Deep learning intravoxel incoherent motion modeling: Exploring the impact of training features and learning strategies.

PURPOSE: The development of advanced estimators for intravoxel incoherent motion (IVIM) modeling is often motivated by a desire to produce smoother parameter maps than least squares (LSQ). Deep neural networks show promise to this end, yet performance may be conditional on a myriad of choices regarding the learning strategy. In this work, we have explored potential impacts of key training features in unsupervised and supervised learning for IVIM model fitting. METHODS: Two synthetic data sets and one in-vivo data set from glioma patients were used in training of unsupervised and supervised networks for assessing generalizability. Network stability for different learning rates and network sizes was assessed in terms of loss convergence. Accuracy, precision, and bias were assessed by comparing estimations against ground truth after using different training data (synthetic and in vivo). RESULTS: A high learning rate, small network size, and early stopping resulted in sub-optimal solutions and correlations in fitted IVIM parameters. Extending training beyond early stopping resolved these correlations and reduced parameter error. However, extensive training resulted in increased noise sensitivity, where unsupervised estimates displayed variability similar to LSQ. In contrast, supervised estimates demonstrated improved precision but were strongly biased toward the mean of the training distribution, resulting in relatively smooth, yet possibly deceptive parameter maps. Extensive training also reduced the impact of individual hyperparameters. CONCLUSION: Voxel-wise deep learning for IVIM fitting demands sufficiently extensive training to minimize parameter correlation and bias for unsupervised learning, or demands a close correspondence between the training and test sets for supervised learning.

Neural networks for parameter estimation in microstructural MRI: Application to a diffusion-relaxation model of white matter.

Specific features of white matter microstructure can be investigated by using biophysical models to interpret relaxation-diffusion MRI brain data. Although more intricate models have the potential to reveal more details of the tissue, they also incur time-consuming parameter estimation that may converge to inaccurate solutions due to a prevalence of local minima in a degenerate fitting landscape. Machine-learning fitting algorithms have been proposed to accelerate the parameter estimation and increase the robustness of the attained estimates. So far, learning-based fitting approaches have been restricted to microstructural models with a reduced number of independent model parameters where dense sets of training data are easy to generate. Moreover, the degree to which machine learning can alleviate the degeneracy problem is poorly understood. For conventional least-squares solvers, it has been shown that degeneracy can be avoided by acquisition with optimized relaxation-diffusion-correlation protocols that include tensor-valued diffusion encoding. Whether machine-learning techniques can offset these acquisition requirements remains to be tested. In this work, we employ artificial neural networks to vastly accelerate the parameter estimation for a recently introduced relaxation-diffusion model of white matter microstructure. We also develop strategies for assessing the accuracy and sensitivity of function fitting networks and use those strategies to explore the impact of the acquisition protocol. The developed learning-based fitting pipelines were tested on relaxation-diffusion data acquired with optimal and sub-optimal acquisition protocols. Networks trained with an optimized protocol were observed to provide accurate parameter estimates within short computational times. Comparing neural networks and least-squares solvers, we found the performance of the former to be less affected by sub-optimal protocols; however, model fitting networks were still susceptible to degeneracy issues and their use could not fully replace a careful design of the acquisition protocol.

Improved unsupervised physics-informed deep learning for intravoxel incoherent motion modeling and evaluation in pancreatic cancer patients.

PURPOSE: Earlier work showed that IVIM-NETorig , an unsupervised physics-informed deep neural network, was faster and more accurate than other state-of-the-art intravoxel-incoherent motion (IVIM) fitting approaches to diffusion-weighted imaging (DWI). This study presents a substantially improved version, IVIM-NEToptim , and characterizes its superior performance in pancreatic cancer patients. METHOD: In simulations (signal-to-noise ratio [SNR] = 20), the accuracy, independence, and consistency of IVIM-NET were evaluated for combinations of hyperparameters (fit S0, constraints, network architecture, number of hidden layers, dropout, batch normalization, learning rate), by calculating the normalized root-mean-square error (NRMSE), Spearman's ρ, and the coefficient of variation (CVNET ), respectively. The best performing network, IVIM-NEToptim was compared to least squares (LS) and a Bayesian approach at different SNRs. IVIM-NEToptim 's performance was evaluated in an independent dataset of 23 patients with pancreatic ductal adenocarcinoma. Fourteen of the patients received no treatment between two repeated scan sessions and nine received chemoradiotherapy between the repeated sessions. Intersession within-subject standard deviations (wSD) and treatment-induced changes were assessed. RESULTS: In simulations (SNR = 20), IVIM-NEToptim outperformed IVIM-NETorig in accuracy (NRMSE(D) = 0.177 vs 0.196; NMRSE(f) = 0.220 vs 0.267; NMRSE(D*) = 0.386 vs 0.393), independence (ρ(D*, f) = 0.22 vs 0.74), and consistency (CVNET (D) = 0.013 vs 0.104; CVNET (f) = 0.020 vs 0.054; CVNET (D*) = 0.036 vs 0.110). IVIM-NEToptim showed superior performance to the LS and Bayesian approaches at SNRs < 50. In vivo, IVIM-NEToptim showed significantly less noisy parameter maps with lower wSD for D and f than the alternatives. In the treated cohort, IVIM-NEToptim detected the most individual patients with significant parameter changes compared to day-to-day variations. CONCLUSION: IVIM-NEToptim is recommended for accurate, informative, and consistent IVIM fitting to DWI data.

Relative Enhanced Diffusivity in Prostate Cancer: Protocol Optimization and Diagnostic Potential.

BACKGROUND: Relative enhanced diffusivity (RED) is a potential biomarker for indirectly measuring perfusion in tissue using diffusion-weighted magnetic resonance imaging (MRI) with 3 b values. PURPOSE: To optimize the RED MRI protocol for the prostate, and to investigate its potential for prostate cancer (PCa) diagnosis. STUDY TYPE: Prospective. POPULATION: Ten asymptomatic healthy volunteers and 35 patients with clinical suspicion of PCa. SEQUENCE: 3T T2 - and diffusion-weighted MRI with b values: b = 0, 50, [100], 150, [200], 250, [300], 400, 800 s/mm2 (values in brackets were only used for patients). ASSESSMENT: Monte Carlo simulations were performed to assess noise sensitivity of RED as a function of intermediate b value. Volunteers were scanned 3 times to assess repeatability of RED. Patient data were used to investigate RED's potential for discriminating between biopsy-confirmed cancer and healthy tissue, and between true and false positive radiological findings. STATISTICAL TESTS: Within-subject coefficient of variation (WCV) to assess repeatability and receiver-operating characteristic curve analysis and logistic regression to assess diagnostic performance of RED. RESULTS: The repeatability was acceptable (WCV = 0.2-0.3) for all intermediate b values tested, apart from b = 50 s/mm2 (WCV = 0.3-0.4). The simulated RED values agreed well with the experimental data, showing that an intermediate b value between 150-250 s/mm2 minimizes noise sensitivity in both peripheral zone (PZ) and transition zone (TZ). RED calculated with the b values 0, 150 and 800 s/mm2 was significantly higher in tumors than in healthy tissue in both PZ (P < 0.001, area under the curve [AUC] = 0.85) and PZ + TZ (P < 0.001, AUC = 0.84). RED was shown to aid apparent diffusion coefficient (ADC) in differentiating between false-positive findings and true-positive PCa in the PZ (AUC; RED = 0.71, ADC = 0.74, RED+ADC = 0.77). DATA CONCLUSION: RED is a repeatable biomarker that may have value for prostate cancer diagnosis. An intermediate b value in the range of 150-250 s/mm2 minimizes the influence of noise and maximizes repeatability. LEVEL OF EVIDENCE: 2 Technical Efficacy Stage: 1 J. Magn. Reson. Imaging 2020;51:1900-1910.

Accuracy of breast cancer lesion classification using intravoxel incoherent motion diffusion-weighted imaging is improved by the inclusion of global or local prior knowledge with bayesian methods.

BACKGROUND: Diffusion-weighted MRI (DWI) has potential to noninvasively characterize breast cancer lesions; models such as intravoxel incoherent motion (IVIM) provide pseudodiffusion parameters that reflect tissue perfusion, but are dependent on the details of acquisition and analysis strategy. PURPOSE: To examine the effect of fitting algorithms, including conventional least-squares (LSQ) and segmented (SEG) methods as well as Bayesian methods with global shrinkage (BSP) and local spatial (FBM) priors, on the power of IVIM parameters to differentiate benign and malignant breast lesions. STUDY TYPE: Prospective patient study. SUBJECTS: 61 patients with confirmed breast lesions. FIELD STRENGTH/SEQUENCE: DWI (bipolar SE-EPI, 13 b values) was included in a clinical MR protocol including T2 -weighted and dynamic contrast-enhanced MRI on a 3T scanner. ASSESSMENT: The IVIM model was fitted voxelwise in lesion regions of interest (ROIs), and derived parameters were compared across methods within benign and malignant subgroups (correlation, coefficients of variation). Area under receiver operator characteristic curves (ROC AUCs) were calculated to determine discriminatory power of parameter combinations from all fitting methods. STATISTICAL TESTS: Kruskal-Wallis, Mann-Whitney, Pearson correlation. RESULTS: All methods provided useful IVIM parameters; D was well-correlated across all methods (r > 0.8), with a wider range for f and D* (0.3-0.7). Fitting methods gave detectable differences in parameters, but all showed increased f and decreased D in malign lesions. D was the most discriminatory single parameter, with LSQ performing least well (AUC 0.83). In general, ROC AUCs were maximized by the inclusion of pseudodiffusion parameters, and by the use of Bayesian methods incorporating prior information (maximum AUC of 0.92 for BSP). DATA CONCLUSION: DWI performs well at classifying breast lesions, but careful consideration of analysis procedure can improve performance. D is the most discriminatory single parameter, but including pseudodiffusion parameters (f and D*) increases ROC AUC. Bayesian methods outperformed conventional least-squares and segmented fitting methods for breast lesion classification. LEVEL OF EVIDENCE: 3 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2019;50:1478-1488.

Relative enhanced diffusivity: noise sensitivity, protocol optimization, and the relation to intravoxel incoherent motion.

OBJECTIVE: To explore the relationship between relative enhanced diffusivity (RED) and intravoxel incoherent motion (IVIM), as well as the impact of noise and the choice of intermediate diffusion weighting (b value) on the RED parameter. MATERIALS AND METHODS: A mathematical derivation was performed to cast RED in terms of the IVIM parameters. Noise analysis and b value optimization was conducted by using Monte Carlo calculations to generate diffusion-weighted imaging data appropriate to breast and liver tissue at three different signal-to-noise ratios. RESULTS: RED was shown to be approximately linearly proportional to the IVIM parameter f, inversely proportional to D and to follow an inverse exponential decay with respect to D*. The choice of intermediate b value was shown to be important in minimizing the impact of noise on RED and in maximizing its discriminatory power. RED was shown to be essentially a reparameterization of the IVIM estimates for f and D obtained with three b values. CONCLUSION: RED imaging in the breast and liver should be performed with intermediate b values of 100 and 50 s/mm2, respectively. Future clinical studies involving RED should also estimate the IVIM parameters f and D using three b values for comparison.

A comparative simulation study of bayesian fitting approaches to intravoxel incoherent motion modeling in diffusion-weighted MRI.

PURPOSE: To assess the performance of various least squares and Bayesian modeling approaches to parameter estimation in intravoxel incoherent motion (IVIM) modeling of diffusion-weighted MRI data. METHODS: Simulated tissue models of different type (breast/liver) and morphology (discrete/continuous) were used to generate noisy data according to the IVIM model at several signal-to-noise ratios. IVIM parameter maps were generated using six different approaches, including full nonlinear least squares (LSQ), segmented least squares (SEG), Bayesian modeling with a Gaussian shrinkage prior (BSP) and Bayesian modeling with a spatial homogeneity prior (FBM), plus two modified approaches. Estimators were compared by calculating the median absolute percentage error and deviation, and median percentage bias. RESULTS: The Bayesian modeling approaches consistently outperformed the least squares approaches, with lower relative error and deviation, and provided cleaner parameter maps with reduced erroneous heterogeneity. However, a weakness of the Bayesian approaches was exposed, whereby certain tissue features disappeared completely in regions of high parameter uncertainty. Lower error and deviation were generally afforded by FBM compared with BSP, at the cost of higher bias. CONCLUSIONS: Bayesian modeling is capable of producing more visually pleasing IVIM parameter maps than least squares approaches, but their potential to mask certain tissue features demands caution during implementation. Magn Reson Med 78:2373-2387, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Minimum maximum temperature gradient coil design.

Ohmic heating is a serious problem in gradient coil operation. A method is presented for redesigning cylindrical gradient coils to operate at minimum peak temperature, while maintaining field homogeneity and coil performance. To generate these minimaxT coil windings, an existing analytic method for simulating the spatial temperature distribution of single layer gradient coils is combined with a minimax optimization routine based on sequential quadratic programming. Simulations are provided for symmetric and asymmetric gradient coils that show considerable improvements in reducing maximum temperature over existing methods. The winding patterns of the minimaxT coils were found to be heavily dependent on the assumed thermal material properties and generally display an interesting "fish-eye" spreading of windings in the dense regions of the coil. Small prototype coils were constructed and tested for experimental validation and these demonstrate that with a reasonable estimate of material properties, thermal performance can be improved considerably with negligible change to the field error or standard figures of merit.

Minimax current density gradient coils: analysis of coil performance and heating.

Standard gradient coils are designed by minimizing the inductance or resistance for an acceptable level of gradient field nonlinearity. Recently, a new method was proposed to minimize the maximum value of the current density in a coil additionally. The stated aim of that method was to increase the minimum wire spacing and to reduce the peak temperature in a coil for fixed efficiency. These claims are tested in this study with experimental measurements of magnetic field and temperature as well as simulations of the performance of many coils. Experimental results show a 90% increase in minimum wire spacing and 40% reduction in peak temperature for equal coil efficiency and field linearity. Simulations of many more coils indicate increase in minimum wire spacing of between 50 and 340% for the coils studied here. This method is shown to be able to increase coil efficiency when constrained by minimum wire spacing rather than switching times or total power dissipation. This increase in efficiency could be used to increase gradient strength, duty cycle, or buildability.

Magnetic Lenz lenses improve the limit-of-detection in nuclear magnetic resonance.

A high NMR detection sensitivity is indispensable when dealing with mass and volume-limited samples, or whenever a high spatial resolution is required. The use of miniaturised RF coils is a proven way to increase sensitivity, but situations may arise where space restrictions could prevent the use of a small resonant coil, e.g., in the interior of the smallest practicable micro-coils. We present the use of magnetic lenses, denoted as Lenz lenses due to their working principle, to focus the magnetic flux of an RF coil into a smaller volume and thereby locally enhance the sensitivity of the NMR experiment-at the expense of the total sensitive volume. Besides focusing, such lenses facilitate re-guiding or re-shaping of magnetic fields much like optical lenses do with light beams. For the first time we experimentally demonstrate the use of Lenz lenses in magnetic resonance and provide a compact mathematical description of the working principle. Through simulations we show that optimal arrangements can be found.

Novel selective TOCSY method enables NMR spectral elucidation of metabolomic mixtures.

Complex mixture analysis is routinely encountered in NMR-based investigations. With the aim of component identification, spectral complexity may be addressed chromatographically or spectroscopically, the latter being favored to reduce sample handling requirements. An attractive experiment is selective total correlation spectroscopy (sel-TOCSY), which is capable of providing tremendous spectral simplification and thereby enhancing assignment capability. Unfortunately, isolating a well resolved resonance is increasingly difficult as the complexity of the mixture increases and the assumption of single spin system excitation is no longer robust. We present TOCSY optimized mixture elucidation (TOOMIXED), a technique capable of performing spectral assignment particularly in the case where the assumption of single spin system excitation is relaxed. Key to the technique is the collection of a series of 1D sel-TOCSY experiments as a function of the isotropic mixing time (τm), resulting in a series of resonance intensities indicative of the underlying molecular structure. By comparing these τm-dependent intensity patterns with a library of pre-determined component spectra, one is able to regain assignment capability. After consideration of the technique's robustness, we tested TOOMIXED firstly on a model mixture. As a benchmark we were able to assign a molecule with high confidence in the case of selectively exciting an isolated resonance. Assignment confidence was not compromised when performing TOOMIXED on a resonance known to contain multiple overlapping signals, and in the worst case the method suggested a follow-up sel-TOCSY experiment to confirm an ambiguous assignment. TOOMIXED was then demonstrated on two realistic samples (whisky and urine), where under our conditions an approximate limit of detection of 0.6mM was determined. Taking into account literature reports for the sel-TOCSY limit of detection, the technique should reach on the order of 10µM sensitivity. We anticipate this technique will be highly attractive to various analytical fields facing mixture analysis, including metabolomics, foodstuff analysis, pharmaceutical analysis, and forensics.

Electromagnetic fields in the human body due to switched transverse gradient coils in MRI.

Magnetic resonance imaging scans impose large gradient magnetic fields on the patient. Modern imaging techniques require this magnetic field to be switched rapidly for good resolution. However, it is believed that this can also lead to the unwanted side effect of peripheral nerve stimulation, which proves to be a limiting factor to the advancement of MRI technology. This paper establishes an analytical model for the fields produced within an MRI scanner by transverse gradient coils of known current density. Expressions are obtained for the magnetic induction vector and the electric field vector, as well as for the surface charge and current densities that are induced on the patient's body. The expressions obtained are general enough to allow the study of any combination of gradient coils whose behaviour can be approximated by Fourier series. For a realistic example coil current density and switching function, it is found that spikes of surface charge density are induced on the patient's body as the gradient field is switched, as well as loops of surface current density that mimic the coil current density. For a 10 mT m(-1) gradient field with a rise time of 100 micros, the magnitude of the radial electric field at the body is found to be 10.3 V m(-1). It is also found that there is a finite limit to radial electric field strength as rise time approaches zero.

Designing MR shim arrays with irregular coil geometry: theoretical considerations.

In magnetic resonance imaging and spectroscopy, a highly uniform magnetic field is desired for minimizing image distortions and line broadening, respectively. Typically, shim coils are employed to provide correcting fields for inhomogeneities brought about by magnetic interactions with the sample under study. Flexible field modeling is possible using an array of regularly shaped conducting loops that are independently electrically driven. In this paper, a design method is presented for generating coil winding patterns for shim arrays with irregular geometry elements. These designs are compared theoretically to the use of circular loop arrays and are shown to provide considerable improvements in field accuracy and efficiency for generating low-order correcting fields.

Theoretical design of gradient coils with minimum power dissipation: accounting for the discretization of current density into coil windings.

Gradient coil windings are typically constructed from either variable width copper tracks or fixed width wires. Excessive power dissipation within these windings during gradient coil operation limits the maximum drive current or duty cycle of the coil. It is common to design gradient coils in terms of a continuous minimum power current density and to perform a discretization to obtain the locations of the coil tracks or wires. However, the existence of finite gaps between these conductors and a maximum conductor width leads to an underestimation of coil resistance when calculated using the continuous current density. Put equivalently, the actual current density within the tracks or wires is higher than that used in the optimization and this departure results in suboptimal coil designs. In this work, a mapping to an effective current density is proposed to account for these effects and provide the correct contribution to the power dissipation. This enables the design of gradient coils that are genuinely optimal in terms of power minimization, post-discretization. The method was applied to the theoretical design of a variety of small x- and z-gradient coils for use in small animal imaging and coils for human head imaging. Computer-driven comparisons were made between coils designed with and without the current density mapping, in terms of simulated power dissipation. For coils to be built using variable width tracks, the method provides slight reductions in power dissipation in most cases and substantial gains only in cases where the minimum separation between track centre-lines is less than twice the gap size. However, for coils to be built using fixed width wires, very considerable reductions in dissipated power are consistently attainable (up to 60%) when compared to standard approaches of coil optimization.

Minimizing hot spot temperature in asymmetric gradient coil design.

Heating caused by gradient coils is a considerable concern in the operation of magnetic resonance imaging (MRI) scanners. Hot spots can occur in regions where the gradient coil windings are closely spaced. These problem areas are particularly common in the design of gradient coils with asymmetrically located target regions. In this paper, an extension of an existing coil design method is described, to enable the design of asymmetric gradient coils with reduced hot spot temperatures. An improved model is presented for predicting steady-state spatial temperature distributions for gradient coils. A great amount of flexibility is afforded by this model to consider a wide range of geometries and system material properties. A feature of the temperature distribution related to the temperature gradient is used in a relaxed fixed point iteration routine for successively altering coil windings to have a lower hot spot temperature. Results show that significant reductions in peak temperature are possible at little or no cost to coil performance when compared to minimum power coils of equivalent field error.

3D gradient coil design for open MRI systems.

Existing gradient coil design methods typically require some predetermined surface to be specified upon which the precise locations of coil windings are optimised with respect to gradient homogeneity and other measures of coil performance. In contrast, in this paper an analytic inverse method is presented for the theoretical design of 3D gradient coils in which the precise 3D geometry of the coils is obtained as part of the optimisation process. This method has been described previously for cylindrical whole-body gradients and is extended here for open MRI systems. A 3D current density solution is obtained using Fourier series combined with Tikhonov regularisation. The examples presented involve a minimum power penalty function and an optional shielding constraint. A discretised set of 3D coil windings is obtained using an equi-flux streamline seeding method. Results for an unshielded example display a concentration of windings within the portion of the coil volume nearest the imaging region and looped return path windings taken away from this region. However, for a shielded example the coil windings are found to lie almost exclusively on biplanar surfaces, suggesting that this is the optimum geometry for a shielded minimum power open coil.

Designing gradient coils with reduced hot spot temperatures.

Gradient coil temperature is an important concern in the design and construction of MRI scanners. Closely spaced gradient coil windings cause temperature hot spots within the system as a result of Ohmic heating associated with large current being driven through resistive material, and can strongly affect the performance of the coils. In this paper, a model is presented for predicting the spatial temperature distribution of a gradient coil, including the location and extent of temperature hot spots. Subsequently, a method is described for designing gradient coils with improved temperature distributions and reduced hot spot temperatures. Maximum temperature represents a non-linear constraint and a relaxed fixed point iteration routine is proposed to adjust coil windings iteratively to minimise this coil feature. Several examples are considered that assume different thermal material properties and cooling mechanisms for the gradient system. Coil winding solutions are obtained for all cases considered that display a considerable drop in hot spot temperature (>20%) when compared to standard minimum power gradient coils with equivalent gradient homogeneity, efficiency and inductance. The method is semi-analytical in nature and can be adapted easily to consider other non-linear constraints in the design of gradient coils or similar systems.

3-D gradient coil design--initial theoretical framework.

An analytic inverse method is presented for the theoretical design of 3-D transverse gradient coils. Existing gradient coil design methods require the basic geometry of the coil to be predetermined before optimization. Typically, coil windings are constrained to lie on cylindrical, planar, spherical, or conical surfaces. In this paper, a fully 3-D region in the solution space is explored and the precise geometry of the gradient coils is obtained as part of the optimization process. Primary interest lies in minimizing the field error between induced and target gradient fields within a spherical target region. This is achieved using regularization, in which the field error is minimized along with the total coil power, to obtain a 3-D current density solution within the coil volume. A novel priority streamline technique is used to create 3-D coil windings that approximate this current density, and a secondary optimization is performed to obtain appropriate coil currents. The 3-D coil windings display an interesting general geometric form involving sets of closed loops plus spiral-type coils, and a number of examples are presented and discussed. The corresponding induced magnetic field is found to be highly linear within the region of interest, and a shielding constraint may be implemented to minimize the field outside the coil volume.

3D Gradient coil design - toroidal surfaces.

Gradient coil design typically involves optimisation of current densities or coil windings on familiar cylindrical, planar, spherical or conical surfaces. In this paper, an analytic inverse method is presented for the theoretical design of toroidal transverse gradient coils. This novel geometry is based on previous work involving a 3D current density solution, in which the precise geometry of the gradient coils was obtained as part of the optimisation process. Regularisation is used to solve for the toroidal current densities, whereby the field error is minimised in conjunction with the total power of the coil. The method is applied to the design of unshielded and shielded, whole-body and head coil gradient systems. Preliminary coil windings displaying high gradient homogeneity, low inductance, high efficiency and good force balancing are displayed and discussed. Potential benefits associated with this morphology include self-shielding gradient sets, greater access to cooling mechanisms, a reduction in acoustic noise due to force-balancing, a lessening of patient claustrophobia and greater patient access for clinicians.