Anisotropic conductivity tensor by analyzing diffusion tensor for electrical brain stimulation (EBS)

Electrical brain stimulation (EBS) is a promising medical treatment method for brain neurological disorders through the direct or indirect excitation by injecting an electric current. At present, it is difficult to directly measure the distribution of the electric current delivered by electrodes inside tissues. By applying low-frequency (<1 kHz) external electrical brain stimulation (EBS), the lowfrequency conductivity around the cells is uneven due to asymmetric cellular structures. We propose a method of electrical property imaging using the measured one component magnetic flux density by EBS and diffusion tensor imaging (DTI). The low-frequency electrical anisotropic conductivity tensor can be decomposed into the ion concentration and the mobility tensor of charge carriers. By analyzing the role of the diffusion tensor, we reconstruct the apparent anisotropic tensor by EBS using the z -component of measured magnetic flux density data and the estimated diffusion tensor. Using only the measured z -component of magnetic flux density, the orthotropic conductivity tensor can be approximately recovered. The orthotropic conductivity tensor is not exact, but only reflects the extracellular space (ECS) effects. By comparing the components of orthotropic tensor and diffusion tensor, we stably determine a scale factor which primarily reflects the concentration of total ions in the extracellular space (ECS). Animal experiments verify that the proposed method recovers the anisotropic conductivity tensor which can visualize electrical properties during EBS of the brain. A direct reconstruction method for the apparent anisotropic conductivity tensor imaging during EBS was proposed to analyze unknown effects to brain tissue.