PurposeReconstructing tissue magnetic susceptibility (QSM) from MRI phase data involves solving multiple consecutive ill-posed inverse problems such as phase unwrapping, background field removal, and field-to-source inversion. Multi-echo acquisitions present an additional challenge, as the magnetization field is typically computed from the multiple phase data prior to reconstructing the susceptibility map. Processing the multiple phase data introduces errors during the field estimation, violating assumptions of the subsequent inverse problems, manifesting as streaking artifacts in the susceptibility map. To address this challenge, we propose a multi-echo field-to-source forward model that forgoes the field estimation step. Moreover, we propose a fully general underestimation correction step to recover susceptibility sources that were regularized away during the field-to-source inversion. MethodsThe multi-echo forward model and correction step were validated on the QSM Challenge 2.0 datasets and compared to the standard single field-to-source model in in vivo human brains using different types of deconvolution algorithms. ResultsOn the QSM Challenge 2.0 datasets the multi-echo forward model and correction step attain state-of-the-art results on all metrics by a wide margin. Experiments in in vivo brains show that the multi-echo model is in agreement with the single field-to-source model and that the proposed forward model and correction step can be used with any available dipole inversion method. ConclusionA multi-echo field-to-source forward model forgoes the need to fit multi-echo phase data and achieves state-of-the-art results on the QSM Challenge 2.0 data. Underestimated low-frequency susceptibility distributions can be partially recovered using a correction step.

PurposeTo develop a deep neural network to recover filtered phase from clinical MR phase images to enable the computation of QSMs.MethodsEighteen deep learning networks were trained to recover combinations of 13 SWI phase‐filtering pipelines. SWI‐filtered data were computed offline from five multiorientation, multiecho MRI scans yielding 132 3D volumes (118/7/7 training/validation/testing). Two experiments were conducted to show the efficacy of the networks. First, using QSM processing, local fields were computed from the raw phase and subsequently filtered using the SWI‐filtering pipelines. The networks were then trained to invert the filtering operation. Second, the trained networks were fine‐tuned to recover unfiltered local fields from filtered local fields computed by applying QSM processing to the SWI‐filtered phase. Susceptibility maps were computed from the recovered fields and compared with gold standard multiple orientation sampling reconstructions.ResultsSusceptibility maps computed from the raw phase using standard QSM processing have a normalized root mean square error (NRMSE) of 0.732 ± 0.095. Susceptibility maps computed from the recovered phase obtained NRMSEs of 0.725 ± 0.095. The network trained using all 13 processing methods generalized well, obtaining NRMSEs of 0.725 ± 0.89 on filters it has not seen, while matching the reconstruction accuracy of networks trained to recover a single filter.ConclusionIt is feasible to recover SWI‐filtered phase using deep learning. QSM can be computed from the recovered phase from SWI acquisition with comparable accuracy to standard QSM processing.

In MRI the transverse relaxation rate, R2 = 1/T2, shows dependence on the orientation of ordered tissue relative to the main magnetic field. In previous studies, orientation effects of R2 relaxation in the mature brain's white matter have been found to be described by a susceptibility-based model of diffusion through local magnetic field inhomogeneities created by the diamagnetic myelin sheaths. Orientation effects in human newborn white matter have not yet been investigated. The newborn brain is known to contain very little myelin and is therefore expected to exhibit a decrease in orientation dependence driven by susceptibility-based effects. We measured R2 orientation dependence in the white matter of human newborns. R2 data were acquired with a 3D Gradient and Spin Echo (GRASE) sequence and fiber orientation was mapped with diffusion tensor imaging (DTI). We found orientation dependence in newborn white matter that is not consistent with the susceptibility-based model and is best described by a model of residual dipolar coupling. In the near absence of myelin in the newborn brain, these findings suggest the presence of residual dipolar coupling between rotationally restricted water molecules. This has important implications for quantitative imaging methods such as myelin water imaging, and suggests orientation dependence of R2 as a potential marker in early brain development.

In Bayesian parameter estimation, models make simplifying assumptions to make parameter inference feasible. If learned inference methods are trained using data simulated by models, however, distributional differences between simulated and observed data may lead to biased inference results on the observed data. In this work, we introduce a semi-supervised learned Bayesian inference method which makes use of both simulated data -- for which the underlying parameters are known by construction -- and unlabeled data, which may depend on nuissance parameters not captured by the simulation procedure. A conditional variational autoencoder (CVAE) is trained to perform approximate inference simultaneously on the sets of labeled simulated data and unlabeled data, where the unlabeled data is initialized with arbitrary pseudo labels. At each training iteration, new candidate pseudo labels are drawn from the CVAE posterior and the pseudo labels are updated using the Metropolis-Hastings algorithm. This process results in a Markov chain of bootstrapped pseudo labels for each unlabeled datum, effectively performing online Markov chain Monte Carlo (MCMC) inference wherein the proposal distribution is a CVAE informed by labeled simulated data, producing proposals which are increasingly likely to be accepted as training proceeds. The resulting CVAE is able to efficiently produce samples from the posterior distributions of both the simulated and unlabeled data, implicitly marginalizing over nuissance parameters in the unlabeled data. We demonstrate the effectiveness of this method in magnetic resonance imaging (MRI) where MCMC is computationally impractical to due the (3+1)D nature of the images, showing improvement against traditional MCMC inference in both speed and posterior quality.

Bayesian parameter estimation methods are robust techniques for quantifying properties of physical systems which cannot be observed directly. In estimating such parameters, one first requires a physics model of the phenomenon to be studied. Often, such a model follows a series of assumptions to make parameter inference feasible. When simplified models are used for inference, however, systematic differences between model predictions and observed data may propagate throughout the parameter estimation process, biasing inference results. In this work, we use generative adversarial networks (GANs) based on the maximum mean discrepancy (MMD) to learn small stochastic corrections to physics models in order to minimize inference bias. We further propose a hybrid training procedure utilizing both the MMD and the standard GAN objective functionals. We demonstrate the ability to learn stochastic model corrections and eliminate inference bias on a toy problem wherein the true data distribution is known. Subsequently, we apply these methods to a mildly ill-posed inference problem in magnetic resonance imaging (MRI), showing improvement over an established inference method. Finally, because 3D MRI images often contain millions of voxels which would each require parameter inference, we train a conditional variational autoencoder (CVAE) network on the corrected MRI physics model to perform fast inference and make this approach practical.

Combinations of multiple exponentially decaying signals are found across many disciplines of science. Decomposition of these multi-exponential signals into their individual components provides insight into the various contributors to the signal. Magnetic resonance images, for instance, can be acquired with multiple gradient or spin echoes to provide voxel by voxel multi-exponential T2* or T2 decays, respectively. With their millions of voxels, these images make the task of decomposition into individual exponentials computationally challenging. Current implementations take several hours, which is prohibitively long in many settings, such as on-scanner calculation for clinical applications. Here, we present a fast approach for the decomposition of multi-exponential signals. The method is applied to multi echo spin echo MRI scans and computes myelin water maps of the whole brain in under 2 min, and luminal water maps of the prostate in under 1 min.

The multiexponential T 2 decay of the magnetic resonance imaging (MRI) signal from cerebral white matter can be separated into short components sensitive to myelin water and long components related to intra- and extracellular water. In this study we investigated to what degree the myelin water fraction (MWF) depends on the angle between white matter fibers and the main magnetic filed. Maps of MWF were acquired using multi echo CPMG and GRASE sequences. The CPMG sequence was acquired with a TR of 1073 ms, 1500 ms and 2000 ms. The fiber orientation was mapped with diffusion tensor imaging. By angle-wise pooling the voxels across the brain’s white matter, an orientation dependent MWF curve was generated. We found that MWF varied between 25% and 35% across different fiber orientations. The orientation dependency of the MWF is characterized by a dipole-dipole interaction model. Furthermore, the selection of the TR influences the orientation dependent and global white matter MWF. White matter fiber orientation induces a strong systematic bias on the estimation of MWF. This finding has important implications for future research and the interpretation of MWI results in previously published studies.

Brain myelin and iron content are important parameters in neurodegenerative diseases such as multiple sclerosis (MS). Both myelin and iron content influence the brain's R2* relaxation rate. However, their quantification based on R2* maps requires a realistic tissue model that can be fitted to the measured data. In structures with low myelin content, such as deep gray matter, R2* shows a linear increase with increasing iron content. In white matter, R2* is not only affected by iron and myelin but also by the orientation of the myelinated axons with respect to the external magnetic field. Here, we propose a numerical model which incorporates iron and myelin, as well as fibre orientation, to simulate R2* decay in white matter. Applying our model to fibre orientation-dependent in vivo R2* data, we are able to determine a unique solution of myelin and iron content in global white matter. We determine an averaged myelin volume fraction of 16.02 ± 2.07% in non-lesional white matter of patients with MS, 17.32 ± 2.20% in matched healthy controls, and 18.19 ± 2.98% in healthy siblings of patients with MS. Averaged iron content was 35.6 ± 8.9 mg/kg tissue in patients, 43.1 ± 8.3 mg/kg in controls, and 47.8 ± 8.2 mg/kg in siblings. All differences in iron content between groups were significant, while the difference in myelin content between MS patients and the siblings of MS patients was significant. In conclusion, we demonstrate that a model that combines myelin-induced orientation-dependent and iron-induced orientation-independent components is able to fit in vivo R2* data.

We investigated the effects of brain tissue orientation, diffusion, and perivascular spaces on dynamic susceptibility contrast MRI. A 3D numerical model of a white matter voxel was created that consists of an isotropic capillary bed and anisotropic vessels that run in parallel with white matter tracts and are surrounded by perivascular spaces. The signal within the voxel was simulated by solving the Bloch-Torrey equation. Experimental perfusion data were acquired with a gradient echo dynamic susceptibility contrast scan. White matter fibre orientation was mapped with diffusion tensor imaging. Our numerical model of the contrast agent induced increase in R 2 * , as a function of tissue orientation, was fit to dynamic susceptibility contrast MRI data from thirteen subjects by minimizing the bias-corrected Akaike information criterion. White matter blood volume fraction in both the isotropic and the anisotropic vessels was determined as a free parameter, and results were analyzed as a function of diffusivity and perivascular space size. Total white matter blood volume was found to be 2.57%, with one third of the blood residing in blood vessels that run parallel with white matter tracts. Gradient echo dynamic susceptibility contrast MRI strongly depended on white matter tissue orientation and, according to the numerical simulations, this effect is amplified by diffusion and perivascular spaces.

Blood vessel related magnetic resonance imaging (MRI) contrast provides a window into the brain's metabolism and function. Here, we show that the spin echo dynamic susceptibility contrast (DSC) MRI signal of the brain's white matter (WM) strongly depends on the angle between WM tracts and the main magnetic field. The apparent cerebral blood flow and volume are 20% larger in fibres perpendicular to the main magnetic field compared to parallel fibres. We present a rapid numerical framework for the solution of the Bloch-Torrey equation that allows us to explore the isotropic and anisotropic components of the vascular tree. By fitting the simulated spin echo DSC signal to the measured data, we show that half of the WM vascular volume is comprised of vessels running in parallel with WM fibre tracts. The WM blood volume corresponding to the best fit to the experimental data was 2.82%, which is close to the PET gold standard of 2.6%.

BACKGROUND:In situ pinning, a low-risk treatment for slipped capital femoral epiphysis (SCFE), leaves the slipped femoral head in place and may reduce range of motion (ROM) and cause impingement. It is unclear when a more complex surgery should be considered, because the relationships between severity, slip stability, remodeling, impingement, and ROM are unknown.RESEARCH QUESTIONS:(1) Do more severe acute SCFE deformities (no bony remodeling) result in a greater loss of flexion ROM?(2) Does the presence or location of impingement on the pelvis vary with severity of acute SCFE deformity?METHODS:We developed a 3D geometric model of acute SCFE deformity from 1 computed tomography scan of a normal adolescent hip. Ethics board approval was obtained from our institution. Bone models were created from the segmented pelvis, epiphysis, and subphyseal femur.In total, 3721 SCFE deformities were simulated by combining posterior and inferior slips in the axial and coronal planes, respectively. Southwick angles were estimated from a frog-leg lateral projection. Deformities were divided into mild (0 to 30 degrees), moderate (30 to 60 degrees), and severe (≥60 degrees) Southwick groups. Each joint was flexed in combination with internal/external rotation until contact occurred. A total of 121 ROM trials, with different degrees of internal/external rotation (0 to 90 degrees at 1.5-degree steps) were performed for each deformity.RESULTS:In total, 3355 simulated SCFE deformities (363 could not be rotated out of impingement) were analyzed.Increasing slip severity reduced flexion ROM across the range of internal/external rotation. Contact occurred for most mild deformities, and for all moderate and severe deformities in at least 1 ROM trial. Impingement was observed mainly on the anterosuperior aspect of the acetabulum.CONCLUSIONS:Increasing slip severity in acute SCFE reduced flexion and increased incidence of impingement, primarily occurring on the anterosuperior aspect of the acetabulum. The impingement patterns observed are consistent with damaged cartilage locations seen in clinical literature.CLINICAL RELEVANCE:In this experimental model, moderate and severe acute slips in SCFE lead to reduced ROM and impingement with the acetabulum. This suggests that in situ pinning may result in impingement of moderate and severe acute SCFE slips.

OBJECTIVE:Slipped capital femoral epiphysis (SCFE) is a hip disorder where the femoral head slips relative to the neck at the physis. Appropriate treatment of SCFE depends on the severity of the slip, commonly categorised using the Southwick (SW) angle. The SW angle is measured in the frog-lateral leg position, which can be painful and potentially unattainable for patients. The purpose of this study is to determine how errors in frog-lateral radiograph positioning affect measured SW angles and slip classifications. METHODS:Models of SCFE hips were produced from one CT scan of a normal hip; 360 deformities were created. SW angles were measured from a simulated frog-lateral position. Femoral lateral head-neck angles (LHNA; equivalent to SW in incorrect frog-lateral plane) were measured over a range of 837 incorrect frog-lateral leg positions with positioning errors in flexion and/or internal/external rotation. RESULTS:Seventy-six per cent of all imaging position-deformity combinations had error in the reported angle (>1° difference between LHNA and SW). Of those, 70% had <5°, 24% had 5° to 10°, and 6% had >10° of error from the actual SW angle. Three per cent of LHNAs that had >10° error resulted from <10° of positioning error. CONCLUSIONS:If the patient is limited in flexion or external rotation, more diagnostic testing should be considered if error in the reported slip measurement would affect treatment decisions or if accurate severity classification is needed for research. Small positioning errors in moderate and severe slips can cause a > 10° LHNA error; additional three-dimensional imaging should be considered.

We propose a two-pass multi-echo nonlinear dipole inversion method. In the first pass an initial susceptibility map is obtained. The susceptibility map is then further processed by deconvolving the residual of the forward computed phase and the input phase to recover remnant low frequency susceptibility sources. The proposed method attains a NRMSE of 18.8 on the QSM Reconstruction Challenge 2.0 calcification dataset (Sim2Snr1), decisively outperforming the best scoring submissions of the challenge (NRMSE 26.3, 28.3, 28.5).

$$$T_2$$$ distributions are typically computed using point estimates such as nonnegative least-squares (NNLS). This characterizes the most likely $$$T_2$$$-distribution arising from the data, but disregards other plausible solutions - of which there are many, due to the ill-posed nature of the inverse problem. Here, we instead propose to use Bayesian posterior sampling methods. To guide the difficult high-dimensional sampling problem, a data-driven domain transformation is learned alongside a deep generative prior. The resulting posterior samples produce more spatially consistent myelin water fraction (MWF) maps compared to NNLS, despite the purely voxelwise analysis, and additionally yields novel MWF uncertainty estimates.

In this study, we investigated the orientation dependence of T2 in fresh and fixed spinal cord white matter (WM). Scans from three pig spinal cord tissues were acquired at 7T at 6 different orientations with respect to the main magnetic field. We found a considerable orientation dependence in the short fraction relaxation rate R2 (=1/T2) in fresh WM as opposed to a weak orientation effect in fixed WM. To our knowledge, this is the first direct comparison of orientation dependence in a WM tissue sample in the fresh and fixed state. Orientation dependence was not observed in long fraction R2.

In this work we studied the orientation dependence of diffusivities measured in DTI of healthy human white matter in vivo. The observed orientation dependence of the mean diffusivity can be explained by the effects of diffusion-mediated dephasing in the presence of diamagnetic myelin. Orientation dependence was markedly different for the radial and axial components of the diffusivity and suggests the presence of residual dipole-dipole interaction between water molecules.

The MRI signal in white matter tissue is composed of constituent signals from two different water pools: intra/extracellular water and myelin water. When using a multi spin-echo acquisition, the relaxation rate measured in each pool has been shown to depend on the orientation of the containing white matter fibre with respect to the main magnetic field. Here, we show an additional influence of the acquisition echo spacing on the apparent intra/extracellular rate relaxation rate, and using numerical simulation, we provide evidence that decoherence mediated by diffusion through local field inhomogeneities created by blood vessels cannot explain the observed orientation dependence.