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

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.

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.

Static and dynamic BOLD fMRI components along white matter fibre tracts and their dependence on the orientation of the local diffusion tensor axis relative to the B0-field

Recent studies have reported functional MRI (fMRI) activation within cerebral white matter (WM) using blood-oxygenation-level-dependent (BOLD) contrast. Many blood vessels in WM run parallel to the fibre bundles, and other studies observed dependence of susceptibility contrast-based measures of blood volume on the local orientation of the fibre bundles relative to the magnetic field or B₀ axis. Motivated by this, we characterized the dependence of gradient-echo BOLD fMRI on fibre orientation (estimated by the local diffusion tensor) relative to the B₀ axis to test whether the alignment between bundles and vessels imparts an orientation dependence on resting-state BOLD fluctuations in the WM. We found that the baseline signal level of the T₂*-weighted data is 11% higher in voxels containing fibres parallel to B₀ than those containing perpendicular fibres, consistent with a static influence of either fibre or vessel orientation on local T₂* values. We also found that BOLD fluctuations in most bundles exhibit orientation effects expected from oxygenation changes, with larger amplitudes from voxels containing perpendicular fibres. Different magnitudes of this orientation effect were observed across the major WM bundles, with inferior fasciculus, corpus callosum and optic radiation exhibiting 14-19% higher fluctuations in voxels containing perpendicular compared to parallel fibres.

Imaging perivascular space structure and function using brain MRI

In this article, we provide an overview of current neuroimaging methods for studying perivascular spaces (PVS) in humans using brain MRI. In recent years, an increasing number of studies highlighted the role of PVS in cerebrospinal/interstial fluid circulation and clearance of cerebral waste products and their association with neurological diseases. Novel strategies and techniques have been introduced to improve the quantification of PVS and to investigate their function and morphological features in physiological and pathological conditions. After a brief introduction on the anatomy and physiology of PVS, we examine the latest technological developments to quantitatively analyze the structure and function of PVS in humans with MRI. We describe the applications, advantages, and limitations of these methods, providing guidance and suggestions on the acquisition protocols and analysis techniques that can be applied to study PVS in vivo. Finally, we review the human neuroimaging studies on PVS across the normative lifespan and in the context of neurological disorders.

New imaging features of tuberous sclerosis complex: A 7 T MRI study

Few in vivo studies have focused on the perivenous association of tubers and iron deposition in the deep gray nuclei in patients with tuberous sclerosis complex (TSC). We investigated this possible relationship in TSC patients using susceptibility weighted imaging (SWI) at 7 T. SWI with high spatial resolution and enhanced sensitivity was performed on 11 TSC patients in comparison with 15 age- and sex-matched healthy controls. The relationship between tubers and veins was evaluated. In addition, the phase images of SWI were processed to produce local field shift (LFS) maps to quantify iron deposition. The mean LFS in the deep gray nuclei was compared between the TSC patients and healthy controls using a covariance analysis. Venous involvement was observed in 211 of the 231 (91.3%) cortical tubers on SWI. The slender tubers often oriented around the long axis of penetrating veins, possibly because cortical tubers typically developed and/or migrated along venous vasculatures. A significant difference in LFS of the thalamus was detected between the TSC patients and healthy controls (3.36 ± 0.50 versus 3.01 ± 0.39, p < 0.01). The new in vivo imaging features observed at 7 T provide valuable insights into the possible venous association of TSC lesions and iron accumulation in the deep gray nuclei. Our results may lead to a better understanding of the pathological changes involved in TSC under in vivo conditions.

Diffusion-informed spatial smoothing of fMRI data in white matter using spectral graph filters

Brain activation mapping using functional magnetic resonance imaging (fMRI) has been extensively studied in brain gray matter (GM), whereas in large disregarded for probing white matter (WM). This unbalanced treatment has been in part due to controversies in relation to the nature of the blood oxygenation level-dependent (BOLD) contrast in WM and its detectability. However, an accumulating body of studies has provided solid evidence of the functional significance of the BOLD signal in WM and has revealed that it exhibits anisotropic spatio-temporal correlations and structure-specific fluctuations concomitant with those of the cortical BOLD signal. In this work, we present an anisotropic spatial filtering scheme for smoothing fMRI data in WM that accounts for known spatial constraints on the BOLD signal in WM. In particular, the spatial correlation structure of the BOLD signal in WM is highly anisotropic and closely linked to local axonal structure in terms of shape and orientation, suggesting that isotropic Gaussian filters conventionally used for smoothing fMRI data are inadequate for denoising the BOLD signal in WM. The fundamental element in the proposed method is a graph-based description of WM that encodes the underlying anisotropy observed across WM, derived from diffusion-weighted MRI data. Based on this representation, and leveraging graph signal processing principles, we design subject-specific spatial filters that adapt to a subject's unique WM structure at each position in the WM that they are applied at. We use the proposed filters to spatially smooth fMRI data in WM, as an alternative to the conventional practice of using isotropic Gaussian filters. We test the proposed filtering approach on two sets of simulated phantoms, showcasing its greater sensitivity and specificity for the detection of slender anisotropic activations, compared to that achieved with isotropic Gaussian filters. We also present WM activation mapping results on the Human Connectome Project's 100-unrelated subject dataset, across seven functional tasks, showing that the proposed method enables the detection of streamline-like activations within axonal bundles.

Quantitative Susceptibility Mapping of Venous Vessels in Neonates with Perinatal Asphyxia

BACKGROUND AND PURPOSE

Cerebral venous oxygen saturation can be used as an indirect measure of brain health, yet it often requires either an invasive procedure or a noninvasive technique with poor sensitivity. We aimed to test whether cerebral venous oxygen saturation could be measured using quantitative susceptibility mapping, an MR imaging technique, in 3 distinct groups: healthy term neonates, injured term neonates, and preterm neonates.

MATERIALS AND METHODS

We acquired multiecho gradient-echo MR imaging data in 16 neonates with perinatal asphyxia and moderate or severe hypoxic-ischemic encephalopathy (8 term age: average, 40.0 [SD, 0.8]  weeks' gestational age; 8 preterm, 33.5 [SD, 2.0]  weeks' gestational age) and in 8 healthy term-age controls (39.3 [SD, 0.6] weeks, for a total of n = 24. Data were postprocessed as quantitative susceptibility mapping images, and magnetic susceptibility was measured in cerebral veins by thesholding out 99.95% of lower magnetic susceptibility values.

RESULTS

The mean magnetic susceptibility value of the cerebral veins was found to be 0.36 (SD, 0.04) ppm in healthy term neonates, 0.36 (SD, 0.06) ppm in term injured neonates, and 0.29 (SD, 0.04) ppm in preterm injured neonates. Correspondingly, the derived cerebral venous oxygen saturation values were 73.6% (SD, 2.8%), 71.5% (SD, 7.4%), and 72.2% (SD, 5.9%). There was no statistically significant difference in cerebral venous oxygen saturation among the 3 groups (P = .751).

CONCLUSIONS

Quantitative susceptibility mapping-derived oxygen saturation values in preterm and term neonates agreed well with values in past literature. Cerebral venous oxygen saturation in preterm and term neonates with hypoxic-ischemic encephalopathy, however, was not found to be significantly different between neonates or healthy controls.

White Matter Neuroplasticity: Motor Learning Activates the Internal Capsule and Reduces Hemodynamic Response Variability

Numerous studies have noted the importance of white matter changes in motor learning, but existing literature only focuses on structural and microstructural MRI changes, as there are limited tools available for in vivo investigations of white matter function. One method that has gained recent prominence is the application of blood oxygen level dependent (BOLD) fMRI to white matter, with high-field scanners now being able to better detect the smaller hemodynamic changes present in this tissue type compared to those in the gray matter. However, fMRI techniques have yet to be applied to investigations of neuroplastic change with motor learning in white matter. White matter function represents an unexplored component of neuroplasticity and is essential for gaining a complete understanding of learning-based changes occurring throughout the whole brain. Twelve healthy, right-handed participants completed fine motor and gross motor tasks with both hands, using an MRI compatible computer mouse. Using a crossover design along with a prior analysis approach to establish WM activation, participants received a baseline scan followed by 2 weeks of training, returning for a midpoint and endpoint scan. The motor tasks were designed to be selectively difficult for the left hand, leading to a training effect only in that condition. Analysis targeted the comparison and detection of training-associated right vs left hand changes. A statistically significant improvement in motor task score was only noted for the left-hand motor condition. A corresponding change in the temporal characteristics of the white matter hemodynamic response was shown within only the right corticospinal tract. The hemodynamic response exhibited a reduction in the dispersion characteristics after the training period. To our knowledge, this is the first report of MRI detectable functional neuroplasticity in white matter, suggesting that modifications in temporal characteristics of white matter hemodynamics may underlie functional neuroplasticity in this tissue.

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.

Myelin water imaging and R2* mapping in neonates: Investigating R2* dependence on myelin and fibre orientation in whole brain white matter

R₂^* relaxation provides a semiquantitative method of detecting myelin, iron and white matter fibre orientation angles. Compared with standard histogram-based analyses, angle-resolved analysis of R₂^* has previously been shown to substantially improve the detection of subtle differences in the brain between healthy siblings of subjects with multiple sclerosis and unrelated healthy controls. Neonates, who are born with very little myelin and iron, and an underdeveloped connectome, provide researchers with an opportunity to investigate whether R₂^* is intimately linked with fibre-angle or myelin content as it is in adults, which may in future studies be explored as a potential white matter developmental biomarker. Five healthy adult volunteers (mean age [±SD] = 31.2 [±8.3] years; three males) were recruited from Vancouver, Canada. Eight term neonates (mean age = 38.6 ± 1.2 weeks; five males) were recruited from the Children's Hospital of Chongqing Medical University neonatal ward. All subjects were scanned on identical 3 T Philips Achieva scanners equipped with an eight-channel SENSE head coil and underwent a multiecho gradient echo scan, a 32-direction DTI scan and a myelin water imaging scan. For both neonates and adults, bin-averaged R₂^* variation across the brain's white matter was found to be best explained by fibre orientation. For adults, this represented a difference in R₂^* values of 3.5 Hz from parallel to perpendicular fibres with respect to the main magnetic field. In neonates, the fibre orientation dependency displayed a cosine wave shape, with a small R₂^* range of 0.4 Hz. This minor relationship in neonates provides further evidence for the key role myelin probably plays in creating this fibre orientation dependence later in life, but suggests limited clinical application in newborn populations. Future studies should investigate fibre-orientation dependency in infants in the first 5 years, when substantial myelin development occurs.

Venous contribution to sodium MRI in the human brain

PURPOSE

Sodium MRI shows great promise as a marker for cerebral metabolic dysfunction in stroke, brain tumor, and neurodegenerative pathologies. However, cerebral blood vessels, whose volume and function are perturbed in these pathologies, have elevated sodium concentrations relative to surrounding tissue. This study aims to assess whether this fluid compartment could bias measurements of tissue sodium using MRI.

METHODS

Density-weighted and B₁ corrected sodium MRI of the brain was acquired in 9 healthy participants at 4.7T. Veins were identified using co-registered ¹ H T 2 ∗ -weighted images and venous partial volume estimates were calculated by down-sampling the finer spatial resolution venous maps from the T 2 ∗ -weighted images to the coarser spatial resolution of the sodium data. Linear regressions of venous partial volume estimates and sodium signal were performed for regions of interest including just gray matter, just white matter, and all brain tissue.

RESULTS

Linear regression demonstrated a significant venous sodium contribution above the underlying tissue signal. The apparent venous sodium concentrations derived from regression were 65.8 ± 4.5 mM (all brain tissue), 71.0 ± 7.4 mM (gray matter), and 55.0 ± 4.7 mM (white matter).

CONCLUSION

Although the partial vein linear regression did not yield the expected sodium concentration in blood (~87 mM), likely the result of point spread function smearing, this regression highlights that blood compartments may bias brain tissue sodium signals across neurological conditions where blood volumes may differ.

Image processing approaches to enhance perivascular space visibility and quantification using MRI

Imaging the perivascular spaces (PVS), also known as Virchow-Robin space, has significant clinical value, but there remains a need for neuroimaging techniques to improve mapping and quantification of the PVS. Current technique for PVS evaluation is a scoring system based on visual reading of visible PVS in regions of interest, and often limited to large caliber PVS. Enhancing the visibility of the PVS could support medical diagnosis and enable novel neuroscientific investigations. Increasing the MRI resolution is one approach to enhance the visibility of PVS but is limited by acquisition time and physical constraints. Alternatively, image processing approaches can be utilized to improve the contrast ratio between PVS and surrounding tissue. Here we combine T1- and T2-weighted images to enhance PVS contrast, intensifying the visibility of PVS. The Enhanced PVS Contrast (EPC) was achieved by combining T1- and T2-weighted images that were adaptively filtered to remove non-structured high-frequency spatial noise. EPC was evaluated on healthy young adults by presenting them to two expert readers and also through automated quantification. We found that EPC improves the conspicuity of the PVS and aid resolving a larger number of PVS. We also present a highly reliable automated PVS quantification approach, which was optimized using expert readings.

Diffusion Kurtosis Imaging as a Tool in Neurotoxicology

This commentary serves as an introduction to the magnetic resonance imaging (MRI) technique called diffusion kurtosis imaging (DKI) employed in the study by Arab et al. in the present issue of Neurotoxicology Research. In their study, DKI is employed for longitudinal investigation of a methamphetamine intoxication model of Parkinson's disease. The study employs an impressive number of animals and combines DKI with behavioral analysis at multiple time points. The commentary discusses some aspects of the study design especially the strength of combining behavioral analysis with MRI in an effort to provide as thorough a characterization and validity assessment of the animal model and cohort as possible. The potential clinical value of combining multiple MRI techniques (multimodal MRI) in PD is discussed as well as the benefit of multimodal MRI combined with behavioral analysis and subsequent histological analysis for in-depth characterization of animal models.

Dependence of resting-state fMRI fluctuation amplitudes on cerebral cortical orientation relative to the direction of B0 and anatomical axes

Functional magnetic resonance imaging (fMRI) is now capable of sub-millimetre scale measurements over the entire human brain, however with such high resolutions each voxel is influenced by the local fine-scale details of the cerebral cortical vascular anatomy. The cortical vasculature is structured with the pial vessels lying tangentially along the grey matter surface, intracortical diving arterioles and ascending venules running perpendicularly to the surface, and a randomly oriented capillary network within the parenchyma. It is well-known that the amplitude of the blood-oxygenation level dependent (BOLD) signal emanating from a vessel depends on its orientation relative to the B0-field. Thus the vascular geometric hierarchy will impart an orientation dependence to the BOLD signal amplitudes and amplitude differences due to orientation differences constitute a bias for interpreting neuronal activity. Here, we demonstrate a clear effect of cortical orientation to B0 in the resting-state BOLD-fMRI amplitude (quantified as the coefficient of temporal signal variation) for 1.1 mm isotropic data at 7T and 2 mm isotropic at 3T. The maximum bias, i.e. the fluctuation amplitude difference between regions where cortex is perpendicular to vs. parallel to B0, is about +70% at the pial surface at 7T and +11% at 3T. The B0 orientation bias declines with cortical depth, becomes progressively smaller closer to the white matter surface, but then increases again to a local maximum within the white matter just beneath the cortical grey matter, suggesting a distinct tangential network of white matter vessels that also generate a BOLD orientation effect. We further found significant (negative) biases with the cortex orientation to the anterior-posterior anatomical axis of the head: a maximum negative bias of about -30% at the pial surface at 7T and about -13% at 3T. The amount of signal variance explained by the low frequency drift, motion and the respiratory cycle also showed a cortical orientation dependence; only the cardiac cycle induced signal variance was independent of cortical orientation, suggesting that the cardiac induced component of the image time-series fluctuations is not related to a significant change in susceptibility. Although these orientation effects represent a signal bias, and are likely to be a nuisance in high-resolution analyses, they may help characterize the vascular influences on candidate fMRI acquisitions and, thereby, may be exploited to improve the neuronal specificity of fMRI.

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.

The influence of brain iron on myelin water imaging

With myelin playing a vital role in normal brain integrity and function and thus in various neurological disorders, myelin sensitive magnetic resonance imaging (MRI) techniques are of great importance. In particular, multi-exponential T₂ relaxation was shown to be highly sensitive to myelin. The myelin water imaging (MWI) technique allows to separate the T₂ decay into short components, specific to myelin water, and long components reflecting the intra- and extracellular water. The myelin water fraction (MWF) is the ratio of the short components to all components. In the brain's white matter (WM), myelin and iron are closely linked via the presence of iron in the myelin generating oligodendrocytes. Iron is known to decrease T₂ relaxation times and may therefore mimic myelin. In this study, we investigated if variations in WM iron content can lead to apparent MWF changes. We performed MWI in post mortem human brain tissue prior and after chemical iron extraction. Histology for iron and myelin confirmed a decrease in iron content and no change in myelin content after iron extraction. In MRI, iron extraction lead to a decrease in MWF by 26%-28% in WM. Thus, a change in MWF does not necessarily reflect a change in myelin content. This observation has important implications for the interpretation of MWI findings in previously published studies and future research.

Perivascular space fluid contributes to diffusion tensor imaging changes in white matter

Diffusion tensor imaging (DTI) has been extensively used to map changes in brain tissue related to neurological disorders. Among the most widespread DTI findings are increased mean diffusivity and decreased fractional anisotropy of white matter tissue in neurodegenerative diseases. Here we utilize multi-shell diffusion imaging to separate diffusion signal of the brain parenchyma from non-parenchymal fluid within the white matter. We show that unincorporated anisotropic water in perivascular space (PVS) significantly, and systematically, biases DTI measures, casting new light on the biological validity of many previously reported findings. Despite the challenge this poses for interpreting these past findings, our results suggest that multi-shell diffusion MRI provides a new opportunity for incorporating the PVS contribution, ultimately strengthening the clinical and scientific value of diffusion MRI.

Characterization of the hemodynamic response function in white matter tracts for event-related fMRI

Accurate estimates of the BOLD hemodynamic response function (HRF) are crucial for the interpretation and analysis of event-related functional MRI data. To date, however, there have been no comprehensive measurements of the HRF in white matter (WM) despite increasing evidence that BOLD signals in WM change after a stimulus. We performed an event-related cognitive task (Stroop color-word interference) to measure the HRF in selected human WM pathways. The task was chosen in order to produce robust, distributed centers of activity throughout the cortex. To measure the HRF in WM, fiber tracts were reconstructed between each pair of activated cortical areas. We observed clear task-specific HRFs with reduced magnitudes, delayed onsets and prolonged initial dips in WM tracts compared with activated grey matter, thus calling for significant changes to current standard models for accurately characterizing the HRFs in WM and for modifications of standard methods of analysis of functional imaging data.