Joint eigenvector estimation from mutually anisotropic tensors improves susceptibility tensor imaging of the brain, kidney, and heart

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.

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.

Quantitative susceptibility mapping (QSM) of the cardiovascular system: challenges and perspectives

Quantitative susceptibility mapping (QSM) is a powerful, non-invasive, magnetic resonance imaging (MRI) technique that relies on measurement of magnetic susceptibility. So far, QSM has been employed mostly to study neurological disorders characterized by iron accumulation, such as Parkinson's and Alzheimer's diseases. Nonetheless, QSM allows mapping key indicators of cardiac disease such as blood oxygenation and myocardial iron content. For this reason, the application of QSM offers an unprecedented opportunity to gain a better understanding of the pathophysiological changes associated with cardiovascular disease and to monitor their evolution and response to treatment. Recent studies on cardiovascular QSM have shown the feasibility of a non-invasive assessment of blood oxygenation, myocardial iron content and myocardial fibre orientation, as well as carotid plaque composition. Significant technical challenges remain, the most evident of which are related to cardiac and respiratory motion, blood flow, chemical shift effects and susceptibility artefacts. Significant work is ongoing to overcome these challenges and integrate the QSM technique into clinical practice in the cardiovascular field.

Can myocardial susceptibility quantification be an imaging biomarker for cardiac amyloidosis?

Purpose

This study aimed to evaluate whether quantification of myocardial susceptibility by cardiac magnetic resonance imaging (CMR) can be an imaging biomarker for cardiac amyloidosis (CA).

Materials and methods

Twenty-six patients with CA underwent CMR, including magnetic phase imaging with a 3.0-T magnetic resonance imaging scanner. Myocardial susceptibility was quantified as a phase shift slope value by magnetic phase analysis. Those values from patients with CA were compared with corresponding values from 18 controls and 15 healthy volunteers. A univariate logistic regression analysis was conducted to identify significant parameters related to CA.

Results

The phase shift slope, a quantitative parameter of myocardial susceptibility, was significantly lower in the CA group compared with the control group and compared with healthy volunteers (p < 0.01). From a total of 17 tested variables, 6 were considered to be significant predictors of CA (p ≤ 0.05) during the univariate analysis. The phase shift slope yielded the best AUC of 0.89 (95% CI = 0.79–0.98) for the prediction of CA (p < 0.01). The phase shift slope was significantly correlated with the end-diastolic thickness of the interventricular septum (r =  − 0.39, p < 0.01) and posterior wall of the left ventricle (r =  − 0.35, p = 0.02).

Conclusion

Myocardial susceptibility analysis by CMR helps in the diagnosis of patients with CA and can be a new quantitative imaging biomarker for CA.

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.

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

Susceptibility tensor imaging (STI) has been proposed as an alternative to diffusion tensor imaging (DTI) for non-invasive in vivo characterization of brain tissue microstructure and white matter fiber architecture, potentially benefitting from its high spatial resolution. In spite of different biophysical mechanisms, animal studies have demonstrated white matter fiber directions measured using STI to be reasonably consistent with those from diffusion tensor imaging (DTI). However, human brain STI is hampered by its requirement of acquiring data at more than 10 head rotations and a complicated processing pipeline. In this paper, we propose a diffusion-regularized STI method (DRSTI) that employs a tensor spectral decomposition constraint to regularize the STI solution using the fiber directions estimated by DTI as a priori. We then explore the high-resolution DRSTI with MR phase images acquired at only 6 head orientations. Compared to other STI approaches, the DRSTI generated susceptibility tensor components, mean magnetic susceptibility (MMS), magnetic susceptibility anisotropy (MSA) and fiber direction maps with fewer artifacts, especially in regions with large susceptibility variations, and with less erroneous quantifications. In addition, the DRSTI method allows us to distinguish more structural features that could not be identified in DTI, especially in deep gray matters. DRSTI enables a more accurate susceptibility tensor estimation with a reduced number of sampling orientations, and achieves better tracking of fiber pathways than previous STI attempts on in vivo human brain.

Multimodal integration of diffusion MRI for better characterization of tissue biology

The contrast in diffusion-weighted MR images is due to variations of diffusion properties within the examined specimen. Certain microstructural information on the underlying tissues can be inferred through quantitative analyses of the diffusion-sensitized MR signals. In the first part of the paper, we review two types of approach for characterizing diffusion MRI signals: Bloch's equations with diffusion terms, and statistical descriptions. Specifically, we discuss expansions in terms of cumulants and orthogonal basis functions, the confinement tensor formalism and tensor distribution models. Further insights into the tissue properties may be obtained by integrating diffusion MRI with other techniques, which is the subject of the second part of the paper. We review examples involving magnetic susceptibility, structural tensors, internal field gradients, transverse relaxation and functional MRI. Integrating information provided by other imaging modalities (MR based or otherwise) could be a key to improve our understanding of how diffusion MRI relates to physiology and biology.

Spin echo based cardiac diffusion imaging at 7T: An ex vivo study of the porcine heart at 7T and 3T

Purpose of this work was to assess feasibility of cardiac diffusion tensor imaging (cDTI) at 7 T in a set of healthy, unfixed, porcine hearts using various parallel imaging acceleration factors and to compare SNR and derived cDTI metrics to a reference measured at 3 T. Magnetic resonance imaging was performed on 7T and 3T whole body systems using a spin echo diffusion encoding sequence with echo planar imaging readout. Five reference (b = 0 s/mm2) images and 30 diffusion directions (b = 700 s/mm2) were acquired at both 7 T and 3 T using a GRAPPA acceleration factor R = 1. Scans at 7 T were repeated using R = 2, R = 3, and R = 4. SNR evaluation was based on 30 reference (b = 0 s/mm2) images of 30 slices of the left ventricle and cardiac DTI metrics were compared within AHA segmentation. The number of hearts scanned at 7 T and 3 T was n = 11. No statistically significant differences were found for evaluated helix angle, secondary eigenvector angle, fractional anisotropy and apparent diffusion coefficient at the different field strengths, given sufficiently high SNR and geometrically undistorted images. R≥3 was needed to reduce susceptibility induced geometric distortions to an acceptable amount. On average SNR in myocardium of the left ventricle was increased from 29±3 to 44±6 in the reference image (b = 0 s/mm2) when switching from 3 T to 7 T. Our study demonstrates that high resolution, ex vivo cDTI is feasible at 7 T using commercial hardware.

Susceptibility tensor imaging and tractography of collagen fibrils in the articular cartilage

PURPOSE

To investigate the B0 orientation-dependent magnetic susceptibility of collagen fibrils within the articular cartilage and to determine whether susceptibility tensor imaging (STI) can detect the 3D collagen network within cartilage.

METHODS

Multiecho gradient echo datasets (100-μm isotropic resolution) were acquired from fixed porcine articular cartilage specimens at 9.4 T. The susceptibility tensor was calculated using phase images acquired at 12 or 15 different orientations relative to B0 . The susceptibility anisotropy of the collagen fibril was quantified and diffusion tensor imaging (DTI) was compared against STI. 3D tractography was performed to visualize and track the collagen fibrils with DTI and STI.

RESULTS

STI experiments showed the distinct and significant anisotropic magnetic susceptibility of collagen fibrils within the articular cartilage. STI can be used to measure and quantify susceptibility anisotropy maps. Furthermore, STI provides orientation information of the underlying collagen network via 3D tractography.

CONCLUSION

The findings of this study demonstrate that STI can characterize the orientation variation of collagen fibrils where diffusion anisotropy fails. We believe that STI could serve as a sensitive and noninvasive marker to study the collagen fibrils microstructure. Magn Reson Med 78:1683-1690, 2017. © 2017 International Society for Magnetic Resonance in Medicine.