A 3-DIMENSIONAL FINITE-ELEMENT METHOD FOR COMPUTING MAGNETICALLY INDUCED CURRENTS IN TISSUES

Time-varying magnetic fields used both in nerve stimulation and in mag netic resonance imaging induce electric fields and currents in conduct ing tissues. Knowledge of the spatial distributions of these induced e lectric fields and currents in the tissues is very limited because of the complex geometry and inhomogeneous, anisotropic conductivities of the tissues, as well as the spatial nonuniformity of the applied magne tic fields. In this paper, we present a finite element solution method that can be used to Compute the induced electric field and current de nsity distributions in tissues when the time rate of change of the app lied magnetic field is low enough that the propagation time and magnet ic diffusion time in the conductive tissues are negligible, and when t he conduction current in the tissues is substantially larger than the displacement current. This finite element implementation is tested for some simple conductive models with both spatially uniform and nonunif orm magnetic fields. Our solutions for a homogeneous isotropic conduct ive slab and a homogeneous anisotropic conductive slab exposed to a un iform magnetic field are in good agreement with analytical results. Th e finite element approach enables us to include conductive inhomogenei ty and anisotropy. It allows us to closely model the complex geometry of the tissues. Therefore, it is well suited for realistic models of t he conductive anatomy of biological tissues.