Reconstruction of intra- and extra-neurite conductivity tensors via conductivity at Larmor frequency and DWI data patterns

Abstract

The developed magnetic resonance electrical properties tomography (MREPT) techniques visualize the internal conductivity distribution at Larmor frequency by measuring the B1 transceive phase data. In biological tissues, electrical conductivity is influenced by ion concentrations and mobility. To visualize the anisotropic conductivity tensor of biological tissues, we use the Einstein–Smoluchowski equation, which links the diffusion coefficient to particle mobility. By assuming a correlation between ion mobility and water diffusivity, we aim to decompose the internal isotropic conductivity at Larmor frequency into anisotropic conductivity tensors within the intra- and extra-neurite compartments. The multi-compartment spherical mean technique (MC-SMT), utilizing both high and low $b$-value diffusion-weighted imaging (DWI) data, characterizes the diffusion of water molecules within and across the intra- and extra-neurite compartments by analyzing the microstructural intricacies and the foundational architectural arrangement of the brain’s tissues. By analyzing the relationships between the measured DWI data, the microscopic diffusion signal, and the fiber orientation distribution function, we predict the DWI data for the intra- and extra-neurite compartments using spherical harmonic decomposition. Using the predicted DWI data for the intra- and extra-neurite compartments, we develop a conductivity tensor imaging method that operates specifically within the separated compartments. Human brain experiments, involving four healthy volunteers and a brain tumor patient, were performed to assess and confirm the reliability of the proposed method.