Opening a new window on MR-based Electrical Properties Tomography with deep learning

Validation of conductivity tensor imaging against diffusion tensor magnetic resonance electrical impedance tomography

Diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) and electrodeless conductivity tensor imaging (CTI) are two emerging modalities that can quantify low-frequency tissue anisotropic conductivity properties by assuming similar properties underlie ionic mobility and water diffusion. While both methods have potential applications to estimating neuro-modulation fields or formulating forward models used for electrical source imaging, a direct comparison of the two modalities has not yet been performed in-vitro or in-vivo. Therefore, the aim of this study was to test the equivalence of these two modalities. We scanned a tissue phantom and the head of human subject using DT-MREIT and CTI protocols and reconstructed conductivity tensor and effective low frequency conductivities. We found both gray and white matter conductivities recovered by each technique were equivalent within 0.05 S/m. Both DT-MREIT and CTI require multiple processing steps, and we further assess the effects of each factor on reconstructions and evaluate the extent to which different measurement mechanisms potentially cause discrepancies between the two methods. Finally, we discuss the implications for spectral models of measuring conductivity using these techniques. The study further establishes the credibility of CTI as an electrodeless non-invasive method of measuring low frequency conductivity properties.

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.

Unrolled Optimization via Physics-Assisted Convolutional Neural Network for MR-Based Electrical Properties Tomography: A Numerical Investigation

Magnetic Resonance imaging based Electrical Properties Tomography (MR-EPT) is a non-invasive technique that measures the electrical properties (EPs) of biological tissues. In this work, we present and numerically investigate the performance of an unrolled, physics-assisted method for 2D MR-EPT reconstructions, where a cascade of Convolutional Neural Networks is used to compute the contrast update. Each network takes in input the EPs and the gradient descent direction (encoding the physics underlying the adopted scattering model) and returns as output the updated contrast function. The network is trained and tested in silico using 2D slices of realistic brain models at 128 MHz. Results show the capability of the proposed procedure to reconstruct EPs maps with quality comparable to that of the popular Contrast Source Inversion-EPT, while significantly reducing the computational time.

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.

Quantification of tissue property and perfusion uncertainties in hyperthermia treatment planning: Multianalysis using polynomial chaos expansion

INTRODUCTION

Hyperthermia treatment planning (HTP) tools can guide treatment delivery, particularly with locoregional radiative phased array systems. Uncertainties in tissue and perfusion property values presently lead to quantitative inaccuracy of HTP, leading to sub-optimal treatment. Assessment of these uncertainties would allow for better judgement of the reliability of treatment plans and improve their value for treatment guidance. However, systematically investigating the impact of all uncertainties on treatment plans is a complex, high-dimensional problem and too computationally expensive for traditional Monte Carlo approaches. This study aims to systematically quantify the treatment-plan impact of tissue property uncertainties by investigating their individual contribution to, and combined impact on predicted temperature distributions.

METHODS

A novel Polynomial Chaos Expansion (PCE)-based HTP uncertainty quantification was developed and applied for locoregional hyperthermia of modelled tumours in the pancreatic head, prostate, rectum, and cervix. Patient models were based on the Duke and Ella digital human models. Using Plan2Heat, treatment plans were created to optimise tumour temperature (represented by T90) for treatment using the Alba4D system. For all 25-34 modelled tissues, the impact of tissue property uncertainties was analysed individually i.e., electrical and thermal conductivity, permittivity, density, specific heat capacity and perfusion. Next, combined analyses were performed on the top 30 uncertainties with the largest impact.

RESULTS

Uncertainties in thermal conductivity and heat capacity were found to have negligible impact on the predicted temperature ( < 1 × 10-10 °C), density and permittivity uncertainties had a small impact (< 0.3 °C). Uncertainties in electrical conductivity and perfusion can lead to large variations in predicted temperature. However, variations in muscle properties result in the largest impact at locations that could limit treatment quality, with a standard deviation up to almost 6 °C (pancreas) and 3.5 °C (prostate) for perfusion and electrical conductivity, respectively. The combined influence of all significant uncertainties leads to large variations with a standard deviation up to 9.0, 3.6, 3.7 and 4.1 °C for the pancreatic, prostate, rectal and cervical cases, respectively.

CONCLUSION

Uncertainties in tissue and perfusion property values can have a large impact on predicted temperatures from hyperthermia treatment planning. PCE-based analysis helps to identify all major uncertainties, their impact and judge the reliability of treatment plans.

Correlation between standardized uptake value of 18F-FDG PET/CT and conductivity with pathologic prognostic factors in breast cancer

We investigated the correlation between standardized uptake value (SUV) of 18F-fluorodeoxyglucose (FDG) positron emission tomography (PET)/computed tomography (CT) and conductivity parameters in breast cancer and explored the feasibility of conductivity as an imaging biomarker. Both SUV and conductivity have the potential to reflect the tumors' heterogeneous characteristics, but their correlations have not been investigated until now. Forty four women diagnosed with breast cancer who underwent breast MRI and 18F-FDG PET/CT at the time of diagnosis were included. Among them, 17 women received neoadjuvant chemotherapy followed by surgery and 27 women underwent upfront surgery. For conductivity parameters, maximum and mean values of the tumor region-of-interests were examined. For SUV parameters, SUVmax, SUVmean, and SUVpeak of the tumor region-of-interests were examined. Correlations between conductivity and SUV were evaluated, and among them, the highest correlation was observed between mean conductivity and SUVpeak (Spearman's correlation coefficient = 0.381). In a subgroup analysis for 27 women with upfront surgery, tumors with lymphovascular invasion (LVI) showed higher mean conductivity than those without LVI (median: 0.49 S/m vs 0.06 S/m, p < 0.001). In conclusion, our study shows a low positive correlation between SUVpeak and mean conductivity in breast cancer. Furthermore, conductivity showed a potential to noninvasively predict LVI status.

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.

Measurement and image-based estimation of dielectric properties of biological tissues —past, present, and future—

The dielectric properties of biological tissues are fundamental pararmeters that are essential for electromagnetic modeling of the human body. The primary database of dielectric properties compiled in 1996 on the basis of dielectric measurements at frequencies from 10 Hz to 20 GHz has attracted considerable attention in the research field of human protection from non-ionizing radiation. This review summarizes findings on the dielectric properties of biological tissues at frequencies up to 1 THz since the database was developed. Although the 1996 database covered general (normal) tissues, this review also covers malignant tissues that are of interest in the research field of medical applications. An intercomparison of dielectric properties based on reported data is presented for several tissue types. Dielectric properties derived from image-based estimation techniques developed as a result of recent advances in dielectric measurement are also included. Finally, research essential for future advances in human body modeling is discussed.

A Method for Electrical Property Tomography Based on a Three-Dimensional Integral Representation of the Electric Field

Magnetic resonance electrical properties tomography (MREPT) noninvasively reconstructs high-resolution electrical property (EP) maps using MRI scanners and is useful for diagnosing cancerous tissues. However, conventional MREPT methods have limitations: sensitivity to noise in the numerical Laplacian operation, difficulty in reconstructing three-dimensional (3D) EPs and convergence not guaranteed in the iterative process. We propose a novel, iterative 3D reconstruction MREPT method without a numerical Laplacian operation. We derive an integral representation of the electric field using its Helmholtz decomposition with Maxwell's equations, under the assumption that the EPs are known on the boundary of the region of interest with the approximation that the unmeasurable magnetic field components are zero. Then, we solve the simultaneous equations composed of the integral representation and Ampere's law using a convex projection algorithm whose convergence is theoretically guaranteed. The efficacy of the proposed method was validated through numerical simulations and a phantom experiment. The results showed that this method is effective in reconstructing 3D EPs and is robust to noise. It was also shown that our proposed method with the unmeasurable component H^- enhances the accuracy of the EPs in a background and that with all the components of the magnetic field reduces the artifacts at the center of the slices except when all the components of the electric field are close to zero.

Physics-Coupled Neural Network Magnetic Resonance Electrical Property Tomography (MREPT) for Conductivity Reconstruction

The electrical property (EP) of human tissues is a quantitative biomarker that facilitates early diagnosis of cancerous tissues. Magnetic resonance electrical properties tomography (MREPT) is an imaging modality that reconstructs EPs by the radio-frequency field in an MRI system. MREPT reconstructs EPs by solving analytic models numerically based on Maxwell's equations. Most MREPT methods suffer from artifacts caused by inaccuracy of the hypotheses behind the models, and/or numerical errors. These artifacts can be mitigated by adding coefficients to stabilize the models, however, the selection of such coefficient has been empirical, which limit its medical application. Alternatively, end-to-end Neural networks-based MREPT (NN-MREPT) learns to reconstruct the EPs from training samples, circumventing Maxwell's equations. However, due to its pattern-matching nature, it is difficult for NN-MREPT to produce accurate reconstructions for new samples. In this work, we proposed a physics-coupled NN for MREPT (PCNN-MREPT), in which an analytic model, cr-MREPT, works with diffusion and convection coefficients, learned by NNs from the difference between the reconstructed and ground-truth EPs to reduce artifacts. With two simulated datasets, three generalization experiments in which test samples deviate gradually from the training samples, and one noise-robustness experiment were conducted. The results show that the proposed PCNN-MREPT achieves higher accuracy than two representative analytic methods. Moreover, compared with an end-to-end NN-MREPT, the proposed method attained higher accuracy in two critical generalization tests. This is an important step to practical MREPT medical diagnoses.

Combining deep learning and 3D contrast source inversion in MR-based electrical properties tomography

Magnetic resonance electrical properties tomography (MR-EPT) is a technique used to estimate the conductivity and permittivity of tissues from MR measurements of the transmit magnetic field. Different reconstruction methods are available; however, all these methods present several limitations, which hamper the clinical applicability. Standard Helmholtz-based MR-EPT methods are severely affected by noise. Iterative reconstruction methods such as contrast source inversion electrical properties tomography (CSI-EPT) are typically time-consuming and are dependent on their initialization. Deep learning (DL) based methods require a large amount of training data before sufficient generalization can be achieved. Here, we investigate the benefits achievable using a hybrid approach, that is, using MR-EPT or DL-EPT as initialization guesses for standard 3D CSI-EPT. Using realistic electromagnetic simulations at 3 and 7 T, the accuracy and precision of hybrid CSI reconstructions are compared with those of standard 3D CSI-EPT reconstructions. Our results indicate that a hybrid method consisting of an initial DL-EPT reconstruction followed by a 3D CSI-EPT reconstruction would be beneficial. DL-EPT combined with standard 3D CSI-EPT exploits the power of data-driven DL-based EPT reconstructions, while the subsequent CSI-EPT facilitates a better generalization by providing data consistency.

Deep Learning and Its Application to Function Approximation for MR in Medicine: An Overview

This article presents an overview of deep learning (DL) and its applications to function approximation for MR in medicine. The aim of this article is to help readers develop various applications of DL. DL has made a large impact on the literature of many medical sciences, including MR. However, its technical details are not easily understandable for non-experts of machine learning (ML).The first part of this article presents an overview of DL and its related technologies, such as artificial intelligence (AI) and ML. AI is explained as a function that can receive many inputs and produce many outputs. ML is a process of fitting the function to training data. DL is a kind of ML, which uses a composite of many functions to approximate the function of interest. This composite function is called a deep neural network (DNN), and the functions composited into a DNN are called layers. This first part also covers the underlying technologies required for DL, such as loss functions, optimization, initialization, linear layers, non-linearities, normalization, recurrent neural networks, regularization, data augmentation, residual connections, autoencoders, generative adversarial networks, model and data sizes, and complex-valued neural networks.The second part of this article presents an overview of the applications of DL in MR and explains how functions represented as DNNs are applied to various applications, such as RF pulse, pulse sequence, reconstruction, motion correction, spectroscopy, parameter mapping, image synthesis, and segmentation.

An insight into electrical resistivity of white matter and brain tumors

BACKGROUND

There is a lack of information regarding electrical properties of white matter and brain tumors.

OBJECTIVE

To investigate the feasibility of in-vivo measurement of electrical resistivity during brain surgery and establish a better understanding of the resistivity patterns of brain tumors in correlation to the white matter.

METHODS

A bipolar probe was used to measure electrical resistivity during surgery in a prospective cohort of patients with brain tumors. For impedance measurement, the probe applied a constant current of 0.7 μA with a frequency of 140 Hz. The measurement was performed in the white matter within and outside peritumoral edema as well as in non-enhancing, enhancing and necrotic tumor areas. Resistivity values expressed in ohmmeter (Ω∗m) were compared between different intracranial tissues and brain tumors.

RESULTS

Ninety-two patients (gliomas WHO II:16, WHO III:10, WHO IV:33, metastasis:33) were included. White matter outside peritumoral edema had higher resistivity values (13.3 ± 1.7 Ω∗m) than within peritumoral edema (8.5 ± 1.6 Ω∗m), and both had higher values than brain tumors including non-enhancing (WHO II:6.4 ± 1.3 Ω∗m, WHO III:6.3 ± 0.9 Ω∗m), enhancing (WHO IV:5 ± 1 Ω∗m, metastasis:5.4 ± 1.3 Ω∗m) and necrotic tumor areas (WHO IV:3.9 ± 1.1 Ω∗m, metastasis:4.3 ± 1.3 Ω∗m), p=<0.001. No difference was found between low-grade and anaplastic gliomas, p = 0.808, while resistivity values in both were higher than the highest values found in glioblastomas, p = 0.003 and p = 0.004, respectively.

CONCLUSIONS

The technique we applied enabled us to measure electrical resistivity of white matter and brain tumors in-vivo presumably with a significant effect with regard to dielectric polarization. Our results suggest that there are significant differences within different areas and subtypes of brain tumors and that white matter exhibits higher electrical resistivity than brain tumors.

Magnetic-resonance-based measurement of electromagnetic fields and conductivity in vivo using single current administration-A machine learning approach

Diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) is a newly developed technique that combines MR-based measurements of magnetic flux density with diffusion tensor MRI (DT-MRI) data to reconstruct electrical conductivity tensor distributions. DT-MREIT techniques normally require injection of two independent current patterns for unique reconstruction of conductivity characteristics. In this paper, we demonstrate an algorithm that can be used to reconstruct the position dependent scale factor relating conductivity and diffusion tensors, using flux density data measured from only one current injection. We demonstrate how these images can also be used to reconstruct electric field and current density distributions. Reconstructions were performed using a mimetic algorithm and simulations of magnetic flux density from complementary electrode montages, combined with a small-scale machine learning approach. In a biological tissue phantom, we found that the method reduced relative errors between single-current and two-current DT-MREIT results to around 10%. For in vivo human experimental data the error was about 15%. These results suggest that incorporation of machine learning may make it easier to recover electrical conductivity tensors and electric field images during neuromodulation therapy without the need for multiple current administrations.

High-frequency electrical properties tomography at 9.4T as a novel contrast mechanism for brain tumors

PURPOSE

To establish high-frequency magnetic resonance electrical properties tomography (MREPT) as a novel contrast mechanism for the assessment of glioblastomas using a rat brain tumor model.

METHODS

Six F98 intracranial tumor bearing rats were imaged longitudinally 8, 11 and 14 days after tumor cell inoculation. Conductivity and mean diffusivity maps were generated using MREPT and Diffusion Tensor Imaging. These maps were co-registered with T2 -weighted images and volumes of interests (VOIs) were segmented from the normal brain, ventricles, edema, viable tumor, tumor rim, and tumor core regions. Longitudinal changes in conductivity and mean diffusivity (MD) values were compared in these regions. A correlation analysis was also performed between conductivity and mean diffusivity values.

RESULTS

The conductivity of ventricles, edematous area and tumor regions (tumor rim, viable tumor, tumor core) was significantly higher (P < .01) compared to the contralateral cortex. The conductivity of the tumor increased over time while MD from the tumor did not change. A marginal positive correlation was noted between conductivity and MD values for tumor rim and viable tumor, whereas this correlation was negative for the tumor core.

CONCLUSION

We demonstrate a novel contrast mechanism based on ionic concentration and mobility, which may aid in providing complementary information to water diffusion in probing the microenvironment of brain tumors.

Advanced patient-specific hyperthermia treatment planning

Hyperthermia treatment planning (HTP) is valuable to optimize tumor heating during thermal therapy delivery. Yet, clinical hyperthermia treatment plans lack quantitative accuracy due to uncertainties in tissue properties and modeling, and report tumor absorbed power and temperature distributions which cannot be linked directly to treatment outcome. Over the last decade, considerable progress has been made to address these inaccuracies and therefore improve the reliability of hyperthermia treatment planning. Patient-specific electrical tissue conductivity derived from MR measurements has been introduced to accurately model the power deposition in the patient. Thermodynamic fluid modeling has been developed to account for the convective heat transport in fluids such as urine in the bladder. Moreover, discrete vasculature trees have been included in thermal models to account for the impact of thermally significant large blood vessels. Computationally efficient optimization strategies based on SAR and temperature distributions have been established to calculate the phase-amplitude settings that provide the best tumor thermal dose while avoiding hot spots in normal tissue. Finally, biological modeling has been developed to quantify the hyperthermic radiosensitization effect in terms of equivalent radiation dose of the combined radiotherapy and hyperthermia treatment. In this paper, we review the present status of these developments and illustrate the most relevant advanced elements within a single treatment planning example of a cervical cancer patient. The resulting advanced HTP workflow paves the way for a clinically feasible and more reliable patient-specific hyperthermia treatment planning.

High-frequency conductivity at Larmor-frequency in human brain using moving local window multilayer perceptron neural network

Magnetic resonance electrical properties tomography (MREPT) aims to visualize the internal high-frequency conductivity distribution at Larmor frequency using the B1 transceive phase data. From the magnetic field perturbation by the electrical field associated with the radiofrequency (RF) magnetic field, the high-frequency conductivity and permittivity distributions inside the human brain have been reconstructed based on the Maxwell’s equation. Starting from the Maxwell’s equation, the complex permittivity can be described as a second order elliptic partial differential equation. The established reconstruction algorithms have focused on simplifying and/or regularizing the elliptic partial differential equation to reduce the noise artifact. Using the nonlinear relationship between the Maxwell’s equation, measured magnetic field, and conductivity distribution, we design a deep learning model to visualize the high-frequency conductivity in the brain, directly derived from measured magnetic flux density. The designed moving local window multi-layer perceptron (MLW-MLP) neural network by sliding local window consisting of neighboring voxels around each voxel predicts the high-frequency conductivity distribution in each local window. The designed MLW-MLP uses a family of multiple groups, consisting of the gradients and Laplacian of measured B1 phase data, as the input layer in a local window. The output layer of MLW-MLP returns the conductivity values in each local window. By taking a non-local mean filtering approach in the local window, we reconstruct a noise suppressed conductivity image while maintaining spatial resolution. To verify the proposed method, we used B1 phase datasets acquired from eight human subjects (five subjects for training procedure and three subjects for predicting the conductivity in the brain).

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.

Electrical Properties Tomography: A Methodological Review

Electrical properties tomography (EPT) is an imaging method that uses a magnetic resonance (MR) system to non-invasively determine the spatial distribution of the conductivity and permittivity of the imaged object. This manuscript starts by providing clear definitions about the data required for, and acquired in, EPT, followed by comprehensively formulating the physical equations underlying a large number of analytical EPT techniques. This thorough mathematical overview of EPT harmonizes several EPT techniques in a single type of formulation and gives insight into how they act on the data and what their data requirements are. Furthermore, the review describes machine learning-based algorithms. Matlab code of several differential and iterative integral methods is available upon request.

MRSaiFE: An AI-based Approach Towards the Real-Time Prediction of Specific Absorption Rate

The purpose of this study is to investigate feasibility of estimating the specific absorption rate (SAR) in MRI in real time. To this goal, SAR maps are predicted from 3T- and 7T-simulated magnetic resonance (MR) images in 10 realistic human body models via a convolutional neural network. Two-dimensional (2-D) U-Net architectures with varying contraction layers and different convolutional filters were designed to estimate the SAR distribution in realistic body models. Sim4Life (ZMT, Switzerland) was used to create simulated anatomical images and SAR maps at 3T and 7T imaging frequencies for Duke, Ella, Charlie, and Pregnant Women (at 3, 7, and 9 month gestational stages) body models. Mean squared error (MSE) was used as the cost function and the structural similarity index (SSIM) was reported. A 2-D U-Net with 4 contracting (and 4 expanding) layers and 64 convolutional filters at the initial stage showed the best compromise to estimate SAR distributions. Adam optimizer outperformed stochastic gradient descent (SGD) for all cases with an average SSIM of 90.5∓3.6 % and an average MSE of 0.7∓0.6% for head images at 7T, and an SSIM of >85.1∓6.2 % and an MSE of 0.4∓0.4% for 3T body imaging. Algorithms estimated the SAR maps for 224×224 slices under 30 ms. The proposed methodology shows promise to predict real-time SAR in clinical imaging settings without using extra mapping techniques or patient-specific calibrations.

Brain Tissue Conductivity Measurements with MR-Electrical Properties Tomography: An In Vivo Study

First in vivo brain conductivity reconstructions using Helmholtz MR-Electrical Properties Tomography (MR-EPT) have been published. However, a large variation in the reconstructed conductivity values is reported and these values differ from ex vivo conductivity measurements. Given this lack of agreement, we performed an in vivo study on eight healthy subjects to provide reference in vivo brain conductivity values. MR-EPT reconstructions were performed at 3 T for eight healthy subjects. Mean conductivity and standard deviation values in the white matter, gray matter and cerebrospinal fluid (σWM, σGM, and σCSF) were computed for each subject before and after erosion of regions at tissue boundaries, which are affected by typical MR-EPT reconstruction errors. The obtained values were compared to the reported ex vivo literature values. To benchmark the accuracy of in vivo conductivity reconstructions, the same pipeline was applied to simulated data, which allow knowledge of ground truth conductivity. Provided sufficient boundary erosion, the in vivo σWM and σGM values obtained in this study agree for the first time with literature values measured ex vivo. This could not be verified for the CSF due to its limited spatial extension. Conductivity reconstructions from simulated data verified conductivity reconstructions from in vivo data and demonstrated the importance of discarding voxels at tissue boundaries. The presented σWM and σGM values can therefore be used for comparison in future studies employing different MR-EPT techniques.

Low frequency conductivity reconstruction based on a single current injection via MREIT

Conventional magnetic resonance electrical impedance tomography (MREIT) reconstruction methods require administration of two linearly independent currents via at least two electrode pairs. This requires long scanning times and inhibits coordination of MREIT measurements with electrical neuromodulation strategies. We sought to develop an isotropic conductivity reconstruction algorithm in MREIT based on a single current injection, both to decrease scanning time by a factor of two and enable MREIT measurements to be conveniently adapted to general transcranial- or implanted-electrode neurostimulation protocols. In this work, we propose and demonstrate an iterative algorithm that extends previously published MREIT work using two-current administration approaches. The proposed algorithm is a single-current adaptation of the harmonic B _z algorithm. Forward modeling of electric potentials is used to capture changes of conductivity along current directions that would normally be invisible using data from a single-current administration. Computational and experimental results show that the reconstruction algorithm is capable of reconstructing isotropic conductivity images that agree well in terms of L ² error and structural similarity with exact conductivity distributions or two-current-based MREIT reconstructions. We conclude that it is possible to reconstruct high quality electrical conductivity images using MREIT techniques and one current injection only.

Magnetic-Resonance-Based Electrical Property Mapping Using Global Maxwell Tomography With an 8-Channel Head Coil at 7 Tesla: A Simulation Study

OBJECTIVE

Global Maxwell Tomography (GMT) is a recently introduced volumetric technique for noninvasive estimation of electrical properties (EP) from magnetic resonance measurements. Previous work evaluated GMT using ideal radiofrequency (RF) excitations. The aim of this simulation study was to assess GMT performance with a realistic RF coil.

METHODS

We designed a transmit-receive RF coil with 8 decoupled channels for 7T head imaging. We calculated the RF transmit field ( B₁⁺) inside heterogeneous head models for different RF shimming approaches, and used them as input for GMT to reconstruct EP for all voxels.

RESULTS

Coil tuning/decoupling remained relatively stable when the coil was loaded with different head models. Mean error in EP estimation changed from [Formula: see text] to [Formula: see text] and from [Formula: see text] to [Formula: see text] for relative permittivity and conductivity, respectively, when changing head model without re-tuning the coil. Results slightly improved when an SVD-based RF shimming algorithm was applied, in place of excitation with one coil at a time. Despite errors in EP, RF transmit field ( B₁⁺) and absorbed power could be predicted with less than [Formula: see text] error over the entire head. GMT could accurately detect a numerically inserted tumor.

CONCLUSION

This work demonstrates that GMT can reliably reconstruct EP in realistic simulated scenarios using a tailored 8-channel RF coil design at 7T. Future work will focus on construction of the coil and optimization of GMT's robustness to noise, to enable in-vivo GMT experiments.

SIGNIFICANCE

GMT could provide accurate estimations of tissue EP, which could be used as biomarkers and could enable patient-specific estimation of RF power deposition, which is an unsolved problem for ultra-high-field magnetic resonance imaging.

Deep learning-based reconstruction of in vivo pelvis conductivity with a 3D patch-based convolutional neural network trained on simulated MR data

PURPOSE

To demonstrate that mapping pelvis conductivity at 3T with deep learning (DL) is feasible.

METHODS

210 dielectric pelvic models were generated based on CT scans of 42 cervical cancer patients. For all dielectric models, electromagnetic and MR simulations with realistic accuracy and precision were performed to obtain B 1 + and transceive phase (ϕ^± ). Simulated B 1 + and ϕ^± served as input to a 3D patch-based convolutional neural network, which was trained in a supervised fashion to retrieve the conductivity. The same network architecture was retrained using only ϕ^± in input. Both network configurations were tested on simulated MR data and their conductivity reconstruction accuracy and precision were assessed. Furthermore, both network configurations were used to reconstruct conductivity maps from a healthy volunteer and two cervical cancer patients. DL-based conductivity was compared in vivo and in silico to Helmholtz-based (H-EPT) conductivity.

RESULTS

Conductivity maps obtained from both network configurations were comparable. Accuracy was assessed by mean error (ME) with respect to ground truth conductivity. On average, ME < 0.1 Sm^-1 for all tissues. Maximum MEs were 0.2 Sm^-1 for muscle and tumour, and 0.4 Sm^-1 for bladder. Precision was indicated with the difference between 90^th and 10^th conductivity percentiles, and was below 0.1 Sm^-1 for fat, bone and muscle, 0.2 Sm^-1 for tumour and 0.3 Sm^-1 for bladder. In vivo, DL-based conductivity had median values in agreement with H-EPT values, but a higher precision.

CONCLUSION

Anatomically detailed, noise-robust 3D conductivity maps with good sensitivity to tissue conductivity variations were reconstructed in the pelvis with DL.

A deep learning method for image-based subject-specific local SAR assessment

Purpose

Local specific absorption rate (SAR) cannot be measured and is usually evaluated by offline numerical simulations using generic body models that of course will differ from the patient's anatomy. An additional safety margin is needed to include this intersubject variability. In this work, we present a deep learning–based method for image‐based subject‐specific local SAR assessment. We propose to train a convolutional neural network to learn a “surrogate SAR model” to map the relation between subject‐specific B1+ maps and the corresponding local SAR.

Method

Our database of 23 subject‐specific models with an 8–transmit channel body array for prostate imaging at 7 T was used to build 5750 training samples. These synthetic complex B1+ maps and local SAR distributions were used to train a conditional generative adversarial network. Extra penalization for local SAR underestimation errors was included in the loss function. In silico and in vivo validation were performed.

Results

In silico cross‐validation shows a good qualitative and quantitative match between predicted and ground‐truth local SAR distributions. The peak local SAR estimation error distribution shows a mean overestimation error of 15% with 13% probability of underestimation. The higher accuracy of the proposed method allows the use of less conservative safety factors compared with standard procedures. In vivo validation shows that the method is applicable with realistic measurement data with impressively good qualitative and quantitative agreement to simulations.

Conclusion

The proposed deep learning method allows online image‐based subject‐specific local SAR assessment. It greatly reduces the uncertainty in current state‐of‐the‐art SAR assessment methods, reducing the time in the examination protocol by almost 25%.

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.