Magnetic Resonance-Electrical Properties Tomography by Directly Solving Maxwell’s Curl Equations

Jieru Chi,Yaohui Wang,Chunyi Liu,Qinghuo Liu,Aurelien Destruel,Jie Yang,Xuegang Xin,Mingyan Li,Lei Guo,Feng Liu,Ewald Weber

doi:10.3390/app10093318

Abstract

Magnetic Resonance-Electrical Properties Tomography (MR-EPT) is a method to reconstruct the electrical properties (EPs) of bio-tissues from the measured radiofrequency (RF) field in Magnetic Resonance Imaging (MRI). Current MR-EPT approaches reconstruct the EP profile by solving a second-order partial differential wave equation problem, which is sensitive to noise and can induce large reconstruction artefacts near tissue boundaries and areas with inaccurate field measurements. In this paper, a novel MR-EPT approach is proposed, which is based on a direct solution to Maxwell’s curl equations. The distribution of EPs is calculated by iteratively fitting the RF field calculated by the finite-difference-time-domain (FDTD) technique to the measured values. To solve the time-consuming problem of the iterative fitting, a graphics processing unit (GPU) is used to accelerate the FDTD technique to process the field calculation kernel. The new EPT method was evaluated by investigating a numerical head phantom, and it was found that EP values can be accurately calculated and were relatively insensitive to simulated RF field errors. The feasibility of the proposed method was further validated using phantom-based experimental data collected from a 9.4 Tesla (T) Magnetic Resonance Imaging (MRI) system. The results also indicated that more accurate EP values could be reconstructed from the new method compared with conventional methods. Moreover, even in the absence of phase information of the RF field, the proposed approach is still capable of offering robust EPT solutions, thus having improved practicality for potential clinical applications.

Highlights

Magnetic Resonance-Electrical Properties Tomography (MR-EPT) is an imaging technique which maps the electrical properties of a subject by analyzing the radiofrequency (RF) magnetic field measured during an MR scan
The concept of MR-EPT was introduced by Haacke et al in 1991 [5], and Wen et al [6] verified this concept through experiments in 2003
The new EPT method was +further verified by using experimental data obtained from the 9.4T Magnetic Resonance Imaging (MRI)

Summary

Introduction

Magnetic Resonance-Electrical Properties Tomography (MR-EPT) is an imaging technique which maps the electrical properties (permittivity and conductivity) of a subject by analyzing the radiofrequency (RF) magnetic field measured during an MR scan. This technique has shown promise for clinical diagnosis and interests in ultra-high field Magnetic Resonance Imaging (MRI), because of its potential in the evaluation of patient-specific absorption rate (SAR) [1]. The initial development of MR-EPT was based on the utilization of the Helmholtz equation, in which the permittivity and conductivity were assumed constant ( known as the “local homogeneity assumption” (LHA)) [7,8]. Additional regularization terms were added to solve the EPT inverse problem [11,12], the Laplacian operator was replaced with a surface integral [8,13], the k-space data were weighted properly [14], and the region of interest (ROI) was expanded with more voxels [15]

Methods

Results

Conclusion