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

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

doi:10.3390/diagnostics12112627

Cited by 10 publications

(8 citation statements)

References 51 publications

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“…Our method can directly reconstruct the EPs from noisy measurements, unlike previous supervised deep learning-based EPT methods [31]- [34], [36] that require a large amount of known data pairs to supervise the training. Compared with previous hybrid deep learning EPT methods [37], [38] which combine deep learning and CR-EPT to solve EP from convection-reaction equations, our method directly trains a neural network (EP Net) to represent the EPs based on measured data and the Helmholtz PDE without requiring any boundary conditions and hyperparameter tuning for the diffusion coefficient. Finally, we observed that PIFON-EPT would always de-noise and reconstruct the B + 1 values first before the EP reconstruction, as shown in the red dotted box of Fig.…”

Section: Discussionmentioning

confidence: 99%

“…These hybrid methods offer a better generalization, however, repeated electromagnetic simulations are still required to generate training data, which can be very expensive and time-consuming. Another hybrid deep learning EPT method was proposed to directly reconstruct conductivity from input transceive phases [38]. Precisely, a neural network is trained to represent the input transceive phase map, where the gradients of the phase are computed by automatic differentiation [39] and then used to solve the phase-only convectionreaction EPT.…”

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confidence: 99%

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

Yu¹,

Serralles²,

Giannakopoulos³

et al. 2023

Preprint

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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

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Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

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

Yu¹,

Serralles²,

Giannakopoulos³

et al. 2023

Preprint

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“…PINNs have already been used in fields such as biochemistry [40], hydrogeology [41], and astronomy [42]. They are also frequently used to solve ordinary and partial differential equations [43,44]. However, PINNs have not yet been applied to the conceptual Koren-Feingold model, which consists of nonlinear delayed differential equations.…”

Section: Artificial Neural Network and Physics-informed Neural Networkmentioning

confidence: 99%

Predicting and Reconstructing Aerosol–Cloud–Precipitation Interactions with Physics-Informed Neural Networks

Hu,

Kabala

2023

Atmosphere

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Interactions between clouds, aerosol, and precipitation are crucial aspects of weather and climate. The simple Koren–Feingold conceptual model is important for providing deeper insight into the complex aerosol–cloud–precipitation system. Recently, artificial neural networks (ANNs) and physics-informed neural networks (PINNs) have been used to study multiple dynamic systems. However, the Koren–Feingold model for aerosol–cloud–precipitation interactions has not yet been studied with either ANNs or PINNs. It is challenging for pure data-driven models, such as ANNs, to accurately predict and reconstruct time series in a small data regime. The pure data-driven approach results in the ANN becoming a “black box” that limits physical interpretability. We demonstrate how these challenges can be overcome by combining a simple ANN with physical laws into a PINN model (not purely data-driven, good for the small data regime, and interpretable). This paper is the first to use PINNs to learn about the original and modified Koren–Feingold models in a small data regime, including external forcings such as wildfire-induced aerosols or the diurnal cycle of clouds. By adding external forcing, we investigate the effects of environmental phenomena on the aerosol–cloud–precipitation system. In addition to predicting the system’s future, we also use PINN to reconstruct the system’s past: a nontrivial task because of time delay. So far, most research has focused on using PINNs to predict the future of dynamic systems. We demonstrate the PINN’s ability to reconstruct the past with limited data for a dynamic system with nonlinear delayed differential equations, such as the Koren–Feingold model, which remains underexplored in the literature. The main reason that this is possible is that the model is non-diffusive. We also demonstrate for the first time that PINNs have significant advantages over traditional ANNs in predicting the future and reconstructing the past of the original and modified Koren–Feingold models containing external forcings in the small data regime. We also show that the accuracy of the PINN is not sensitive to the value of the regularization factor (λ), a key parameter for the PINN that controls the weight for the physics loss relative to the data loss, for a broad range (from λ=1×103 to λ=1×105).

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“…Therefore, the development of new sensing technologies is needed, such as sensing materials for detection. In the past, conductive tissue-like phantoms had been used to measure the thermal effects of electromagnetic exposure [15,16], evaluation of medical imaging techniques [17,18], conductivity influence in electrical stimulation [19][20][21], that can mimic the tissue hardness [22], but it has not been reported as a sensing material for 3D localization.…”

Section: Introductionmentioning

confidence: 99%

Electro-localization method using a muscle conductive phantom for needle position detection towards medical training

Gomez-Tames,

2023

Biomed. Phys. Eng. Express

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Simulation in healthcare can help train, improve, and evaluate medical personnel's skills. In the case of needle insertion/manipulation inside the muscle during an nEMG examination, a training simulator requires estimating the position of the needle to output the electrical muscle activity in real-time according to the training plan. External cameras can be used to estimate the needle location; however, different error sources can make its implementation difficult and new medical sensing technologies are needed. This study introduces and demonstrates the feasibility of a conductive phantom that serves as the medium for needle insertion and senses the 3D needle position based on a technique named electro-localization for the first time. The proposed conductive phantom is designed so that different voltage distributions are generated in the phantom using electrodes placed on its borders. The needle is inserted in the phantom, and the recorded voltages are mapped to spatial coordinates using a finite element method (FEM)-based computational model of the conductive phantom to estimate the 3D needle tip position. Experimental and simulation results of phantom voltage distributions agreed. In 2D mapping (no depth consideration), the needle position error was 1.7 mm, which was marginally reduced if only the central area of the phantom was used (1.5 mm). In 3D mapping, the error was 4 mm. This study showed the feasibility of using a conductive muscle phantom as a new embedded sensor that estimates needle position for medical training of nEMG without relying on external sensors.

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

Cited by 10 publications

References 51 publications

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

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

Predicting and Reconstructing Aerosol–Cloud–Precipitation Interactions with Physics-Informed Neural Networks

Electro-localization method using a muscle conductive phantom for needle position detection towards medical training

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