Imaging the Electric Properties of Human Tissue with MRI

Abstract

Electric property（EP）imaging inside the human body has attracted considerable attention as a new modality for cancer diagnosis. This paper presents the mathematical foundation on an inverse problem to reconstruct the three-dimensional distribution of the electrical conductivity and permittivity of human tissue from radiofrequency magnetic fields measured using usual magnetic resonance scanners. First, the problem is formulated with Maxwellʼs equations. The conventional methods are then introduced: i）a standard method based on the assumption that the spatial changes of the electric properties are small, and ii）a finite-element-based method with no EP restrictions. However, it is shown that these methods are sensitive to measurement noise since it is necessary to compute the second-order derivatives of the measured magnetic field data. Finally, our proposed method is introduced based on which the electric properties at arbitrary positions inside the human body can be reconstructed in a closed form in terms of the first-order derivatives and integrals of the measured magnetic field data.