Physics Informed Neural Networks (PINN) for Low Snr Magnetic Resonance Electrical Properties Tomography (MREPT)

Adan Jafet Garcia Inda; Shao Ying Huang; Nevrez İmamoğlu; Ruian Qin; Tianyi Yang; Tiao Chen; Zilong Yuan; Wenwei Yu

doi:10.3390/diagnostics12112627

Physics Informed Neural Networks (PINN) for Low Snr Magnetic Resonance Electrical Properties Tomography (MREPT)

Diagnostics (Basel). 2022 Oct 29;12(11):2627. doi: 10.3390/diagnostics12112627.

Authors

Adan Jafet Garcia Inda¹, Shao Ying Huang^{2

3}, Nevrez İmamoğlu⁴, Ruian Qin¹, Tianyi Yang¹, Tiao Chen⁵, Zilong Yuan⁵, Wenwei Yu^{1

6}

Affiliations

¹ Department of Medical Engineering, Chiba University, Chiba 263-8522, Japan.
² Department of Surgery, National University of Singapore, Singapore 119077, Singapore.
³ Engineering Product Development Department, Singapore University of Technology and Design, Singapore 487372, Singapore.
⁴ Digital Architecture Research Center, National Institute of Advanced Industrial Science and Technology, Tokyo 135-0064, Japan.
⁵ Department of Radiology, Hubei Cancer Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan 430079, China.
⁶ Center for Frontier Medical Engineering, Chiba University, Chiba 263-8522, Japan.

Abstract

Electrical properties (EPs) of tissues facilitate early detection of cancerous tissues. Magnetic resonance electrical properties tomography (MREPT) is a technique to non-invasively probe the EPs of tissues from MRI measurements. Most MREPT methods rely on numerical differentiation (ND) to solve partial differential Equations (PDEs) to reconstruct the EPs. However, they are not practical for clinical data because ND is noise sensitive and the MRI measurements for MREPT are noisy in nature. Recently, Physics informed neural networks (PINNs) have been introduced to solve PDEs by substituting ND with automatic differentiation (AD). To the best of our knowledge, it has not been applied to MREPT due to the challenges in using PINN on MREPT as (i) a PINN requires part of ground-truth EPs as collocation points to optimize the network's AD, (ii) the noisy input data disrupts the optimization of PINNs despite the noise-filtering nature of NNs and additional denoising processes. In this work, we propose a PINN-MREPT model based on a canonical analytic MREPT model. A reference padding layer with known EPs was added to surround the region of interest for providing additive collocation points. Moreover, an optimizable diffusion coefficient was embedded in the analytic MREPT model used in the PINN-MREPT. The noise robustness of the proposed PINN-MREPT for single-sample reconstruction was tested by using numerical phantoms of human brain with extra tumor-like tissues at different noise levels. The results of numerical experiments show that PINN-MREPT outperforms two typical numerical MREPT methods in terms of reconstruction accuracy, sensitivity to the extra tissues, and the correlations of line profiles in the regions of interest. The advantage of the PINN-MREPT is shown by the results of an experiment on phantom measurement, too. Moreover, it is found that the diffusion term plays an important role to achieve a noise-robust PINN-MREPT. This is an important step moving forward to a clinical application of MREPT.

Keywords: MREPT; PINN; machine learning; neural network; physics informed neural network.

Grants and funding

This research received no external funding.