Regarding your project to model microwave radiation passing through an inhomogeneous body (human head), back in 1997 I corresponded with Le-Wei (Joshua) Li (unfortunately now deceased) of the Antennas & Scattering Lab & EM Research Group at the National University of Singapore regarding his paper A Spheroidal Vector Wave Function Analysis of Field and SAR Distributions in a Dielectric Prolate Spheroidal Human Head Model and, later, his book Spheroidal Wave Functions in Electromagnetic Theory.

Le-Wei used Mathematica and described his project as follows:

Primarily it is utilized in the analysis of airborne antenna radomes and antennas of the oblate and prolate shapes, as well as the interaction between human head (modeled as an inhomogenous spheroidal media) and a mobile phone where closed form solution of the electrical fields and specific absorption ratio (SAR) can be found.

The reason for my interest was that my MSc student, Peter Falloon, wrote his computational thesis on the Theory and Computation of the Spheroidal Harmonics with General Complex Arguments which, eventually, resulted in the built-in spheroidal functionality. Interestingly, Peter's thesis was submitted and examined as a series of Mathematica Notebooks.