A three-dimensional finite element method for computing magnetically induced currents in tissues

Time-varying magnetic fields used both in nerve stimulation and in magnetic resonance imaging induce electric fields and currents in conducting tissues. Knowledge of the spatial distributions of these induced electric 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 magnetic fields. In this paper, we present a finite element solution method that can be used to compute the induced electric field and current density distributions in tissues when the time rate of change of the applied magnetic field is low enough that the propagation time and magnetic diffusion time in the conductive tissues are negligible, and when the 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 nonuniform magnetic fields. Our solutions for a homogeneous isotropic conductive slab and a homogeneous anisotropic conductive slab exposed to a uniform magnetic field are in good agreement with analytical results. The finite element approach enables us to include conductive inhomogeneity and anisotropy. I allows us to closely model the complex geometry of the tissues. Therefore, it is well suited for realistic models of the conductive anatomy of biological tissues