Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI

Comparison of different neurite density metrics with brain asymmetry evaluation

The standard diffusion MRI model with intra- and extra-axonal water pools offers a set of microstructural parameters describing brain white matter architecture. However, non-linearities in the standard model and diffusion data contamination by noise and imaging artefacts make estimation of diffusion metrics challenging. In order to develop reliable diffusion approaches and to avoid computational model degeneracy, additional theoretical assumptions allowing stable numerical implementations are required. Advanced diffusion approaches allow for estimation of intra-axonal water fraction (AWF), describing a key structural characteristic of brain tissue. AWF can be interpreted as an indirect measure or proxy of neurite density and has a potential as useful clinical biomarker. Established diffusion approaches such as white matter tract integrity, neurite orientation dispersion and density imaging (NODDI), and spherical mean technique provide estimates of AWF within their respective theoretical frameworks. In the present study, we estimated AWF metrics using different diffusion approaches and compared measures of brain asymmetry between the different metrics in a sub-sample of 182 subjects from the UK Biobank. Multivariate decomposition by mean of linked independent component analysis revealed that the various AWF proxies derived from the different diffusion approaches reflect partly non-overlapping variance of independent components, with distinct anatomical distributions and sensitivity to age. Further, voxel-wise analysis revealed age-related differences in AWF-based brain asymmetry, indicating less apparent left-right hemisphere difference with higher age. Finally, we demonstrated that NODDI metrics suffer from a quite strong dependence on used numerical algorithms and post-processing pipeline. The analysis based on AWF metrics strongly depends on the used diffusion approach and leads to poorly reproducible results.

A deep learning approach to multi-fiber parameter estimation and uncertainty quantification in diffusion MRI

Diffusion MRI (dMRI) is the primary imaging modality used to study brain microstructure in vivo. Reliable and computationally efficient parameter inference for common dMRI biophysical models is a challenging inverse problem, due to factors such as variable dimensionalities (reflecting the unknown number of distinct white matter fiber populations in a voxel), low signal-to-noise ratios, and non-linear forward models. These challenges have led many existing methods to use biologically implausible simplified models to stabilize estimation, for instance, assuming shared microstructure across all fiber populations within a voxel. In this work, we introduce a novel sequential method for multi-fiber parameter inference that decomposes the task into a series of manageable subproblems. These subproblems are solved using deep neural networks tailored to problem-specific structure and symmetry, and trained via simulation. The resulting inference procedure is largely amortized, enabling scalable parameter estimation and uncertainty quantification across all model parameters. Simulation studies and real imaging data analysis using the Human Connectome Project (HCP) demonstrate the advantages of our method over standard alternatives. In the case of the standard model of diffusion, our results show that under HCP-like acquisition schemes, estimates for extra-cellular parallel diffusivity are highly uncertain, while those for the intra-cellular volume fraction can be estimated with relatively high precision.

Isotropic sampling of tensor-encoded diffusion MRI

PURPOSE

The purpose of this study is to develop a method for selecting uniform wave vectors for double diffusion encoding (DDE) to improve the accuracy and reliability of diffusion measurements.

METHODS

The method relies on identifying orthogonal wave vectors with rotations, and representing these rotations as points on a three-dimensional sphere in four dimensions using quaternions. This enables an electrostatic repulsion algorithm to achieve a uniform distribution of these points. The optimal points are then converted back into orthogonal wave vectors (or rotations).

RESULTS

The method was validated by comparing the distribution of directions to those generated by uniform sampling and by evaluating the error in the powder-averaged signal for various models. Our results demonstrate that the electrostatic repulsion approach effectively achieves a uniform distribution of wave vectors.

CONCLUSION

The proposed method provides a systematic way to generate uniform diffusion directions suitable, for example, for DDE, enhancing the precision of diffusion measurements and reducing potential bias in experimental results. The method is also capable of generating uniform sets of B-tensors, and is thus applicable for general free waveform encoding.

Uncertainty mapping and probabilistic tractography using Simulation-based Inference in diffusion MRI: A comparison with classical Bayes

Simulation-Based Inference (SBI) has recently emerged as a powerful framework for Bayesian inference: Neural networks are trained on simulations from a forward model, and learn to rapidly estimate posterior distributions. We here present an SBI framework for parametric spherical deconvolution of diffusion MRI data of the brain. We demonstrate its utility for estimating white matter fibre orientations, mapping uncertainty of voxel-based estimates and performing probabilistic tractography by spatially propagating fibre orientation uncertainty. We conduct an extensive comparison against established Bayesian methods based on Markov-Chain Monte-Carlo (MCMC) and find that: a) in-silico training can lead to calibrated SBI networks with accurate parameter estimates and uncertainty mapping for both single- and multi-shell diffusion MRI, b) SBI allows amortised inference of the posterior distribution of model parameters given unseen observations, which is orders of magnitude faster than MCMC, c) SBI-based tractography yields reconstructions that have a high level of agreement with their MCMC-based counterparts, equal to or higher than scan-rescan reproducibility of estimates. We further demonstrate how SBI design considerations (such as dealing with noise, defining priors and handling model selection) can affect performance, allowing us to identify optimal practices. Taken together, our results show that SBI provides a powerful alternative to classical Bayesian inference approaches for fast and accurate model estimation and uncertainty mapping in MRI.

White matter microstructure links with brain, bodily and genetic attributes in adolescence, mid- and late life

Advanced diffusion magnetic resonance imaging (dMRI) allows one to probe and assess brain white matter (WM) organisation and microstructure in vivo. Various dMRI models with different theoretical and practical assumptions have been developed, representing partly overlapping characteristics of the underlying brain biology with potentially complementary value in the cognitive and clinical neurosciences. To which degree the different dMRI metrics relate to clinically relevant geno- and phenotypes is still debated. Hence, we investigate how tract-based and whole WM skeleton parameters from different dMRI approaches associate with clinically relevant and white matter-related phenotypes (sex, age, pulse pressure (PP), body-mass-index (BMI), brain asymmetry) and genetic markers in the UK Biobank (UKB, n=52,140) and the Adolescent Brain Cognitive Development (ABCD) Study (n=5,844). In general, none of the imaging approaches could explain all examined phenotypes, though the approaches were overall similar in explaining variability of the examined phenotypes. Nevertheless, particular diffusion parameters of the used dMRI approaches stood out in explaining some important phenotypes known to correlate with general human health outcomes. A multi-compartment Bayesian dMRI approach provided the strongest WM associations with age, and together with diffusion tensor imaging, the largest accuracy for sex-classifications. We find a similar pattern of metric and tract-dependent asymmetries across datasets, with stronger asymmetries in ABCD data. The magnitude of WM associations with polygenic scores as well as PP depended more on the sample, and likely age, than dMRI metrics. However, kurtosis was most indicative of BMI and potentially of bipolar disorder polygenic scores. We conclude that WM microstructure is differentially associated with clinically relevant pheno- and genotypes at different points in life.

Denoising Improves Cross-Scanner and Cross-Protocol Test-Retest Reproducibility of Diffusion Tensor and Kurtosis Imaging

The clinical translation of diffusion magnetic resonance imaging (dMRI)-derived quantitative contrasts hinges on robust reproducibility, minimizing both same-scanner and cross-scanner variability. As multi-site data sets, including multi-shell dMRI, expand in scope, enhancing reproducibility across variable MRI systems and MRI protocols becomes crucial. This study evaluates the reproducibility of diffusion kurtosis imaging (DKI) metrics (beyond conventional diffusion tensor imaging (DTI)), at the voxel and region-of-interest (ROI) levels on magnitude and complex-valued dMRI data, using denoising with and without harmonization. We compared same-scanner, cross-scanner, and cross-protocol variability for a multi-shell dMRI protocol (2-mm isotropic resolution, b = 0, 1000, 2000 s/mm2) in 20 subjects. We first evaluated the effectiveness of Marchenko-Pastur Principal Component Analysis (MPPCA) based denoising strategies for both magnitude and complex data to mitigate noise-induced bias and variance, to improve dMRI parametric maps and reproducibility. Next, we examined the impact of denoising under different population analysis approaches, specifically comparing voxel-wise versus region of interest (ROI)-based methods. We also evaluated the role of denoising when harmonizing dMRI across scanners and protocols. The results indicate that DTI and DKI maps visually improve after MPPCA denoising, with noticeably fewer outliers in kurtosis maps. Denoising, either using magnitude or complex dMRI, enhances voxel-wise reproducibility, with test-retest variability of kurtosis indices reduced from 15%-20% without denoising to 5%-10% after denoising. Complex dMRI denoising reduces the noise floor by up to 60%. Denoising not only reduced variability across scans and protocols, but also increased statistical power for low SNR voxel-wise comparisons when comparing cross sectional groups. In conclusion, MPPCA denoising, either over magnitude or complex dMRI data, enhances the reproducibility and precision of higher-order diffusion metrics across same-scanner, cross-scanner, and cross-protocol assessments. The enhancement in data quality and precision facilitates the broader application and acceptance of these advanced imaging techniques in both clinical practice and large-scale neuroimaging studies.

SE(3) group convolutional neural networks and a study on group convolutions and equivariance for DWI segmentation

We present an SE(3) Group Convolutional Neural Network along with a series of networks with different group actions for segmentation of Diffusion Weighted Imaging data. These networks gradually incorporate group actions that are natural for this type of data, in the form of convolutions that provide equivariant transformations of the data. This knowledge provides a potentially important inductive bias and may alleviate the need for data augmentation strategies. We study the effects of these actions on the performances of the networks by training and validating them using the diffusion data from the Human Connectome project. Unlike previous works that use Fourier-based convolutions, we implement direct convolutions, which are more lightweight. We show how incorporating more actions - using the SE(3) group actions - generally improves the performances of our segmentation while limiting the number of parameters that must be learned.

Characterization of neurite and soma organization in the brain and spinal cord with diffusion MRI

The central nervous system (CNS), comprised of both the brain and spinal cord, and is a complex network of white and gray matter responsible for sensory, motor, and cognitive functions. Advanced diffusion MRI (dMRI) techniques offer a promising mechanism to non-invasively characterize CNS architecture, however, most studies focus on the brain or spinal cord in isolation. Here, we implemented a clinically feasible dMRI protocol on a 3T scanner to simultaneously characterize neurite and soma microstructure of both the brain and spinal cord. The protocol enabled the use of Diffusion Tensor Imaging (DTI), Standard Model Imaging (SMI), and Soma and Neurite Density Imaging (SANDI), representing the first time SMI and SANDI have been evaluated in the cord, and in the cord and brain simultaneously. Our results demonstrate high image quality even at high diffusion weightings, reproducibility of SMI and SANDI derived metrics similar to those of DTI with few exceptions, and biologically feasible contrasts between and within white and gray matter regions. Reproducibility and contrasts were decreased in the cord compared to that of the brain, revealing challenges due to partial volume effects and image preprocessing. This study establishes a harmonized approach for brain and cord microstructural imaging, and the opportunity to study CNS pathologies and biomarkers of structural integrity across the neuroaxis.

Improving the Assessment of Axonal Injury in Early Multiple Sclerosis

RATIONALE AND OBJECTIVES

Several quantitative magnetic resonance imaging (MRI) methods are available to measure tissue injury in multiple sclerosis (MS), but their pathological specificity remains limited. The multi-compartment diffusion imaging using the spherical mean technique (SMT) overcomes several technical limitations of the diffusion-weighted image signal, thus delivering metrics with increased pathological specificity. Given these premises, here we assess whether the SMT-derived apparent axonal volume (Vax) provides a better tissue classifier than the diffusion tensor imaging (DTI)-derived axial diffusivity (AD) in the white matter (WM) of MS brains.

METHODS

Forty-three treatment-naïve people with newly diagnosed MS, clinically isolated syndrome, or radiologically isolated syndrome and 18 healthy controls (HCs) underwent a 3.0 Tesla MRI inclusive of T1-weighted (T1-w) and T2-w fluid-attenuated inversion recovery (FLAIR) sequences, and multi-b shell diffusion-weighted imaging. In patients only, pre- and post-gadolinium diethylenetriamine penta-acetic acid T1-w sequences were obtained for the evaluation of contrast-active lesions (CELs). Vax and AD were calculated in T2-lesions, chronic black holes (cBHs), and normal appearing (NAWM) in patients and normal WM (NWM) in HCs. Vax and AD values were compared across all the possible combinations of these regions. CELs were excluded from the analyses.

RESULTS

Vax differed in all comparisons (p ≤ 0.047 by paired t-test); AD differed in most comparisons (p < 0.001) except between NAWM and NWM, and between cBHs and T2-lesions. Vax had higher accuracy (p ≤ 0.029 by DeLong test) and larger effect size (p ≤ 0.038 by paired t-test) than AD in differentiating areas with even minimal tissue injury.

CONCLUSIONS

Vax provides a better radiological quantitative discriminator of different degrees of axonal-mediated tissue injury even between areas with expected minimal pathology. Our data support further studies to assess the readiness of Vax as a measure of outcome for clinical trials on neuroprotection in MS.

In vivo human neurite exchange imaging (NEXI) at 500 mT/m diffusion gradients

Evaluating tissue microstructure and membrane integrity in the living human brain through diffusion-water exchange imaging is challenging due to requirements for a high signal-to-noise ratio and short diffusion times dictated by relatively fast exchange processes. The goal of this work was to demonstrate the feasibility of in vivo imaging of tissue micro-geometries and water exchange within the brain gray matter using the state-of-the-art Connectome 2.0 scanner equipped with an ultra-high-performance gradient system (maximum gradient strength=500 mT/m, maximum slew rate=600 T/m/s). We performed diffusion MRI measurements in 15 healthy volunteers at multiple diffusion times (13-30 ms) and b -values up to 17.5 ms/μm2. The anisotropic Kärger model was applied to estimate the exchange time between intra-neurite and extracellular water in gray matter. The estimated exchange time across the cortical ribbon was around (median±interquartile range) 13±8 ms on Connectome 2.0, substantially faster than that measured using an imaging protocol compatible with Connectome 1.0-alike systems on the same cohort. Our investigation suggested that the NEXI exchange time estimation using a Connectome 1.0 compatible protocol was more prone to residual noise floor biases due to the small time-dependent signal contrasts across diffusion times when the exchange is fast (≤20 ms). Furthermore, spatial variation of exchange time was observed across the cortex, where the motor cortex, somatosensory cortex and visual cortex exhibit longer exchange times compared to other cortical regions. Non-linear fitting for the anisotropic Kärger model was accelerated 100 times using a GPU-based pipeline compared to the conventional CPU-based approach. This study highlighted the importance of the chosen diffusion times and measures to address Rician noise in dMRI data, which can have a substantial impact on the estimated NEXI exchange time and require extra attention when comparing NEXI results between various hardware setups.

Microstructurally informed subject-specific parcellation of the corpus callosum using axonal water fraction

The corpus callosum (CC) is the most important interhemispheric white matter (WM) structure composed of several anatomically and functionally distinct WM tracts. Resolving these tracts is a challenge since the callosum appears relatively homogenous in conventional structural imaging. Commonly used callosal parcellation methods such as Hofer and Frahm scheme rely on rigid geometric guidelines to separate the substructures that are limited to consider individual variation. Here we present a novel subject-specific and microstructurally-informed method for callosal parcellation based on axonal water fraction (ƒ) known as a diffusion metric reflective of axon caliber and density. We studied 30 healthy subjects from the Human Connectome Project dataset with multi-shell diffusion MRI. The biophysical parameter ƒ was derived from compartment-specific WM modeling. Inflection points were identified where there were concavity changes in ƒ across the CC to delineate callosal subregions. We observed relatively higher ƒ in anterior and posterior areas known to consist of a greater number of small diameter fibers and lower ƒ in posterior body areas of the CC known to consist of a greater number of large diameter fibers. Based on the degree of change in ƒ along the callosum, seven callosal subregions were consistently delineated for each individual. Therefore, this method provides microstructurally informed callosal parcellation in a subject-specific way, allowing for more accurate analysis in the corpus callosum.

Introducing µGUIDE for quantitative imaging via generalized uncertainty-driven inference using deep learning

This work proposes µGUIDE: a general Bayesian framework to estimate posterior distributions of tissue microstructure parameters from any given biophysical model or signal representation, with exemplar demonstration in diffusion-weighted magnetic resonance imaging. Harnessing a new deep learning architecture for automatic signal feature selection combined with simulation-based inference and efficient sampling of the posterior distributions, µGUIDE bypasses the high computational and time cost of conventional Bayesian approaches and does not rely on acquisition constraints to define model-specific summary statistics. The obtained posterior distributions allow to highlight degeneracies present in the model definition and quantify the uncertainty and ambiguity of the estimated parameters.

Rebalance the Inhibitory System in the Elderly Brain: Influence of Balance Learning on GABAergic Inhibition and Functional Connectivity

Aging involves complex processes that impact the structure, function, and metabolism of the human brain. Declines in both structural and functional integrity along with reduced local inhibitory tone in the motor areas, as indicated by reduced γ-aminobutyric acid (GABA) levels, are often associated with compromised motor performance in elderly adults. Using multimodal neuroimaging techniques including magnetic resonance spectroscopy (MRS), diffusion magnetic resonance imaging (MRI), functional MRI as well as transcranial magnetic stimulation to assess short-interval intracortical inhibition (SICI), this study explores whether these age-related changes can be mitigated by motor learning. The investigation focused on the effects of long-term balance learning (3 months) on intracortical inhibition, metabolism, structural, and functional connectivity in the cortical sensorimotor network among an elderly cohort. We found that after 3 months of balance learning, subjects significantly improved balance performance, upregulated sensorimotor cortical GABA levels and ventral sensorimotor network functional connectivity (VSN-FC) compared to a passive control group. Furthermore, correlation analysis suggested a positive association between baseline VSN-FC and balance performance, between baseline VSN-FC and SICI, and between improvements in balance performance and upregulation in SICI in the training group, though these correlations did not survive the false discovery rate correction. These findings demonstrate that balance learning has the potential to counteract aging-related decline in functional connectivity and cortical inhibition on the "tonic" (MRS) and "functional" (SICI) level and shed new light on the close interplay between the GABAergic system, functional connectivity, and behavior.

The Diffusion Exchange Ratio (DEXR): A minimal sampling of diffusion exchange spectroscopy to probe exchange, restriction, and time-dependence

Water exchange is increasingly recognized as an important biological process that can affect the study of biological tissue using diffusion MR. Methods to measure exchange, however, remain immature as opposed to those used to characterize restriction, with no consensus on the optimal pulse sequence (s) or signal model (s). In general, the trend has been towards data-intensive fitting of highly parameterized models. We take the opposite approach and show that a judicious sub-sample of diffusion exchange spectroscopy (DEXSY) data can be used to robustly quantify exchange, as well as restriction, in a data-efficient manner. This sampling produces a ratio of two points per mixing time: (i) one point with equal diffusion weighting in both encoding periods, which gives maximal exchange contrast, and (ii) one point with the same total diffusion weighting in just the first encoding period, for normalization. We call this quotient the Diffusion EXchange Ratio (DEXR). Furthermore, we show that it can be used to probe time-dependent diffusion by estimating the velocity autocorrelation function (VACF) over intermediate to long times (∼2-500ms). We provide a comprehensive theoretical framework for the design of DEXR experiments in the case of static or constant gradients. Data from Monte Carlo simulations and experiments acquired in fixed and viable ex vivo neonatal mouse spinal cord using a permanent magnet system are presented to test and validate this approach. In viable spinal cord, we report the following apparent parameters from just 6 data points: τk=17±4ms, fNG=0.72±0.01, Reff=1.05±0.01μm, and κeff=0.19±0.04μm/ms, which correspond to the exchange time, restricted or non-Gaussian signal fraction, an effective spherical radius, and permeability, respectively. For the VACF, we report a long-time, power-law scaling with ≈t-2.4, which is approximately consistent with disordered domains in 3-D. Overall, the DEXR method is shown to be highly efficient, capable of providing valuable quantitative diffusion metrics using minimal MR data.

White Matter Microstructural Changes Using Ultra-Strong Diffusion Gradient MRI in Adult-Onset Idiopathic Focal Cervical Dystonia

BACKGROUND AND OBJECTIVES

Adult-onset idiopathic focal cervical dystonia (AOIFCD) involves abnormal posturing of the cervical musculature and, in some individuals, an associated head tremor. Existing neuroimaging studies have implicated key motor networks. However, measures used to date lack specificity toward underlying pathophysiologic differences. We aim to assess white matter motor pathways for localized, microstructural differences, which may aid in understanding underlying mechanisms.

METHODS

Individuals diagnosed with AOIFCD and an age- and sex-matched control group were prospectively recruited through the Welsh Movement Disorders Research Network. All participants underwent in-depth clinical phenotyping and MRI (structural and diffusion sequences) using ultra-strong diffusion gradients. Tractography (whole-tract median values) and tractometry (along tract profiling) were performed for key white matter motor pathways assessing diffusion kurtosis imaging (DKI), neurite orientation dispersion and density imaging (NODDI), and standard model parameters. Groups were compared using linear model analysis with Bonferroni multiple comparison correction.

RESULTS

Fifty participants with AOIFCD and 30 healthy control participants were recruited, with 46 with AOIFCD and 30 healthy controls included for analysis (33 without head tremor, 13 with head tremor). Significant differences were observed in the anterior thalamic radiations (lower mid-tract fractional anisotropy [estimate = -0.046, p = 3.07 × 10-3], radial kurtosis [estimate = -0.165, p = 1.42 × 10-4], f-intra-axonal signal fraction [estimate = -0.044, p = 2.78 × 10-3], p2 orientation coherence [estimate = -0.043, p = 1.64 × 10-3], higher Orientation Dispersion Index [ODI, estimate = 0.023, p = 2.22 × 10-3]) and thalamopremotor tracts (higher mid-tract mean kurtosis [estimate = 0.064, p = 7.56 × 10-4], lower Neurite Density Index [estimate = 0.062, p = 2.1 × 10-3], higher distal tract ODI [estimate = 0.062, p = 3.1 × 10-3], lower f [estimate = -0.1, p = 2.3 × 10-3], and striatopremotor tracts [proximal lower f: estimate = -0.075, p = 1.06 × 10-3]). These measures correlated with clinical measures: dystonia duration (right thalamopremotor distal ODI: r = -0.9, p = 1.29 × 10-14), psychiatric symptoms (obsessive compulsive symptoms: left anterior thalamic radiation p2 r = 0.92, p = 2.797 × 10-11), sleep quality (Sleep Disorders Questionnaire Score: left anterior thalamic radiation ODI: r = -0.84, p = 4.84 × 10-11), pain (left anterior thalamic radiation ODI: r = -0.89, p = 1.4 × 10-13), and cognitive functioning (paired associated learning task p2, r = 0.94, p = 6.68 × 10-20).

DISCUSSION

Overall, localized microstructural differences were identified within tracts linking the prefrontal and premotor cortices with thalamic and basal ganglia regions, suggesting pathophysiologic processes involve microstructural aberrances of motor system modulatory pathways, particularly involving intra-axonal and fiber orientation dispersion measures.

The Diffusion Exchange Ratio (DEXR): A minimal sampling of diffusion exchange spectroscopy to probe exchange, restriction, and time-dependence

Water exchange is increasingly recognized as an important biological process that can affect the study of biological tissue using diffusion MR. Methods to measure exchange, however, remain immature as opposed to those used to characterize restriction, with no consensus on the optimal pulse sequence(s) or signal model(s). In general, the trend has been towards data-intensive fitting of highly parameterized models. We take the opposite approach and show that a judicious sub-sample of diffusion exchange spectroscopy (DEXSY) data can be used to robustly quantify exchange, as well as restriction, in a data-efficient manner. This sampling produces a ratio of two points per mixing time: (i) one point with equal diffusion weighting in both encoding periods, which gives maximal exchange contrast, and (ii) one point with the same total diffusion weighting in just the first encoding period, for normalization. We call this quotient the Diffusion EXchange Ratio (DEXR). Furthermore, we show that it can be used to probe time-dependent diffusion by estimating the velocity autocorrelation function (VACF) over intermediate to long times (~ 2-500 ms). We provide a comprehensive theoretical framework for the design of DEXR experiments in the case of static or constant gradients. Data from Monte Carlo simulations and experiments acquired in fixed and viable ex vivo neonatal mouse spinal cord using a permanent magnet system are presented to test and validate this approach. In viable spinal cord, we report the following apparent parameters from just 6 data points:τ k = 17 ± 4 m s ,f N G = 0.71 ± 0.01 ,R e f f = 1.10 ± 0.01 μ m , andκ eff = 0.21 ± 0.06 μ m / m s , which correspond to the exchange time, restricted or non-Gaussian signal fraction, an effective spherical radius, and permeability, respectively. For the VACF, we report a long-time, power-law scaling with ≈ t - 2.4 , which is approximately consistent with disordered domains in 3-D. Overall, the DEXR method is shown to be highly efficient, capable of providing valuable quantitative diffusion metrics using minimal MR data.

The Larmor frequency shift of a white matter magnetic microstructure model with multiple sources

Magnetic susceptibility imaging may provide valuable information about chemical composition and microstructural organization of tissue. However, its estimation from the MRI signal phase is particularly difficult as it is sensitive to magnetic tissue properties ranging from the molecular to the macroscopic scale. The MRI Larmor frequency shift measured in white matter (WM) tissue depends on the myelinated axons and other magnetizable sources such as iron-filled ferritin. We have previously derived the Larmor frequency shift arising from a dense medium of cylinders with scalar susceptibility and arbitrary orientation dispersion. Here, we extend our model to include microscopic WM susceptibility anisotropy as well as spherical inclusions with scalar susceptibility to represent subcellular structures, biologically stored iron, and so forth. We validate our analytical results with computer simulations and investigate the feasibility of estimating susceptibility using simple iterative linear least squares without regularization or preconditioning. This is done in a digital brain phantom synthesized from diffusion MRI measurements of an ex vivo mouse brain at ultra-high field.

Compartmental anisotropy of filtered exchange imaging (FEXI) in human white matter: What is happening in FEXI?

PURPOSE

To investigate the effects of compartmental anisotropy on filtered exchange imaging (FEXI) in white matter (WM).

THEORY AND METHODS

FEXI signals were measured using multiple combinations of diffusion filter and detection directions in five healthy volunteers. Additional filters, including a trace-weighted diffusion filter with trapezoidal gradients, a spherical b-tensor encoded diffusion filter, and a T2 filter, were tested with trace-weighted diffusion detection.

RESULTS

A large range of apparent exchange rates (AXR) and both positive and negative filter efficiencies (σ) were found depending on the mutual orientation of the filter and detection gradients relative to WM fiber orientation. The data demonstrated that the fast-diffusion compartment suppressed by diffusional filtering is not exclusively extra-cellular, but also intra-cellular. While not comprehensive, a simple two-compartment diffusion tensor model with water exchange was able to account qualitatively for the trends in positive and negative filtering efficiencies, while standard model imaging (SMI) without exchange could not. This two-compartment diffusion tensor model also demonstrated smaller AXR variances across subjects. When employing trace-weighted diffusion detection, AXR values were on the order of the R1 (=1/T1) of water at 3T for crossing fibers, while being less than R1 for parallel fibers.

CONCLUSION

Orientation-dependent AXR and σ values were observed when using multi-orientation filter and detection gradients in FEXI, indicating that WM FEXI models need to account for compartmental anisotropy. When using trace-weighted detection, AXR values were on the order of or less than R1, complicating the interpretation of FEXI results in WM in terms of biological exchange properties. These findings may contribute toward better understanding of FEXI results in WM.

Investigating apparent differences between standard DKI and axisymmetric DKI and its consequences for biophysical parameter estimates

PURPOSE

The purpose of the study is to identify differences between axisymmetric diffusion kurtosis imaging (DKI) and standard DKI, their consequences for biophysical parameter estimates, and the protocol choice influence on parameter estimation.

METHODS

Noise-free and noisy, synthetic diffusion MRI human brain data is simulated using standard DKI for a standard and the fast "199" acquisition protocol. First the noise-free "baseline" difference between both DKI models is estimated and the influence of fiber complexity is investigated. Noisy data is used to establish the signal-to-noise ratio at which the baseline difference exceeds noise variability. The influence of protocol choices and denoising is investigated. The five axisymmetric DKI tensor metrics (AxTM), the parallel and perpendicular diffusivity and kurtosis and mean of the kurtosis tensor are used to compare both DKI models. Additionally, the baseline difference is also estimated for the five parameters of the WMTI-Watson model.

RESULTS

The parallel and perpendicular kurtosis and all of the WMTI-Watson parameters had large baseline differences. Using a Westin or FA mask reduced the number of voxels with large baseline difference, that is, by selecting voxels with less complex fibers. For the noisy data, precision was worsened by the fast "199" protocol but adaptive denoising can help counteract these effects.

CONCLUSION

For the diffusivities and mean of the kurtosis tensor, axisymmetric DKI with a standard protocol delivers similar results as standard DKI. Fiber complexity is one main driver of the baseline differences. Using the "199" protocol worsens precision in noisy data but adaptive denoising mitigates these effects.

Constrained alternating minimization for parameter mapping (CAMP)

OBJECTIVE

To improve image quality in highly accelerated parameter mapping by incorporating a linear constraint that relates consecutive images.

APPROACH

In multi-echo T1 or T2 mapping, scan time is often shortened by acquiring undersampled but complementary measures of k-space at each TE or TI. However, residual undersampling artifacts from the individual images can then degrade the quality of the final parameter maps. In this work, a new reconstruction method, dubbed Constrained Alternating Minimization for Parameter mapping (CAMP), is introduced. This method simultaneously extracts T2 or T1* maps in addition to an image for each TE or TI from accelerated datasets, leveraging the constraints of the decay to improve the reconstructed image quality. The model enforces exponential decay through a linear constraint, resulting in a biconvex objective function that lends itself to alternating minimization. The method was tested in four in vivo volunteer experiments and validated in phantom studies and healthy subjects, using T2 and T1 mapping, with accelerations of up to 12.

MAIN RESULTS

CAMP is demonstrated for accelerated radial and Cartesian acquisitions in T2 and T1 mapping. The method is even applied to generate an entire T2 weighted image series from a single TSE dataset, despite the blockwise k-space sampling at each echo time. Experimental undersampled phantom and in vivo results processed with CAMP exhibit reduced artifacts without introducing bias.

SIGNIFICANCE

For a wide array of applications, CAMP linearizes the model cost function without sacrificing model accuracy so that the well-conditioned and highly efficient reconstruction algorithm improves the image quality of accelerated parameter maps.

Complemental Value of Microstructural and Macrostructural MRI in the Discrimination of Neurodegenerative Parkinson Syndromes

PURPOSE

Various MRI-based techniques were tested for the differentiation of neurodegenerative Parkinson syndromes (NPS); the value of these techniques in direct comparison and combination is uncertain. We thus compared the diagnostic performance of macrostructural, single compartmental, and multicompartmental MRI in the differentiation of NPS.

METHODS

We retrospectively included patients with NPS, including 136 Parkinson's disease (PD), 41 multiple system atrophy (MSA) and 32 progressive supranuclear palsy (PSP) and 27 healthy controls (HC). Macrostructural tissue probability values (TPV) were obtained by CAT12. The microstructure was assessed using a mesoscopic approach by diffusion tensor imaging (DTI), neurite orientation dispersion and density imaging (NODDI), and diffusion microstructure imaging (DMI). After an atlas-based read-out, a linear support vector machine (SVM) was trained on a training set (n = 196) and validated in an independent test cohort (n = 40). The diagnostic performance of the SVM was compared for different inputs individually and in combination.

RESULTS

Regarding the inputs separately, we observed the best diagnostic performance for DMI. Overall, the combination of DMI and TPV performed best and correctly classified 88% of the patients. The corresponding area under the receiver operating characteristic curve was 0.87 for HC, 0.97 for PD, 1.0 for MSA, and 0.99 for PSP.

CONCLUSION

We were able to demonstrate that (1) MRI parameters that approximate the microstructure provided substantial added value over conventional macrostructural imaging, (2) multicompartmental biophysically motivated models performed better than the single compartmental DTI and (3) combining macrostructural and microstructural information classified NPS and HC with satisfactory performance, thus suggesting a complementary value of both approaches.

Cerebral microstructural alterations in Post-COVID-condition are related to cognitive impairment, olfactory dysfunction and fatigue

After contracting COVID-19, a substantial number of individuals develop a Post-COVID-Condition, marked by neurologic symptoms such as cognitive deficits, olfactory dysfunction, and fatigue. Despite this, biomarkers and pathophysiological understandings of this condition remain limited. Employing magnetic resonance imaging, we conduct a comparative analysis of cerebral microstructure among patients with Post-COVID-Condition, healthy controls, and individuals that contracted COVID-19 without long-term symptoms. We reveal widespread alterations in cerebral microstructure, attributed to a shift in volume from neuronal compartments to free fluid, associated with the severity of the initial infection. Correlating these alterations with cognition, olfaction, and fatigue unveils distinct affected networks, which are in close anatomical-functional relationship with the respective symptoms.

Optimisation of quantitative brain diffusion-relaxation MRI acquisition protocols with physics-informed machine learning

Diffusion-relaxation MRI aims to extract quantitative measures that characterise microstructural tissue properties such as orientation, size, and shape, but long acquisition times are typically required. This work proposes a physics-informed learning framework to extract an optimal subset of diffusion-relaxation MRI measurements for enabling shorter acquisition times, predict non-measured signals, and estimate quantitative parameters. In vivo and synthetic brain 5D-Diffusion-T1-T2∗-weighted MRI data obtained from five healthy subjects were used for training and validation, and from a sixth participant for testing. One fully data-driven and two physics-informed machine learning methods were implemented and compared to two manual selection procedures and Cramér-Rao lower bound optimisation. The physics-informed approaches could identify measurement-subsets that yielded more consistently accurate parameter estimates in simulations than other approaches, with similar signal prediction error. Five-fold shorter protocols yielded error distributions of estimated quantitative parameters with very small effect sizes compared to estimates from the full protocol. Selected subsets commonly included a denser sampling of the shortest and longest inversion time, lowest echo time, and high b-value. The proposed framework combining machine learning and MRI physics offers a promising approach to develop shorter imaging protocols without compromising the quality of parameter estimates and signal predictions.

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.

Neural orientation distribution fields for estimation and uncertainty quantification in diffusion MRI

Inferring brain connectivity and structure in-vivo requires accurate estimation of the orientation distribution function (ODF), which encodes key local tissue properties. However, estimating the ODF from diffusion MRI (dMRI) signals is a challenging inverse problem due to obstacles such as significant noise, high-dimensional parameter spaces, and sparse angular measurements. In this paper, we address these challenges by proposing a novel deep-learning based methodology for continuous estimation and uncertainty quantification of the spatially varying ODF field. We use a neural field (NF) to parameterize a random series representation of the latent ODFs, implicitly modeling the often ignored but valuable spatial correlation structures in the data, and thereby improving efficiency in sparse and noisy regimes. An analytic approximation to the posterior predictive distribution is derived which can be used to quantify the uncertainty in the ODF estimate at any spatial location, avoiding the need for expensive resampling-based approaches that are typically employed for this purpose. We present empirical evaluations on both synthetic and real in-vivo diffusion data, demonstrating the advantages of our method over existing approaches.

Purpose in life as a resilience factor for brain health: diffusion MRI findings from the Midlife in the U.S. study

Introduction

A greater sense of purpose in life is associated with several health benefits relevant for active aging, but the mechanisms remain unclear. We evaluated if purpose in life was associated with indices of brain health.

Methods

We examined data from the Midlife in the United States (MIDUS) Neuroscience Project. Diffusion weighted magnetic resonance imaging data (n=138; mean age 65.2 years, age range 48-95; 80 females; 37 black, indigenous, and people of color) were used to estimate microstructural indices of brain health such as axonal density, and axonal orientation. The seven-item purpose in life scale was used. Permutation analysis of linear models was used to examine associations between purpose in life scores and the diffusion metrics in white matter and in the bilateral hippocampus, adjusting for age, sex, education, and race.

Results and discussion

Greater sense of purpose in life was associated with brain microstructural features consistent with better brain health. Positive associations were found in both white matter and the right hippocampus, where multiple convergent associations were detected. The hippocampus is a brain structure involved in learning and memory that is vulnerable to stress but retains the capacity to grow and adapt through old age. Our findings suggest pathways through which an enhanced sense of purpose in life may contribute to better brain health and promote healthy aging. Since purpose in life is known to decline with age, interventions and policy changes that facilitate a greater sense of purpose may extend and improve the brain health of individuals and thus improve public health.

Insights and improvements in correspondence between axonal volume fraction measured with diffusion-weighted MRI and electron microscopy

Biophysical diffusion-weighted imaging (DWI) models are increasingly used in neuroscience to estimate the axonal water fraction (f AW ), which in turn is key for noninvasive estimation of the axonal volume fraction (f A ). These models require thorough validation by comparison with a reference method, for example, electron microscopy (EM). While EM studies often neglect the unmyelinated axons and solely report the fraction of myelinated axons, in DWI both myelinated and unmyelinated axons contribute to the DWI signal. However, DWI models often include simplifications, for example, the neglect of differences in the compartmental relaxation times or fixed diffusivities, which in turn might affect the estimation off AW . We investigate whether linear calibration parameters (scaling and offset) can improve the comparability between EM- and DWI-based metrics off A . To this end, we (a) used six DWI models based on the so-called standard model of white matter (WM), including two models with fixed compartmental diffusivities (e.g., neurite orientation dispersion and density imaging, NODDI) and four models that fitted the compartmental diffusivities (e.g., white matter tract integrity, WMTI), and (b) used a multimodal data set including ex vivo diffusion DWI and EM data in mice with a broad dynamic range of fibre volume metrics. We demonstrated that the offset is associated with the volume fraction of unmyelinated axons and the scaling factor is associated with different compartmentalT 2 and can substantially enhance the comparability between EM- and DWI-based metrics off A . We found that DWI models that fitted compartmental diffusivities provided the most accurate estimates of the EM-basedf A . Finally, we introduced a more efficient hybrid calibration approach, where only the offset is estimated but the scaling is fixed to a theoretically predicted value. Using this approach, a similar one-to-one correspondence to EM was achieved for WMTI. The method presented can pave the way for use of validated DWI-based models in clinical research and neuroscience.

Assessment of Precision and Accuracy of Brain White Matter Microstructure using Combined Diffusion MRI and Relaxometry

Joint modeling of diffusion and relaxation has seen growing interest due to its potential to provide complementary information about tissue microstructure. For brain white matter, we designed an optimal diffusion-relaxometry MRI protocol that samples multiple b-values, B-tensor shapes, and echo times (TE). This variable-TE protocol (27 min) has as subsets a fixed-TE protocol (15 min) and a 2-shell dMRI protocol (7 min), both characterizing diffusion only. We assessed the sensitivity, specificity and reproducibility of these protocols with synthetic experiments and in six healthy volunteers. Compared with the fixed-TE protocol, the variable-TE protocol enables estimation of free water fractions while also capturing compartmental T 2 relaxation times. Jointly measuring diffusion and relaxation offers increased sensitivity and specificity to microstructure parameters in brain white matter with voxelwise coefficients of variation below 10%.

Incorporating the effect of white matter microstructure in the estimation of magnetic susceptibility in ex vivo mouse brain

PURPOSE

To extend quantitative susceptibility mapping to account for microstructure of white matter (WM) and demonstrate its effect on ex vivo mouse brain at 16.4T.

THEORY AND METHODS

Previous studies have shown that the MRI measured Larmor frequency also depends on local magnetic microstructure at the mesoscopic scale. Here, we include effects from WM microstructure using our previous results for the mesoscopic Larmor frequencyΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ of cylinders with arbitrary orientations. We scrutinize the validity of our model and QSM in a digital brain phantom includingΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ from a WM susceptibility tensor and biologically stored iron with scalar susceptibility. We also apply susceptibility tensor imaging to the phantom and investigate how the fitted tensors are biased fromΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ . Last, we demonstrate how to combine multi-gradient echo and diffusion MRI images of ex vivo mouse brains acquired at 16.4T to estimate an apparent scalar susceptibility without sample rotations.

RESULTS

Our new model improves susceptibility estimation compared to QSM for the brain phantom. Applying susceptibility tensor imaging to the phantom withΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ from WM axons with scalar susceptibility produces a highly anisotropic susceptibility tensor that mimics results from previous susceptibility tensor imaging studies. For the ex vivo mouse brain we find theΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ due to WM microstructure to be substantial, changing susceptibility in WM up to 25% root-mean-squared-difference.

CONCLUSION

Ω ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ impacts susceptibility estimates and biases susceptibility tensor imaging fitting substantially. Hence, it should not be neglected when imaging structurally anisotropic tissue such as brain WM.

A simulation-driven supervised learning framework to estimate brain microstructure using diffusion MRI

We propose a framework to train supervised learning models on synthetic data to estimate brain microstructure parameters using diffusion magnetic resonance imaging (dMRI). Although further validation is necessary, the proposed framework aims to seamlessly incorporate realistic simulations into dMRI microstructure estimation. Synthetic data were generated from over 1,000 neuron meshes converted from digital neuronal reconstructions and linked to their neuroanatomical parameters (such as soma volume and neurite length) using an optimized diffusion MRI simulator that produces intracellular dMRI signals from the solution of the Bloch-Torrey partial differential equation. By combining random subsets of simulated neuron signals with a free diffusion compartment signal, we constructed a synthetic dataset containing dMRI signals and 40 tissue microstructure parameters of 1.45 million artificial brain voxels. To implement supervised learning models we chose multilayer perceptrons (MLPs) and trained them on a subset of the synthetic dataset to estimate some microstructure parameters, namely, the volume fractions of soma, neurites, and the free diffusion compartment, as well as the area fractions of soma and neurites. The trained MLPs perform satisfactorily on the synthetic test sets and give promising in-vivo parameter maps on the MGH Connectome Diffusion Microstructure Dataset (CDMD). Most importantly, the estimated volume fractions showed low dependence on the diffusion time, the diffusion time independence of the estimated parameters being a desired property of quantitative microstructure imaging. The synthetic dataset we generated will be valuable for the validation of models that map between the dMRI signals and microstructure parameters. The surface meshes and microstructures parameters of the aforementioned neurons have been made publicly available.

Microstructurally Informed Subject-Specific Parcellation of the Corpus Callosum using Axonal Water Fraction

The corpus callosum (CC) is the most important interhemispheric white matter (WM) structure composed of several anatomically and functionally distinct WM tracts. Resolving these tracts is a challenge since the callosum appears relatively homogenous in conventional structural imaging. Commonly used callosal parcellation methods such as the Hofer/Frahm scheme rely on rigid geometric guidelines to separate the substructures that are limited to consider individual variation. Here we present a novel subject-specific and microstructurally-informed method for callosal parcellation based on axonal water fraction (ƒ) known as a diffusion metric reflective of axon caliber and density. We studied 30 healthy subjects from the Human Connectome Project (HCP) dataset with multi-shell diffusion MRI. The biophysical parameter ƒ was derived from compartment-specific WM modeling. Inflection points were identified where there were concavity changes in ƒ across the CC to delineate callosal subregions. We observed relatively higher ƒ in anterior and posterior areas consisting of a greater number of small diameter fibers and lower ƒ in posterior body areas of the CC consisting of a greater number of large diameter fibers. Based on degree of change in ƒ along the callosum, seven callosal subregions can be consistently delineated for each individual. We observe that ƒ can capture differences in underlying tissue microstructures and seven subregions can be identified across CC. Therefore, this method provides microstructurally informed callosal parcellation in a subject-specific way, allowing for more accurate analysis in the corpus callosum.

Probing brain tissue microstructure with MRI: principles, challenges, and the role of multidimensional diffusion-relaxation encoding

Diffusion MRI uses the random displacement of water molecules to sensitize the signal to brain microstructure and to properties such as the density and shape of cells. Microstructure modeling techniques aim to estimate these properties from acquired data by separating the signal between virtual tissue 'compartments' such as the intra-neurite and the extra-cellular space. A key challenge is that the diffusion MRI signal is relatively featureless compared with the complexity of brain tissue. Another challenge is that the tissue microstructure is wildly different within the gray and white matter of the brain. In this review, we use results from multidimensional diffusion encoding techniques to discuss these challenges and their tentative solutions. Multidimensional encoding increases the information content of the data by varying not only the b-value and the encoding direction but also additional experimental parameters such as the shape of the b-tensor and the echo time. Three main insights have emerged from such encoding. First, multidimensional data contradict common model assumptions on diffusion and T2 relaxation, and illustrates how the use of these assumptions cause erroneous interpretations in both healthy brain and pathology. Second, many model assumptions can be dispensed with if data are acquired with multidimensional encoding. The necessary data can be easily acquired in vivo using protocols optimized to minimize Cramér-Rao lower bounds. Third, microscopic diffusion anisotropy reflects the presence of axons but not dendrites. This insight stands in contrast to current 'neurite models' of brain tissue, which assume that axons in white matter and dendrites in gray matter feature highly similar diffusion. Nevertheless, as an axon-based contrast, microscopic anisotropy can differentiate gray and white matter when myelin alterations confound conventional MRI contrasts.

Mapping the macrostructure and microstructure of the in vivo human hippocampus using diffusion MRI

The hippocampus is classically divided into mesoscopic subfields which contain varying microstructure that contribute to their unique functional roles. It has been challenging to characterize this microstructure with current magnetic resonance based neuroimaging techniques. In this work, we used diffusion magnetic resonance imaging (dMRI) and a novel surface-based approach in the hippocampus which revealed distinct microstructural distributions of neurite density and dispersion, T1w/T2w ratio as a proxy for myelin content, fractional anisotropy, and mean diffusivity. We used the neurite orientation dispersion and density imaging (NODDI) model optimized for grey matter diffusivity to characterize neurite density and dispersion. We found that neurite dispersion was highest in the cornu ammonis (CA) 1 and subiculum subfields which likely captures the large heterogeneity of tangential and radial fibres, such as the Schaffer collaterals, perforant path, and pyramidal neurons. Neurite density and T1w/T2w were highest in the subiculum and CA3 and lowest in CA1, which may reflect known myeloarchitectonic differences between these subfields. Using a simple logistic regression model, we showed that neurite density, dispersion, and T1w/T2w measures were separable across the subfields, suggesting that they may be sensitive to the known variability in subfield cyto- and myeloarchitecture. We report macrostructural measures of gyrification, thickness, and curvature that were in line with ex vivo descriptions of hippocampal anatomy. We employed a multivariate orthogonal projective non-negative matrix factorization (OPNNMF) approach to capture co-varying regions of macro- and microstructure across the hippocampus. The clusters were highly variable along the medial-lateral (proximal-distal) direction, likely reflecting known differences in morphology, cytoarchitectonic profiles, and connectivity. Finally, we show that by examining the main direction of diffusion relative to canonical hippocampal axes, we could identify regions with stereotyped microstructural orientations that may map onto specific fibre pathways, such as the Schaffer collaterals, perforant path, fimbria, and alveus. These results highlight the value of combining in vivo dMRI with computational approaches for capturing hippocampal microstructure, which may provide useful features for understanding cognition and for diagnosis of disease states.

The impact of head orientation with respect to B0 on diffusion tensor MRI measures

Diffusion tensor MRI (DT-MRI) remains the most commonly used approach to characterise white matter (WM) anisotropy. However, DT estimates may be affected by tissue orientation w.r.t. B → 0 due to local gradients and intrinsic T 2 orientation dependence induced by the microstructure. This work aimed to investigate whether and how diffusion tensor MRI-derived measures depend on the orientation of the head with respect to the static magnetic field, B → 0 . By simulating WM as two compartments, we demonstrated that compartmental T 2 anisotropy can induce the dependence of diffusion tensor measures on the angle between WM fibres and the magnetic field. In in vivo experiments, reduced radial diffusivity and increased axial diffusivity were observed in white matter fibres perpendicular to B → 0 compared to those parallel to B → 0 . Fractional anisotropy varied by up to 20 % as a function of the angle between WM fibres and the orientation of the main magnetic field. To conclude, fibre orientation w.r.t. B → 0 is responsible for up to 7 % variance in diffusion tensor measures across the whole brain white matter from all subjects and head orientations. Fibre orientation w.r.t. B → 0 may introduce additional variance in clinical research studies using diffusion tensor imaging, particularly when it is difficult to control for (e.g., fetal or neonatal imaging, or when the trajectories of fibres change due to, e.g., space occupying lesions).

Mapping tissue microstructure across the human brain on a clinical scanner with soma and neurite density image metrics

Soma and neurite density image (SANDI) is an advanced diffusion magnetic resonance imaging biophysical signal model devised to probe in vivo microstructural information in the gray matter (GM). This model requires acquisitions that include b values that are at least six times higher than those used in clinical practice. Such high b values are required to disentangle the signal contribution of water diffusing in soma from that diffusing in neurites and extracellular space, while keeping the diffusion time as short as possible to minimize potential bias due to water exchange. These requirements have limited the use of SANDI only to preclinical or cutting-edge human scanners. Here, we investigate the potential impact of neglecting water exchange in the SANDI model and present a 10-min acquisition protocol that enables to characterize both GM and white matter (WM) on 3 T scanners. We implemented analytical simulations to (i) evaluate the stability of the fitting of SANDI parameters when diminishing the number of shells; (ii) estimate the bias due to potential exchange between neurites and extracellular space in such reduced acquisition scheme, comparing it with the bias due to experimental noise. Then, we demonstrated the feasibility and assessed the repeatability and reproducibility of our approach by computing microstructural metrics of SANDI with AMICO toolbox and other state-of-the-art models on five healthy subjects. Finally, we applied our protocol to five multiple sclerosis patients. Results suggest that SANDI is a practical method to characterize WM and GM tissues in vivo on performant clinical scanners.

Origins of brain tissue elasticity under multiple loading modes by analyzing the microstructure-based models

Constitutive behaviors and material properties of brain tissue play an essential role in accurately modeling its mechanical responses. However, the measured mechanical behaviors of brain tissue exhibit a large variability, and the reported elastic modulus can differ by orders of magnitude. Here we develop the micromechanical models based on the actual microstructure of the longitudinally anisotropic plane of brain tissue to investigate the microstructural origins of the large variability. Specifically, axonal fiber bundles with the specified configurations are distributed in an equivalent matrix. All micromechanical models are subjected to multiple loading modes, such as tensile, compressive, and shear loading, under periodic boundary conditions. The predicted results agree well with the experimental results. Furthermore, we investigate how brain tissue elasticity varies with its microstructural features. It is revealed that the large variability in brain tissue elasticity stems from the volume fraction of axonal fiber, the aspect ratio of axonal fiber, and the distribution of axonal fiber orientation. The volume fraction has the greatest impact on the mechanical behaviors of brain tissue, followed by the distribution of axonal fiber orientation, then the aspect ratio. This study provides critical insights for understanding the microstructural origins of the large variability in brain tissue elasticity.

Artificial intelligence for diffusion MRI-based tissue microstructure estimation in the human brain: an overview

Artificial intelligence (AI) has made significant advances in the field of diffusion magnetic resonance imaging (dMRI) and other neuroimaging modalities. These techniques have been applied to various areas such as image reconstruction, denoising, detecting and removing artifacts, segmentation, tissue microstructure modeling, brain connectivity analysis, and diagnosis support. State-of-the-art AI algorithms have the potential to leverage optimization techniques in dMRI to advance sensitivity and inference through biophysical models. While the use of AI in brain microstructures has the potential to revolutionize the way we study the brain and understand brain disorders, we need to be aware of the pitfalls and emerging best practices that can further advance this field. Additionally, since dMRI scans rely on sampling of the q-space geometry, it leaves room for creativity in data engineering in such a way that it maximizes the prior inference. Utilization of the inherent geometry has been shown to improve general inference quality and might be more reliable in identifying pathological differences. We acknowledge and classify AI-based approaches for dMRI using these unifying characteristics. This article also highlighted and reviewed general practices and pitfalls involving tissue microstructure estimation through data-driven techniques and provided directions for building on them.

The influence of axonal beading and undulation on axonal diameter mapping

We consider the effect of non-cylindrical axonal shape on axonal diameter mapping with diffusion MRI. Practical sensitivity to axon diameter is attained at strong diffusion weightings b , where the deviation from the 1 / b scaling yields the finite transverse diffusivity, which is then translated into axon diameter. While axons are usually modeled as perfectly straight, impermeable cylinders, the local variations in diameter (caliber variation or beading) and direction (undulation) have been observed in microscopy data of human axons. Here we quantify the influence of cellular-level features such as caliber variation and undulation on axon diameter estimation. For that, we simulate the diffusion MRI signal in realistic axons segmented from 3-dimensional electron microscopy of a human brain sample. We then create artificial fibers with the same features and tune the amplitude of their caliber variations and undulations. Numerical simulations of diffusion in fibers with such tunable features show that caliber variations and undulations result in under- and over-estimation of axon diameters, correspondingly; this bias can be as large as 100%. 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.

Temporal trajectories of normal myelination and axonal development assessed by quantitative macromolecular and diffusion MRI: Ultrastructural and immunochemical validation in a rabbit model

INTRODUCTION

Quantitative and non-invasive measures of brain myelination and maturation during development are of great importance to both clinical and translational research communities. While the metrics derived from diffusion tensor imaging, are sensitive to developmental changes and some pathologies, they remain difficult to relate to the actual microstructure of the brain tissue. The advent of advanced model-based microstructural metrics requires histological validation. The purpose of the study was to validate novel, model-based MRI techniques, such as macromolecular proton fraction mapping (MPF) and neurite orientation and dispersion indexing (NODDI), against histologically derived indexes of myelination and microstructural maturation at various stages of development.

METHODS

New Zealand White rabbit kits underwent serial in-vivo MRI examination at postnatal days 1, 5, 11, 18, and 25, and as adults. Multi-shell, diffusion-weighted experiments were processed to fit NODDI model to obtain estimates, intracellular volume fraction (ICVF) and orientation dispersion index (ODI). Macromolecular proton fraction (MPF) maps were obtained from three source (MT-, PD-, and T1-weighted) images. After MRI sessions, a subset of animals was euthanized and regional samples of gray and white matter were taken for western blot analysis, to determine myelin basic protein (MBP), and electron microscopy, to estimate axonal, myelin fractions and g-ratio.

RESULTS

MPF of white matter regions showed a period of fast growth between P5 and P11 in the internal capsule, with a later onset in the corpus callosum. This MPF trajectory was in agreement with levels of myelination in the corresponding brain region, as assessed by western blot and electron microscopy. In the cortex, the greatest increase of MPF occurred between P18 and P26. In contrast, myelin, according to MBP western blot, saw the largest hike between P5 and P11 in the sensorimotor cortex and between P11 and P18 in the frontal cortex, which then seemingly plateaued after P11 and P18 respectively. G-ratio by MRI markers decreased with age in the white matter. However, electron microscopy suggest a relatively stable g-ratio throughout development.

CONCLUSION

Developmental trajectories of MPF accurately reflected regional differences of myelination rate in different cortical regions and white matter tracts. MRI-derived estimation of g-ratio was inaccurate during early development, likely due to the overestimation of axonal volume fraction by NODDI due to the presence of a large proportion of unmyelinated axons.

Deep learning prediction of diffusion MRI data with microstructure-sensitive loss functions

Deep learning prediction of diffusion MRI (DMRI) data relies on the utilization of effective loss functions. Existing losses typically measure the signal-wise differences between the predicted and target DMRI data without considering the quality of derived diffusion scalars that are eventually utilized for quantification of tissue microstructure. Here, we propose two novel loss functions, called microstructural loss and spherical variance loss, to explicitly consider the quality of both the predicted DMRI data and derived diffusion scalars. We apply these loss functions to the prediction of multi-shell data and enhancement of angular resolution. Evaluation based on infant and adult DMRI data indicates that both microstructural loss and spherical variance loss improve the quality of derived diffusion scalars.

Larmor frequency shift from magnetized cylinders with arbitrary orientation distribution

The magnetic susceptibility of tissue can provide valuable information about its chemical composition and microstructural organization. However, the relation between the magnetic microstructure and the measurable Larmor frequency shift is understood only for a few idealized cases. Here we analyze the microstructure formed by magnetized, NMR-invisible infinite cylinders suspended in an NMR-reporting fluid. Through simulations, we scrutinize various geometries of mesoscopic Lorentz cavities and inclusions, and show that the cavity size should be approximately one order of magnitude larger than the width of the inclusions. We also analytically derive the Larmor frequency shift for a population of cylinders with arbitrary orientation dispersion and show that it is determined by the l = 2 Laplace expansion coefficients p 2 m of the cylinders' orientation distribution function. Our work underscores the need to account for microstructural organization when estimating magnetic tissue properties.

Parameter estimation for WMTI-Watson model of white matter using encoder-decoder recurrent neural network

PURPOSE

Biophysical modeling of the diffusion MRI (dMRI) signal provides estimates of specific microstructural tissue properties. Although non-linear least squares (NLLS) is the most widespread fitting method, it suffers from local minima and high computational cost. Deep learning approaches are steadily replacing NLLS, but come with the limitation that the model needs to be retrained for each acquisition protocol and noise level. In this study, a novel fitting approach was proposed based on the encoder-decoder recurrent neural network (RNN) to accelerate model estimation with good generalization to various datasets.

METHODS

The white matter tract integrity (WMTI)-Watson model as an implementation of the Standard Model of diffusion in white matter derives its parameters indirectly from the diffusion and kurtosis tensors (DKI). The RNN-based solver, which estimates the WMTI-Watson model from DKI, is therefore more readily translatable to various data, irrespective of acquisition protocols as long as the DKI was pre-computed from the signal. An embedding approach was also used to render the model insensitive to potential differences in distributions between training data and experimental data. The analytical solution, NLLS, RNN-, and a multilayer perceptron (MLP)-based methods were evaluated on synthetic and in vivo datasets of rat and human brain.

RESULTS

The proposed RNN solver showed highly reduced computation time over the analytical solution and NLLS, with similar accuracy but improved robustness, and superior generalizability over MLP.

CONCLUSION

The RNN estimator can be easily applied to various datasets without retraining, which shows great potential for a widespread use.

Linear multi-scale modeling of diffusion MRI data: A framework for characterization of oriented structures across length scales

Diffusion-weighted magnetic resonance imaging (DW-MRI) has evolved to provide increasingly sophisticated investigations of the human brain's structural connectome in vivo. Restriction spectrum imaging (RSI) is a method that reconstructs the orientation distribution of diffusion within tissues over a range of length scales. In its original formulation, RSI represented the signal as consisting of a spectrum of Gaussian diffusion response functions. Recent technological advances have enabled the use of ultra-high b-values on human MRI scanners, providing higher sensitivity to intracellular water diffusion in the living human brain. To capture the complex diffusion time dependence of the signal within restricted water compartments, we expand upon the RSI approach to represent restricted water compartments with non-Gaussian response functions, in an extended analysis framework called linear multi-scale modeling (LMM). The LMM approach is designed to resolve length scale and orientation-specific information with greater specificity to tissue microstructure in the restricted and hindered compartments, while retaining the advantages of the RSI approach in its implementation as a linear inverse problem. Using multi-shell, multi-diffusion time DW-MRI data acquired with a state-of-the-art 3 T MRI scanner equipped with 300 mT/m gradients, we demonstrate the ability of the LMM approach to distinguish different anatomical structures in the human brain and the potential to advance mapping of the human connectome through joint estimation of the fiber orientation distributions and compartment size characteristics.

Axial and radial axonal diffusivities and radii from single encoding strongly diffusion-weighted MRI

We enable the estimation of the per-axon axial diffusivity from single encoding, strongly diffusion-weighted, pulsed gradient spin echo data. Additionally, we improve the estimation of the per-axon radial diffusivity compared to estimates based on spherical averaging. The use of strong diffusion weightings in magnetic resonance imaging (MRI) allows to approximate the signal in white matter as the sum of the contributions from only axons. At the same time, spherical averaging leads to a major simplification of the modeling by removing the need to explicitly account for the unknown distribution of axonal orientations. However, the spherically averaged signal acquired at strong diffusion weightings is not sensitive to the axial diffusivity, which cannot therefore be estimated although needed for modeling axons - especially in the context of multi-compartmental modeling. We introduce a new general method for the estimation of both the axial and radial axonal diffusivities at strong diffusion weightings based on kernel zonal modeling. The method could lead to estimates that are free from partial volume bias with gray matter or other isotropic compartments. The method is tested on publicly available data from the MGH Adult Diffusion Human Connectome project. We report reference values of axonal diffusivities based on 34 subjects, and derive estimates of axonal radii from only two shells. The estimation problem is also addressed from the angle of the required data preprocessing, the presence of biases related to modeling assumptions, current limitations, and future possibilities.

Axisymmetric diffusion kurtosis imaging with Rician bias correction: A simulation study

PURPOSE

To compare the estimation accuracy of axisymmetric diffusion kurtosis imaging (DKI) and standard DKI in combination with Rician bias correction (RBC).

METHODS

Axisymmetric DKI is more robust against noise-induced variation in the measured signal than standard DKI because of its reduced parameter space. However, its susceptibility to Rician noise bias at low signal-to-noise ratios (SNR) is unknown. Here, we investigate two main questions: first, does RBC improve estimation accuracy of axisymmetric DKI?; second, is estimation accuracy of axisymmetric DKI increased compared to standard DKI? Estimation accuracy was investigated on the five axisymmetric DKI tensor metrics (AxTM): the parallel and perpendicular diffusivity and kurtosis and mean of the kurtosis tensor, using a noise simulation study based on synthetic data of tissues with varying fiber alignment and in-vivo data focusing on white matter.

RESULTS

RBC mainly increased accuracy for the parallel AxTM in tissues with highly to moderately aligned fibers. For the perpendicular AxTM, axisymmetric DKI without RBC performed slightly better than with RBC. However, the combination of axisymmetric DKI with RBC was the overall best performing algorithm across all five AxTM in white matter and axisymmetric DKI itself substantially improved accuracy in axisymmetric tissues with low fiber alignment.

CONCLUSION

Combining axisymmetric DKI with RBC facilitates accurate DKI parameter estimation at unprecedented low SNRs ( ≈ 15 $$ \approx 15 $$ ) in white matter, possibly making it a valuable tool for neuroscience and clinical research studies where scan time is a limited resource. The tools used here are available in the open-source ACID toolbox for SPM.

Optimized rectification of fiber orientation density function with background threshold

PURPOSE

To describe an optimized fiber orientation density function (fODF) rectification procedure that removes negative values and absorbs all features below a specified threshold into a constant background.

THEORY AND METHODS

The fODF for a white matter imaging voxel describes the angular density of axons. Because of signal noise and Gibbs ringing, fODFs estimated with diffusion MRI may take on unphysical negative values in some directions and contain spurious peaks. In order to suppress such artifacts, an fODF rectification procedure is proposed that both eliminates all negative values and incorporates all features below a specified threshold, η, into a constant background while at the same time minimizing the mean square deviation from the original, unrectified fODF. Calculating this fODF is straightforward, and the directions and shapes of peaks not absorbed into the background are preserved. The rectification method is illustrated for an analytic fODF model and for experimental diffusion MRI data obtained in healthy human brain, with the original fODFs being obtained from fiber ball imaging.

RESULTS

Examples of optimal rectified fODFs are given for three choices of the background threshold referred to as minimal rectification (η = 0), average-level rectification (η ≈ 0.08), and fractional-anisotropy-axonal-based rectification (η ≈ 0.1). As η is increased, artifacts and other small features are more strongly suppressed, but the major fODF peaks are largely unaffected for the range of η values illustrated by these three alternatives.

CONCLUSION

Artifactual features of fODFs estimated with diffusion MRI can be effectively suppressed by applying the proposed optimized rectification procedure. Since it minimizes fODF distortion in the mean square sense, it may be useful in the study of how fODF fine structure is affected by aging and disease.

Differentiation of Perilesional Edema in Glioblastomas and Brain Metastases: Comparison of Diffusion Tensor Imaging, Neurite Orientation Dispersion and Density Imaging and Diffusion Microstructure Imaging

Although the free water content within the perilesional T2 hyperintense region should differ between glioblastomas (GBM) and brain metastases based on histological differences, the application of classical MR diffusion models has led to inconsistent results regarding the differentiation between these two entities. Whereas diffusion tensor imaging (DTI) considers the voxel as a single compartment, multicompartment approaches such as neurite orientation dispersion and density imaging (NODDI) or the recently introduced diffusion microstructure imaging (DMI) allow for the calculation of the relative proportions of intra- and extra-axonal and also free water compartments in brain tissue. We investigate the potential of water-sensitive DTI, NODDI and DMI metrics to detect differences in free water content of the perilesional T2 hyperintense area between histopathologically confirmed GBM and brain metastases. Respective diffusion metrics most susceptible to alterations in the free water content (MD, V-ISO, V-CSF) were extracted from T2 hyperintense perilesional areas, normalized and compared in 24 patients with GBM and 25 with brain metastases. DTI MD was significantly increased in metastases (p = 0.006) compared to GBM, which was corroborated by an increased DMI V-CSF (p = 0.001), while the NODDI-derived ISO-VF showed only trend level increase in metastases not reaching significance (p = 0.060). In conclusion, diffusion MRI metrics are able to detect subtle differences in the free water content of perilesional T2 hyperintense areas in GBM and metastases, whereas DMI seems to be superior to DTI and NODDI.

Diffusion microstructure imaging in progressive supranuclear palsy: reduced axonal volumes in the superior cerebellar peduncles, dentato-rubro-thalamic tracts, ventromedial thalami, and frontomesial white matter

Differentiating between Parkinson's disease (PD) and atypical Parkinson syndromes such as progressive supranuclear palsy (PSP), multiple system atrophy (MSA), and corticobasal degeneration is challenging. Diffusion microstructure imaging (DMI) was analyzed in patients with clinically suspected atypical Parkinson syndromes and healthy controls. In an exploration cohort, the spatial distribution of PSP-related changes of DMI parameters were evaluated in a voxel-wise analysis and a region-of-interest (ROI)-based approach was established. The diagnostic performance was subsequently tested in an independent validation cohort. In the exploration cohort, 53 PSP patients were compared to a pooled comparison group of 19 patients with PD, 26 patients with MSA, 7 patients with corticobasal syndrome, and 25 healthy controls. PSP patients showed widespread axonal loss in the superior cerebellar peduncles, the dentato-rubro-thalamic tracts, the thalami and the frontal white matter (each P < 0.001). In the validation cohort consisting of 12 patients with PSP vs. 13 patients with other movement disorders, the accuracy of this ROI-based approach for identifying the PSP was highest in the thalamus and the frontal white matter (accuracy 0.96 each). This DMI approach can identify PSP patients on an individual level in a collective with suspected atypical Parkinson syndromes and allows further insight on microstructural alterations in vivo.

Minimal number of sampling directions for robust measures of the spherical mean diffusion weighted signal: Effects of sampling directions, b-value, signal-to-noise ratio, hardware, and fitting strategy

Several recent multi-compartment diffusion MRI investigations and modeling strategies have utilized the orientationally-averaged, or spherical mean, diffusion-weighted signal to study tissue microstructure of the central nervous system. Most experimental designs sample a large number of diffusion weighted directions in order to calculate the spherical mean signal, however, sampling a subset of these directions may increase scanning efficiency and enable either a decrease in scan time or the ability to sample more diffusion weightings. Here, we aim to determine the minimum number of gradient directions needed for a robust measurement of the spherical mean signal. We used computer simulations to characterize the variation of the measured spherical mean signal as a function of the number of gradient directions, while also investigating the effects of diffusion weighting (b-value), signal-to-noise ratio (SNR), available hardware, and spherical mean fitting strategy. We then utilize empirically acquired data in the brain and spinal cord to validate simulations, showing experimental results are in good agreement with simulations. We summarize these results by providing an intuitive lookup table to facilitate the determination of the minimal number of sampling directions needed for robust spherical mean measurements, and give recommendations based on SNR and experimental conditions.

Bundle geodesic convolutional neural network for diffusion-weighted imaging segmentation

Purpose

Applying machine learning techniques to magnetic resonance diffusion-weighted imaging (DWI) data is challenging due to the size of individual data samples and the lack of labeled data. It is possible, though, to learn general patterns from a very limited amount of training data if we take advantage of the geometry of the DWI data. Therefore, we present a tissue classifier based on a Riemannian deep learning framework for single-shell DWI data.

Approach

The framework consists of three layers: a lifting layer that locally represents and convolves data on tangent spaces to produce a family of functions defined on the rotation groups of the tangent spaces, i.e., a (not necessarily continuous) function on a bundle of rotational functions on the manifold; a group convolution layer that convolves this function with rotation kernels to produce a family of local functions over each of the rotation groups; a projection layer using maximization to collapse this local data to form manifold based functions.

Results

Experiments show that our method achieves the performance of the same level as state-of-the-art while using way fewer parameters in the model ( < 10 % ). Meanwhile, we conducted a model sensitivity analysis for our method. We ran experiments using a proportion (69.2%, 53.3%, and 29.4%) of the original training set and analyzed how much data the model needs for the task. Results show that this does reduce the overall classification accuracy mildly, but it also boosts the accuracy for minority classes.

Conclusions

This work extended convolutional neural networks to Riemannian manifolds, and it shows the potential in understanding structural patterns in the brain, as well as in aiding manual data annotation.