Analytical Solution for the Forward Problem of Magnetic Induction Tomography with Multi-layer Sphere Model

A 4-layer sphere model of human head was built for the forward problem of Magnetic Induction Tomography(MIT). The layers represent the brain, the CFS, the skull, and the scalp, respectively. Helmholtz equation in the spherical coordinates was constructed as control equation, and the vector magnetic potential was taken as a variable, the Variable Separation Method(VSM) was used to solve the equation companying with the boundary and interface conditions. The eddy current distribution in the model was obtained. As a result, the contour line of the eddy current field was plotted, the influence of the frequency to the induced voltage was analyzed. The simulation results demonstrate that this analytical method is validated in solving the forward problem of magnetic induction tomography. It may be used as a fast calculation method to generate the sensitivity matrix of the MIT inverse problem.