PIFON-EPT: MR-Based Electrical Property Tomography Using Physics-Informed Fourier Networks

Abstract

In this paper, we introduce Physics-Informed Fourier Networks (PIFONs) for Electrical Properties (EP) Tomography (EPT). Our novel deep learning-based method is capable of learning EPs globally by solving an inverse scattering problem based on noisy and/or incomplete magnetic resonance (MR) measurements. Methods: We use two separate fully-connected neural networks, namely B + 1 Net and EP Net, to learn the B + 1 field and EPs at any location. A random Fourier features mapping is embedded into B + 1 Net, which allows it to learn the B + 1 field more efficiently. These two neural networks are trained jointly by minimizing the combination of a physicsinformed loss and a data mismatch loss via gradient descent. Results: We showed that PIFON-EPT could provide physically consistent reconstructions of EPs and transmit field in the whole domain of interest even when half of the noisy MR measurements of the entire volume was missing. The average error was 2.49%, 4.09% and 0.32% for the relative permittivity, conductivity and B + 1 , respectively, over the entire volume of the phantom. In experiments that admitted a zero assumption of Bz, PIFON-EPT could yield accurate EP predictions near the interface between regions of different EP values without requiring any boundary conditions. Conclusion: This work demonstrated the feasibility of PIFON-EPT, suggesting it could be an accurate and effective method for electrical properties estimation. Significance: PIFON-EPT can efficiently de-noise MR measurements, which shows the potential to improve other MR-based EPT techniques. Furthermore, it is the first time that MR-based EPT methods can reconstruct the EPs and B + 1 field simultaneously from incomplete simulated noisy MR measurements.Index terms-Electrical Property Mapping, Physics Informed Neural Networks, Fourier Features Mapping. I. INTRODUCTIONElectrical properties (EP), namely relative permittivity and electric conductivity, determine the interactions between electromagnetic waves and biological tissue [1], [2]. EPs have the potential to be employed as biomarkers for pathologies

Data‐driven electrical conductivity brain imaging using 3 T MRI

“…As a future study, uncertainty estimations could be added to the proposed method (Gal & Ghahramani, 2016;Glang et al, 2020;Jung et al, 2022;Roy et al, 2019;Tanno et al, 2021), thus evaluating network instability, for example, by employing dropout with Bayesian approximation. As another option, physicsinformed networks (Inda et al, 2022;Lim & Psaltis, 2022;Raissi et al, 2019;Yu et al, 2023) can be considered. Nevertheless, since B z information is required to solve the full Helmholtz equation, it may still be difficult to apply the method in practice for phase-based EPT reconstruction algorithms.…”