Magnetic stimulation for non-homogeneous biological structures

Background: Magnetic stimulation has gained relatively wide application in studying nervous system structures. This technology has the advantage of reduced excitation of sensory nerve endings, and hence results in quasi-painless action. It has become clinically accepted modality for brain stimulation. However, theoretical and practical solutions for assessment of induced current distribution need more detailed and accurate consideration. Some possible analyses are proposed for distribution of the current induced from excitation current contours of different shape and disposition. Relatively non-difficult solutions are shown, applicable for two- and three-dimensional analysis. Methods: The boundary conditions for field analysis by the internal Dirichlet problem are introduced, based on the vector potential field excited by external current coils. The feedback from the induced eddy currents is neglected. Finite element modeling is applied for obtaining the electromagnetic fields distribution in a non-homogeneous domain. Results: The distributions were obtained in a non-homogeneous structure comprised of homogeneous layers. A tendency was found of the induced currents to follow paths in lower resistivity layers, deviating from the expected theoretical course for a homogeneous domain. Current density concentrations occur at the boundary between layers, suggesting the possibility for focusing on, or predicting of, a zone of stimulation. Conclusion: The theoretical basis and simplified approach for generation of 3D FEM networks for magnetic stimulation analysis are presented, applicable in non-homogeneous and non-linear media. The inconveniences of introducing external excitation currents are avoided. Thus, the possibilities are improved for analysis of distributions induced by time-varying currents from contours of various geometry and position with respect to the medium.