White matter microstructure from nonparametric axon diameter distribution mapping

Diffusion tensor subspace imaging of double diffusion-encoded MRI delineates small fibers and gray-matter microstructure not visible with single encoding techniques

PURPOSE

Double diffusion encoding (DDE) acquisition strategies promise specificity for small-dimensional structures inaccessible to single diffusion encoding (SDE). For DDE-weighted MRI scans to become relevant for whole brain imaging, signal reconstruction frameworks must accurately report microstructural features of interest-especially microscale anisotropy in complex tissue environments. This study examined the recently developed diffusion tensor subspace imaging (DiTSI) framework and its radial and spherical anisotropy metrics (RA and SA, respectively) in postmortem human brain tissue specimens.

METHODS

MRI microscopy including multishell SDE-weighted and DDE-weighted imaging was performed for healthy brain stem and temporal lobe specimens and for specimens with Alzheimer's disease pathology and neurodegeneration. The DiTSI framework was compared with four other diffusion MRI frameworks, and angular and radial DDE sampling were evaluated.

RESULTS

DDE acquisition and the DiTSI metric maps of SA and RA in temporal lobe and brain-stem specimens were found to be distinct from fractional anisotropy and orientation dispersion index in providing complementary and selective contrast of microscale anisotropy at the gray-matter/white-matter interface in the cortex and in hippocampal layers. DiTSI maps also unmasked small fascicles in the brain stem that were not detectable by SDE techniques and provided selective contrast across the major fiber pathways. Results also revealed prominent reductions of SA and RA in tissue with Alzheimer's disease pathology that were not observed for any other framework.

CONCLUSIONS

New contrasts were evident for DiTSI framework metrics over a range of tissue environments with promise toward providing novel markers of pathology.

Evaluation of diffusion time-dependent changes in radial diffusivity as a surrogate for axon diameter

PURPOSE

To experimentally evaluate the change in radial diffusivity with diffusion time (∆ D ⊥ $$ \Delta {\mathrm{D}}_{\perp } $$ ) as a simple estimate of axon diameter.

METHODS

Ex vivo ferret spinal cords were imaged via MRI and scanning electron microscopy. Region-of-interest comparisons were made between∆ D ⊥ $$ \Delta {\mathrm{D}}_{\perp } $$ and area-weighted mean axon diameter,d eff $$ \left\langle {\mathrm{d}}_{\mathrm{eff}}\right\rangle $$ , derived from scanning electron microscopy. Additional comparisons were made between∆ D ⊥ $$ \Delta {\mathrm{D}}_{\perp } $$ and quantitative MRI myelin metrics.

RESULTS

A strong linear correlation was found between∆ D ⊥ $$ \Delta {\mathrm{D}}_{\perp } $$ andd eff $$ \left\langle {\mathrm{d}}_{\mathrm{eff}}\right\rangle $$ . Negative correlations were found between myelin water fraction and∆ D ⊥ $$ \Delta {\mathrm{D}}_{\perp } $$ as well as bound pool fraction and∆ D ⊥ $$ \Delta {\mathrm{D}}_{\perp } $$ .

CONCLUSION

The value of∆ D ⊥ $$ \Delta {\mathrm{D}}_{\perp } $$ is shown to be a good estimate of axon size in ex vivo spinal cords regardless of variations in myelin content, as indicated by quantitative MRI.

QSI and DTI of Inherited White Matter Disorders in Rat Spinal Cord: Early Detection and Comparison with Quantitative Electron Microscopy Findings

Background: Inherited white matter (WM) disorders of the central nervous systems (CNS), or leukodystrophies, are devastating diseases that primarily affect children, many of whom die early in life or suffer from long-term disability. Methods: q-Space diffusion MR imaging (QSI) and diffusion tensor MR imaging (DTI) with the same resolution and timing parameters were used to study the spinal cords (SCs) of two myelin mutants that are experimental models of WM diseases of different severity, namely the 28-day-old taiep and Long-Evans Shaker (les) rats. The aim was to verify if and which of the diffusion methodologies used is more suitable for early detection of the milder taiep pathology and to characterize its early phase. We also aimed to compare the diffusion MRI results with quantitative electron microscopy (EM) findings. Results: We found that at this early age (28 days), both QSI and DTI were able to detect the severe les WM pathology, while the milder WM pathology in the SC of the taiep rats was detected only by QSI. An increase in the mean radial displacement (RaDis), representing the MRI axon diameter (AD), and a decrease in the probability for zero displacement (PZD) were observed in the dorsal column (ROI 1) of the taiep SCs. In other WM areas, the same trends were observed but the differences were not of statistical significance. In DTI, we found some lower fractional anisotropy (FA) values in the taiep SCs compared to the controls; however, these differences were not statistically significant. For the more severe les pathology, we observed a dramatic increase in the RaDis values and a large decrease in PZD values in all ROIs examined. There, even the FA values were lower than that of the control SCs in all ROIs, albeit with much smaller statistical significance. These MRI results, which show a higher detectability of WM pathology with heavier diffusion weighting, followed histological findings that showed significant myelin deficiency in the dorsal column in the taiep SCs and a practically complete myelin loss in all WM areas in the les SCs. This study also revealed that, under the experimental conditions used here, the apparent increase in RaDis agrees better with myelin thickness and not with average AD extracted form EM, probably reflecting the effect of water exchange. Conclusions: These results, corroborated by diffusion time-dependent QSI, also imply that while diffusion MRI in general and QSI in particular provide acceptable apparent axon diameter estimations in heathy and mature WM, this appears not to be the case in severely damaged WM where exchange appears to play a more important role.

A genetic optimisation and iterative reconstruction framework for sparse multi-dimensional diffusion-relaxation correlation MRI

Multi-dimensional diffusion-relaxation correlation (DRC) magnetic resonance imaging (MRI) techniques have recently been developed to investigate tissue microstructures. Sub-voxel tissue heterogeneity is resolved from the local correlation distributions of relaxation time and molecular diffusivity. However, the implementation of these techniques considerably increases the total acquisition time, and simply reducing the scan time may be at the expense of detailed structural resolution. To overcome these limitations, an optimised framework was proposed for acquiring microstructural maps of the human brain on a clinically feasible timescale. First, the acquisition parameters of the multi-dimensional DRC MRI method were sparsely optimised using a genetic algorithm with a fitness function according to the spectral resolution of the correlation map, hardware requirements, and total scan time. Next, the acquired DRC MRI data were processed using a proposed numerical algorithm based on the dynamic inverse Laplace transform (ILT). Prior knowledge from one-dimensional data was then utilised in the iterative procedure to improve the spectral resolution. Finally, the proposed framework was validated using Monte Carlo simulations and experimental data acquired from healthy participants on an MRI scanner. The results demonstrated that the suggested approach is feasible for offering high-resolution DRC maps that correspond to distinct microstructures with a limited amount of optimised acquisition data from two-dimensional DRC sampling space. By significantly reducing scan time while retaining structural resolution, this approach may enable multi-dimensional DRC MRI to be more widely used for quantitative evaluation in biological and medical settings.

The effects of axonal beading and undulation on axonal diameter estimation from diffusion MRI: Insights from simulations in human axons segmented from three-dimensional electron microscopy

The increasing availability of high-performance gradient systems in human MRI scanners has generated great interest in diffusion microstructural imaging applications such as axonal diameter mapping. Practically, sensitivity to axon diameter in diffusion MRI is attained at strong diffusion weightings b , where the deviation from the expected 1 / b scaling in white matter yields a finite transverse diffusivity, which is then translated into an axon diameter estimate. While axons are usually modeled as perfectly straight, impermeable cylinders, local variations in diameter (caliber variation or beading) and direction (undulation) are known to influence axonal diameter estimates and have been observed in microscopy data of human axons. In this study, we performed Monte Carlo simulations of diffusion in axons reconstructed from three-dimensional electron microscopy of a human temporal lobe specimen using simulated sequence parameters matched to the maximal gradient strength of the next-generation Connectome 2.0 human MRI scanner ( ≲ 500 mT/m). We show that axon diameter estimation is accurate for nonbeaded, nonundulating fibers; however, in fibers with caliber variations and undulations, the axon diameter is heavily underestimated due to caliber variations, and this effect overshadows the known overestimation of the axon diameter due to undulations. This unexpected underestimation may originate from variations in the coarse-grained axial diffusivity due to caliber variations. Given that increased axonal beading and undulations have been observed in pathological tissues, such as traumatic brain injury and ischemia, the interpretation of axon diameter alterations in pathology may be significantly confounded.

Mapping the individual human cortex using multidimensional MRI and unsupervised learning

Human evolution has seen the development of higher-order cognitive and social capabilities in conjunction with the unique laminar cytoarchitecture of the human cortex. Moreover, early-life cortical maldevelopment has been associated with various neurodevelopmental diseases. Despite these connections, there is currently no noninvasive technique available for imaging the detailed cortical laminar structure. This study aims to address this scientific and clinical gap by introducing an approach for imaging human cortical lamina. This method combines diffusion-relaxation multidimensional MRI with a tailored unsupervised machine learning approach that introduces enhanced microstructural sensitivity. This new imaging method simultaneously encodes the microstructure, the local chemical composition and importantly their correlation within complex and heterogenous tissue. To validate our approach, we compared the intra-cortical layers obtained using our ex vivo MRI-based method with those derived from Nissl staining of postmortem human brain specimens. The integration of unsupervised learning with diffusion-relaxation correlation MRI generated maps that demonstrate sensitivity to areal differences in cytoarchitectonic features observed in histology. Significantly, our observations revealed layer-specific diffusion-relaxation signatures, showing reductions in both relaxation times and diffusivities at the deeper cortical levels. These findings suggest a radial decrease in myelin content and changes in cell size and anisotropy, reflecting variations in both cytoarchitecture and myeloarchitecture. Additionally, we demonstrated that 1D relaxation and high-order diffusion MRI scalar indices, even when aggregated and used jointly in a multimodal fashion, cannot disentangle the cortical layers. Looking ahead, our technique holds the potential to open new avenues of research in human neurodevelopment and the vast array of disorders caused by disruptions in neurodevelopment.

Double pulsed field gradient diffusion MRI to assess skeletal muscle microstructure

PURPOSE

Preliminary study to determine whether double pulsed field gradient (PFG) diffusion MRI is sensitive to key features of muscle microstructure related to function.

METHODS

The restricted diffusion profile of molecules in models of muscle microstructure derived from histology were systematically simulated using a numerical simulation approach. Diffusion tensor subspace imaging analysis of the diffusion signal was performed, and spherical anisotropy (SA) was calculated for each model. Linear regression was used to determine the predictive capacity of SA on the fiber area, fiber diameter, and surface area to volume ratio of the models. Additionally, a rat model of muscle hypertrophy was scanned using a single PFG and a double PFG pulse sequence, and the restricted diffusion measurements were compared with histological measurements of microstructure.

RESULTS

Excellent agreement between SA and muscle fiber area (r2  = 0.71; p < 0.0001), fiber diameter (r2  = 0.83; p < 0.0001), and surface area to volume ratio (r2  = 0.97; p < 0.0001) in simulated models was found. In a scanned rat leg, the distribution of these microstructural features measured from histology was broad and demonstrated that there is a wide variance in the microstructural features observed, similar to the SA distributions. However, the distribution of fractional anisotropy measurements in the same tissue was narrow.

CONCLUSIONS

This study demonstrates that SA-a scalar value from diffusion tensor subspace imaging analysis-is highly sensitive to muscle microstructural features predictive of function. Furthermore, these techniques and analysis tools can be translated to real experiments in skeletal muscle. The increased dynamic range of SA compared with fractional anisotropy in the same tissue suggests increased sensitivity to detecting changes in tissue microstructure.

Estimating axon radius using diffusion-relaxation MRI: calibrating a surface-based relaxation model with histology

Axon radius is a potential biomarker for brain diseases and a crucial tissue microstructure parameter that determines the speed of action potentials. Diffusion MRI (dMRI) allows non-invasive estimation of axon radius, but accurately estimating the radius of axons in the human brain is challenging. Most axons in the brain have a radius below one micrometer, which falls below the sensitivity limit of dMRI signals even when using the most advanced human MRI scanners. Therefore, new MRI methods that are sensitive to small axon radii are needed. In this proof-of-concept investigation, we examine whether a surface-based axonal relaxation process could mediate a relationship between intra-axonal T2 and T1 times and inner axon radius, as measured using postmortem histology. A unique in vivo human diffusion-T1-T2 relaxation dataset was acquired on a 3T MRI scanner with ultra-strong diffusion gradients, using a strong diffusion-weighting (i.e., b = 6,000 s/mm2) and multiple inversion and echo times. A second reduced diffusion-T2 dataset was collected at various echo times to evaluate the model further. The intra-axonal relaxation times were estimated by fitting a diffusion-relaxation model to the orientation-averaged spherical mean signals. Our analysis revealed that the proposed surface-based relaxation model effectively explains the relationship between the estimated relaxation times and the histological axon radius measured in various corpus callosum regions. Using these histological values, we developed a novel calibration approach to predict axon radius in other areas of the corpus callosum. Notably, the predicted radii and those determined from histological measurements were in close agreement.

Adult lifespan maturation and degeneration patterns in gray and white matter: A mean apparent propagator (MAP) MRI study

The relationship between brain microstructure and aging has been the subject of intense study, with diffusion MRI perhaps the most effective modality for elucidating these associations. Here, we used the mean apparent propagator (MAP)-MRI framework, which is suitable to characterize complex microstructure, to investigate age-related cerebral differences in a cohort of cognitively unimpaired participants and compared the results to those derived using diffusion tensor imaging. We studied MAP-MRI metrics, among them the non-Gaussianity (NG) and propagator anisotropy (PA), and established an opposing pattern in white matter of higher NG alongside lower PA among older adults, likely indicative of axonal degradation. In gray matter, however, these two indices were consistent with one another, and exhibited regional pattern heterogeneity compared to other microstructural parameters, which could indicate fewer neuronal projections across cortical layers along with an increased glial concentration. In addition, we report regional variations in the magnitude of age-related microstructural differences consistent with the posterior-anterior shift in aging paradigm. These results encourage further investigations in cognitive impairments and neurodegeneration.

COnstrained Reference frame diffusion TEnsor Correlation Spectroscopic (CORTECS) MRI: A practical framework for high-resolution diffusion tensor distribution imaging

High-resolution imaging studies have consistently shown that in cortical tissue water diffuses preferentially along radial and tangential orientations with respect to the cortical surface, in agreement with histology. These dominant orientations do not change significantly even if the relative contributions from microscopic water pools to the net voxel signal vary across experiments that use different diffusion times, b-values, TEs, and TRs. With this in mind, we propose a practical new framework for imaging non-parametric diffusion tensor distributions (DTDs) by constraining the microscopic diffusion tensors of the DTD to be diagonalized using the same orthonormal reference frame of the mesoscopic voxel. In each voxel, the constrained DTD (cDTD) is completely determined by the correlation spectrum of the microscopic principal diffusivities associated with the axes of the voxel reference frame. Consequently, all cDTDs are inherently limited to the domain of positive definite tensors and can be reconstructed efficiently using Inverse Laplace Transform methods. Moreover, the cDTD reconstruction can be performed using only data acquired efficiently with single diffusion encoding, although it also supports datasets with multiple diffusion encoding. In tissues with a well-defined architecture, such as the cortex, we can further constrain the cDTD to contain only cylindrically symmetric diffusion tensors and measure the 2D correlation spectra of principal diffusivities along the radial and tangential orientation with respect to the cortical surface. To demonstrate this framework, we perform numerical simulations and analyze high-resolution dMRI data from a fixed macaque monkey brain. We estimate 2D cDTDs in the cortex and derive, in each voxel, the marginal distributions of the microscopic principal diffusivities, the corresponding distributions of the microscopic fractional anisotropies and mean diffusivities along with their 2D correlation spectra to quantify the cDTD shape-size characteristics. Signal components corresponding to specific bands in these cDTD-derived spectra show high specificity to cortical laminar structures observed with histology. Our framework drastically simplifies the measurement of non-parametric DTDs in high-resolution datasets with mesoscopic voxel sizes much smaller than the radius of curvature of the underlying anatomy, e.g., cortical surface, and can be applied retrospectively to analyze existing diffusion MRI data from fixed cortical tissues.

Connectome 2.0: Developing the next-generation ultra-high gradient strength human MRI scanner for bridging studies of the micro-, meso- and macro-connectome

The first phase of the Human Connectome Project pioneered advances in MRI technology for mapping the macroscopic structural connections of the living human brain through the engineering of a whole-body human MRI scanner equipped with maximum gradient strength of 300 mT/m, the highest ever achieved for human imaging. While this instrument has made important contributions to the understanding of macroscale connectional topology, it has also demonstrated the potential of dedicated high-gradient performance scanners to provide unparalleled in vivo assessment of neural tissue microstructure. Building on the initial groundwork laid by the original Connectome scanner, we have now embarked on an international, multi-site effort to build the next-generation human 3T Connectome scanner (Connectome 2.0) optimized for the study of neural tissue microstructure and connectional anatomy across multiple length scales. In order to maximize the resolution of this in vivo microscope for studies of the living human brain, we will push the diffusion resolution limit to unprecedented levels by (1) nearly doubling the current maximum gradient strength from 300 mT/m to 500 mT/m and tripling the maximum slew rate from 200 T/m/s to 600 T/m/s through the design of a one-of-a-kind head gradient coil optimized to minimize peripheral nerve stimulation; (2) developing high-sensitivity multi-channel radiofrequency receive coils for in vivo and ex vivo human brain imaging; (3) incorporating dynamic field monitoring to minimize image distortions and artifacts; (4) developing new pulse sequences to integrate the strongest diffusion encoding and highest spatial resolution ever achieved in the living human brain; and (5) calibrating the measurements obtained from this next-generation instrument through systematic validation of diffusion microstructural metrics in high-fidelity phantoms and ex vivo brain tissue at progressively finer scales with accompanying diffusion simulations in histology-based micro-geometries. We envision creating the ultimate diffusion MRI instrument capable of capturing the complex multi-scale organization of the living human brain - from the microscopic scale needed to probe cellular geometry, heterogeneity and plasticity, to the mesoscopic scale for quantifying the distinctions in cortical structure and connectivity that define cyto- and myeloarchitectonic boundaries, to improvements in estimates of macroscopic connectivity.

Quantitative diffusion MRI of the abdomen and pelvis

Diffusion MRI has enormous potential and utility in the evaluation of various abdominal and pelvic disease processes including cancer and noncancer imaging of the liver, prostate, and other organs. Quantitative diffusion MRI is based on acquisitions with multiple diffusion encodings followed by quantitative mapping of diffusion parameters that are sensitive to tissue microstructure. Compared to qualitative diffusion-weighted MRI, quantitative diffusion MRI can improve standardization of tissue characterization as needed for disease detection, staging, and treatment monitoring. However, similar to many other quantitative MRI methods, diffusion MRI faces multiple challenges including acquisition artifacts, signal modeling limitations, and biological variability. In abdominal and pelvic diffusion MRI, technical acquisition challenges include physiologic motion (respiratory, peristaltic, and pulsatile), image distortions, and low signal-to-noise ratio. If unaddressed, these challenges lead to poor technical performance (bias and precision) and clinical outcomes of quantitative diffusion MRI. Emerging and novel technical developments seek to address these challenges and may enable reliable quantitative diffusion MRI of the abdomen and pelvis. Through systematic validation in phantoms, volunteers, and patients, including multicenter studies to assess reproducibility, these emerging techniques may finally demonstrate the potential of quantitative diffusion MRI for abdominal and pelvic imaging applications.

The link between gliomas infiltration and white matter architecture investigated with electron microscopy and diffusion tensor imaging

Diffuse low-grade gliomas (DLGG) display different preferential locations in eloquent and secondary associative brain areas. The reason for this tendency is still unknown. We hypothesized that the intrinsic architecture and water diffusion properties of the white matter bundles in these regions may facilitate gliomas infiltration. Magnetic resonance imaging of sixty-seven diffuse low-grade gliomas patients were normalized to/and segmented in MNI space to create three probabilistic infiltration weighted gradient maps according to the molecular status of each tumor group (IDH mutated, IDH wild-type and IDH mutated/1p19q co-deleted). Diffusion tensor imaging (DTI)- based parameters were derived for five major white matter bundles, displaying regional differences in the grade of infiltration, averaged over 20 healthy individuals acquired from the Human connectome project (HCP) database. Transmission electron microscopy (TEM) was used to analyze fiber density, fiber diameter and g-ratio in 100 human white matter regions, sampled from cadaver specimens, reflecting areas with different gliomas infiltration in each white matter bundle. Histological results and DTI-based parameters were compared in anatomical regions of high- and low grade of infiltration (HIF and LIF) respectively. We detected differences in the white matter infiltration of five major white matter bundles in three groups. Astrocytomas IDHm infiltrated left fronto-temporal subcortical areas. Astrocytomas IDHwt were detected in the posterior-temporal and temporo-parietal regions bilaterally. Oligodendrogliomas IDHm/1p19q infiltrated anterior subcortical regions of the frontal lobes bilaterally. Regional differences within the same white matter bundles were detected by both TEM- and DTI analysis linked to different topographical variables. Our multimodal analysis showed that HIF regions, common to all the groups, displayed a smaller fiber diameter, lower FA and higher RD compared with LIF regions. Our results suggest that the both morphological features and diffusion parameters of the white matter may be different in regions linked to the preferential location of DLGG.

MR cell size imaging with temporal diffusion spectroscopy

Cytological features such as cell size and intracellular morphology provide fundamental information on cell status and hence may provide specific information on changes that arise within biological tissues. Such information is usually obtained by invasive biopsy in current clinical practice, which suffers several well-known disadvantages. Recently, novel MRI methods such as IMPULSED (imaging microstructural parameters using limited spectrally edited diffusion) have been developed for direct measurements of mean cell size non-invasively. The IMPULSED protocol is based on using temporal diffusion spectroscopy (TDS) to combine measurements of water diffusion over a wide range of diffusion times to probe cellular microstructure over varying length scales. IMPULSED has been shown to provide rapid, robust, and reliable mapping of mean cell size and is suitable for clinical imaging. More recently, cell size distributions have also been derived by appropriate analyses of data acquired with IMPULSED or similar sequences, which thus provides MRI-cytometry. This review summarizes the basic principles, practical implementations, validations, and example applications of MR cell size imaging based on TDS and demonstrates how cytometric information can be used in various applications. In addition, the limitations and potential future directions of MR cytometry are identified including the diagnosis of nonalcoholic steatohepatitis of the liver and the assessment of treatment response of cancers.

MRI-cytometry: Mapping nonparametric cell size distributions using diffusion MRI

PURPOSE

This report introduces and validates a new diffusion MRI-based method, termed MRI-cytometry, which can noninvasively map intravoxel, nonparametric cell size distributions in tissues.

METHODS

MRI was used to acquire diffusion MRI signals with a range of diffusion times and gradient factors, and a model was fit to these data to derive estimates of cell size distributions. We implemented a 2-step fitting method to avoid noise-induced artificial peaks and provide reliable estimates of tumor cell size distributions. Computer simulations in silico, experimental measurements on cultured cells in vitro, and animal xenografts in vivo were used to validate the accuracy and precision of the method. Tumors in 7 patients with breast cancer were also imaged and analyzed using this MRI-cytometry approach on a clinical 3 Tesla MRI scanner.

RESULTS

Simulations and experimental results confirm that MRI-cytometry can reliably map intravoxel, nonparametric cell size distributions and has the potential to discriminate smaller and larger cells. The application in breast cancer patients demonstrates the feasibility of direct translation of MRI-cytometry to clinical applications.

CONCLUSION

The proposed MRI-cytometry method can characterize nonparametric cell size distributions in human tumors, which potentially provides a practical imaging approach to derive specific histopathological information on biological tissues.

Multidimensional correlation MRI

Multidimensional correlation spectroscopy is emerging as a novel MRI modality that is well suited for microstructure and microdynamic imaging studies, especially of biological specimens. Conventional MRI methods only provide voxel-averaged and mostly macroscopically averaged information; these methods cannot disentangle intra-voxel heterogeneity on the basis of both water mobility and local chemical interactions. By correlating multiple MR contrast mechanisms and processing the data in an integrated manner, correlation spectroscopy is able to resolve the distribution of water populations according to their chemical and physical interactions with the environment. The use of a non-parametric, phenomenological representation of the multidimensional MR signal makes no assumptions about tissue structure, thereby allowing the study of microscopic structure and composition of complex heterogeneous biological systems. However, until recently, vast data requirements have confined these types of measurement to non-localized NMR applications and prevented them from being widely and successfully used in conjunction with imaging. Recent groundbreaking advancements have allowed this powerful NMR methodology to be migrated to MRI, initiating its emergence as a promising imaging approach. This review is not intended to cover the entire field of multidimensional MR; instead, it focuses on pioneering imaging applications and the challenges involved. In addition, the background and motivation that have led to multidimensional correlation MR development are discussed, along with the basic underlying mathematical concepts. The goal of the present work is to provide the reader with a fundamental understanding of the techniques developed and their potential benefits, and to provide guidance to help refine future applications of this technology.

In vivo observation and biophysical interpretation of time-dependent diffusion in human cortical gray matter

The dependence of the diffusion MRI signal on the diffusion time t is a hallmark of tissue microstructure at the scale of the diffusion length. Here we measure the time-dependence of the mean diffusivity D(t) and mean kurtosis K(t) in cortical gray matter and in 25 ​gray matter sub-regions, in 10 healthy subjects. Significant diffusivity and kurtosis time-dependence is observed for t=21.2-100 ​ms, and is characterized by a power-law tail ∼t-ϑ with dynamical exponent ϑ. To interpret our measurements, we systematize the relevant scenarios and mechanisms for diffusion time-dependence in the brain. Using the effective medium theory formalism, we derive an exact relation between the power-law tails in D(t) and K(t). The estimated dynamical exponent ϑ≃1/2 in both D(t) and K(t) is consistent with one-dimensional diffusion in the presence of randomly positioned restrictions along neurites. We analyze the short-range disordered statistics of synapses on axon collaterals in the cortex, and perform one-dimensional Monte Carlo simulations of diffusion restricted by permeable barriers with a similar randomness in their placement, to confirm the ϑ=1/2 exponent. In contrast, the Kärger model of exchange is less consistent with the data since it does not capture the diffusivity time-dependence, and the estimated exchange time from K(t) falls below our measured t-range. Although we cannot exclude exchange as a contributing factor, we argue that structural disorder along neurites is mainly responsible for the observed time-dependence of diffusivity and kurtosis. Our observation and theoretical interpretation of the t-1/2 tail in D(t) and K(t) altogether establish the sensitivity of a macroscopic MRI signal to micrometer-scale structural heterogeneities along neurites in human gray matter in vivo.

Double diffusion encoding and applications for biomedical imaging

Diffusion Magnetic Resonance Imaging (dMRI) is one of the most important contemporary non-invasive modalities for probing tissue structure at the microscopic scale. The majority of dMRI techniques employ standard single diffusion encoding (SDE) measurements, covering different sequence parameter ranges depending on the complexity of the method. Although many signal representations and biophysical models have been proposed for SDE data, they are intrinsically limited by a lack of specificity. Advanced dMRI methods have been proposed to provide additional microstructural information beyond what can be inferred from SDE. These enhanced contrasts can play important roles in characterizing biological tissues, for instance upon diseases (e.g. neurodegenerative, cancer, stroke), aging, learning, and development. In this review we focus on double diffusion encoding (DDE), which stands out among other advanced acquisitions for its versatility, ability to probe more specific diffusion correlations, and feasibility for preclinical and clinical applications. Various DDE methodologies have been employed to probe compartment sizes (Section 3), decouple the effects of microscopic diffusion anisotropy from orientation dispersion (Section 4), probe displacement correlations, study exchange, or suppress fast diffusing compartments (Section 6). DDE measurements can also be used to improve the robustness of biophysical models (Section 5) and study intra-cellular diffusion via magnetic resonance spectroscopy of metabolites (Section 7). This review discusses all these topics as well as important practical aspects related to the implementation and contrast in preclinical and clinical settings (Section 9) and aims to provide the readers a guide for deciding on the right DDE acquisition for their specific application.

Direct and specific assessment of axonal injury and spinal cord microenvironments using diffusion correlation imaging

We describe a practical two-dimensional (2D) diffusion MRI framework to deliver specificity and improve sensitivity to axonal injury in the spinal cord. This approach provides intravoxel distributions of correlations of water mobilities in orthogonal directions, revealing sub-voxel diffusion components. Here we use it to investigate water diffusivities along axial and radial orientations within spinal cord specimens with confirmed, tract-specific axonal injury. First, we show using transmission electron microscopy and immunohistochemistry that tract-specific axonal beading occurs following Wallerian degeneration in the cortico-spinal tract as direct sequelae to closed head injury. We demonstrate that although some voxel-averaged diffusion tensor imaging (DTI) metrics are sensitive to this axonal injury, they are non-specific, i.e., they do not reveal an underlying biophysical mechanism of injury. Then we employ 2D diffusion correlation imaging (DCI) to improve discrimination of different water microenvironments by measuring and mapping the joint water mobility distributions perpendicular and parallel to the spinal cord axis. We determine six distinct diffusion spectral components that differ according to their microscopic anisotropy and mobility. We show that at the injury site a highly anisotropic diffusion component completely disappears and instead becomes more isotropic. Based on these findings, an injury-specific MR image of the spinal cord was generated, and a radiological-pathological correlation with histological silver staining % area was performed. The resulting strong and significant correlation (r=0.70,p < 0.0001) indicates the high specificity with which DCI detects injury-induced tissue alterations. We predict that the ability to selectively image microstructural changes following axonal injury in the spinal cord can be useful in clinical and research applications by enabling specific detection and increased sensitivity to injury-induced microstructural alterations. These results also encourage us to translate DCI to higher spatial dimensions to enable assessment of traumatic axonal injury, and possibly other diseases and disorders in the brain.

The present and the future of microstructure MRI: From a paradigm shift to normal science

The aspiration of imaging tissue microstructure with MRI is to uncover micrometer-scale tissue features within millimeter-scale imaging voxels, in vivo. This kind of super-resolution has fueled a paradigm shift within the biomedical imaging community. However, what feels like an ongoing revolution in MRI, has been conceptually experienced in physics decades ago; from this point of view, our current developments can be seen as Thomas Kuhn's "normal science" stage of progress. While the concept of model-based quantification below the nominal imaging resolution is not new, its possibilities in neuroscience and neuroradiology are only beginning to be widely appreciated. This disconnect calls for communicating the progress of tissue microstructure MR imaging to its potential users. Here, a number of recent research developments are outlined in terms of the overarching concept of coarse-graining the tissue structure over an increasing diffusion length. A variety of diffusion models and phenomena are summarized on the phase diagram of diffusion MRI, with the unresolved problems and future directions corresponding to its unexplored domains.

Microstructure with diffusion MRI: what scale we are sensitive to?

Diffusion-weighted MRI is the forerunner of the rapidly developed microstructure MRI (μMRI) aimed at in vivo evaluation of the cellular tissue architecture. This brief review focuses on the spatiotemporal scales of the microstructure that are accessible using different diffusion MRI techniques and the need to weight the measurability against the interpretability of results. Diffusion phenomena and models are first classified in two-dimensional space (the q-t-plane) of the measurement with narrow gradient pulses. Three-dimensional parameter space of the Stejskal-Tanner diffusion weighting adds more phenomena to this collection. Modern measurement techniques with larger number of parameters are briefly discussed under the overarching idea of diffusion weighting matching the geometry of the targeted cell species.

The impact of realistic axonal shape on axon diameter estimation using diffusion MRI

To study axonal microstructure with diffusion MRI, axons are typically modeled as straight impermeable cylinders, whereby the transverse diffusion MRI signal can be made sensitive to the cylinder’s inner diameter. However, the shape of a real axon varies along the axon direction, which couples the longitudinal and transverse diffusion of the overall axon direction. Here we develop a theory of the intra-axonal diffusion MRI signal based on coarse-graining of the axonal shape by 3-dimensional diffusion. We demonstrate how the estimate of the inner diameter is confounded by the diameter variations (beading), and by the local variations in direction (undulations) along the axon. We analytically relate diffusion MRI metrics, such as time-dependent radial diffusivity D_⊥(t) and kurtosis K_⊥(t), to the axonal shape, and validate our theory using Monte Carlo simulations in synthetic undulating axons with randomly positioned beads, and in realistic axons reconstructed from electron microscopy images of mouse brain white matter. We show that (i) In the narrow pulse limit, the inner diameter from D_⊥(t) is overestimated by about twofold due to a combination of axon caliber variations and undulations (each contributing a comparable effect size); (ii) The narrow-pulse kurtosis K_⊥∣_t→∞ deviates from that in an ideal cylinder due to caliber variations; we also numerically calculate the fourth-order cumulant for an ideal cylinder in the wide pulse limit, which is relevant for inner diameter overestimation; (iii) In the wide pulse limit, the axon diameter overestimation is mainly due to undulations at low diffusion weightings b; and (iv) The effect of undulations can be considerably reduced by directional averaging of high-b signals, with the apparent inner diameter given by a combination of the axon caliber (dominated by the thickest axons), caliber variations, and the residual contribution of undulations.

MRI of tumor T cell infiltration in response to checkpoint inhibitor therapy

BACKGROUND

Immune checkpoint inhibitors, the most widespread class of immunotherapies, have demonstrated unique response patterns that are not always adequately captured by traditional response criteria such as the Response Evaluation Criteria in Solid Tumors or even immune-specific response criteria. These response metrics rely on monitoring tumor growth, but an increase in tumor size and/or appearance after starting immunotherapy does not always represent tumor progression, but also can be a result of T cell infiltration and thus positive treatment response. Therefore, non-invasive and longitudinal monitoring of T cell infiltration are needed to assess the effects of immunotherapies such as checkpoint inhibitors. Here, we proposed an innovative concept that a sufficiently large influx of tumor infiltrating T cells, which have a smaller diameter than cancer cells, will change the diameter distribution and decrease the average size of cells within a volume to a degree that can be quantified by non-invasive MRI.

METHODS

We validated our hypothesis by studying tumor response to combination immune-checkpoint blockade (ICB) of anti-PD-1 and anti-CTLA4 in a mouse model of colon adenocarcinoma (MC38). The response was monitored longitudinally using Imaging Microstructural Parameters Using Limited Spectrally Edited Diffusion (IMPULSED), a diffusion MRI-based method which has been previously shown to non-invasively map changes in intracellular structure and cell sizes with the spatial resolution of MRI, in cell cultures and in animal models. Tumors were collected for immunohistochemical and flow cytometry analyzes immediately after the last imaging session.

RESULTS

Immunohistochemical analysis revealed that increased T cell infiltration of the tumors results in a decrease in mean cell size (eg, a 10% increase of CD3+ T cell fraction results a ~1 µm decrease in the mean cell size). IMPULSED showed that the ICB responders, mice with tumor volumes were less than 250 mm3 or had tumors with stable or decreased volumes, had significantly smaller mean cell sizes than both Control IgG-treated tumors and ICB non-responder tumors.

CONCLUSIONS

IMPULSED-derived cell size could potentially serve as an imaging marker for differentiating responsive and non-responsive tumors after checkpoint inhibitor therapies, a current clinical challenge that is not solved by simply monitoring tumor growth.

Double Diffusion Encoding for Probing Radiation-Induced Microstructural Changes in a Tumor Model: A Proof-of-Concept Study With Comparison to the Apparent Diffusion Coefficient and Histology

BACKGROUND

Microstructure analyses are gaining interest in cancer MRI as an alternative to the conventional apparent diffusion coefficient (ADC), of which the determinants remain unclear.

PURPOSE

To assess the sensitivity of parameters calculated from a double diffusion encoding (DDE) sequence to changes in a tumor's microstructure early after radiotherapy and to compare them with ADC and histology.

STUDY TYPE

Cohort study on experimental tumors.

ANIMAL MODEL

Sixteen WAG/Rij rats grafted with one rhabdomyosarcoma fragment in each thigh. Thirty-one were imaged at days 1 and 4, of which 17 tumors received a 20 Gy radiation dose after the first imagery.

FIELD STRENGTH/SEQUENCE

3T. Diffusion-weighted imaging, DDE with flow compensated, and noncompensated measurements.

ASSESSMENTS

1) To compare, after irradiation, DDE-derived parameters (intracellular fraction, cell size, and cell density) to their histological counterparts (fraction of stained area, minimal Feret diameter, and nuclei count, respectively). 2) To compare percentage changes in DDE-derived parameters and ADC. 3) To evaluate the evolution of DDE-derived parameters describing perfusion.

STATISTICAL TESTS

Wilcoxon rank sum test.

RESULTS

1) Intracellular fraction, cell size, and cell density were respectively lower (-24%, P < 0.001), higher (+7.5%, P < 0.001) and lower (-38%, P < 0.001) in treated tumors as compared to controls. Fraction of stained area, minimal Feret diameter, and nuclei count were respectively lower (-20%, P < 0.001), higher (+28%, P < 0.001), and lower (-34%, P < 0.001) in treated tumors. 2) The magnitude of ADC's percentage change due to irradiation (16.4%) was superior to the one of cell size (8.4%, P < 0.01) but inferior to those of intracellular fraction (35.5%, P < 0.001) and cell density (42%, P < 0.001). 3) After treatment, the magnitude of the vascular fraction's decrease was higher than the increase of flow velocity (33.3%, vs. 13.3%, P < 0.001).

DATA CONCLUSION

The DDE sequence allows quantitatively monitoring the effects of radiotherapy on a tumor's microstructure, whereas ADC only reveals global changes.

EVIDENCE LEVEL

2.

TECHNICAL EFFICACY

Stage 4. J. Magn. Reson. Imaging 2020;52:941-951.

Robust Monte-Carlo Simulations in Diffusion-MRI: Effect of the Substrate Complexity and Parameter Choice on the Reproducibility of Results

Monte-Carlo Diffusion Simulations (MCDS) have been used extensively as a ground truth tool for the validation of microstructure models for Diffusion-Weighted MRI. However, methodological pitfalls in the design of the biomimicking geometrical configurations and the simulation parameters can lead to approximation biases. Such pitfalls affect the reliability of the estimated signal, as well as its validity and reproducibility as ground truth data. In this work, we first present a set of experiments in order to study three critical pitfalls encountered in the design of MCDS in the literature, namely, the number of simulated particles and time steps, simplifications in the intra-axonal substrate representation, and the impact of the substrate's size on the signal stemming from the extra-axonal space. The results obtained show important changes in the simulated signals and the recovered microstructure features when changes in those parameters are introduced. Thereupon, driven by our findings from the first studies, we outline a general framework able to generate complex substrates. We show the framework's capability to overcome the aforementioned simplifications by generating a complex crossing substrate, which preserves the volume in the crossing area and achieves a high packing density. The results presented in this work, along with the simulator developed, pave the way toward more realistic and reproducible Monte-Carlo simulations for Diffusion-Weighted MRI.

Retaining information from multidimensional correlation MRI using a spectral regions of interest generator

Multidimensional correlation magnetic resonance imaging (MRI) is an emerging imaging modality that is capable of disentangling highly heterogeneous and opaque systems according to chemical and physical interactions of water within them. Using this approach, the conventional three dimensional MR scalar images are replaced with spatially resolved multidimensional spectra. The ensuing abundance in microstructural and chemical information is a blessing that incorporates a real challenge: how does one distill and refine it into images while retaining its significant components? In this paper we introduce a general framework that preserves the spectral information from spatially resolved multidimensional data. Equal weight is given to significant spectral components at the single voxel level, resulting in a summarized image spectrum. This spectrum is then used to define spectral regions of interest that are utilized to reconstruct images of sub-voxel components. Using numerical simulations we first show that, contrary to the conventional approach, the proposed framework preserves spectral resolution, and in turn, sensitivity and specificity of the reconstructed images. The retained spectral resolution allows, for the first time, to observe an array of distinct [Formula: see text]-[Formula: see text]-[Formula: see text] components images of the human brain. The robustly generated images of sub-voxel components overcome the limited spatial resolution of MRI, thus advancing multidimensional correlation MRI to fulfilling its full potential.

JEDI: Joint Estimation Diffusion Imaging of macroscopic and microscopic tissue properties

PURPOSE

A new method for enhancing the sensitivity of diffusion MRI (dMRI) by combining the data from single (sPFG) and double (dPFG) pulsed field gradient experiments is presented.

METHODS

This method uses our JESTER framework to combine microscopic anisotropy information from dFPG experiments using a new method called diffusion tensor subspace imaging (DiTSI) to augment the macroscopic anisotropy information from sPFG data analyzed using our guided by entropy spectrum pathways method. This new method, called joint estimation diffusion imaging (JEDI), combines the sensitivity to macroscopic diffusion anisotropy of sPFG with the sensitivity to microscopic diffusion anisotropy of dPFG methods.

RESULTS

Its ability to produce significantly more detailed anisotropy maps and more complete fiber tracts than existing methods within both brain white matter (WM) and gray matter (GM) is demonstrated on normal human subjects on data collected using a novel fast, robust, and clinically feasible sPFG/dPFG acquisition.

CONCLUSIONS

The potential utility of this method is suggested by an initial demonstration of its ability to mitigate the problem of gyral bias. The capability of more completely characterizing the tissue structure and connectivity throughout the entire brain has broad implications for the utility and scope of dMRI in a wide range of research and clinical applications.

Magnetic resonance measurements of cellular and sub-cellular membrane structures in live and fixed neural tissue

We develop magnetic resonance (MR) methods for real-time measurement of tissue microstructure and membrane permeability of live and fixed excised neonatal mouse spinal cords. Diffusion and exchange MR measurements are performed using the strong static gradient produced by a single-sided permanent magnet. Using tissue delipidation methods, we show that water diffusion is restricted solely by lipid membranes. Most of the diffusion signal can be assigned to water in tissue which is far from membranes. The remaining 25% can be assigned to water restricted on length scales of roughly a micron or less, near or within membrane structures at the cellular, organelle, and vesicle levels. Diffusion exchange spectroscopy measures water exchanging between membrane structures and free environments at 100 s^-1.

Single- and double-Diffusion encoding MRI for studying ex vivo apparent axon diameter distribution in spinal cord white matter

Mapping average axon diameter (AAD) and axon diameter distribution (ADD) in neuronal tissues non-invasively is a challenging task that may have a tremendous effect on our understanding of the normal and diseased central nervous system (CNS). Water diffusion is used to probe microstructure in neuronal tissues, however, the different water populations and barriers that are present in these tissues turn this into a complex task. Therefore, it is not surprising that recently we have witnessed a burst in the development of new approaches and models that attempt to obtain, non-invasively, detailed microstructural information in the CNS. In this work, we aim at challenging and comparing the microstructural information obtained from single diffusion encoding (SDE) with double diffusion encoding (DDE) MRI. We first applied SDE and DDE MR spectroscopy (MRS) on microcapillary phantoms and then applied SDE and DDE MRI on an ex vivo porcine spinal cord (SC), using similar experimental conditions. The obtained diffusion MRI data were fitted by the same theoretical model, assuming that the signal in every voxel can be approximated as the superposition of a Gaussian-diffusing component and a series of restricted components having infinite cylindrical geometries. The diffusion MRI results were then compared with histological findings. We found a good agreement between the fittings and the experimental data in white matter (WM) voxels of the SC in both diffusion MRI methods. The microstructural information and apparent AADs extracted from SDE MRI were found to be similar or somewhat larger than those extracted from DDE MRI especially when the diffusion time was set to 40 ms. The apparent ADDs extracted from SDE and DDE MRI show reasonable agreement but somewhat weaker correspondence was observed between the diffusion MRI results and histology. The apparent subtle differences between the microstructural information obtained from SDE and DDE MRI are briefly discussed.

Construction of a rat spinal cord atlas of axon morphometry

Atlases of the central nervous system are essential for understanding the pathophysiology of neurological diseases, which remains one of the greatest challenges in neuroscience research today. These atlases provide insight into the underlying white matter microstructure and have been created from a variety of animal models, including rats. Although existing atlases of the rat spinal cord provide some details of axon microstructure, there is currently no histological dataset that quantifies axon morphometry exhaustively in the entire spinal cord. In this study, we created the first comprehensive rat spinal cord atlas of the white matter microstructure with quantifiable axon and myelin morphometrics. Using full-slice scanning electron microscopy images and state-of-the-art segmentation algorithms, we generated an atlas of microstructural metrics such as axon diameter, axonal density and g-ratio. After registering the Watson spinal cord white matter atlas to our template, we computed statistics across metrics, spinal levels and tracts. We notably found that g-ratio is relatively constant, whereas axon diameter showed the greatest variation. The atlas, data and full analysis code are freely available at: https://github.com/neuropoly/atlas-rat.

ActiveAxADD : Toward non-parametric and orientationally invariant axon diameter distribution mapping using PGSE

PURPOSE

Non-invasive axon diameter distribution (ADD) mapping using diffusion MRI is an ill-posed problem. Current ADD mapping methods require knowledge of axon orientation before performing the acquisition. Instead, ActiveAx uses a 3D sampling scheme to estimate the orientation from the signal, providing orientationally invariant estimates. The mean diameter is estimated instead of the distribution for the solution to be tractable. Here, we propose an extension (ActiveAx_ADD ) that provides non-parametric and orientationally invariant estimates of the whole distribution.

THEORY

The accelerated microstructure imaging with convex optimization (AMICO) framework accelerates mean diameter estimation using a linear formulation combined with Tikhonov regularization to stabilize the solution. Here, we implement a new formulation (ActiveAx_ADD ) that uses Laplacian regularization to provide robust estimates of the whole ADD.

METHODS

The performance of ActiveAx_ADD was evaluated using Monte Carlo simulations on synthetic white matter samples mimicking axon distributions reported in histological studies.

RESULTS

ActiveAx_ADD provided robust ADD reconstructions when considering the isolated intra-axonal signal. However, our formulation inherited some common microstructure imaging limitations. When accounting for the extra axonal compartment, estimated ADDs showed spurious peaks and increased variability because of the difficulty of disentangling intra and extra axonal contributions.

CONCLUSION

Laplacian regularization solves the ill-posedness regarding the intra axonal compartment. ActiveAx_ADD can potentially provide non-parametric and orientationally invariant ADDs from isolated intra-axonal signals. However, further work is required before ActiveAx_ADD can be applied to real data containing extra-axonal contributions, as disentangling the 2 compartment appears to be an overlooked challenge that affects microstructure imaging methods in general.

High-gradient diffusion MRI reveals distinct estimates of axon diameter index within different white matter tracts in the in vivo human brain

Axon diameter and density are important microstructural metrics that offer valuable insight into the structural organization of white matter throughout the human brain. We report the systematic acquisition and analysis of a comprehensive diffusion MRI data set acquired with 300 mT/m maximum gradient strength in a cohort of 20 healthy human subjects that yields distinct and consistent patterns of axon diameter index in white matter tracts of arbitrary orientation. We use a straightforward, previously validated approach to estimating indices of axon diameter and volume fraction that involves interpolating the diffusion signal perpendicular to the principal fiber orientation and fitting a three-compartment model of intra-axonal, extra-axonal and free water diffusion. The resultant maps confirm the presence of larger diameter indices in the body of corpus callosum compared to the genu and splenium, as previously reported, and show larger axon diameter index in the corticospinal tracts compared to adjacent white matter tracts such as the cingulum. An anterior-to-posterior gradient in axon diameter index is also observed, with smaller diameter indices in the frontal lobes and larger diameter indices in the parieto-occipital white matter. These observations are consistent with known trends from prior histologic studies in humans and non-human primates. Rather than serving as fully quantitative measures of axon diameter and density, our results may be considered as axon diameter- and volume fraction-weighted images that appear to be modulated by the underlying microstructure and may capture broad trends in axonal size and packing density, acknowledging that the precise origin of such modulation requires further investigation that will be facilitated by the availability of high gradient strengths for in vivo human imaging.

Diffusion MRI microstructural models in the cervical spinal cord - Application, normative values, and correlations with histological analysis

Multi-compartment tissue modeling using diffusion magnetic resonance imaging has proven valuable in the brain, offering novel indices sensitive to the tissue microstructural environment in vivo on clinical MRI scanners. However, application, characterization, and validation of these models in the spinal cord remain relatively under-studied. In this study, we apply a diffusion "signal" model (diffusion tensor imaging, DTI) and two commonly implemented "microstructural" models (neurite orientation dispersion and density imaging, NODDI; spherical mean technique, SMT) in the human cervical spinal cord of twenty-one healthy controls. We first provide normative values of DTI, SMT, and NODDI indices in a number of white matter ascending and descending pathways, as well as various gray matter regions. We then aim to validate the sensitivity and specificity of these diffusion-derived contrasts by relating these measures to indices of the tissue microenvironment provided by a histological template. We find that DTI indices are sensitive to a number of microstructural features, but lack specificity. The microstructural models also show sensitivity to a number of microstructure features; however, they do not capture the specific microstructural features explicitly modelled. Although often regarded as a simple extension of the brain in the central nervous system, it may be necessary to re-envision, or specifically adapt, diffusion microstructural models for application to the human spinal cord with clinically feasible acquisitions - specifically, adjusting, adapting, and re-validating the modeling as it relates to both theory (i.e. relevant biology, assumptions, and signal regimes) and parameter estimation (for example challenges of acquisition, artifacts, and processing).

Along-axon diameter variation and axonal orientation dispersion revealed with 3D electron microscopy: implications for quantifying brain white matter microstructure with histology and diffusion MRI

Tissue microstructure modeling of diffusion MRI signal is an active research area striving to bridge the gap between macroscopic MRI resolution and cellular-level tissue architecture. Such modeling in neuronal tissue relies on a number of assumptions about the microstructural features of axonal fiber bundles, such as the axonal shape (e.g., perfect cylinders) and the fiber orientation dispersion. However, these assumptions have not yet been validated by sufficiently high-resolution 3-dimensional histology. Here, we reconstructed sequential scanning electron microscopy images in mouse brain corpus callosum, and introduced a random-walker (RaW)-based algorithm to rapidly segment individual intra-axonal spaces and myelin sheaths of myelinated axons. Confirmed by a segmentation based on human annotations initiated with conventional machine-learning-based carving, our semi-automatic algorithm is reliable and less time-consuming. Based on the segmentation, we calculated MRI-relevant estimates of size-related parameters (inner axonal diameter, its distribution, along-axon variation, and myelin g-ratio), and orientation-related parameters (fiber orientation distribution and its rotational invariants; dispersion angle). The reported dispersion angle is consistent with previous 2-dimensional histology studies and diffusion MRI measurements, while the reported diameter exceeds those in other mouse brain studies. Furthermore, we calculated how these quantities would evolve in actual diffusion MRI experiments as a function of diffusion time, thereby providing a coarse-graining window on the microstructure, and showed that the orientation-related metrics have negligible diffusion time-dependence over clinical and pre-clinical diffusion time ranges. However, the MRI-measured inner axonal diameters, dominated by the widest cross sections, effectively decrease with diffusion time by ~ 17% due to the coarse-graining over axonal caliber variations. Furthermore, our 3d measurement showed that there is significant variation of the diameter along the axon. Hence, fiber orientation dispersion estimated from MRI should be relatively stable, while the "apparent" inner axonal diameters are sensitive to experimental settings, and cannot be modeled by perfectly cylindrical axons.

Brain networks and their relevance for stroke rehabilitation

Stroke has long been regarded as focal disease with circumscribed damage leading to neurological deficits. However, advances in methods for assessing the human brain and in statistics have enabled new tools for the examination of the consequences of stroke on brain structure and function. Thereby, it has become evident that stroke has impact on the entire brain and its network properties and can therefore be considered as a network disease. The present review first gives an overview of current methodological opportunities and pitfalls for assessing stroke-induced changes and reorganization in the human brain. We then summarize principles of plasticity after stroke that have emerged from the assessment of networks. Thereby, it is shown that neurological deficits do not only arise from focal tissue damage but also from local and remote changes in white-matter tracts and in neural interactions among wide-spread networks. Similarly, plasticity and clinical improvements are associated with specific compensatory structural and functional patterns of neural network interactions. Innovative treatment approaches have started to target such network patterns to enhance recovery. Network assessments to predict treatment response and to individualize rehabilitation is a promising way to enhance specific treatment effects and overall outcome after stroke.

Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation

We review, systematize and discuss models of diffusion in neuronal tissue, by putting them into an overarching physical context of coarse-graining over an increasing diffusion length scale. From this perspective, we view research on quantifying brain microstructure as occurring along three major avenues. The first avenue focusses on transient, or time-dependent, effects in diffusion. These effects signify the gradual coarse-graining of tissue structure, which occurs qualitatively differently in different brain tissue compartments. We show that transient effects contain information about the relevant length scales for neuronal tissue, such as the packing correlation length for neuronal fibers, as well as the degree of structural disorder along the neurites. The second avenue corresponds to the long-time limit, when the observed signal can be approximated as a sum of multiple nonexchanging anisotropic Gaussian components. Here, the challenge lies in parameter estimation and in resolving its hidden degeneracies. The third avenue employs multiple diffusion encoding techniques, able to access information not contained in the conventional diffusion propagator. We conclude with our outlook on future directions that could open exciting possibilities for designing quantitative markers of tissue physiology and pathology, based on methods of studying mesoscopic transport in disordered systems.

The role of diffusion MRI in neuroscience

Diffusion-weighted imaging has pushed the boundaries of neuroscience by allowing us to examine the white matter microstructure of the living human brain. By doing so, it has provided answers to fundamental neuroscientific questions, launching a new field of research that had been largely inaccessible. We briefly summarize key questions that have historically been raised in neuroscience concerning the brain's white matter. We then expand on the benefits of diffusion-weighted imaging and its contribution to the fields of brain anatomy, functional models and plasticity. In doing so, this review highlights the invaluable contribution of diffusion-weighted imaging in neuroscience, presents its limitations and proposes new challenges for future generations who may wish to exploit this powerful technology to gain novel insights.

Modeling conduction delays in the corpus callosum using MRI-measured g-ratio

Conduction of action potentials along myelinated axons is affected by their structural features, such as the axonal g-ratio, the ratio between the inner and outer diameters of the myelin sheath surrounding the axon. The effect of g-ratio variance on conduction properties has been quantitatively evaluated using single-axon models. It has recently become possible to estimate a g-ratio weighted measurement in vivo using quantitative MRI. Nevertheless, it is still unclear whether the variance in the g-ratio in the healthy human brain leads to significant differences in conduction velocity. In this work we tested whether the g-ratio MRI measurement can be used to predict conduction delays in the corpus callosum. We present a comprehensive framework in which the structural properties of fibers (i.e. length and g-ratio, measured using MRI), are incorporated in a biophysical model of axon conduction, to model conduction delays of long-range white matter fibers. We applied this framework to the corpus callosum, and found conduction delay estimates that are compatible with previously estimated values of conduction delays. We account for the variance in the velocity given the axon diameter distribution in the splenium, mid-body and genu, to further compare the fibers within the corpus callosum. Conduction delays have been suggested to increase with age. Therefore, we investigated whether there are differences in the g-ratio and the fiber length between young and old adults, and whether this leads to a difference in conduction speed and delays. We found very small differences between the predicted delays of the two groups in the motor fibers of the corpus callosum. We also found that the motor fibers of the corpus callosum have the fastest conduction estimates. Using the axon diameter distributions, we found that the occipital fibers have the slowest estimations, while the frontal and motor fiber tracts have similar estimates. Our study provides a framework for predicting conduction latencies in vivo. The framework could have major implications for future studies of white matter diseases and large range network computations. Our results highlight the need for improving additional in vivo measurements of white matter microstructure.

Generalized Mean Apparent Propagator MRI to Measure and Image Advective and Dispersive Flows in Medicine and Biology

Water transport in biological systems spans different regimes with distinct physical behaviors: diffusion, advection, and dispersion. Identifying these regimes is of paramount importance in many in vivo applications, among them, measuring microcirculation of blood in capillary networks and cerebrospinal fluid transport in the glymphatic system. Diffusion magnetic resonance imaging (dMRI) can be used to encode water displacements, and a Fourier transform of the acquired signal furnishes a displacement probability density function known as the propagator. This transformation normally requires the use of a fast Fourier transform (FFT), which presents major feasibility challenges when scanning in vivo, mainly because of dense signal sampling, resulting in long acquisition times. A second approach to reconstruct the propagator is by using analytical representation of the signal, overcoming many of the FFT's limitations. In all analytical implementations of dMRI to date, the translational motion of water has been assumed to be exclusively diffusive, which is the case only in the absence of flow. However, retaining the phase information from the diffusion signal provides the ability to measure both mean coherent velocity and random diffusion from a single experiment. We implement and extend an analytical framework, mean apparent propagator (MAP), which can account for non-zero flow conditions. We call this method generalized MAP or GMAP. We describe a numerical optimization scheme and implement it on data from an MRI flow phantom constructed from a pack of 10- [Formula: see text] beads. The advantages of GMAP over the FFT-based method in the context of sampling density and low-flow detection were demonstrated, and analytically derived propagator moments were shown to agree with theoretical values even after data subsampling. GMAP would enable the detection of microflow in vivo that could help elucidate many important biological processes.

Water mobility spectral imaging of the spinal cord: Parametrization of model-free Laplace MRI

Diffusion magnetic resonance imaging (dMRI) of biological systems most often results in non-monoexponential signal, due to their complexity and heterogeneity. One approach to interpreting dMRI data without imposing tissue microstructural models is to fit the signal to a multiexponential function, which is sometimes referred to as an inverse Laplace transformation, and to display the coefficients as a distribution of the diffusivities, or water mobility spectra. Until recently, this method has not been used in a voxelwise manner, mainly because of heavy data requirements. With recent advancements in processing and experimental design, voxelwise Laplace MRI approaches are becoming feasible and attractive. The rich spectral information, combined with a three-dimensional image, presents a challenge because it tremendously increases the dimensionality of the data and requires a robust method for interpretation and analysis. In this work, we suggest parameterizing the empirically measured water mobility spectra using a bimodal lognormal function. This approach allows for a compact representation of the spectrum, and it also resolves overlapping spectral peaks, which allows for a robust extraction of their signal fraction. We apply the method on a fixed spinal cord sample and use it to generate robust intensity images of slow- and fast-diffusion components. Using the parametric variables, we create novel image contrasts, among them the information entropy of the water mobility spectrum, which pack unique features of the individual diffusion regimes in the investigated system.

Rapid detection of the presence of diffusion exchange

Diffusion exchange spectroscopy (DEXSY) provides a detailed picture of how fluids in different microenvironments communicate with one another but requires a large amount of data. For DEXSY MRI, a simple measure of apparent exchanging fractions may suffice to characterize and differentiate materials and tissues. Reparameterizing signal intensity from a PGSE-storage-PGSE experiment as a function of the sum, b_s=b₁+b₂, and difference b_d=b₂-b₁ of the diffusion encodings separates diffusion weighting from exchange weighting. Exchange leads to upward curvature along a slice of constant b_s. Exchanging fractions can be measured rapidly by a finite difference approximation of the curvature using four data points. The method is generalized for non-steady-state and multi-site exchange. We apply the method to image exchanging fractions and calculate exchange rates of water diffusing across the bulk water interface of a glass capillary array.

What dominates the time dependence of diffusion transverse to axons: Intra- or extra-axonal water?

Brownian motion of water molecules provides an essential length scale, the diffusion length, commensurate with cell dimensions in biological tissues. Measuring the diffusion coefficient as a function of diffusion time makes in vivo diffusion MRI uniquely sensitive to the cellular features about three orders of magnitude below imaging resolution. However, there is a longstanding debate, regarding which contribution - intra- or extra-cellular - is more relevant in the overall time-dependence of the MRI-derived diffusion metrics. Here we resolve this debate in the human brain white matter. By varying not just the diffusion time, but also the gradient pulse duration of a standard diffusion MRI sequence, we identify a functional form of the measured time-dependent diffusion coefficient transverse to white matter tracts in 10 healthy volunteers. This specific functional form is shown to originate from the extra-axonal space, and provides estimates of the fiber packing correlation length for axons in a bundle. Our results offer a metric for the outer axonal diameter, a promising candidate marker for demyelination in neurodegenerative diseases. From the methodological perspective, our analysis demonstrates how competing models, which describe different physics yet interpolate standard measurements equally well, can be distinguished based on their prediction for an independent "orthogonal" measurement.

Microstructural imaging of the human brain with a 'super-scanner': 10 key advantages of ultra-strong gradients for diffusion MRI

The key component of a microstructural diffusion MRI 'super-scanner' is a dedicated high-strength gradient system that enables stronger diffusion weightings per unit time compared to conventional gradient designs. This can, in turn, drastically shorten the time needed for diffusion encoding, increase the signal-to-noise ratio, and facilitate measurements at shorter diffusion times. This review, written from the perspective of the UK National Facility for In Vivo MR Imaging of Human Tissue Microstructure, an initiative to establish a shared 300 mT/m-gradient facility amongst the microstructural imaging community, describes ten advantages of ultra-strong gradients for microstructural imaging. Specifically, we will discuss how the increase of the accessible measurement space compared to a lower-gradient systems (in terms of Δ, b-value, and TE) can accelerate developments in the areas of 1) axon diameter distribution mapping; 2) microstructural parameter estimation; 3) mapping micro-vs macroscopic anisotropy features with gradient waveforms beyond a single pair of pulsed-gradients; 4) multi-contrast experiments, e.g. diffusion-relaxometry; 5) tractography and high-resolution imaging in vivo and 6) post mortem; 7) diffusion-weighted spectroscopy of metabolites other than water; 8) tumour characterisation; 9) functional diffusion MRI; and 10) quality enhancement of images acquired on lower-gradient systems. We finally discuss practical barriers in the use of ultra-strong gradients, and provide an outlook on the next generation of 'super-scanners'.

Using double pulsed-field gradient MRI to study tissue microstructure in traumatic brain injury (TBI)

Double pulsed-field gradient (dPFG) MRI is proposed as a new sensitive tool to detect and characterize tissue microstructure following diffuse axonal injury. In this study dPFG MRI was used to estimate apparent mean axon diameter in a diffuse axonal injury animal model and in healthy fixed mouse brain. Histological analysis was used to verify the presence of the injury detected by MRI.

Experimental Traumatic Brain Injury Identifies Distinct Early and Late Phase Axonal Conduction Deficits of White Matter Pathophysiology, and Reveals Intervening Recovery

Traumatic brain injury (TBI) patients often exhibit slowed information processing speed that can underlie diverse symptoms. Processing speed depends on neural circuit function at synapses, in the soma, and along axons. Long axons in white matter (WM) tracts are particularly vulnerable to TBI. We hypothesized that disrupted axon–myelin interactions that slow or block action potential conduction in WM tracts may contribute to slowed processing speed after TBI. Concussive TBI in male/female mice was used to produce traumatic axonal injury in the corpus callosum (CC), similar to WM pathology in human TBI cases. Compound action potential velocity was slowed along myelinated axons at 3 d after TBI with partial recovery by 2 weeks, suggesting early demyelination followed by remyelination. Ultrastructurally, dispersed demyelinated axons and disorganized myelin attachment to axons at paranodes were apparent within CC regions exhibiting traumatic axonal injury. Action potential conduction is exquisitely sensitive to paranode abnormalities. Molecular identification of paranodes and nodes of Ranvier detected asymmetrical paranode pairs and abnormal heminodes after TBI. Fluorescent labeling of oligodendrocyte progenitors in NG2CreER;mTmG mice showed increased synthesis of new membranes extended along axons to paranodes, indicating remyelination after TBI. At later times after TBI, an overall loss of conducting axons was observed at 6 weeks followed by CC atrophy at 8 weeks. These studies identify a progression of both myelinated axon conduction deficits and axon–myelin pathology in the CC, implicating WM injury in impaired information processing at early and late phases after TBI. Furthermore, the intervening recovery reveals a potential therapeutic window.

SIGNIFICANCE STATEMENT Traumatic brain injury (TBI) is a major global health concern. Across the spectrum of TBI severities, impaired information processing can contribute to diverse functional deficits that underlie persistent symptoms. We used experimental TBI to exploit technical advantages in mice while modeling traumatic axonal injury in white matter tracts, which is a key pathological feature of human TBI. A combination of approaches revealed slowed and failed signal conduction along with damage to the structure and molecular composition of myelinated axons in the white matter after TBI. An early regenerative response was not sustained yet reveals a potential time window for intervention. These insights into white matter abnormalities underlying axon conduction deficits can inform strategies to improve treatment options for TBI patients.

Validation strategies for the interpretation of microstructure imaging using diffusion MRI

Extracting microanatomical information beyond the image resolution of MRI would provide valuable tools for diagnostics and neuroscientific research. A number of mathematical models already suggest microstructural interpretations of diffusion MRI (dMRI) data. Examples of such microstructural features could be cell bodies and neurites, e.g. the axon's diameter or their orientational distribution for global connectivity analysis using tractography, and have previously only been possible to access through conventional histology of post mortem tissue or invasive biopsies. The prospect of gaining the same knowledge non-invasively from the whole living human brain could push the frontiers for the diagnosis of neurological and psychiatric diseases. It could also provide a general understanding of the development and natural variability in the healthy brain across a population. However, due to a limited image resolution, most of the dMRI measures are indirect estimations and may depend on the whole chain from experimental parameter settings to model assumptions and implementation. Here, we review current literature in this field and highlight the integrative work across anatomical length scales that is needed to validate and trust a new dMRI method. We encourage interdisciplinary collaborations and data sharing in regards to applying and developing new validation techniques to improve the specificity of future dMRI methods.

On modeling

Mapping tissue microstructure with MRI holds great promise as a noninvasive window into tissue organization at the cellular level. Having originated within the realm of diffusion NMR in the late 1970s, this field is experiencing an exponential growth in the number of publications. At the same time, model-based approaches are also increasingly incorporated into advanced MRI acquisition and reconstruction techniques. However, after about two decades of intellectual and financial investment, microstructural mapping has yet to find a single commonly accepted clinical application. Here, we suggest that slow progress in clinical translation may signify unresolved fundamental problems. We outline such problems and related practical pitfalls, as well as review strategies for developing and validating tissue microstructure models, to provoke a discussion on how to bridge the gap between our scientific aspirations and the clinical reality. We argue for recalibrating the efforts of our community toward a more systematic focus on fundamental research aimed at identifying relevant degrees of freedom affecting the measured MR signal. Such a focus is essential for realizing the truly revolutionary potential of noninvasive three-dimensional in vivo microstructural mapping.

Studying brain microstructure with magnetic susceptibility contrast at high-field

A rapidly developing application of high field MRI is the study of brain anatomy and function with contrast based on the magnetic susceptibility of tissues. To study the subtle variations in susceptibility contrast between tissues and with changes in brain activity, dedicated scan techniques such as susceptibility-weighted MRI and blood-oxygen level dependent functional MRI have been developed. Particularly strong susceptibility contrast has been observed with systems that operate at 7T and above, and their recent widespread use has led to an improved understanding of contributing sources and mechanisms. To interpret magnetic susceptibility contrast, analysis approaches have been developed with the goal of extracting measures that report on local tissue magnetic susceptibility, a physical quantity that, under certain conditions, allows estimation of blood oxygenation, local tissue iron content, and quantification of its changes with disease. Interestingly, high field studies have also brought to light that not only the makeup of tissues affects MRI susceptibility contrast, but that also a tissue's sub-voxel structure at scales all the way down to the molecular level plays an important role as well. In this review, various ways will be discussed by which sub-voxel structure can affect the MRI signal in general, and magnetic susceptibility in particular, sometimes in a complex fashion. In the light of this complexity, it appears likely that accurate, brain-wide quantification of iron will require the combination of multiple contrasts that may include diffusion and magnetization transfer information with susceptibility-weighted contrast. On the other hand, this complexity also offers opportunities to use magnetic susceptibility contrast to inform about specific microstructural aspects of brain tissue. Details and several examples will be presented in this review.