Data-driven electrical conductivity brain imaging using 3 T MRI

MR electrical properties mapping using vision transformers and canny edge detectors

PURPOSE

We developed a 3D vision transformer-based neural network to reconstruct electrical properties (EP) from magnetic resonance measurements.

THEORY AND METHODS

Our network uses the magnitude of the transmit magnetic field of a birdcage coil, the associated transceive phase, and a Canny edge mask that identifies the object boundaries as inputs to compute the EP maps. We trained our network on a dataset of 10 000 synthetic tissue-mimicking phantoms and fine-tuned it on a dataset of 11 000 realistic head models. We assessed performance in-distribution simulated data and out-of-distribution head models, with and without synthetic lesions. We further evaluated our network in experiments for an inhomogeneous phantom and a volunteer.

RESULTS

The conductivity and permittivity maps had an average peak normalized absolute error (PNAE) of 1.3% and 1.7% for the synthetic phantoms, respectively. For the realistic heads, the average PNAE for the conductivity and permittivity was 1.8% and 2.7%, respectively. The location of synthetic lesions was accurately identified, with reconstructed conductivity and permittivity values within 15% and 25% of the ground-truth, respectively. The conductivity and permittivity for the phantom experiment yielded 2.7% and 2.1% average PNAEs with respect to probe-measured values, respectively. The in vivo EP reconstruction truthfully preserved the subject's anatomy with average values over the entire head similar to the expected literature values.

CONCLUSION

We introduced a new learning-based approach for reconstructing EP from MR measurements obtained with a birdcage coil, marking an important step towards the development of clinically-usable in vivo EP reconstruction protocols.

A joint three-plane physics-constrained deep learning based polynomial fitting approach for MR electrical properties tomography

Magnetic resonance electrical properties tomography can extract the electrical properties of in-vivo tissue. To estimate tissue electrical properties, various reconstruction algorithms have been proposed. However, physics-based reconstructions are prone to various artifacts such as noise amplification and boundary artifact. Deep learning-based approaches are robust to these artifacts but need extensive training datasets and suffer from generalization to unseen data. To address these issues, we introduce a joint three-plane physics-constrained deep learning framework for polynomial fitting MR-EPT by merging physics-based weighted polynomial fitting with deep learning. Within this framework, deep learning is used to discern the optimal polynomial fitting weights for a physics based polynomial fitting reconstruction on the complex B1+ data. For the prediction of optimal fitting coefficients, three neural networks were separately trained on simulated heterogeneous brain models to predict optimal polynomial weighting parameters in three orthogonal planes. Then, the network weights were jointly optimized to estimate the polynomial weights in each plane for a combined conductivity reconstruction. Based on this physics-constrained deep learning approach, we achieved an improvement of conductivity estimation accuracy in comparison to a single plane estimation and a reduction of computational load. The results demonstrate that the proposed method based on 3D data exhibits superior performance in comparison to conventional polynomial fitting methods in terms of capturing anatomical detail and homogeneity. Crucially, in-vivo application of the proposed method showed that the method generalizes well to in-vivo data, without introducing significant errors or artifacts. This generalization makes the presented method a promising candidate for use in clinical applications.

Deep Network Regularization for Phase-Based Magnetic Resonance Electrical Properties Tomography With Stein's Unbiased Risk Estimator

Magnetic resonance imaging (MRI) can estimate tissue conductivity values using phase-based magnetic resonance electrical properties tomography (MR-EPT). However, this method is prone to noise amplification due to the Laplacian operator's sensitivity. To address this issue, we propose a novel unsupervised preprocessing denoiser for MRI transceive phase images. Our approach draws inspiration from the deep image prior (DIP) technique, utilizing the random initialization of a convolutional neural network (CNN) to enforce implicit regularization. Additionally, we incorporate Stein.s unbiased risk estimator (SURE) to optimize the network, which serves as an unbiased estimator of mean square error, thereby eliminating the need for labeled data. This modification mitigates the overfitting commonly associated with the DIP approach, enabling a fully unsupervised framework. Furthermore, we process real and imaginary images instead of phase images, aligning more closely with the theoretical basis of the risk estimator. Our generative model does not require pre-training or extensive training datasets, maintaining adaptability across different resolutions and signal-to-noise ratio levels. In our evaluations, the proposed method significantly reduced residual noise in phase maps, improving both quantitative and qualitative outcomes in phantom and simulated brain data. It also outperformed existing denoising techniques by reducing noise amplification and boundary errors. Applied to data from healthy volunteers and patients, our method yielded conductivity maps with reduced errors and values consistent with established literature. To our knowledge, this is the first blind, fully unsupervised approach capable of implementing a 2D phase-based MR-EPT reconstruction algorithm.

A reusable 3D printed brain-like phantom for benchmarking electrical properties tomography reconstructions

PURPOSE

In MR electrical properties tomography (MR-EPT), electrical properties (EPs, conductivity and permittivity) are reconstructed from MR measurements. Phantom measurements are important to characterize the performance of MR-EPT reconstruction methods, since they allow knowledge of reference EPs values. To assess reconstruction methods in a more realistic scenario, it is important to test the methods using phantoms with realistic shapes, internal structures, and dielectric properties. In this work, we present a 3D printing procedure for the creation of realistic brain-like phantoms to benchmark MR-EPT reconstructions.

METHODS

We created two brain-like geometries with three different compartments using 3D printing. The first geometry was filled once, while the second geometry was filled three times with different saline-gelatin solutions, resulting in a total of four phantoms with different EPs. The saline solutions were characterized using a probe. 3D MR-EPT reconstructions were performed from MR measurements at 3T. The reconstructed conductivity values were compared to reference values of the saline-gelatin solutions. The measured fields were also compared to simulated fields using the same phantom geometry and electrical properties.

RESULTS

The measured fields were consistent with simulated fields. Reconstructed conductivity values were consistent with the reference (probe) conductivity values. This indicated the suitability of such phantoms for benchmarking MR-EPT reconstructions.

CONCLUSION

We presented a new workflow to 3D print realistic brain-like phantoms in an easy and affordable way. These phantoms are suitable to benchmark MR-EPT reconstructions, but can also be used for benchmarking other quantitative MR methods.

MR-based electrical property tomography using a physics-informed network at 3 and 7 T

Magnetic resonance electrical propert tomography promises to retrieve electrical properties (EPs) quantitatively and non-invasively in vivo, providing valuable information for tissue characterization and pathology diagnosis. However, its clinical implementation has been hindered by, for example, B1 measurement accuracy, reconstruction artifacts resulting from inaccuracies in underlying models, and stringent hardware/software requirements. To address these challenges, we present a novel approach aimed at accurate and high-resolution EPs reconstruction based on water content maps by using a physics-informed network (PIN-wEPT). The proposed method utilizes standard clinical protocols and conventional multi-channel receive arrays that have been routinely equipped in clinical settings, thus eliminating the need for specialized RF sequence/coil configurations. Compared with the original wEPT method, the network generates accurate water content maps that effectively eliminate the influence ofB → 1 + andB → 1 - by incorporating data mismatch with electrodynamic constraints derived from the Helmholtz equation. Subsequent regression analysis develops a broad relationship between water content and EPs across various types of brain tissue. A series of numerical simulations was conducted at 7 T to assess the feasibility and performance of the method, which encompassed four normal head models and models with tumorous tissues incorporated, and the results showed normalized mean square error below 1.0% in water content, below 11.7% in conductivity, and below 1.1% in permittivity reconstructions for normal brain tissues. Moreover, in vivo validations conducted over five healthy subjects at both 3 and 7 T showed reasonably good consistency with empirical EPs values across the white matter, gray matter, and cerebrospinal fluid. The PIN-wEPT method, with its demonstrated efficacy, flexibility, and compatibility with current MRI scanners, holds promising potential for future clinical application.

Changes of in vivo electrical conductivity in the brain and torso related to age, fat fraction and sex using MRI

This work was inspired by the observation that a majority of MR-electrical properties tomography studies are based on direct comparisons with ex vivo measurements carried out on post-mortem samples in the 90's. As a result, the in vivo conductivity values obtained from MRI in the megahertz range in different types of tissues (brain, liver, tumors, muscles, etc.) found in the literature may not correspond to their ex vivo equivalent, which still serves as a reference for electromagnetic modelling. This study aims to pave the way for improving current databases since the definition of personalized electromagnetic models (e.g. for Specific Absorption Rate estimation) would benefit from better estimation. Seventeen healthy volunteers underwent MRI of both brain and thorax/abdomen using a three-dimensional ultrashort echo-time (UTE) sequence. We estimated conductivity (S/m) in several classes of macroscopic tissue using a customized reconstruction method from complex UTE images, and give general statistics for each of these regions (mean-median-standard deviation). These values are used to find possible correlations with biological parameters such as age, sex, body mass index and/or fat volume fraction, using linear regression analysis. In short, the collected in vivo values show significant deviations from the ex vivo values in conventional databases, and we show significant relationships with the latter parameters in certain organs for the first time, e.g. a decrease in brain conductivity with age.