GPU-accelerated Bloch simulations and MR-STAT reconstructions using the Julia programming language.

PURPOSE: MR-STAT is a relatively new multiparametric quantitative MRI technique in which quantitative paramater maps are obtained by solving a large-scale nonlinear optimization problem. Managing reconstruction times is one of the main challenges of MR-STAT. In this work we leverage GPU hardware to reduce MR-STAT reconstruction times. A highly optimized, GPU-compatible Bloch simulation toolbox is developed as part of this work that can be utilized for other quantitative MRI techniques as well. METHODS: The Julia programming language was used to develop a flexible yet highly performant and GPU-compatible Bloch simulation toolbox called BlochSimulators.jl. The runtime performance of the toolbox is benchmarked against other Bloch simulation toolboxes. Furthermore, a (partially matrix-free) modification of a previously presented (matrix-free) MR-STAT reconstruction algorithm is proposed and implemented using the Julia language on GPU hardware. The proposed algorithm is combined with BlochSimulators.jl and the resulting MR-STAT reconstruction times on GPU hardware are compared to previously presented MR-STAT reconstruction times. RESULTS: The BlochSimulators.jl package demonstrates superior runtime performance on both CPU and GPU hardware when compared to other existing Bloch simulation toolboxes. The GPU-accelerated partially matrix-free MR-STAT reconstruction algorithm, which relies on BlochSimulators.jl, allows for reconstructions of 68 seconds per two-dimensional (2D slice). CONCLUSION: By combining the proposed Bloch simulation toolbox and the partially matrix-free reconstruction algorithm, 2D MR-STAT reconstructions can be performed in the order of one minute on a modern GPU card. The Bloch simulation toolbox can be utilized for other quantitative MRI techniques as well, for example for online dictionary generation for MR Fingerprinting.

An improved method to measure transfer functions using MRI.

PURPOSE: A previously published method for MRI-based transfer function assessment makes use of the so-called transceive phase assumption (TPA). This limits its applicability to shorter leads and/or lower field strengths. A new method is presented where the background electric field is determined from both B 1 + $$ {\mathrm{B}}_1^{+} $$ - and B 1 - $$ {\mathrm{B}}_1^{-} $$ -field distributions, avoiding the TPA and making it more generally applicable. THEORY AND METHODS: These B 1 $$ {\mathrm{B}}_1 $$ -distributions are determined from a spoiled gradient echo multiflip angle acquisition. From the separated B 1 $$ {\mathrm{B}}_1 $$ -components the background electrical field and the induced current are computed. Further improvement is achieved by recasting the B 1 $$ {\mathrm{B}}_1 $$ -field model as a "magnitude squared least squares" problem. The proposed reconstruction method is used to determine transfer functions of various copper wire lengths up to 40 cm inside an elliptical ASTM phantom. The method is first tested on EM-simulated data and subsequently phantom and bench measurements are used to determine transfer functions experimentally. RESULTS: In silica reconstructions demonstrate the validity of the proposed B 1 $$ {\mathrm{B}}_1 $$ -field model resulting in highly accurate reconstructed B 1 $$ {\mathrm{B}}_1 $$ -fields, currents, incident electric fields and transfer functions. The experimental results show slight deviations in the field model, however, resulting transfer functions are accurately determined with high similarity to simulations and comparable to bench measurements. CONCLUSION: A more generally applicable method for MRI-based transfer function assessment is presented. The proposed method circumvents phase assumptions making it applicable for longer objects and/or higher field strengths. Additional improvements are implemented in the B 1 $$ {\mathrm{B}}_1 $$ -mapping method and the solution algorithm.

High SNR full brain relaxometry at 7T by accelerated MR-STAT.

PURPOSE: To demonstrate the feasibility and robustness of the Magnetic Resonance Spin TomogrAphy in Time-domain (MR-STAT) framework for fast, high SNR relaxometry at 7T. METHODS: To deploy MR-STAT on 7T-systems, we designed optimized flip-angles using the BLAKJac-framework that incorporates the SAR-constraints. Transmit RF-inhomogeneities were mitigated by including a measured B 1 + $$ {B}_1^{+} $$ -map in the reconstruction. Experiments were performed on a gel-phantom and on five volunteers to explore the robustness of the sequence and its sensitivity to B 1 + $$ {B}_1^{+} $$ inhomogeneities. The SNR-gain at 7T was explored by comparing phantom and in vivo results to MR-STAT at 3T in terms of SNR-efficiency. RESULTS: The higher SNR at 7T enabled two-fold acceleration with respect to current 2D MR-STAT protocols at lower field strengths. The resulting scan had whole-brain coverage, with 1 x 1 x 3 mm3 resolution (1.5 mm slice-gap) and was acquired within 3 min including the B 1 + $$ {B}_1^{+} $$ -mapping. After B 1 + $$ {B}_1^{+} $$ -correction, the estimated T1 and T2 in a phantom showed a mean relative error of, respectively, 1.7% and 4.4%. In vivo, the estimated T1 and T2 in gray and white matter corresponded to the range of values reported in literature with a variation over the subjects of 1.0%-2.1% (WM-GM) for T1 and 4.3%-5.3% (WM-GM) for T2. We measured a higher SNR-efficiency at 7T (R = 2) than at 3T for both T1 and T2 with, respectively, a 4.1 and 2.3 times increase in SNR-efficiency. CONCLUSION: We presented an accelerated version of MR-STAT tailored to high field (7T) MRI using a low-SAR flip-angle train and showed high quality parameter maps with an increased SNR-efficiency compared to MR-STAT at 3T.

Water diffusion and T2 quantification in transient-state MRI: the effect of RF pulse sequence.

In quantitative measurement of the T 2 value of tissues, the diffusion of water molecules has been recognized as a confounder. This is most notably so for transient-state quantitative mapping techniques, which allow simultaneous estimation of T 1 and T 2 . In prior work, apparently conflicting conclusions are presented on the level of diffusion-induced bias on the T2 estimate. So far there is a lack of studies on the effect of the RF pulse angle sequence on the level of diffusion-induced bias. In this work, we show that the specific transient-state RF pulse sequence has a large effect on this level of bias. In particular, the bias level is strongly influenced by the mean value of the RF pulse angles. Also, for realistic values of the spoiling gradient area, we infer that the diffusion-induced bias is negligible for non-liquid human tissues; yet, for phantoms, the effect can be substantial (15% of the true T 2 value) for some RF pulse sequences. This should be taken into account in validation procedures.

A three-dimensional Magnetic Resonance Spin Tomography in Time-domain protocol for high-resolution multiparametric quantitative magnetic resonance imaging.

Magnetic Resonance Spin TomogrAphy in Time-domain (MR-STAT) is a multiparametric quantitative MR framework, which allows for simultaneously acquiring quantitative tissue parameters such as T1, T2, and proton density from one single short scan. A typical two-dimensional (2D) MR-STAT acquisition uses a gradient-spoiled, gradient-echo sequence with a slowly varying RF flip-angle train and Cartesian readouts, and the quantitative tissue maps are reconstructed by an iterative, model-based optimization algorithm. In this work, we design a three-dimensional (3D) MR-STAT framework based on previous 2D work, in order to achieve better image signal-to-noise ratio, higher though-plane resolution, and better tissue characterization. Specifically, we design a 7-min, high-resolution 3D MR-STAT sequence, and the corresponding two-step reconstruction algorithm for the large-scale dataset. To reduce the long acquisition time, Cartesian undersampling strategies such as SENSE are adopted in our transient-state quantitative framework. To reduce the computational burden, a data-splitting scheme is designed for decoupling the 3D reconstruction problem into independent 2D reconstructions. The proposed 3D framework is validated by numerical simulations, phantom experiments, and in vivo experiments. High-quality knee quantitative maps with 0.8 × 0.8 × 1.5 mm3 resolution and bilateral lower leg maps with 1.6 mm isotropic resolution can be acquired using the proposed 7-min acquisition sequence and the 3-min-per-slice decoupled reconstruction algorithm. The proposed 3D MR-STAT framework could have wide clinical applications in the future.

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 ignore B 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.

Multi-echo MR thermometry in the upper leg at 7 T using near-harmonic 2D reconstruction for initialization.

PURPOSE: The aim of this work is the development of a thermometry method to measure temperature increases in vivo, with a precision and accuracy sufficient for validation against thermal simulations. Such an MR thermometry model would be a valuable tool to get an indication on one of the major safety concerns in MR imaging: the tissue heating occurring due to radiofrequency (RF) exposure. To prevent excessive temperature rise, RF power deposition, expressed as specific absorption rate, cannot exceed predefined thresholds. Using these thresholds, MRI has demonstrated an extensive history of safe usage. Nevertheless, MR thermometry would be a valuable tool to address some of the unmet needs in the area of RF safety assessment, such as validation of specific absorption rate and thermal simulations, investigation of local peak temperatures during scanning, or temperature-based safety guidelines. METHODS: The harmonic initialized model-based multi-echo approach is proposed. The method combines a previously published model-based multi-echo water/fat separated approach with an also previously published near-harmonic 2D reconstruction method. The method is tested on the human thigh with a multi-transmit array at 7 T, in three volunteers, and for several RF shims. RESULTS: Precision and accuracy are improved considerably compared to a previous fat-referenced method (precision: 0.09 vs. 0.19°C). Comparison of measured temperature rise distributions to subject-specific simulated counterparts show good relative agreement for multiple RF shim settings. CONCLUSION: The high precision shows promising potential for validation purposes and other RF safety applications.

Efficient performance analysis and optimization of transient-state sequences for multiparametric magnetic resonance imaging.

In transient-state multiparametric MRI sequences such as Magnetic Resonance Spin TomogrAphy in Time-domain (MR-STAT), MR fingerprinting, or hybrid-state imaging, the flip angle pattern of the RF excitation varies over the sequence. This gives considerable freedom to choose an optimal pattern of flip angles. For pragmatic reasons, most optimization methodologies choose for a single-voxel approach (i.e., without taking the spatial encoding scheme into account). Particularly in MR-STAT, the context of spatial encoding is important. In the current study, we present a methodology, called BLock Analysis of a K-space-domain Jacobian (BLAKJac), which is sufficiently fast to optimize a sequence in the context of a predetermined phase-encoding pattern. Based on MR-STAT acquisitions and reconstructions, we show that sequences optimized using BLAKJac are more reliable in terms of actually achieved precision than conventional single-voxel-optimized sequences. In addition, BLAKJac provides analytical tools that give insights into the performance of the sequence in a very limited computation time. Our experiments are based on MR-STAT, but the theory is equally valid for other transient-state multiparametric methods.

Tier-based formalism for safety assessment of custom-built radio-frequency transmit coils.

The purpose of this work is to propose a tier-based formalism for safety assessment of custom-built radio-frequency (RF) coils that balances validation effort with the effort put in determinating the safety factor. The formalism has three tier levels. Higher tiers require increased effort when validating electromagnetic simulation results but allow for less conservative safety factors. In addition, we propose a new method to calculate modeling uncertainty between simulations and measurements and a new method to propagate uncertainties in the simulation into a safety factor that minimizes the risk of underestimating the peak specific absorption rate (SAR). The new safety assessment procedure was completed for all tier levels for an eight-channel dipole array for prostate imaging at 7 T and an eight-channel dipole array for head imaging at 10.5 T, using data from two different research sites. For the 7 T body array, the validation procedure resulted in a modeling uncertainty of 77% between measured and simulated local SAR distributions. For a situation where RF shimming is performed on the prostate, average power limits of 2.4 and 4.5 W/channel were found for tiers 2 and 3, respectively. When the worst-case peak SAR among all phase settings was calculated, power limits of 1.4 and 2.7 W/channel were found for tiers 2 and 3, respectively. For the 10.5 T head array, a modeling uncertainty of 21% was found based on B1 + mapping. For the tier 2 validation, a power limit of 2.6 W/channel was calculated. The demonstrated tier system provides a strategy for evaluating modeling inaccuracy, allowing for the rapid translation of novel coil designs with conservative safety factors and the implementation of less conservative safety factors for frequently used coil arrays at the expense of increased validation effort.

Synthetic MRI with Magnetic Resonance Spin TomogrAphy in Time-Domain (MR-STAT): Results from a Prospective Cross-Sectional Clinical Trial.

BACKGROUND: Magnetic Resonance Spin TomogrAphy in Time-domain (MR-STAT) can reconstruct whole-brain multi-parametric quantitative maps (eg, T1 , T2 ) from a 5-minute MR acquisition. These quantitative maps can be leveraged for synthetization of clinical image contrasts. PURPOSE: The objective was to assess image quality and overall diagnostic accuracy of synthetic MR-STAT contrasts compared to conventional contrast-weighted images. STUDY TYPE: Prospective cross-sectional clinical trial. POPULATION: Fifty participants with a median age of 45 years (range: 21-79 years) consisting of 10 healthy participants and 40 patients with neurological diseases (brain tumor, epilepsy, multiple sclerosis or stroke). FIELD STRENGTH/SEQUENCE: 3T/Conventional contrast-weighted imaging (T1 /T2 weighted, proton density [PD] weighted, and fluid-attenuated inversion recovery [FLAIR]) and a MR-STAT acquisition (2D Cartesian spoiled gradient echo with varying flip angle preceded by a non-selective inversion pulse). ASSESSMENT: Quantitative T1 , T2 , and PD maps were computed from the MR-STAT acquisition, from which synthetic contrasts were generated. Three neuroradiologists blinded for image type and disease randomly and independently evaluated synthetic and conventional datasets for image quality and diagnostic accuracy, which was assessed by comparison with the clinically confirmed diagnosis. STATISTICAL TESTS: Image quality and consequent acceptability for diagnostic use was assessed with a McNemar's test (one-sided α = 0.025). Wilcoxon signed rank test with a one-sided α = 0.025 and a margin of Δ = 0.5 on the 5-level Likert scale was used to assess non-inferiority. RESULTS: All data sets were similar in acceptability for diagnostic use (≥3 Likert-scale) between techniques (T1 w:P = 0.105, PDw:P = 1.000, FLAIR:P = 0.564). However, only the synthetic MR-STAT T2 weighted images were significantly non-inferior to their conventional counterpart; all other synthetic datasets were inferior (T1 w:P = 0.260, PDw:P = 1.000, FLAIR:P = 1.000). Moreover, true positive/negative rates were similar between techniques (conventional: 88%, MR-STAT: 84%). DATA CONCLUSION: MR-STAT is a quantitative technique that may provide radiologists with clinically useful synthetic contrast images within substantially reduced scan time. EVIDENCE LEVEL: 1 Technical Efficacy: Stage 2.

The Coax Dipole: A fully flexible coaxial cable dipole antenna with flattened current distribution for body imaging at 7 Tesla.

PURPOSE: The coax dipole antenna, a flexible antenna for body imaging at 7T is presented. Similar to the high impedance coil, this coaxial cable antenna is fed on the central conductor and through gaps in the shield, the current passes to the outside of the antenna to generate B1 field. This could achieve more favorable current distributions and better adaptation to the body curvature. METHODS: Finite difference time domain (FDTD) simulations are performed to optimize the positions of the gaps in the shield for a flat current profile. Lumped inductors are added to each end to reduce losses. The performance of a single antenna is compared to a fractionated dipole using B1 maps and MR thermometry. Finally, an array of eight coax dipoles is evaluated in simulations and used for in-vivo scanning. RESULTS: An optimal configuration is found with gaps located at 10 cm from the center and inductor values of 28 nH. In comparison to the fractionated dipole antenna, in single antenna phantom measurements the coax dipole achieves similar B1 amplitude with 18% lower peak temperature. In simulations, the eight-channel array of coax dipoles improved B1 homogeneity by 18%, along with small improvements in transmit efficiency and specific absorption rate (SAR). MRI measurements on three volunteers show more consistent performance for the coax dipoles. CONCLUSION: The coax dipole is a novel antenna design with a flattened current distribution resulting in beneficial properties. Also, the flexible design of the coax dipoles allows better adaptation to the body curvature and can potentially be used for a wide range of imaging targets.

Transceive phase corrected 2D contrast source inversion-electrical properties tomography.

PURPOSE: To remove the necessity of the tranceive phase assumption for CSI-EPT and show electrical properties maps reconstructed from measured data obtained using a standard 3T birdcage body coil setup. METHODS: The existing CSI-EPT algorithm is reformulated to use the transceive phase rather than relying on the transceive phase assumption. Furthermore, the radio frequency (RF)-shield is numerically implemented to accurately model the RF fields inside the MRI scanner. We verify that the reformulated two-dimensional (2D) CSI-EPT algorithm can reconstruct electrical properties maps given 2D electromagnetic simulations. Afterward, the algorithm is tested with three-dimensional (3D) FDTD simulations to investigate if the 2D CSI-EPT can retrieve the electrical properties for 3D RF fields. Finally, an MR experiment at 3T with a phantom is performed. RESULTS: From the results of the 2D simulations, it is seen that CSI-EPT can reconstruct the electrical properties using MRI accessible quantities. For 3D simulations, it is observed that the electrical properties are underestimated, nonetheless, CSI-EPT has a lower standard deviation than the standard Helmholtz based methods. Finally, the first CSI-EPT reconstructions based on measured data are presented showing comparable accuracy and precision to reconstructions based on simulated data, and demonstrating the feasibility of CSI-EPT. CONCLUSIONS: The CSI-EPT algorithm was rewritten to use MRI accessible quantities. This allows for CSI-EPT to fully exploit the benefits of the higher static magnetic field strengths with a standard quadrature birdcage coil setup.

Nonrigid 3D motion estimation at high temporal resolution from prospectively undersampled k-space data using low-rank MR-MOTUS.

PURPOSE: With the recent introduction of the MR-LINAC, an MR-scanner combined with a radiotherapy LINAC, MR-based motion estimation has become of increasing interest to (retrospectively) characterize tumor and organs-at-risk motion during radiotherapy. To this extent, we introduce low-rank MR-MOTUS, a framework to retrospectively reconstruct time-resolved nonrigid 3D+t motion fields from a single low-resolution reference image and prospectively undersampled k-space data acquired during motion. THEORY: Low-rank MR-MOTUS exploits spatiotemporal correlations in internal body motion with a low-rank motion model, and inverts a signal model that relates motion fields directly to a reference image and k-space data. The low-rank model reduces the degrees-of-freedom, memory consumption, and reconstruction times by assuming a factorization of space-time motion fields in spatial and temporal components. METHODS: Low-rank MR-MOTUS was employed to estimate motion in 2D/3D abdominothoracic scans and 3D head scans. Data were acquired using golden-ratio radial readouts. Reconstructed 2D and 3D respiratory motion fields were, respectively, validated against time-resolved and respiratory-resolved image reconstructions, and the head motion against static image reconstructions from fully sampled data acquired right before and right after the motion. RESULTS: Results show that 2D+t respiratory motion can be estimated retrospectively at 40.8 motion fields per second, 3D+t respiratory motion at 7.6 motion fields per second and 3D+t head-neck motion at 9.3 motion fields per second. The validations show good consistency with image reconstructions. CONCLUSIONS: The proposed framework can estimate time-resolved nonrigid 3D motion fields, which allows to characterize drifts and intra and inter-cycle patterns in breathing motion during radiotherapy, and could form the basis for real-time MR-guided radiotherapy.

Real-time assessment of potential peak local specific absorption rate value without phase monitoring: Trigonometric maximization method for worst-case local specific absorption rate determination.

PURPOSE: Multi-transmit MRI systems are typically equipped with dedicated hardware to sample the reflected/lost power in the transmit channels. After extensive calibration, the amplitude and phase of the signal at the feed of each array element can be accurately determined. However, determining the phase is more difficult and monitoring errors can lead to a hazardous peak local specific absorption rate (pSAR10g ) underestimation. For this purpose, methods were published for online maximum potential pSAR10g estimation without relying on phase monitoring, but these methods produce considerable overestimation. We present a trigonometric maximization method to determine the actual worst-case pSAR10g without any overestimation. THEORY AND METHOD: The proposed method takes advantage of the sinusoidal relation between the SAR10g in each voxel and the phases of input signals, to return the maximum achievable SAR10g in a few iterations. The method is applied to determine the worst-case pSAR10g for three multi-transmit array configurations at 7T: (1) body array with eight fractionated dipoles; (2) head array with eight fractionated dipoles; (3) head array with eight rectangular loops. The obtained worst-case pSAR10g values are compared with the pSAR10g values determined with a commonly used method and with a more efficient method based on reference-phases. RESULTS: For each voxel, the maximum achievable SAR10g is determined in less than 0.1 ms. Compared to the reference-phases-based method, the proposed method reduces the mean overestimation of the actual pSAR10g up to 52%, while never underestimating the true pSAR10g . CONCLUSION: The proposed method can widely improve the performance of parallel transmission MRI systems without phase monitoring.

A single setup approach for the MRI-based measurement and validation of the transfer function of elongated medical implants.

PURPOSE: To propose a single setup using the MRI to both measure and validate the transfer function (TF) of linear implants. Conventionally, the TF of an implant is measured in one bench setup and validated using another. METHODS: It has been shown that the TF can be measured using MRI. To validate this measurement, the implant is exposed to different incident electric fields, while the temperature increase at the tip is monitored. For a good validation, the incident electric fields that the implant is exposed to should be orthogonal. We perform a simulation study on six different methods that change the incident electric field. Afterward, a TF measurement and validation study using the best method from the simulations is performed. This is done with fiberoptic temperature probes at 1.5 T for four linear implant structures using the proposed single setup. RESULTS: The simulation study showed that positioning local transmit coils at different locations along the lead trajectory has a similar validation quality compared with changing the implant trajectory (ie, the conventional validation method). For the validation study that was performed, an R2 ≥ 0.91 was found for the four investigated leads. CONCLUSION: A single setup to both measure and validate the transfer function using local transmit coils has been shown to work. The benefits of using the proposed validation method are that there is only one setup required instead of two and the implant trajectory is not varied; therefore, the relative distance between the leap tip and the temperature probe is constant.

Improving phase-based conductivity reconstruction by means of deep learning-based denoising of B1+ phase data for 3T MRI.

PURPOSE: To denoise B1+ phase using a deep learning method for phase-based in vivo electrical conductivity reconstruction in a 3T MR system. METHODS: For B1+ 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 B1+ 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 B1+ 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 B1+ phase with deep learning. CONCLUSION: The results suggest that the proposed approach can be used as an alternative preprocessing method to denoise B1+ maps for phase-based conductivity reconstruction without relying on image filters or signal averaging.

Fast and accurate modeling of transient-state, gradient-spoiled sequences by recurrent neural networks.

Fast and accurate modeling of MR signal responses are typically required for various quantitative MRI applications, such as MR fingerprinting. This work uses a new extended phase graph (EPG)-Bloch model for accurate simulation of transient-state, gradient-spoiled MR sequences, and proposes a recurrent neural network (RNN) as a fast surrogate of the EPG-Bloch model for computing large-scale MR signals and derivatives. The computational efficiency of the RNN model is demonstrated by comparisons with other existing models, showing one to three orders of acceleration compared with the latest GPU-accelerated, open-source EPG package. By using numerical and in vivo brain data, two used cases, namely, MRF dictionary generation and optimal experimental design, are also provided. Results show that the RNN surrogate model can be efficiently used for computing large-scale dictionaries of transient-state signals and derivatives within tens of seconds, resulting in several orders of magnitude acceleration with respect to state-of-the-art implementations. The practical application of transient-state quantitative techniques can therefore be substantially facilitated.

SAR and temperature distributions in a database of realistic human models for 7 T cardiac imaging.

PURPOSE: To investigate inter-subject variability of B1+ , SAR and temperature rise in a database of human models using a local transmit array for 7 T cardiac imaging. METHODS: Dixon images were acquired of 14 subjects and segmented in dielectric models with an eight-channel local transmit array positioned around the torso for cardiac imaging. EM simulations were done to calculate SAR distributions. Based on the SAR distributions, temperature simulations were performed for exposure times of 6 min and 30 min. Peak local SAR and temperature rise levels were calculated for different RF shim settings. A statistical analysis of the resulting peak local SAR and temperature rise levels was performed to arrive at safe power limits. RESULTS: For RF shim vectors with random phase and uniformly distributed power, a safe average power limit of 35.7 W was determined (first level controlled mode). When RF amplitude and phase shimming was performed on the heart, a safe average power limit of 35.0 W was found. According to Pennes' model, our numerical study suggests a very low probability of exceeding the absolute local temperature limit of 40 °C for a total exposure time of 6 min and a peak local SAR of 20 W/kg. For a 30 min exposure time at 20 W/kg, it was shown that the absolute temperature limit can be exceeded in the case where perfusion does not change with temperature. CONCLUSION: Safe power constraints were found for 7 T cardiac imaging with an eight-channel local transmit array, while considering the inter-subject variability of B1+ , SAR and temperature rise.

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.

Conditional safety margins for less conservative peak local SAR assessment: A probabilistic approach.

PURPOSE: The introduction of a linear safety factor to address peak local specific absorption rate (pSAR10g ) uncertainties (eg, intersubject variation, modeling inaccuracies) bears one considerable drawback: It often results in over-conservative scanning constraints. We present a more efficient approach to define a variable safety margin based on the conditional probability density function of the effectively obtained pSAR10g value, given the estimated pSAR10g value. METHODS: The conditional probability density function can be estimated from previously simulated data. A representative set of true and estimated pSAR10g samples was generated by means of our database of 23 subject-specific models with an 8-fractionated dipole array for prostate imaging at 7 T. The conditional probability density function was calculated for each possible estimated pSAR10g value and used to determine the corresponding safety margin with an arbitrary low probability of underestimation. This approach was applied to five state-of-the-art local SAR estimation methods, namely: (1) using just the generic body model "Duke"; (2) using our model library to assess the maximum pSAR10g value over all models; (3) using the most representative "local SAR model"; (4) using the five most representative local SAR models; and (5) using a recently developed deep learning-based method. RESULTS: Compared with the more conventional safety factor, the conditional safety-margin approach results in lower (up to 30%) mean overestimation for all investigated local SAR estimation methods. CONCLUSION: The proposed probabilistic approach for pSAR10g correction allows more accurate local SAR assessment with much lower overestimation, while a predefined level of underestimation is accepted (eg, 0.1%).