On Modelling Electrical Conductivity of the Cerebral White Matter

The conductivity, in general, of the brain tissues is a characteristic key of functional cerebral changes. White matter electric conductivity appears to be extremely anisotropic, so a tensor (matrix) is needed to describe it. Traditional methods of imaging brain electrical properties fail to capture it and required the interpolation of the diffusion matrix. The electrochemical model is suitable for analysis, while, on the other hand, the volume fraction model is suitable for studying the effect of white matter structural changes in relation to electrical conductivity. It adopts a relevant algorithm, based upon a linear conductivity-to-diffusivity relationship and a volume constraint, respectively. It incorporates the effects of the partial volume of the cerebrospinal fluid and the structure of the neuronal fiber crossing, which was not achieved by the existing algorithms, accomplishing a more accurate estimation of the anisotropic conductivity of the white matter. Diffusion matrix imaging is a powerful noninvasive method for characterizing neuronal tissue in the human brain. The ultimate goal is to study and draw appropriate conclusions, regarding the molecule diffusion in the brain under normal physiological conditions and the changes that occur in development, diseases, and aging. The ability to measure the electrical conductivity of brain tissues in a noninvasive way also helps in characterizing endogenous currents by measuring the associated electromagnetic fields.