is $\sim$ 10$^{2}$. With such a variation it is necessary to consider the effect of boundaries. A model consisting of 2 hemispheres was used in the model with the properties of one hemisphere kept constant at $\sigma_{1}=$0.1Sm$^{-1}$ and $\varepsilon_{r1} = $10 while the properties of the second hemisphere were changed kept at $\sigma_{2}=$0.1Sm$^{-1}$ to 2Sm$^{-1}$ and $\varepsilon_{r2} =$ 10$^{2}$ to 10$^{5}$. A 70 mm diameter double coil was used as the source of the magnetic field. The amplitude of the current in the coil was 5488 A at a frequency of 2.9 kHz. The results show that the electric field, \textbf{E} induced during magnetic stimulation is independent of the relative permittivity, $\varepsilon_{r}$ and varies with the conductivity. Thus the variation in \textbf{E}, calculated with homogeneous and heterogeneous head models was due to variation in conductivity of the tissues and not due to variation in permittivities.