Multi-echo dipole inversion for magnetic susceptibility mapping.

PURPOSE: Reconstructing 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. METHODS: The 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. RESULTS: On 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. CONCLUSION: A 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.

Orientation dependence of R2 relaxation in the newborn brain.

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.

Recovering SWI-filtered phase data using deep learning.

PURPOSE: To develop a deep neural network to recover filtered phase from clinical MR phase images to enable the computation of QSMs. METHODS: Eighteen 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. RESULTS: Susceptibility 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. CONCLUSION: It 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.

Myelin water imaging depends on white matter fiber orientation in the human brain.

PURPOSE: The multi-exponential T2 decay of the MRI signal from cerebral white matter can be separated into short T2 components related to myelin water and long T2 components related to intracellular and extracellular water. In this study, we investigated to what degree the apparent myelin water fraction (MWF) depends on the angle between white matter fibers and the main magnetic field. METHODS: Maps of the apparent MWF were acquired using multi-echo Carr-Purcell-Meiboom-Gill and gradient-echo spin-echo sequences. The Carr-Purcell-Meiboom-Gill sequence was acquired with a TR of 1073 ms, 1500 ms, and 2000 ms. The fiber orientation was mapped with DTI. By angle-wise pooling the voxels across the brain's white matter, orientation-dependent apparent MWF curves were generated. RESULTS: We found that the apparent MWF varied between 25% and 35% across different fiber orientations. Furthermore, the selection of the TR influences the apparent MWF. CONCLUSION: White matter fiber orientation induces a strong systematic bias on the estimation of the apparent MWF. This finding has implications for future research and the interpretation of MWI results in previously published studies.

DECAES - DEcomposition and Component Analysis of Exponential Signals.

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 2min, and luminal water maps of the prostate in under 1min.

The role of iron and myelin in orientation dependent R2* of white matter.

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.

Rapid solution of the Bloch-Torrey equation in anisotropic tissue: Application to dynamic susceptibility contrast MRI of cerebral white matter.

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%.

Southwick angle measurements and SCFE slip severity classifications are affected by frog-lateral positioning.

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.

Relationships Between Severity of Deformity and Impingement in Slipped Capital Femoral Epiphysis.

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.