Vol. 3 No. 1 - Mar 2017

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An MR-Based Viscosity-Type Regularization Method for Electrical Property Tomography Changyou Li 1 , Wenwei Yu 2 , and Shao Ying Huang 3 1 School of Electronics and Information, Northwestern Polytechnical University, China; 2 Center for Frontier Medical Engineering, Chiba University, Japan; and 3 Bio-Medical Group, Engineering Product Development, Singapore University of Technology and Design, Singapore Corresponding Author: Shao Ying Huang Bio-Medical Group, Engineering Product Development, Singapore University of Technology and Design, 487372, Singapore; E-mail: Key Words: magnetic resonance, electrical property tomography, magnetic resonance safety, radio frequency field, partial differential equation, inverse problem Abbreviations: Magnetic resonance electrical property tomography (MREPT), partial differential equation (PDE), magnetic resonance imaging (MRI), electrical properties (EPs), magnetic resonance (MR), Local Maxwell Tomography (LMT), convection–reaction MREPT (cr-MREPT), finite difference (FD), finite element method (FEM), standard MREPT (stdMREPT), stabilized MREPT (stabMREPT), signal-to-noise ratio (SNR), normalized root-mean-square error (NRMSE), Savitzky–Golay (SG), convection–reaction MREPT (cr-MREPT) Here, a method based on viscosity-type regularization is proposed for magnetic resonance electrical prop- erty tomography (MREPT) to mitigate persistent artifacts when it is used to reconstruct a map of electrical properties based on data from a magnetic resonance imaging scanner. The challenges for solving the corre- sponding partial differential equation (PDE) are discussed in detail. The existing artifacts in the numerical results are pointed out and classified. The methods in the literature for MREPT are mainly based on an as- sumption of local homogeneity, which makes the approach simple but leads to artifacts in the transition re- gion where electrical properties vary rapidly. Recent work has focused on eliminating the assumption of lo- cal homogeneity, and one of the solutions is convection–reaction MREPT that is based on a first-order PDE. Numerical solutions of the PDE have persistent artifacts in certain regions and global spurious oscillations. Here, a method based on viscosity-type regularization is proposed to effectively mitigate the aforementioned problems. Finite difference method is used for discretizing the governing PDE. Numerical experiments are presented to analyze the problem in detail. Electrical properties of different phantoms are successfully re- trieved. The efficiency, accuracy, and noise tolerance of the proposed method are illustrated with numerical results. INTRODUCTION Magnetic resonance imaging (MRI)-based magnetic resonance electrical property tomography (MREPT) (1, 2) is a strategy for noninvasively reconstructing electrical properties (EPs) (permit- tivity and electrical conductivity) of the human body without using additional hardware to a magnetic resonance (MR) scan- ner. It has been intensively developed in recent years for recon- structing the EPs of human tissues based on the measurable data (radiofrequency [RF] field distribution called B 1 -map) (3) from an MRI scanner because the B 1 -field carries the information of EP distribution in the human body. MREPT is an important technology in various areas in medicine and biology. The constructed EP map can show the anatomical structure of the human body by the high contrast of EPs between different tissues (4). Cancerous tissues, including those at the early stages, are highly distinguishable from healthy ones (5, 6). Therefore, the EP map provides a good tool for early cancer detection. It can also provide guidance to design body- centric communications (7) and electromagnetics-based thera- pies (8). EP maps can also help in understanding the activities of cells, in particular with exposure to either static or dynamic electromagnetic waves (9). Moreover, an EP map is crucial for accurate calculation of specific absorption rate, which is a main parameter for assessing the risk of RF and microwave radiation and that of ultrahigh-field MRI scanning (10, 11). MREPT was originally proposed by Haacke et al. (12) and first implemented by Wen (13). The Helmholtz equation for homogeneous material was proposed for calculating both con- ductivity and permittivity with positively circularly polarized component of the magnetic field (B 1 1 ), which corresponds to the RF transmit field. Another MREPT method was developed and systematically studied by Katscher et al. (14) and Voigt et al. (15). The integral forms of Faraday's law and Ampère's law were applied to formulate the governing equation based on B 1 1 . How- ever, these methods are based on an assumption of local homo- geneity for simplification. This assumption leads to artifacts in the region where EPs vary either quickly or abruptly (3, 16, 17). The reconstruction errors are rigorously analyzed by Seo et al. (18). A recent work was focused on removing the local homo- geneity assumption (19). RESEARCH ARTICLE ABSTRACT © 2017 The Authors. Published by Grapho Publications, LLC This is an open access article under the CC BY-NC-ND license ( ISSN 2379-1381 50 TOMOGRAPHY.ORG | VOLUME 3 NUMBER 1 | MARCH 2017

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