Adan Jafet Garcia Inda^{1}, Shao Ying Huang^{2,3}, Stefano Mandija^{4,5}, and Wenwei Yu^{1,6}

^{1}Department of Medical Engineering, Chiba University, Chiba, Japan, ^{2}Department of Surgery, National University of Singapore, Singapore, Singapore, ^{3}Engineering Product Development, Singapore University of Technology and Design, Singapore, Singapore, ^{4}Department of Radiotherapy, University Medical Center Utrecht, Utrecht, Netherlands, ^{5}Computational Imaging Group for MR diagnostic & therapy, University Medical Center Utrecht, Utrecht, Netherlands, ^{6}Center for Frontier Medical Engineering, Chiba University, Chiba, Japan

MREPT is a technique used to non-invasively estimate the electrical properties (EPs) of tissues based on Maxwell equations from MRI measurements. However, most reconstruction techniques are susceptible to noise and have severe boundary artifacts. In this work, we designed problem-oriented machine learning methods to improve the MREPT reconstructions. Through numerical experiments with 2-D cylindrical phantoms and comparison with cr-EPT, we demonstrate the feasibility of ML approaches to provide more noise robust EPT reconstructions with lower boundary artifacts.

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Fig. 1 A) Cylindrical structures used with size h = 24 cm, r1 = 5 cm, r2 = 1.5 - 4 cm and r3 = 1 cm, the region of interest is marked by the orange dashed line square. B) High pass birdcage coil at 128 MHz working frequency in green. Coil radius is 24 cm, the leg length is 20 cm and end ring width is 4 cm. Cylindrical structure placement in orange, middle lines show the extracted B1 maps. C) Range of values used.

Fig. 2
The two ML models A) DR-MREPT, inputs pre-processed 70 PCA coefficients used in
network to reconstruct EP’s simultaneously. B) FC-MREPT, inputs used in
encoder-decoder network to reconstruct EP’s independently.

Fig.
3. Permittivity reconstruction for two test samples, two-layered and solid, for
the ML methods and cr-MREPT for comparison. Absolute error map for each
reconstruction is also included. The ringing artifact can be observed on the ML
model reconstructions. The instable PDE solution for cr-MREPT can be observed by
the global spurious artifact.

Fig.
4 Conductivity reconstruction for two test samples, two-layered and solid, for
the ML methods and cr-MREPT for comparison. Absolute error map for each
reconstruction is also included. The ringing artifact can be observed on the ML
model reconstructions. The instable PDE solution for cr-MREPT can be observed
by the global spurious artifact.

Fig. 5 Table of NRMSE reconstruction values for ML and analytical methods. The consistency of ML results, indicates noise robustness across the noise spectrum. Reconstruction time and training time for the ML and cr-MREPT model are also reported. FC-MREPT had the highest accuracy but was the slowest, DR-MREPT accuracy does not vary, but the training time is only one tenth, while reconstruction time is halved.