MR-based electrical property tomography using a modified finite difference scheme

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.

Using the Probability Density Function-Based Channel-Combination Bloch-Siegert Method Realizes Permittivity Imaging at 3T

Magnetic resonance electrical properties tomography (MR EPT) can retrieve permittivity from the B1+ magnitude. However, the accuracy of the permittivity measurement using MR EPT is still not ideal due to the low signal-to-noise ratio (SNR) of B1+ magnitude. In this study, the probability density function (PDF)-based channel-combination Bloch-Siegert (BSS) method was firstly introduced to MR EPT for improving the accuracy of the permittivity measurement. MRI experiments were performed using a 3T scanner with an eight-channel receiver coil. The homogeneous water phantom was scanned for assessing the spatial distribution of B1+ magnitude obtained from the PDF-based channel-combination BSS method. Gadolinium (Gd) phantom and rats were scanned for assessing the feasibility of the PDF-based channel-combination BSS method in MR EPT. The Helmholtz-based EPT reconstruction algorithm was selected. For quantitative comparison, the permittivity measured by the open-ended coaxial probe method was considered as the ground-truth value. The accuracy of the permittivity measurement was estimated by the relative error between the reconstructed value and the ground-truth value. The reconstructed relative permittivity of Gd phantom was 52.413, while that of rat leg muscle was 54.053. The ground-truth values of relative permittivity of Gd phantom and rat leg muscle were 78.86 and 49.04, respectively. The relative error of average permittivity was 33.53% for Gd and 10.22% for rat leg muscle. The results indicated the high accuracy of the permittivity measurement using the PDF-based channel-combination BSS method in MR EPT. This improvement may promote the clinical application of MR EPT technology, such as in the early diagnosis of cancers.

Use of machine learning to improve the estimation of conductivity and permittivity based on longitudinal relaxation time T1 in magnetic resonance at 7 T

Electrical property tomography (EPT) is a noninvasive method that uses magnetic resonance imaging (MRI) to estimate the conductivity and permittivity of tissues, and hence, can be used as a biomarker. One branch of EPT is based on the correlation of water and relaxation time T1 with the conductivity and permittivity of tissues. This correlation was applied to a curve-fitting function to estimate electrical properties, it was found to have a high correlation between permittivity and T1 however the computation of conductivity based on T1 requires to estimate the water content. In this study, we developed multiple phantoms with several ingredients that modify the conductivity and permittivity and explored the use of machine learning algorithms to have a direct estimation of conductivity and permittivity based on MR images and the relaxation time T1. To train the algorithms, each phantom was measured using a dielectric measurement device to acquire the true conductivity and permittivity. MR images were taken for each phantom, and the T1 values were measured. Then, the acquired data were tested using curve fitting, regression learning, and neural fit models to estimate the conductivity and permittivity values based on the T1 values. In particular, the regression learning algorithm based on Gaussian process regression showed high accuracy with a coefficient of determination R2 of 0.96 and 0.99 for permittivity and conductivity, respectively. The estimation of permittivity using regression learning demonstrated a lower mean error of 0.66% compared to the curve fitting method, which resulted in a mean error of 3.6%. The estimation of conductivity also showed that the regression learning approach had a lower mean error of 0.49%, whereas the curve fitting method resulted in a mean error of 6%. The findings suggest that utilizing regression learning models, specifically Gaussian process regression, can result in more accurate estimations for both permittivity and conductivity compared to other methods.

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

PURPOSE

To denoise B 1 + phase using a deep learning method for phase-based in vivo electrical conductivity reconstruction in a 3T MR system.

METHODS

For B 1 + phase deep-learning denoising, a convolutional neural network (U-net) was chosen. Training was performed on data sets from 10 healthy volunteers. Input data were the real and imaginary components of single averaged spin-echo data (SNR = 45), which was used to approximate the B 1 + phase. For label data, multiple signal-averaged spin-echo data (SNR = 128) were used. Testing was performed on in silico and in vivo data. Reconstructed conductivity maps were derived using phase-based conductivity reconstructions. Additionally, we investigated the usability of the network to various SNR levels, imaging contrasts, and anatomical sites (ie, T₁ , T₂ , and proton density-weighted brain images and proton density-weighted breast images. In addition, conductivity reconstructions from deep learning-based denoised data were compared with conventional image filters, which were used for data denoising in electrical properties tomography (ie, the Gaussian filtering and the Savitzky-Golay filtering).

RESULTS

The proposed deep learning-based denoising approach showed improvement for B 1 + phase for both in silico and in vivo experiments with reduced quantitative error measures compared with other methods. Subsequently, this resulted in an improvement of reconstructed conductivity maps from the denoised B 1 + phase with deep learning.

CONCLUSION

The results suggest that the proposed approach can be used as an alternative preprocessing method to denoise B 1 + maps for phase-based conductivity reconstruction without relying on image filters or signal averaging.

Effect of radiofrequency inhomogeneity on water-content based electrical properties tomography and its correction by flip angle maps

Water-content based electrical properties tomography (wEPT) can retrieve electrical properties (EPs) from water-content maps. B₁⁺ field information is not involved in the traditional magnetic resonance electrical properties tomography approach. wEPT can be performed through conventional MR scanning, such as T₁-weighted spin-echo imaging, which provides convenient access to multiple clinical applications. However, the inhomogeneous radiofrequency (RF) field induced by RF coils would cause inaccuracy in wEPT reconstructions during MR scanning. We conducted a detailed investigation to evaluate the effect of inhomogeneous RF field on wEPT reconstructions to guarantee that EP mapping is desired for clinical practice. Two important considerations are involved, namely, multiple typical coil configurations and various flip angles (FAs). We proposed a correction scheme with actual FA mapping to calibrate the RF inhomogeneity and finally validated it by using human imaging at 3 T. This study illustrates a detailed evaluation for wEPT under imperfect RF homogeneity and further provides a feasible correction procedure to mitigate it. The profound knowledge of wEPT provided in our work will benefit its performance in clinical applications.

Individualized SAR calculations using computer vision-based MR segmentation and a fast electromagnetic solver

PURPOSE

We propose a fast, patient-specific workflow for on-line specific absorption rate (SAR) supervision. An individualized electromagnetic model is created while the subject is on the table, followed by rapid SAR estimates for that individual. Our goal is an improved correspondence between the patient and model, reducing reliance on general anatomical body models.

METHODS

A 3D fat-water 3T acquisition (~2 minutes) is automatically segmented using a computer vision algorithm (~1 minute) into what we found to be the most important electromagnetic tissue classes: air, bone, fat, and soft tissues. We then compute the individual's EM field exposure and global and local SAR matrices using a fast electromagnetic integral equation solver. We assess the approach in 10 volunteers and compare to the SAR seen in a standard generic body model (Duke).

RESULTS

The on-the-table workflow averaged 7'44″. Simulation of the simplified Duke models confirmed that only air, bone, fat, and soft tissue classes are needed to estimate global and local SAR with an error of 6.7% and 2.7%, respectively, compared to the full model. In contrast, our volunteers showed a 16.0% and 20.3% population variability in global and local SAR, respectively, which was mostly underestimated by the Duke model.

CONCLUSION

Timely construction and deployment of a patient-specific model is computationally feasible. The benefit of resolving the population heterogeneity compared favorably to the modest modeling error incurred. This suggests that individualized SAR estimates can improve electromagnetic safety in MRI and possibly reduce conservative safety margins that account for patient-model mismatch, especially in non-standard patients.

Statistical analysis of the accuracy of water content-based electrical properties tomography

Water content-based electrical properties tomography (wEPT) can retrieve electrical properties (EPs) from water content maps, thereby eliminating the need for B₁ field measurement in the traditional magnetic resonance electrical properties tomography method. The wEPT is performed by conventional MR scanning, such as T₁ -weighted spin-echo imaging, and thus can be directly applied to clinical settings. However, the random noise propagation involved in wEPT causes inaccuracy in EP mapping. To guarantee the EP estimates desired for clinical practice, this study statically investigates the noise-specific uncertainty of wEPT through probability density function models. We calculated the probability distribution of EP maps with different noise levels and examined the effects of scan parameters on reconstruction accuracy with various flip angles (FAs) and repetition time (TR) settings. The theoretical derivation was validated by Monte Carlo simulations and human imaging experiment at 3 T. Results showed that a serious deviation could occur in tissues with large conductivity value at a low signal-to-noise ratio and quantitatively demonstrate that such deviation could be mitigated by increased FAs or TRs. This study provided useful information for the setup of scan parameters, evaluation of accuracy of the wEPT under specific SNR levels, and promote its clinical applications.

Magnetic resonance electrical property mapping at 21.1 T: a study of conductivity and permittivity in phantoms, ex vivo tissue and in vivo ischemia

Electrical properties (EP), namely conductivity and permittivity, can provide endogenous contrast for tissue characterization. Using electrical property tomography (EPT), maps of EP can be generated from conventional MRI data. This report investigates the feasibility and accuracy of EPT at 21.1 T for multiple RF coils and modes of operation using phantoms. Additionally, it demonstrates the EP of the in vivo rat brain with and without ischemia. Helmholtz-based EPT was implemented in its Full-form, which demands the complex [Formula: see text] field, and a simplified form requiring either just the [Formula: see text] field phase for conductivity or the [Formula: see text] field magnitude for permittivity. Experiments were conducted at 21.1 T using birdcage and saddle coils operated in linear or quadrature transceive mode, respectively. EPT approaches were evaluated using a phantom, ex and in vivo Sprague-Dawley rats under naïve conditions and ischemic stroke via transient middle cerebral artery occlusion. Different conductivity reconstruction approaches applied to the phantom displayed average errors of 12%-73% to the target acquired from dielectric probe measurements. Permittivity reconstructions showed higher agreement and an average 3%-8% error to the target depending on reconstruction approach. Conductivity and permittivity of ex and in vivo rodent brain were measured. Elevated EP in the ischemia region correlated with the increased sodium content and the influx of water intracellularly following ischemia in the lesion were detected. The Full-form technique generated from the linear birdcage provided the best accuracy for EP of the phantom. Phase-based conductivity and magnitude-based permittivity mapping provided reasonable estimates but also demonstrated the limitations of Helmholtz-based EPT at 21.1 T. Permittivity reconstruction was improved significantly over lower fields, suggesting a novel metric for in vivo brain studies. EPT applied to ischemic rat brain proved sensitivity to physiological changes, motivating the future application of more advanced reconstruction approaches.

Integral MR-EPT With the Calculation of Coil Current Distributions

Many integral equation (IE)-based magnetic resonance electrical property tomography (MR-EPT) methods use unloaded incident radio-frequency (RF) fields from simulations that may not fully reflect the real situation and thus lead to reconstruction errors. To improve the accuracy of IE-based MR-EPT methods, a novel approach that enables the calculation of loaded coil current distributions and avoids the explicit use of incident RF fields is presented in this paper. In the proposed method, a hybrid source composed of the current source from the coil and the contrast source from the subject are introduced in the integral equations. Because the loaded coil current distributions can be extracted from the reconstructed hybrid source, the simulated incident RF fields are eliminated from the problem formulations. To improve the convergence performance, a modified conjugate gradient (CG) scheme was used where the gradients of the current source and contrast source were balanced through using different weighting parameters. The proposed method was verified through full-wave simulations at 9.4 and 7 T involving a heterogeneous ball and an anatomical head phantom. The numerical results indicated that by using the proposed method, an accurate coil current distributions and EPs profiles can be reconstructed and the desirable robustness against noise can also be achieved.

Accuracy and precision of electrical permittivity mapping at 3T: the impact of three B 1 + mapping techniques

Purpose

To investigate the sequence‐specific impact of B1+ amplitude mapping on the accuracy and precision of permittivity reconstruction at 3T in the pelvic region.

Methods

B1+ maps obtained with actual flip angle imaging (AFI), Bloch–Siegert (BS), and dual refocusing echo acquisition mode (DREAM) sequences, set to a clinically feasible scan time of 5 minutes, were compared in terms of accuracy and precision with electromagnetic and Bloch simulations and MR measurements. Permittivity maps were reconstructed based on these B1+ maps with Helmholtz‐based electrical properties tomography. Accuracy and precision in permittivity were assessed. A 2‐compartment phantom with properties and size similar to the human pelvis was used for both simulations and measurements. Measurements were also performed on a female volunteer’s pelvis.

Results

Accuracy was evaluated with noiseless simulations on the phantom. The maximum B1+ bias relative to the true B1+ distribution was 1% for AFI and BS and 6% to 15% for DREAM. This caused an average permittivity bias relative to the true permittivity of 7% to 20% for AFI and BS and 12% to 35% for DREAM. Precision was assessed in MR experiments. The lowest standard deviation in permittivity, found in the phantom for BS, measured 22.4 relative units and corresponded to a standard deviation in B1+ of 0.2% of the B1+ average value. As regards B1+ precision, in vivo and phantom measurements were comparable.

Conclusions

Our simulation framework quantitatively predicts the different impact of B1+ mapping techniques on permittivity reconstruction and shows high sensitivity of permittivity reconstructions to sequence‐specific bias and noise perturbation in the B1+ map. These findings are supported by the experimental results.