An Electromagnetic Inverse Problem in the Medical Sciences

Most human tissue is heavily comprised of water and ions; which is dispersive of electromagnetic energy. The definitive goal of this research is to make an accurate determination of dielectric constants and conductivity at different given frequencies of living tissue from measurements outside of the human body. Previous studies used tissue samples or probing mechanisms, but these methods to deduce both the dielectric constant and conductivity values are not necessarily reproducible since the sample itself is not in its natural environment. In the future, the overall goal would be to illuminate the human body with a broad-band pulse of electromagnetic radiation. By doing so, one could measure the dielectric constants or conductivities throughout the body by accumulating reflected and/or transmitted signals. Thus may one deductively determine the electrical coefficients through the use of an inverse problem using the incident and scattered fields as a function of position within the body. The process and technique implemented in this study uses a frequency response function. The inversion process is non-unique unless both the relative permittivity and conductivity are presumed to be differentiable as functions of frequency. The results, as expected, for the dielectric constant are fairly in accord to the true expected value. However, the conductivity values display much variation at the larger ranges of frequency. This implies that the functions lose their authenticity as frequency is increased.