Prediction of magnetically induced electric fields in biological tissue

Noninvasive magnetic stimulation of neurons in the brain can be realized by high-intensity rapidly changing magnetic fields. 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 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 the Biot-Savart rule (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.