Reconstruction of conductivity distribution of brain tissue from two components magnetic flux density

In this paper the recent Magnetic resonance electrical impedance imaging (MREIT) technique is used to image non-invasively the three-dimensional continuous conductivity distribution of the head tissues. With the feasibility of the human head being rotated twice in the magnetic resonance imaging (MRI) system, a continuous conductivity reconstruction MREIT algorithm based on two components of the measured magnetic flux density is introduced. The reconstructed conductivity image could be obtained through solving iteratively a non-linear matrix equation. According to the present algorithm of using two magnetic flux density components, numerical simulations were performed on a concentric three-sphere and realistic human head model (consisting of the scalp, skull and brain) with the uniform and non-uniform isotropic target conductivity distributions. Based on the algorithm, the reconstruction of scalp and brain conductivity ratios could be figured out even under the condition that only one current is injected into the brain. The present results show that the three-dimensional continuous conductivity reconstruction method with two magnetic flux density components for the realistic head could get better results than the method with only one magnetic flux density component. Given the skull conductivity ratio, the relative errors of scalp and brain conductivity values were reduced to less than 1% with the uniform conductivity distribution and less than 6.5% with the non-uniform distribution for different noise levels. Furthermore, the algorithm also shows fast convergence and improved robustness against noise.