Improving phase-based conductivity reconstruction by means of deep learning-based denoising of B 1 + phase data for 3T MRI

Feasibility of undersampled spiral trajectories in MREPT for fast conductivity imaging

PURPOSE

To investigate spiral-based imaging including trajectories with undersampling as a fast and robust alternative for phase-based magnetic resonance electrical properties tomography (MREPT) techniques.

METHODS

Spiral trajectories with various undersampling ratios were prescribed to acquire images from an experimental phantom and a healthy volunteer at 3T. The non-Cartesian acquisitions were reconstructed using SPIRiT, and conductivity maps were derived using phase-based cr-MREPT. The resulting maps were compared between different sampling trajectories. Additionally, a conductivity map was obtained using a Cartesian balanced SSFP acquisition from the volunteer to comparatively demonstrate the robustness of the proposed method.

RESULTS

The phantom and volunteer results illustrate the benefits of the spiral acquisitions. Specifically, undersampled spiral acquisitions display improved robustness against field inhomogeneity artifacts and lowered SD values with shortened readout times. Furthermore, average of conductivity values measured for the cerebrospinal fluid with the spiral acquisitions were 1.703 S/m, indicating a close agreement with the theoretical values of 1.794 S/m.

CONCLUSION

A spiral-based acquisition framework for conductivity imaging with and without undersampling is presented. Overall, spiral-based acquisitions improved robustness against field inhomogeneity artifacts, while achieving whole head coverage with multiple averages in less than a minute.

A database for MR-based electrical properties tomography with in silico brain data-ADEPT

PURPOSE

Several reconstruction methods for MR-based electrical properties tomography (EPT) have been developed. However, the lack of common data makes it difficult to objectively compare their performances. This is, however, a necessary precursor for standardizing and introducing this technique in the clinical setting. To enable objective comparison of the performances of reconstruction methods and provide common data for their training and testing, we created ADEPT, a database of simulated data for brain MR-EPT reconstructions.

METHODS

ADEPT is a database containing in silico data for brain EPT reconstructions. This database was created from 25 different brain models, with and without tumors. Rigid geometric augmentations were applied, and different electrical properties were assigned to white matter, gray matter, CSF, and tumors to generate 120 different brain models. These models were used as input for finite-difference time-domain simulations in Sim4Life, used to compute the electromagnetic fields needed for MR-EPT reconstructions.

RESULTS

Electromagnetic fields from 84 healthy and 36 tumor brain models were simulated. The simulated fields relevant for MR-EPT reconstructions (transmit and receive RF fields and transceive phase) and their ground-truth electrical properties are made publicly available through ADEPT. Additionally, nonattainable fields such as the total magnetic field and the electric field are available upon request.

CONCLUSION

ADEPT will serve as reference database for objective comparisons of reconstruction methods and will be a first step toward standardization of MR-EPT reconstructions. Furthermore, it provides a large amount of data that can be exploited to train data-driven methods. It can be accessed from  https://doi.org/10.34894/V0HBJ8.

Data-driven electrical conductivity brain imaging using 3 T MRI

Magnetic resonance electrical properties tomography (MR-EPT) is a non-invasive measurement technique that derives the electrical properties (EPs, e.g., conductivity or permittivity) of tissues in the radiofrequency range (64 MHz for 1.5 T and 128 MHz for 3 T MR systems). Clinical studies have shown the potential of tissue conductivity as a biomarker. To date, model-based conductivity reconstructions rely on numerical assumptions and approximations, leading to inaccuracies in the reconstructed maps. To address such limitations, we propose an artificial neural network (ANN)-based non-linear conductivity estimator trained on simulated data for conductivity brain imaging. Network training was performed on 201 synthesized T2-weighted spin-echo (SE) data obtained from the finite-difference time-domain (FDTD) electromagnetic (EM) simulation. The dataset was composed of an approximated T2-w SE magnitude and transceive phase information. The proposed method was tested three in-silico and in-vivo on two volunteers and three patients' data. For comparison purposes, various conventional phase-based EPT reconstruction methods were used that ignoreB 1 + magnitude information, such as Savitzky-Golay kernel combined with Gaussian filter (S-G Kernel), phase-based convection-reaction EPT (cr-EPT), magnitude-weighted polynomial-fitting phase-based EPT (Poly-Fit), and integral-based phase-based EPT (Integral-based). From the in-silico experiments, quantitative analysis showed that the proposed method provides more accurate and improved quality (e.g., high structural preservation) conductivity maps compared to conventional reconstruction methods. Representatively, in the healthy brain in-silico phantom experiment, the proposed method yielded mean conductivity values of 1.97 ± 0.20 S/m for CSF, 0.33 ± 0.04 S/m for WM, and 0.52 ± 0.08 S/m for GM, which were closer to the ground-truth conductivity (2.00, 0.30, 0.50 S/m) than the integral-based method (2.56 ± 2.31, 0.39 ± 0.12, 0.68 ± 0.33 S/m). In-vivo ANN-based conductivity reconstructions were also of improved quality compared to conventional reconstructions and demonstrated network generalizability and robustness to in-vivo data and pathologies. The reported in-vivo brain conductivity values were in agreement with literatures. In addition, the proposed method was observed for various SNR levels (SNR levels = 10, 20, 40, and 58) and repeatability conditions (the eight acquisitions with the number of signal averages = 1). The preliminary investigations on brain tumor patient datasets suggest that the network trained on simulated dataset can generalize to unforeseen in-vivo pathologies, thus demonstrating its potential for clinical applications.

Repeatability of brain phase-based magnetic resonance electric properties tomography methods and effect of compressed SENSE and RF shimming

Magnetic resonance electrical properties tomography (MREPT) is an emerging imaging modality to noninvasively measure tissue conductivity and permittivity. Implementation of MREPT in the clinic requires repeatable measurements at a short scan time and an appropriate protocol. The aim of this study was to investigate the repeatability of conductivity measurements using phase-based MREPT and the effects of compressed SENSE (CS), and RF shimming on the precision of conductivity measurements. Conductivity measurements using turbo spin echo (TSE) and three-dimensional balanced fast field echo (bFFE) with CS factors were repeatable. Conductivity measurement using bFFE phase showed smaller mean and variance that those measured by TSE. The conductivity measurements using bFFE showed minimal deviation with CS factors up to 8, with deviation increasing at CS factors > 8. Subcortical structures produced less consistent measurements than cortical parcellations at higher CS factors. RF shimming using full slice coverage 2D dual refocusing echo acquisition mode (DREAM) and full coverage 3D dual TR approaches further improved measurement precision. BFFE is a more optimal sequence than TSE for phase-based MREPT in brain. Depending on the area of the brain being measured, the scan can be safely accelerated with compressed SENSE without sacrifice of precision, offering the potential to employ MREPT in clinical research and applications. RF shimming with better field mapping further improves precision of the conductivity measures.

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

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.

Correlation analysis between the complex electrical permittivity and relaxation time of tissue mimicking phantoms in 7 T MRI

Dielectric relaxation theory describes the complex permittivity of a material in an alternating field; in particular, Debye theory relates the time it takes for an applied field to achieve the maximum polarization and the electrical properties of the material. Although, Debye’s equations were proposed for electrical polarization, in this study, we investigate the correlation between the magnetic longitudinal relaxation time T1 and the complex electrical permittivity of tissue-mimicking phantoms using a 7 T magnetic resonance scanner. We created phantoms that mimicked several human tissues with specific electrical properties. The electrical properties of the phantoms were measured using bench-test equipment. T1 values were acquired from phantoms using MRI. The measured values were fitted with functions based on dielectric estimations, using relaxation times of electrical polarization, and the mixture theory for dielectrics. The results show that, T1 and the real permittivity are correlated; therefore, the correlation can be approximated with a rational function in the case of water-based phantoms. The correlation between index loss and T1 was determined using a fitting function based on the Debye equation and mixture theory equation, in which the fraction of the materials was taken into account. This phantom study and analysis provide an insight into the application relaxation times used for estimating dielectric properties. Currently, the measurement of electrical properties based on dielectric relaxation theory is based on an antenna, sometimes invasive, that irradiates an electric field into a small sample; thus, it is not possible to create a map of electrical properties for a complex structure such as the human body. This study could be further used to compute the electrical properties maps of tissues by scanning images and measuring T1 maps.