MRI-Based Electrical Property Retrieval by Applying the Finite-Element Method (FEM)

Abstract

In this study, the finite-element method is applied to reconstruct the electrical properties (conductivity and permittivity) maps of media with 1-D, 2-D, and 3-D inhomogeneities based on the RF magnetic field distributions in a magnetic resonance imaging (MRI) system. The proposed method handles the discontinuity of electrical properties well. It therefore shows high accuracy at the boundary compared to retrieval methods in the literature. The method has successfully been validated using both analytical and numerical data. Moreover, the noise sensitivity of the proposed method is studied. Good accuracy of retrievals can be obtained when proper coils are chosen (e.g., transverse electromagnetic coils). It is an effective approach showing one step further towards accurate electrical property mapping based on MRI data. It helps to pave the way to accurate calculations of specific absorption rate distributions and temperature distributions of human body under MRI scans, which are crucial for the evaluation of the safety of MRI systems. Moreover, the increased accuracy of the electrical property maps of human body show their potential to be a diagnostic tool for tumors and cancers, especially at their early stages. Following-up research is expected to make the proposed method robust and practical for clinical applications.Index Terms-Electrical properties retrieval, electrical property tomography (EPT), finite-element method (FEM), magnetic resonance imaging (MRI).

Individualized SAR calculations using computer vision‐based MR segmentation and a fast electromagnetic solver

“…For example, Homann et al 8 reported a computation time of 45 minutes per Tx channel (eight channels) using a Finite Difference Time Domain (FDTD) solver. Other methods have been proposed for real-time assessment of an individual's local SAR, including approaches based on Electrical Properties Tomography (EPT), [30][31][32][33][34][35][36][37][38][39][40] Global Maxwell Tomography, [41][42][43] and thermoacoustic imaging. 44 However, these methods present other challenges in the accurate and timely calculation of local SAR distributions and are not widely used.…”

Noninvasive Estimation of Electrical Properties From Magnetic Resonance Measurements via Global Maxwell Tomography and Match Regularization

“…Liu et al and Zhang et al extended MR–EPT to the case of multiple transmit coils and incorporated the effective receive fields into their algorithm [14], [15]. Huang et al incorporated finite–element discretization in their MR–EPT implementation to improve conditioning [16], whereas Michel et al proposed a nonlinear filter to denoise b1+ maps prior to MR–EPT in order to reduce reconstruction errors [17]. Wan et al, Lee at al., and Marqués et al proposed versions of MR–EPT that use receive sensitivities (b1−), which are simpler to measure and usually have higher SNR than b1+, to estimate EP [18], [19], [20].…”

“…Sodickson et al proposed the first differential technique free of any assumptions, dubbed Local Maxwell Tomography, which uses both transmit and receive fields from multiple RF coils to reconstruct EP on a voxel–by– voxel basis [25]. Various multi–modal approaches have also been proposed, usually combining MR–EPT with electrical impedance tomography (EIT), which is an invasive method [26], [27], [16], [28]. While most techniques reconstruct EP directly, some recently proposed differential techniques are implemented with iterative reconstruction schemes.…”

An MR-Based Viscosity-Type Regularization Method for Electrical Property Tomography

“…Hafalir et al ( 25 ) then named this method as convection–reaction MREPT (cr-MREPT), as its governing equation is similar to the convection–reaction equation ( 26 ). The first-order PDE was then solved by Hafalir et al ( 25 ) for 2-dimensional reconstruction using a strong form with finite element method (FEM) ( 27 ). An obvious artifact was observed in the region where the gradient of is close to zero.…”