Diffusion-regularized susceptibility tensor imaging (DRSTI) of tissue microstructures in the human brain

Chaos and COSMOS-Considerations on QSM methods with multiple and single orientations and effects from local anisotropy

PURPOSE

Field-to-susceptibility inversion in quantitative susceptibility mapping (QSM) is ill-posed and needs numerical stabilization through either regularization or oversampling by acquiring data at three or more object orientations. Calculation Of Susceptibility through Multiple Orientations Sampling (COSMOS) is an established oversampling approach and regarded as QSM gold standard. It achieves a well-conditioned inverse problem, requiring rotations by 0°, 60° and 120° in the yz-plane. However, this is impractical in vivo, where head rotations are typically restricted to a range of ±25°. Non-ideal sampling degrades the conditioning with residual streaking artifacts whose mitigation needs further regularization. Moreover, susceptibility anisotropy in white matter is not considered in the COSMOS model, which may introduce additional bias. The current work presents a thorough investigation of these effects in primate brain.

METHODS

Gradient-recalled echo (GRE) data of an entire fixed chimpanzee brain were acquired at 7 T (350 μm resolution, 10 orientations) including ideal COSMOS sampling and realistic rotations in vivo. Comparisons of the results included ideal COSMOS, in-vivo feasible acquisitions with 3-8 orientations and single-orientation iLSQR QSM.

RESULTS

In-vivo feasible and optimal COSMOS yielded high-quality susceptibility maps with increased SNR resulting from averaging multiple acquisitions. COSMOS reconstructions from non-ideal rotations about a single axis required additional L2-regularization to mitigate residual streaking artifacts.

CONCLUSION

In view of unconsidered anisotropy effects, added complexity of the reconstruction, and the general challenge of multi-orientation acquisitions, advantages of sub-optimal COSMOS schemes over regularized single-orientation QSM appear limited in in-vivo settings.

A spatially adaptive regularization based three-dimensional reconstruction network for quantitative susceptibility mapping

Objective.Quantitative susceptibility mapping (QSM) is a new imaging technique for non-invasive characterization of the composition and microstructure ofin vivotissues, and it can be reconstructed from local field measurements by solving an ill-posed inverse problem. Even for deep learning networks, it is not an easy task to establish an accurate quantitative mapping between two physical quantities of different units, i.e. field shift in Hz and susceptibility value in ppm for QSM.Approach. In this paper, we propose a spatially adaptive regularization based three-dimensional reconstruction network SAQSM. A spatially adaptive module is specially designed and a set of them at different resolutions are inserted into the network decoder, playing a role of cross-modality based regularization constraint. Therefore, the exact information of both field and magnitude data is exploited to adjust the scale and shift of feature maps, and thus any information loss or deviation occurred in previous layers could be effectively corrected. The network encoding has a dynamic perceptual initialization, which enables the network to overcome receptive field intervals and also strengthens its ability to detect features of various sizes.Main results. Experimental results on the brain data of healthy volunteers, clinical hemorrhage and simulated phantom with calcification demonstrate that SAQSM can achieve more accurate reconstruction with less susceptibility artifacts, while perform well on the stability and generalization even for severe lesion areas.Significance. This proposed framework may provide a valuable paradigm to quantitative mapping or multimodal reconstruction.

A latent code based multi-variable modulation network for susceptibility mapping

Quantitative susceptibility mapping (QSM) is a technique for obtaining quantitative information on tissue susceptibility and has shown promising potential for clinical applications, in which the magnetic susceptibility is calculated by solving an ill-posed inverse problem. Recently, deep learning-based methods are proposed to address this issue, but the diversity of data distribution was not well considered, and thus the model generalization is limited in clinical applications. In this paper, we propose a Latent Code based Multi-Variable modulation network for QSM reconstruction (LCMnet). Particularly, a specific modulation module is exploited to incorporate three variables, i.e., field map, magnitude image, and initial susceptibility. The latent code in the modulated convolution is learned from feature maps of the field data using the encoder-decoder framework. The susceptibility map pre-estimated from simple thresholding is the constant input of the module, thereby enhancing the network stability and accelerating training convergence. As another input, multi-level features generated by a cross-fusion block integrate the information of field and magnitude data effectively. Experimental results on in vivo human brain data, challenge data, clinical data and synthetic data demonstrate that the proposed method LCMnet can achieve outstanding performance on accurate susceptibility measurement and also excellent generalization.

Sub-voxel quantitative susceptibility mapping for assessing whole-brain magnetic susceptibility from ages 4 to 80

The evolution of magnetic susceptibility of the brain is mainly determined by myelin in white matter (WM) and iron deposition in deep gray matter (DGM). However, existing imaging techniques have limited abilities to simultaneously quantify the myelination and iron deposition within a voxel throughout brain development and aging. For instance, the temporal trajectories of iron in the brain WM and myelination in DGM have not been investigated during the aging process. This study aimed to map the age-related iron and myelin changes in the whole brain, encompassing myelin in DGM and iron deposition in WM, using a novel sub-voxel quantitative susceptibility mapping (QSM) method. To achieve this, a cohort of 494 healthy adults (18-80 years old) was studied. The sub-voxel QSM method was employed to obtain the paramagnetic and diamagnetic susceptibility based on the approximatedR 2 ' map from acquiredR 2 * map. The linear relationship betweenR 2 * andR 2 ' maps was established from the regression coefficients on a small cohort data acquired with both 3D gradient recalled echo data andR 2 mapping. Large cohort sub-voxel susceptibility maps were used to create longitudinal and age-specific atlases via group-wise registration. To explore the differential developmental trajectories in the DGM and WM, we employed nonlinear models including exponential and Poisson functions, along with generalized additive models. The constructed atlases reveal the iron accumulation in the posterior part of the putamen and the gradual myelination process in the globus pallidus with aging. Interestingly, the developmental trajectories show that the rate of myelination differs among various DGM regions. Furthermore, the process of myelin synthesis is paralleled by an associated pattern of iron accumulation in the primary WM fiber bundles. In summary, our study offers significant insights into the distinctive developmental trajectories of iron in the brain's WM and myelination/demyelination in the DGM in vivo. These findings highlight the potential of using sub-voxel QSM to uncover new perspectives in neuroscience and improve our understanding of whole-brain myelination and iron deposit processes across the lifespan.

Effect of corticosubcortical iron deposition on dysfunction in CADASIL is mediated by white matter microstructural damage

Iron dysregulation may attenuate cognitive performance in patients with CADASIL. However, the underlying pathophysiological mechanisms remain incompletely understood. Whether white matter microstructural changes mediate these processes is largely unclear. In the present study, 30 cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy (CADASIL) patients were confirmed via genetic analysis and 30 sex- and age-matched healthy controls underwent multimodal MRI examinations and neuropsychological assessments. Quantitative susceptibility mapping and peak width of skeletonized mean diffusivity (PSMD) were analyzed. Mediation effect analysis was performed to explore the interrelationship between iron deposition, white matter microstructural changes and cognitive deficits in CADASIL. Cognitive deterioration was most affected in memory and executive function, followed by attention and working memory in CADASIL. Excessive iron in the temporal-precuneus pathway and deep gray matter specific to CADASIL were identified. Mediation analysis further revealed that PSMD mediated the relationship between iron concentration and cognitive profile in CADASIL. The present findings provide a new perspective on iron deposition in the corticosubcortical circuit and its contribution to disease-related selective cognitive decline, in which iron concentration may affect cognition by white matter microstructural changes in CADASIL.

DeepSTI: Towards tensor reconstruction using fewer orientations in susceptibility tensor imaging

Susceptibility tensor imaging (STI) is an emerging magnetic resonance imaging technique that characterizes the anisotropic tissue magnetic susceptibility with a second-order tensor model. STI has the potential to provide information for both the reconstruction of white matter fiber pathways and detection of myelin changes in the brain at mm resolution or less, which would be of great value for understanding brain structure and function in healthy and diseased brain. However, the application of STI in vivo has been hindered by its cumbersome and time-consuming acquisition requirement of measuring susceptibility induced MR phase changes at multiple head orientations. Usually, sampling at more than six orientations is required to obtain sufficient information for the ill-posed STI dipole inversion. This complexity is enhanced by the limitation in head rotation angles due to physical constraints of the head coil. As a result, STI has not yet been widely applied in human studies in vivo. In this work, we tackle these issues by proposing an image reconstruction algorithm for STI that leverages data-driven priors. Our method, called DeepSTI, learns the data prior implicitly via a deep neural network that approximates the proximal operator of a regularizer function for STI. The dipole inversion problem is then solved iteratively using the learned proximal network. Experimental results using both simulation and in vivo human data demonstrate great improvement over state-of-the-art algorithms in terms of the reconstructed tensor image, principal eigenvector maps and tractography results, while allowing for tensor reconstruction with MR phase measured at much less than six different orientations. Notably, promising reconstruction results are achieved by our method from only one orientation in human in vivo, and we demonstrate a potential application of this technique for estimating lesion susceptibility anisotropy in patients with multiple sclerosis.

APART-QSM: an improved sub-voxel quantitative susceptibility mapping for susceptibility source separation using an iterative data fitting method

The brain tissue phase contrast in MRI sequences reflects the spatial distributions of multiple substances, such as iron, myelin, calcium, and proteins. These substances with paramagnetic and diamagnetic susceptibilities often colocalize in one voxel in brain regions. Both opposing susceptibilities play vital roles in brain development and neurodegenerative diseases. Conventional QSM methods only provide voxel-averaged susceptibility value and cannot disentangle intravoxel susceptibilities with opposite signs. Advanced susceptibility imaging methods have been recently developed to distinguish the contributions of opposing susceptibility sources for QSM. The basic concept of separating paramagnetic and diamagnetic susceptibility proportions is to include the relaxation rate R₂^* with R₂^' in QSM. The magnitude decay kernel, describing the proportionality coefficient between R₂^' and susceptibility, is an essential reconstruction coefficient for QSM separation methods. In this study, we proposed a more comprehensive complex signal model that describes the relationship between 3D GRE signal and the contributions of paramagnetic and diamagnetic susceptibility to the frequency shift and R₂^* relaxation. The algorithm is implemented as a constrained minimization problem in which the voxel-wise magnitude decay kernel and sub-voxel susceptibilities are determined alternately in each iteration until convergence. The calculated voxel-wise magnitude decay kernel could realistically model the relationship between the R₂^' relaxation and the volume susceptibility. Thus, the proposed method effectively prevents the errors of the magnitude decay kernel from propagating to the final susceptibility separation reconstruction. Phantom studies, ex vivo macaque brain experiments, and in vivo human brain imaging studies were conducted to evaluate the ability of the proposed method to distinguish paramagnetic and diamagnetic susceptibility sources. The results demonstrate that the proposed method provides state-of-the-art performances for quantifying brain iron and myelin compared to previous QSM separation methods. Our results show that the proposed method has the potential to simultaneously quantify whole brain iron and myelin during brain development and aging. The proposed model was also deployed with multiple-orientation complex GRE data input measurements, resulting in high-quality QSM separation maps with more faithful tissue delineation between brain structures compared to those reconstructed by single-orientation QSM separation methods.

Orientation dependent proton transverse relaxation in the human brain white matter: The magic angle effect on a cylindrical helix

PURPOSE

To overcome some limitations of previous proton orientation-dependent transverse relaxation formalisms in human brain white matter (WM) by a generalized magic angle effect function.

METHODS

A cylindrical helix model was developed embracing anisotropic rotational and translational diffusion of restricted molecules in WM, with the former characterized by an axially symmetric system. Transverse relaxation rates R₂ and R₂^∗ were divided into isotropic R₂ⁱ and anisotropic parts, R₂^a ∗ f(α,Φ - ε₀), with α denoting an open angle and ε₀ an orientation (Φ) offset from DTI-derived primary diffusivity direction. The proposed framework (Fit A) was compared to prior models without ε₀ on previously published water and methylene proton transverse relaxation rates from developing, healthy, and pathological WM at 3 T. Goodness of fit was represented by root-mean-square error (RMSE). F-test and linear correlation were used with statistical significance set to P ≤ 0.05.

RESULTS

Fit A significantly (P < 0.01) outperformed prior models as demonstrated by reduced RMSEs, e.g., 0.349 vs. 0.724 in myelin water. Fitted ε₀ was in good agreement with calculated ε₀ from directional diffusivities. Compared with those from healthy adult, the fitted R₂ⁱ, R₂^a, and α from neonates were substantially reduced but ε₀ increased, consistent with developing myelination. Significant positive (R₂ⁱ) and negative (α and R₂^a) correlations were found with aging (demyelination) in elderly.

CONCLUSION

The developed framework can better characterize orientation dependences from a wide range of proton transverse relaxation measurements in the human brain WM, thus shedding new light on myelin microstructural alterations at the molecular level.

Phase-shifted transverse relaxation orientation dependences in human brain white matter

This work aimed to demonstrate an essential phase shift ε 0 $$ {\varepsilon}_0 $$ for better quantifying R 2 $$ {R}_2 $$ and R 2 * $$ {R}_2^{\ast } $$ in human brain white matter (WM), and to further elucidate its origin related to the directional diffusivities from standard diffusion tensor imaging (DTI). ε 0 $$ {\varepsilon}_0 $$ was integrated into a proposed generalized transverse relaxation model for characterizing previously published R 2 $$ {R}_2 $$ and R 2 * $$ {R}_2^{\ast } $$ orientation dependence profiles in brain WM, and then comparisons were made with those without ε 0 $$ {\varepsilon}_0 $$ . It was theorized that anisotropic diffusivity direction ε $$ \varepsilon $$ was collinear with an axon fiber subject to all eigenvalues and eigenvectors from an apparent diffusion tensor. To corroborate the origin of ε 0 $$ {\varepsilon}_0 $$ , R 2 $$ {R}_2 $$ orientation dependences referenced by ε $$ \varepsilon $$ were compared with those referenced by the standard principal diffusivity direction Φ $$ \Phi $$ at b-values of 1000 and 2500 (s/mm² ). These R 2 $$ {R}_2 $$ orientation dependences were obtained from T 2 $$ {T}_2 $$ -weighted images (b = 0) of ultrahigh-resolution Connectome DTI datasets in the public domain. A normalized root-mean-square error ( NRMSE % $$ NRMSE\% $$ ) and an F $$ F $$ -test were used for evaluating curve-fittings, and statistical significance was considered to be a p of 0.05 or less. A phase-shifted model resulted in significantly reduced NRMSE % $$ NRMSE\% $$ compared with that without ε 0 $$ {\varepsilon}_0 $$ in quantifying various R 2 $$ {R}_2 $$ and R 2 * $$ {R}_2^{\ast } $$ profiles, both in vivo and ex vivo at multiple B 0 $$ {B}_0 $$ fields. The R 2 $$ {R}_2 $$ profiles based on Φ $$ \Phi $$ manifested a right-shifted phase ( ε 0 > 0 $$ {\varepsilon}_0>0 $$ ) at two b-values, while those based on ε $$ \varepsilon $$ became free from ε 0 $$ {\varepsilon}_0 $$ . For all phase-shifted R 2 $$ {R}_2 $$ and R 2 * $$ {R}_2^{\ast } $$ profiles, ε 0 $$ {\varepsilon}_0 $$ generally depended on the directional diffusivities by tan - 1 D ⊥ / D ∥ $$ {\tan}^{-1}\left({D}_{\perp }/{D}_{\parallel}\right) $$ , as predicted. In summary, a ubiquitous phase shift ε 0 $$ {\varepsilon}_0 $$ has been demonstrated as a prerequisite for better quantifying transverse relaxation orientation dependences in human brain WM. Furthermore, the origin of ε 0 $$ {\varepsilon}_0 $$ associated with the directional diffusivities from DTI has been elucidated. These findings could have a significant impact on interpretations of prior R 2 $$ {R}_2 $$ and R 2 * $$ {R}_2^{\ast } $$ datasets and on future research.

An improved asymmetric susceptibility tensor imaging model with frequency offset correction

PURPOSE

To improve susceptibility tensor imaging (STI) reconstruction using the asymmetric STI model with the correction of non-bulk-magnetic-susceptibility (NBMS) effects.

METHOD

A frequency offset term was introduced into the asymmetric STI model to account for the bias between measured MRI frequency signals and conventional susceptibility tensor models because of NBMS contributions. Experiments were conducted to compare the proposed model with conventional STI, conventional STI with the proposed frequency offset correction, and asymmetric STI on simulation, ex vivo mouse brain, and in vivo human brain data.

RESULTS

In the simulation where NBMS contributions are head rotation-invariant, the proposed method achieves the lowest errors in mean magnetic susceptibility (MMS) and magnetic susceptibility anisotropy (MSA) and is more robust to noise in the estimation of principal eigenvector (PEV). When considering the head orientation dependency of NBMS contributions, the proposed method shows advantages in estimating MSA and PEV. On the mouse and human brain data, the proposed method produces more reliable MSA maps and more consistent white matter fiber directions when referring to those from DTI than the compared STI methods.

CONCLUSION

The proposed method can reduce the effects of NBMS-related frequency shifts on the susceptibility tensors in the brain white matter. This study inspires STI reconstruction from the perspective of better modeling the sources of frequency shifts.

Regularized Asymmetric Susceptibility Tensor Imaging in the Human Brain in vivo

Susceptibility tensor imaging (STI) is a promising tool for studying orientation-dependent tissue magnetic susceptibility and for mapping white matter fiber orientations complementary to diffusion tensor imaging (DTI). However, the limited head rotation range within modern head coils for data acquisition makes in vivo STI reconstruction ill-conditioned. Conventional STI reconstruction method is usually vulnerable to noise and requires sufficiently large head rotations to solve this ill-conditioned inverse problem. In this study, based on the recently proposed asymmetric STI (aSTI) model, a new method termed aSTI+ was proposed to improve in vivo STI reconstruction by enforcing isotropic susceptibility tensor inside cerebrospinal fluid (CSF) and applying morphology constraint in white matter. Experimental results showed superior performance of the proposed method with reduced noise, improved tissue contrast and better fiber orientation estimation over previous methods. Thus aSTI+ may promote in vivo human brain STI studies on white matter and myelin-related brain diseases.

Magnetic susceptibility anisotropy in normal appearing white matter in multiple sclerosis from single-orientation acquisition

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Orientation dependence of QSM is studied in a large cohort of MS patients.

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Apparent magnetic susceptibility anisotropy (MSA) obtained from single-orientation QSM.

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Apparent MSA found decreased in optic radiation (OR) of MS patients.

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Apparent MSA decreases with lesion load in OR and with disease duration in splenium.

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Negative apparent MSA observed in SLF indicates limitations of the proposed method.

Quantitative susceptibility mapping (QSM) has been successfully applied to study changes in deep grey matter nuclei as well as in lesional tissue, but its application to white matter has been complicated by the observed orientation dependence of gradient echo signal. The anisotropic susceptibility tensor is thought to be at the origin of this orientation dependence, and magnetic susceptibility anisotropy (MSA) derived from this tensor has been proposed as a marker of the state and integrity of the myelin sheath and may therefore be of particular interest for the study of demyelinating pathologies such as multiple sclerosis (MS). Reconstruction of the susceptibility tensor, however, requires repeated measurements with multiple head orientations, rendering the approach impractical for clinical applications.

In this study, we combined single-orientation QSM with fibre orientation information to assess apparent MSA in three white matter tracts, i.e., optic radiation (OR), splenium of the corpus callosum (SCC), and superior longitudinal fascicle (SLF), in two cohorts of 64 healthy controls and 89 MS patients. The apparent MSA showed a significant decrease in optic radiation in the MS cohort compared with healthy controls. It decreased in the MS cohort with increasing lesion load in OR and with disease duration in the splenium. All of this suggests demyelination in normal appearing white matter. However, the apparent MSA observed in the SLF pointed to potential systematic issues that require further exploration to realize the full potential of the presented approach. Despite the limitations of such single-orientation ROI-specific estimation, we believe that our clinically feasible approach to study degenerative changes in WM is worthy of further investigation.

Streaking artifact suppression of quantitative susceptibility mapping reconstructions via L1-norm data fidelity optimization (L1-QSM)

PURPOSE

The presence of dipole-inconsistent data due to substantial noise or artifacts causes streaking artifacts in quantitative susceptibility mapping (QSM) reconstructions. Often used Bayesian approaches rely on regularizers, which in turn yield reduced sharpness. To overcome this problem, we present a novel L1-norm data fidelity approach that is robust with respect to outliers, and therefore prevents streaking artifacts.

METHODS

QSM functionals are solved with linear and nonlinear L1-norm data fidelity terms using functional augmentation, and are compared with equivalent L2-norm methods. Algorithms were tested on synthetic data, with phase inconsistencies added to mimic lesions, QSM Challenge 2.0 data, and in vivo brain images with hemorrhages.

RESULTS

The nonlinear L1-norm-based approach achieved the best overall error metric scores and better streaking artifact suppression. Notably, L1-norm methods could reconstruct QSM images without using a brain mask, with similar regularization weights for different data fidelity weighting or masking setups.

CONCLUSION

The proposed L1-approach provides a robust method to prevent streaking artifacts generated by dipole-inconsistent data, renders brain mask calculation unessential, and opens novel challenging clinical applications such asassessing brain hemorrhages and cortical layers.

Asymmetric susceptibility tensor imaging

PURPOSE

To investigate the symmetry constraint in susceptibility tensor imaging.

THEORY

The linear relationship between the MRI frequency shift and the magnetic susceptibility tensor is derived without constraining the tensor to be symmetric. In the asymmetric case, the system matrix is shown to be maximally rank 6. Nonetheless, relaxing the symmetry constraint may still improve tensor estimation because noise and image artifacts do not necessarily follow the constraint.

METHODS

Gradient echo phase data are obtained from postmortem mouse brain and kidney samples. Both symmetric and asymmetric tensor reconstructions are applied to the data. The reconstructions are then used for susceptibility tensor imaging fiber tracking. Simulations with ground truth and at various noise levels are also performed. The reconstruction methods are compared qualitatively and quantitatively.

RESULTS

Compared to regularized and unregularized symmetric reconstructions, the asymmetric reconstruction shows reduced noise and streaking artifacts, better contrast, and more complete fiber tracking. In simulation, the asymmetric reconstruction achieves better mean squared error and better angular difference in the presence of noise. Decomposing the asymmetric tensor into its symmetric and antisymmetric components confirms that the underlying susceptibility tensor is symmetric and that the main sources of asymmetry are noise and streaking artifacts.

CONCLUSION

Whereas the susceptibility tensor is symmetric, asymmetric reconstruction is more effective in suppressing noise and artifacts, resulting in more accurate estimation of the susceptibility tensor.