Prediction of magnetically induced electric fields in biological tissue

There are many potential medical applications in which it is desirable to noninvasively induce electric fields. One such application that serves as the backdrop of this work is that of stimulating neurons in the brain. The magnetic fields necessary must be quite high in magnitude, and fluctuate rapidly in time to induce the internal electric fields necessary for stimulation. Attention is focused on the calculation of the induced electric fields commensurate with rapidly changing magnetic fields in biological tissue. The problem is not a true eddy current problem in that the magnetic fields induced do not influence the source fields. Two techniques are introduced for numerically predicting the fields, each employing a different gauge for the potentials used to represent the electric field. The first method employs a current vector potential (analogous to A in classical magnetic field theory where DEL x A = B) and is best suited to two-dimensional (2-D) models. The second represents the electric field as the sum of a vector plus the gradient of a scalar field; because the vector can be determined quickly using Biot Savart (which for circular coils degenerates to an efficient evaluation employing elliptic integrals), the numerical model is a scalar problem even in the most complicated three dimensional geometry. These two models are solved for the case of a circular current carrying coil near a conducting body with sharp corners.