Magnetic resonance electrical property tomography (MREPT) is an emerging imaging modality using measured B1 maps from magnetic resonance imaging (MRI) to measure a distribution of electric conductivity and permittivity of the subject at the Larmor frequency. Conventional MREPT approaches at single transmit channel system using the Helmholtz equation rely on an assumption that conductivity and permittivity of the subject are locally homogeneous. For small tissue structures and tissue boundaries, in which the assumption of locally homogeneous conductivity and permittivity does not hold, the reconstructed conductivity values deviated from the actual values, so called “Boundary Artifacts.” The aim of this study is to propose new reconstruction processes based on time-harmonic Maxwell's equations to reconstruct conductivity for small tissue structures and tissue boundaries.Methods
Instead of removing the electric fields from the equations as done in the Helmholtz equation, three key identities of circularly polarized and longitudinal components of electric fields, circularly polarized component of magnetic fields, and electric properties from time-harmonic Maxwell's equations are derived. Based on the three key identities, the proposed reconstruction methods determine conductivity, permittivity, and circularly polarized component and longitudinal component of electric fields using the measured H1+. In each iterative step, estimated conductivity, permittivity, electric fields, and artifact-free mask region, Ω where the contribution of the boundary artifacts is small, were updated. Using the estimated values in the artifact-free mask region as boundary conditions, the estimates beyond the mask region were updated. EM simulations were performed on three types of numerical phantoms with very small regions of homogeneous conductivity and permittivity. The performance of the proposed methods was evaluated using the simulated electric and magnetic fields.Results
For the numerical simulation model, the proposed methods significantly reduced the boundary artifacts compared to conventional methods using Helmholtz equations. In addition, previous methods using the Helmholtz equation could measure conductivity of only large anomalies, but the proposed method can measure the conductivity of the small compartments whose size is 2–3 voxels. The proposed approaches are compatible with spatial filtering which can be used to reduce noise. If a good image segmentation is available as a prior information, better initial boundary conditions can be estimated, and thus the proposed approach can be more accurate for small tissue structures.Conclusions
The proposed reconstruction method not only determines electrical properties, but also circularly polarized component and longitudinal component of electric fields using an iterative process. The proposed method can quantitatively detect the conductivity of the small anomalies better than conventional methods.