Evaluation of restricted diffusion in cylinders. Phosphocreatine in rabbit leg muscle

Diffusion MRI with double diffusion encoding and variable mixing times disentangles water exchange from transient kurtosis

Double diffusion encoding (DDE) makes diffusion MRI sensitive to a wide range of microstructural features, and the acquired data can be analysed using different approaches. Correlation tensor imaging (CTI) uses DDE to resolve three components of the diffusional kurtosis: isotropic, anisotropic, and microscopic kurtosis. The microscopic kurtosis is estimated from the contrast between single diffusion encoding (SDE) and parallel DDE signals at the same b-value. Another approach is multi-Gaussian exchange (MGE), which employs DDE to measure exchange. Sensitivity to exchange is obtained by contrasting SDE and DDE signals at the same b-value. CTI and MGE exploit the same signal contrast to quantify microscopic kurtosis and exchange, and this study investigates the interplay between these two quantities. We perform Monte Carlo simulations in different geometries with varying levels of exchange and study the behaviour of the parameters from CTI and MGE. We conclude that microscopic kurtosis from CTI is sensitive to the exchange rate and that intercompartmental exchange and the transient kurtosis of individual compartments are distinct sources of microscopic kurtosis. In an attempt to disentangle these two sources, we propose a heuristic signal representation referred to as tMGE (MGE incorporating transient kurtosis) that accounts for both effects by exploiting the distinct signatures of exchange and transient kurtosis with varying mixing time: exchange causes a slow dependence of the signal on mixing time while transient kurtosis arguably has a much faster dependence. We find that applying tMGE to data acquired with multiple mixing times for both parallel and orthogonal DDE may enable estimation of the exchange rate as well as isotropic, anisotropic, and transient kurtosis.

Tuned exchange imaging: Can the filter exchange imaging pulse sequence be adapted for applications with thin slices and restricted diffusion?

Filter exchange imaging (FEXI) is a double diffusion-encoding (DDE) sequence that is specifically sensitive to exchange between sites with different apparent diffusivities. FEXI uses a diffusion-encoding filtering block followed by a detection block at varying mixing times to map the exchange rate. Long mixing times enhance the sensitivity to exchange, but they pose challenges for imaging applications that require a stimulated echo sequence with crusher gradients. Thin imaging slices require strong crushers, which can introduce significant diffusion weighting and bias exchange rate estimates. Here, we treat the crushers as an additional encoding block and consider FEXI as a triple diffusion-encoding sequence. This allows the bias to be corrected in the case of multi-Gaussian diffusion, but not easily in the presence of restricted diffusion. Our approach addresses challenges in the presence of restricted diffusion and relies on the ability to independently gauge sensitivities to exchange and restricted diffusion for arbitrary gradient waveforms. It follows two principles: (i) the effects of crushers are included in the forward model using signal cumulant expansion; and (ii) timing parameters of diffusion gradients in filter and detection blocks are adjusted to maintain the same level of restriction encoding regardless of the mixing time. This results in the tuned exchange imaging (TEXI) protocol. The accuracy of exchange mapping with TEXI was assessed through Monte Carlo simulations in spheres of identical sizes and gamma-distributed sizes, and in parallel hexagonally packed cylinders. The simulations demonstrate that TEXI provides consistent exchange rates regardless of slice thickness and restriction size, even with strong crushers. However, the accuracy depends on b-values, mixing times, and restriction geometry. The constraints and limitations of TEXI are discussed, including suggestions for protocol adaptations. Further studies are needed to optimize the precision of TEXI and assess the approach experimentally in realistic, heterogeneous substrates.

Validation of conductivity tensor imaging against diffusion tensor magnetic resonance electrical impedance tomography

Diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) and electrodeless conductivity tensor imaging (CTI) are two emerging modalities that can quantify low-frequency tissue anisotropic conductivity properties by assuming similar properties underlie ionic mobility and water diffusion. While both methods have potential applications to estimating neuro-modulation fields or formulating forward models used for electrical source imaging, a direct comparison of the two modalities has not yet been performed in-vitro or in-vivo. Therefore, the aim of this study was to test the equivalence of these two modalities. We scanned a tissue phantom and the head of human subject using DT-MREIT and CTI protocols and reconstructed conductivity tensor and effective low frequency conductivities. We found both gray and white matter conductivities recovered by each technique were equivalent within 0.05 S/m. Both DT-MREIT and CTI require multiple processing steps, and we further assess the effects of each factor on reconstructions and evaluate the extent to which different measurement mechanisms potentially cause discrepancies between the two methods. Finally, we discuss the implications for spectral models of measuring conductivity using these techniques. The study further establishes the credibility of CTI as an electrodeless non-invasive method of measuring low frequency conductivity properties.

Q-space imaging based on Gaussian radial basis function with Laplace regularization

PURPOSE

To introduce the diffusion signal characteristics presented by spherical harmonics (SH) basis into the q-space imaging method based on Gaussian radial basis function (GRBF) to robustly reconstruct ensemble average diffusion propagator (EAP) in diffusion MRI (dMRI).

METHODS

We introduced the Laplacian regularization of the signal into the dMRI imaging method based on GRBF, and derived the relevant indicators of microstructure imaging and the orientation distribution function (ODF) providing fiber bundle direction information based on EAP. In addition, this method is combined with a multi-compartment model to calculate the diameter of fiber bundle axons. The evaluation of the results included qualitative comparisons and quantitative assessments of the signal fitting.

RESULTS

The results show that the proposed method achieves the more significant accuracy improvement in reconstructing signal. Meanwhile, ODFs estimated by the proposed method show the sharper profiles and less spurious peaks, even under the sparse and noisy conditions. In the 36 sets of axon diameter estimation experiments, 34 and 30 sets of results showed that the proposed method reduced the mean and SD of axon diameter estimates, respectively. Moreover, compared with the current state-of-the-art method, the mean and SD of axon diameter estimated by the proposed method are mostly lower, with 32 and 29 of 36 groups.

CONCLUSION

The proposed method outperforms the GRBF regarding signal fitting and the estimation of the EAP and ODF with multi-shell sparse samples. Moreover, it shows the potential to recover important features of microstructures with less uncertainty by using proposed method together with multi-compartment models.

Pore size estimation in axon-mimicking microfibers with diffusion-relaxation MRI

PURPOSE

This study aims to evaluate two distinct approaches for fiber radius estimation using diffusion-relaxation MRI data acquired in biomimetic microfiber phantoms that mimic hollow axons. The methods considered are the spherical mean power-law approach and a T2-based pore size estimation technique.

THEORY AND METHODS

A general diffusion-relaxation theoretical model for the spherical mean signal from water molecules within a distribution of cylinders with varying radii was introduced, encompassing the evaluated models as particular cases. Additionally, a new numerical approach was presented for estimating effective radii (i.e., MRI-visible mean radii) from the ground truth radii distributions, not reliant on previous theoretical approximations and adaptable to various acquisition sequences. The ground truth radii were obtained from scanning electron microscope images.

RESULTS

Both methods show a linear relationship between effective radii estimated from MRI data and ground-truth radii distributions, although some discrepancies were observed. The spherical mean power-law method overestimated fiber radii. Conversely, the T2-based method exhibited higher sensitivity to smaller fiber radii, but faced limitations in accurately estimating the radius in one particular phantom, possibly because of material-specific relaxation changes.

CONCLUSION

The study demonstrates the feasibility of both techniques to predict pore sizes of hollow microfibers. The T2-based technique, unlike the spherical mean power-law method, does not demand ultra-high diffusion gradients, but requires calibration with known radius distributions. This research contributes to the ongoing development and evaluation of neuroimaging techniques for fiber radius estimation, highlights the advantages and limitations of both methods, and provides datasets for reproducible research.

Novel pore size-controlled, susceptibility matched, 3D-printed MRI phantoms

PURPOSE

We report the design concept and fabrication of MRI phantoms, containing blocks of aligned microcapillaires that can be stacked into larger arrays to construct diameter distribution phantoms or fractured, to create a "powder-averaged" emulsion of randomly oriented blocks for vetting or calibrating advanced MRI methods, that is, diffusion tensor imaging, AxCaliber MRI, MAP-MRI, and multiple pulsed field gradient or double diffusion-encoded microstructure imaging methods. The goal was to create a susceptibility-matched microscopically anisotropic but macroscopically isotropic phantom with a ground truth diameter that could be used to vet advanced diffusion methods for diameter determination in fibrous tissues.

METHODS

Two-photon polymerization, a novel three-dimensional printing method is used to fabricate blocks of capillaries. Double diffusion encoding methods were employed and analyzed to estimate the expected MRI diameter.

RESULTS

Susceptibility-matched microcapillary blocks or modules that can be assembled into large-scale MRI phantoms have been fabricated and measured using advanced diffusion methods, resulting in microscopic anisotropy and random orientation.

CONCLUSION

This phantom can vet and calibrate various advanced MRI methods and multiple pulsed field gradient or diffusion-encoded microstructure imaging methods. We demonstrated that two double diffusion encoding methods underestimated the ground truth diameter.

Diffusion of brain metabolites highlights altered brain microstructure in type C hepatic encephalopathy: a 9.4 T preliminary study

Introduction

Type C hepatic encephalopathy (HE) is a decompensating event of chronic liver disease leading to severe motor and cognitive impairment. The progression of type C HE is associated with changes in brain metabolite concentrations measured by 1H magnetic resonance spectroscopy (MRS), most noticeably a strong increase in glutamine to detoxify brain ammonia. In addition, alterations of brain cellular architecture have been measured ex vivo by histology in a rat model of type C HE. The aim of this study was to assess the potential of diffusion-weighted MRS (dMRS) for probing these cellular shape alterations in vivo by monitoring the diffusion properties of the major brain metabolites.

Methods

The bile duct-ligated (BDL) rat model of type C HE was used. Five animals were scanned before surgery and 6- to 7-week post-BDL surgery, with each animal being used as its own control. 1H-MRS was performed in the hippocampus (SPECIAL, TE = 2.8 ms) and dMRS in a voxel encompassing the entire brain (DW-STEAM, TE = 15 ms, diffusion time = 120 ms, maximum b-value = 25 ms/μm2) on a 9.4 T scanner. The in vivo MRS acquisitions were further validated with histological measures (immunohistochemistry, Golgi-Cox, electron microscopy).

Results

The characteristic 1H-MRS pattern of type C HE, i.e., a gradual increase of brain glutamine and a decrease of the main organic osmolytes, was observed in the hippocampus of BDL rats. Overall increased metabolite diffusivities (apparent diffusion coefficient and intra-stick diffusivity-Callaghan's model, significant for glutamine, myo-inositol, and taurine) and decreased kurtosis coefficients were observed in BDL rats compared to control, highlighting the presence of osmotic stress and possibly of astrocytic and neuronal alterations. These results were consistent with the microstructure depicted by histology and represented by a decline in dendritic spines density in neurons, a shortening and decreased number of astrocytic processes, and extracellular edema.

Discussion

dMRS enables non-invasive and longitudinal monitoring of the diffusion behavior of brain metabolites, reflecting in the present study the globally altered brain microstructure in BDL rats, as confirmed ex vivo by histology. These findings give new insights into metabolic and microstructural abnormalities associated with high brain glutamine and its consequences in type C HE.

Diffusion-weighted MR spectroscopy: Consensus, recommendations, and resources from acquisition to modeling

Brain cell structure and function reflect neurodevelopment, plasticity, and aging; and changes can help flag pathological processes such as neurodegeneration and neuroinflammation. Accurate and quantitative methods to noninvasively disentangle cellular structural features are needed and are a substantial focus of brain research. Diffusion-weighted MRS (dMRS) gives access to diffusion properties of endogenous intracellular brain metabolites that are preferentially located inside specific brain cell populations. Despite its great potential, dMRS remains a challenging technique on all levels: from the data acquisition to the analysis, quantification, modeling, and interpretation of results. These challenges were the motivation behind the organization of the Lorentz Center workshop on "Best Practices & Tools for Diffusion MR Spectroscopy" held in Leiden, the Netherlands, in September 2021. During the workshop, the dMRS community established a set of recommendations to execute robust dMRS studies. This paper provides a description of the steps needed for acquiring, processing, fitting, and modeling dMRS data, and provides links to useful resources.

Measuring cardiomyocyte cellular characteristics in cardiac hypertrophy using diffusion-weighted MRI

PURPOSE

This paper presents a hierarchical modeling approach for estimating cardiomyocyte major and minor diameters and intracellular volume fraction (ICV) using diffusion-weighted MRI (DWI) data in ex vivo mouse hearts.

METHODS

DWI data were acquired on two healthy controls and two hearts 3 weeks post transverse aortic constriction (TAC) using a bespoke diffusion scheme with multiple diffusion times (Δ $$ \Delta $$ ), q-shells and diffusion encoding directions. Firstly, a bi-exponential tensor model was fitted separately at each diffusion time to disentangle the dependence on diffusion times from diffusion weightings, that is, b-values. The slow-diffusing component was attributed to the restricted diffusion inside cardiomyocytes. ICV was then extrapolated atΔ = 0 $$ \Delta =0 $$ using linear regression. Secondly, given the secondary and the tertiary diffusion eigenvalue measurements for the slow-diffusing component obtained at different diffusion times, major and minor diameters were estimated assuming a cylinder model with an elliptical cross-section (ECS). High-resolution three-dimensional synchrotron X-ray imaging (SRI) data from the same specimen was utilized to evaluate the biophysical parameters.

RESULTS

Estimated parameters using DWI data were (control 1/control 2 vs. TAC 1/TAC 2): major diameter-17.4μ $$ \mu $$ m/18.0μ $$ \mu $$ m versus 19.2μ $$ \mu $$ m/19.0μ $$ \mu $$ m; minor diameter-10.2μ $$ \mu $$ m/9.4μ $$ \mu $$ m versus 12.8μ $$ \mu $$ m/13.4μ $$ \mu $$ m; and ICV-62%/62% versus 68%/47%. These findings were consistent with SRI measurements.

CONCLUSION

The proposed method allowed for accurate estimation of biophysical parameters suggesting cardiomyocyte diameters as sensitive biomarkers of hypertrophy in the heart.

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.

A Method for In-Vivo Mapping of Axonal Diameter Distributions in the Human Brain Using Diffusion-Based Axonal Spectrum Imaging (AxSI)

In this paper we demonstrate a generalized and simplified pipeline called axonal spectrum imaging (AxSI) for in-vivo estimation of axonal characteristics in the human brain. Whole-brain estimation of the axon diameter, in-vivo and non-invasively, across all fiber systems will allow exploring uncharted aspects of brain structure and function relations with emphasis on connectivity and connectome analysis. While axon diameter mapping is important in and of itself, its correlation with conduction velocity will allow, for the first time, the explorations of information transfer mechanisms within the brain. We demonstrate various well-known aspects of axonal morphometry (e.g., the corpus callosum axon diameter variation) as well as other aspects that are less explored (e.g., axon diameter-based separation of the superior longitudinal fasciculus into segments). Moreover, we have created an MNI based mean axon diameter map over the entire brain for a large cohort of subjects providing the reference basis for future studies exploring relation between axon properties, its connectome representation, and other functional and behavioral aspects of the brain.

Apparent diffusion coefficients of 31P metabolites in the human calf muscle at 7 T

PURPOSE

In this study, we aimed to measure the apparent diffusion coefficients (ADCs) of major phosphorous metabolites in the human calf muscle at 7 T with a diffusion-weighted (DW)-STEAM sequence.

METHODS

A DW-STEAM sequence with bipolar gradients was implemented at 7 T, and DW MR spectra were acquired in three orthogonal directions in the human calf muscle of six healthy volunteers (TE/TM/TR = 15 ms/750 ms/5 s) at three b-values (0, 800, and 1200 s/mm²). Frequency and phase alignments were applied prior to spectral averaging. Averaged DW MR spectra were analyzed with LCModel, and ADCs of ³¹P metabolites were estimated.

RESULTS

Four metabolites (phosphocreatine (PCr), adenosine triphosphate (ATP), inorganic phosphate (Pi) and glycerol phosphorylcholine (GPC)) were quantified at all b-values with mean CRLBs below 10%. The ADC values of PCr, ATP, Pi, and GPC were (0.24 ± 0.02, 0.15 ± 0.04, 0.43 ± 0.14, 0.40 ± 0.09) × 10^-3 mm²/s, respectively.

CONCLUSION

The ADCs of four ³¹P metabolites were successfully measured in the human calf muscle at 7 T, among which those of ATP, Pi and GPC were reported for the first time in humans. This study paves the way to investigate ³¹P metabolite diffusion properties in health and disease on the clinical MR scanner.

Temporal Diffusion Ratio (TDR) for imaging restricted diffusion: Optimisation and pre-clinical demonstration

Temporal Diffusion Ratio (TDR) is a recently proposed dMRI technique (Dell'Acqua et al., proc. ISMRM 2019) which provides contrast between areas with restricted diffusion and areas either without restricted diffusion or with length scales too small for characterisation. Hence, it has a potential for informing on pore sizes, in particular the presence of large axon diameters or other cellular structures. TDR employs the signal from two dMRI acquisitions obtained with the same, large, b-value but with different diffusion gradient waveforms. TDR is advantageous as it employs standard acquisition sequences, does not make any assumptions on the underlying tissue structure and does not require any model fitting, avoiding issues related to model degeneracy. This work for the first time introduces and optimises the TDR method in simulation for a range of different tissues and scanner constraints and validates it in a pre-clinical demonstration. We consider both substrates containing cylinders and spherical structures, representing cell soma in tissue. Our results show that contrasting an acquisition with short gradient duration, short diffusion time and high gradient strength with an acquisition with long gradient duration, long diffusion time and low gradient strength, maximises the TDR contrast for a wide range of pore configurations. Additionally, in the presence of Rician noise, computing TDR from a subset (50% or fewer) of the acquired diffusion gradients rather than the entire shell as proposed originally further improves the contrast. In the last part of the work the results are demonstrated experimentally on rat spinal cord. In line with simulations, the experimental data shows that optimised TDR improves the contrast compared to non-optimised TDR. Furthermore, we find a strong correlation between TDR and histology measurements of axon diameter. In conclusion, we find that TDR has great potential and is a very promising alternative (or potentially complement) to model-based approaches for informing on pore sizes and restricted diffusion in general.

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.

Generalisation of continuous time random walk to anomalous diffusion MRI models with an age-related evaluation of human corpus callosum

Diffusion MRI measures of the human brain provide key insight into microstructural variations across individuals and into the impact of central nervous system diseases and disorders. One approach to extract information from diffusion signals has been to use biologically relevant analytical models to link millimetre scale diffusion MRI measures with microscale influences. The other approach has been to represent diffusion as an anomalous transport process and infer microstructural information from the different anomalous diffusion equation parameters. In this study, we investigated how parameters of various anomalous diffusion models vary with age in the human brain white matter, particularly focusing on the corpus callosum. We first unified several established anomalous diffusion models (the super-diffusion, sub-diffusion, quasi-diffusion and fractional Bloch-Torrey models) under the continuous time random walk modelling framework. This unification allows a consistent parameter fitting strategy to be applied from which meaningful model parameter comparisons can be made. We then provided a novel way to derive the diffusional kurtosis imaging (DKI) model, which is shown to be a degree two approximation of the sub-diffusion model. This link between the DKI and sub-diffusion models led to a new robust technique for generating maps of kurtosis and diffusivity using the sub-diffusion parameters β_SUB and D_SUB. Superior tissue contrast is achieved in kurtosis maps based on the sub-diffusion model. 7T diffusion weighted MRI data for 65 healthy participants in the age range 19-78 years was used in this study. Results revealed that anomalous diffusion model parameters α and β have shown consistent positive correlation with age in the corpus callosum, indicating α and β are sensitive to tissue microstructural changes in ageing.

Diffusion MRI fiber diameter for muscle denervation assessment

BACKGROUND

To develop and evaluate a diffusion MRI-based apparent muscle fiber diameter (AFD) method in patients with muscle denervation. It was hypothesized that AFD differences between denervated, non-denervated and control muscles would be greater than those from standard diffusion metrics.

METHODS

A spin-echo diffusion acquisition with multi-b-valued diffusion sampling was used. An orientation-invariant dictionary approach utilized a cylinder-based forward model and multi-compartment model for obtaining restricted and free fractions. Simulations were performed to determine precision, bias, and optimize dictionary parameters. In all, 18 exams of patients with muscle denervation and 8 exams of healthy subjects were performed at 3T. Six regions of interests (ROIs) within separate shoulder muscles were selected, yielding three groups consisting 47 control (healthy), 36 non-denervated (patients), and 68 denervated (patients) muscle ROIs. Two-sample t-tests (α=0.05) between groups were performed with Holm-Bonferroni correction. T2- and fat fraction (FF)-mapping were acquired for comparison.

RESULTS

Mean AFD was 89.7±13.6 µm in control, 71.6±15.3 µm in non-denervated, and 60.7±15.9 µm in denervated muscles and were significantly different (P<0.001) in paired comparisons and in 10/12 individual muscle region comparisons. Correlation between AFD and FF (-0.331, P<0.001) was low, but correlation between FA and FF was negligible (0.197, P=0.016). Correlation was low between AFD and T2 (-0.395, P<0.001) and between FA and T2 (0.359, P<0.001).

CONCLUSIONS

Diffusion MRI-based AFD complements T2- and FF-mapping techniques to non-invasively assess muscle denervation.

Assessing Myocardial Microstructure With Biophysical Models of Diffusion MRI

Biophysical models are a promising means for interpreting diffusion weighted magnetic resonance imaging (DW-MRI) data, as they can provide estimates of physiologically relevant parameters of microstructure including cell size, volume fraction, or dispersion. However, their application in cardiac microstructure mapping (CMM) has been limited. This study proposes seven new two-compartment models with combination of restricted cylinder models and a diffusion tensor to represent intra- and extracellular spaces, respectively. Three extended versions of the cylinder model are studied here: cylinder with elliptical cross section (ECS), cylinder with Gamma distributed radii (GDR), and cylinder with Bingham distributed axes (BDA). The proposed models were applied to data in two fixed mouse hearts, acquired with multiple diffusion times, q-shells and diffusion encoding directions. The cylinderGDR-pancake model provided the best performance in terms of root mean squared error (RMSE) reducing it by 25% compared to diffusion tensor imaging (DTI). The cylinderBDA-pancake model represented anatomical findings closest as it also allows for modelling dispersion. High-resolution 3D synchrotron X-ray imaging (SRI) data from the same specimen was utilized to evaluate the biophysical models. A novel tensor-based registration method is proposed to align SRI structure tensors to the MR diffusion tensors. The consistency between SRI and DW-MRI parameters demonstrates the potential of compartment models in assessing physiologically relevant parameters.

Does powder averaging remove dispersion bias in diffusion MRI diameter estimates within real 3D axonal architectures?

Noninvasive estimation of axon diameter with diffusion MRI holds the potential to investigate the dynamic properties of the brain network and pathology of neurodegenerative diseases. Recent studies use powder averaging to account for complex white matter architectures, but these have not been validated for real axonal geometries from regions that contain fibre crossings. Here, we present 120-304μm long segmented axons from X-ray nano-holotomography volumes of a splenium and crossing fibre region of a vervet monkey brain. We show that the axons in the complex crossing fibre region, which contains callosal, association, and corticospinal connections, are larger and exhibit a wider distribution than those of the splenium region. To accurately estimate the axon diameter in these regions, therefore, sensitivity to a wide range of diameters is required. We demonstrate how the q-value, b-value, signal-to-noise ratio and the assumed intra-axonal parallel diffusivity influence the range of measurable diameters with powder average approaches. Furthermore, we show how Gaussian distributed noise results in a wider range of measurable diameter at high b-values than Rician distributed noise, even at high signal-to-noise ratios of 100. The number of gradient directions is also shown to impose a lower bound on measurable diameter. Our results indicate that axon diameter estimation can be performed with only few b-shells, and that additional shells do not improve the accuracy of the estimate. For strong gradients available on human Connectom and preclinical scanners, Monte Carlo simulations of diffusion confirm that powder averaging techniques succeed in providing accurate estimates of axon diameter across a range of sequence parameters and diffusion times, even in complex white matter architectures. At relatively low b-values, the diameter estimate becomes sensitive to axonal microdispersion and the intra-axonal parallel diffusivity shows time dependency at both in vivo and ex vivo intrinsic diffusivities.

Validating pore size estimates in a complex microfiber environment on a human MRI system

PURPOSE

Recent advances in diffusion-weighted MRI provide "restricted diffusion signal fraction" and restricting pore size estimates. Materials based on co-electrospun oriented hollow cylinders have been introduced to provide validation for such methods. This study extends this work, exploring accuracy and repeatability using an extended acquisition on a 300 mT/m gradient human MRI scanner, in substrates closely mimicking tissue, that is, non-circular cross-sections, intra-voxel fiber crossing, intra-voxel distributions of pore-sizes, and smaller pore-sizes overall.

METHODS

In a single-blind experiment, diffusion-weighted data were collected from a biomimetic phantom on a 3T Connectom system using multiple gradient directions/diffusion times. Repeated scans established short-term and long-term repeatability. The total scan time (54 min) matched similar protocols used in human studies. The number of distinct fiber populations was estimated using spherical deconvolution, and median pore size estimated through the combination of CHARMED and AxCaliber3D framework. Diffusion-based estimates were compared with measurements derived from scanning electron microscopy.

RESULTS

The phantom contained substrates with different orientations, fiber configurations, and pore size distributions. Irrespective of one or two populations within the voxel, the pore-size estimates (~5 μm) and orientation-estimates showed excellent agreement with the median values of pore-size derived from scanning electron microscope and phantom configuration. Measurement repeatability depended on substrate complexity, with lower values seen in samples containing crossing-fibers. Sample-level repeatability was found to be good.

CONCLUSION

While no phantom mimics tissue completely, this study takes a step closer to validating diffusion microstructure measurements for use in vivo by demonstrating the ability to quantify microgeometry in relatively complex configurations.

SPHERIOUSLY? The challenges of estimating sphere radius non-invasively in the human brain from diffusion MRI

The Soma and Neurite Density Imaging (SANDI) three-compartment model was recently proposed to disentangle cylindrical and spherical geometries, attributed to neurite and soma compartments, respectively, in brain tissue. There are some recent advances in diffusion-weighted MRI signal encoding and analysis (including the use of multiple so-called 'b-tensor' encodings and analysing the signal in the frequency-domain) that have not yet been applied in the context of SANDI. In this work, using: (i) ultra-strong gradients; (ii) a combination of linear, planar, and spherical b-tensor encodings; and (iii) analysing the signal in the frequency domain, three main challenges to robust estimation of sphere size were identified: First, the Rician noise floor in magnitude-reconstructed data biases estimates of sphere properties in a non-uniform fashion. It may cause overestimation or underestimation of the spherical compartment size and density. This can be partly ameliorated by accounting for the noise floor in the estimation routine. Second, even when using the strongest diffusion-encoding gradient strengths available for human MRI, there is an empirical lower bound on the spherical signal fraction and radius that can be detected and estimated robustly. For the experimental setup used here, the lower bound on the sphere signal fraction was approximately 10%. We employed two different ways of establishing the lower bound for spherical radius estimates in white matter. The first, examining power-law relationships between the DW-signal and diffusion weighting in empirical data, yielded a lower bound of 7μm, while the second, pure Monte Carlo simulations, yielded a lower limit of 3μm and in this low radii domain, there is little differentiation in signal attenuation. Third, if there is sensitivity to the transverse intra-cellular diffusivity in cylindrical structures, e.g., axons and cellular projections, then trying to disentangle two diffusion-time-dependencies using one experimental parameter (i.e., change in frequency-content of the encoding waveform) makes spherical radii estimates particularly challenging. We conclude that due to the aforementioned challenges spherical radii estimates may be biased when the corresponding sphere signal fraction is low, which must be considered.

Scan-rescan repeatability of axonal imaging metrics using high-gradient diffusion MRI and statistical implications for study design

Axon diameter mapping using diffusion MRI in the living human brain has attracted growing interests with the increasing availability of high gradient strength MRI systems. A systematic assessment of the consistency of axon diameter estimates within and between individuals is needed to gain a comprehensive understanding of how such methods extend to quantifying differences in axon diameter index between groups and facilitate the design of neurobiological studies using such measures. We examined the scan-rescan repeatability of axon diameter index estimation based on the spherical mean technique (SMT) approach using diffusion MRI data acquired with gradient strengths up to 300 mT/m on a 3T Connectom system in 7 healthy volunteers. We performed statistical power analyses using data acquired with the same protocol in a larger cohort consisting of 15 healthy adults to investigate the implications for study design. Results revealed a high degree of repeatability in voxel-wise restricted volume fraction estimates and tract-wise estimates of axon diameter index derived from high-gradient diffusion MRI data. On the region of interest (ROI) level, across white matter tracts in the whole brain, the Pearson’s correlation coefficient of the axon diameter index estimated between scan and rescan experiments was r = 0.72 with an absolute deviation of 0.18 μm. For an anticipated 10% effect size in studies of axon diameter index, most white matter regions required a sample size of less than 15 people to observe a measurable difference between groups using an ROI-based approach. To facilitate the use of high-gradient strength diffusion MRI data for neuroscientific studies of axonal microstructure, the comprehensive multi-gradient strength, multi-diffusion time data used in this work will be made publicly available, in support of open science and increasing the accessibility of such data to the greater scientific community.

Bundle-Specific Axon Diameter Index as a New Contrast to Differentiate White Matter Tracts

In the central nervous system of primates, several pathways are characterized by different spectra of axon diameters. In vivo methods, based on diffusion-weighted magnetic resonance imaging, can provide axon diameter index estimates non-invasively. However, such methods report voxel-wise estimates, which vary from voxel-to-voxel for the same white matter bundle due to partial volume contributions from other pathways having different microstructure properties. Here, we propose a novel microstructure-informed tractography approach, COMMITAxSize, to resolve axon diameter index estimates at the streamline level, thus making the estimates invariant along trajectories. Compared to previously proposed voxel-wise methods, our formulation allows the estimation of a distinct axon diameter index value for each streamline, directly, furnishing a complementary measure to the existing calculation of the mean value along the bundle. We demonstrate the favourable performance of our approach comparing our estimates with existing histologically-derived measurements performed in the corpus callosum and the posterior limb of the internal capsule. Overall, our method provides a more robust estimation of the axon diameter index of pathways by jointly estimating the microstructure properties of the tissue and the macroscopic organisation of the white matter connectivity.

Cytosolic diffusivity and microscopic anisotropy of N-acetyl aspartate in human white matter with diffusion-weighted MRS at 7 T

Metabolite diffusion measurable in humans in vivo with diffusion-weighted spectroscopy (DW-MRS) provides a window into the intracellular morphology and state of specific cell types. Anisotropic diffusion in white matter is governed by the microscopic properties of the individual cell types and their structural units (axons, soma, dendrites). However, anisotropy is also markedly affected by the macroscopic orientational distribution over the imaging voxel, particularly in DW-MRS, where the dimensions of the volume of interest (VOI) are much larger than those typically used in diffusion-weighted imaging. One way to address the confound of macroscopic structural features is to average the measurements acquired with uniformly distributed gradient directions to mimic a situation where fibers present in the VOI are orientationally uniformly distributed. This situation allows the extraction of relevant microstructural features such as transverse and longitudinal diffusivities within axons and the related microscopic fractional anisotropy. We present human DW-MRS data acquired at 7 T in two different white matter regions, processed and analyzed as described above, and find that intra-axonal diffusion of the neuronal metabolite N-acetyl aspartate is in good correspondence to simple model interpretations, such as multi-Gaussian diffusion from disperse fibers where the transverse diffusivity can be neglected. We also discuss the implications of our approach for current and future applications of DW-MRS for cell-specific measurements.

The variability of MR axon radii estimates in the human white matter

The noninvasive quantification of axonal morphology is an exciting avenue for gaining understanding of the function and structure of the central nervous system. Accurate non-invasive mapping of micron-sized axon radii using commonly applied neuroimaging techniques, that is, diffusion-weighted MRI, has been bolstered by recent hardware developments, specifically MR gradient design. Here the whole brain characterization of the effective MR axon radius is presented and the inter- and intra-scanner test-retest repeatability and reproducibility are evaluated to promote the further development of the effective MR axon radius as a neuroimaging biomarker. A coefficient-of-variability of approximately 10% in the voxelwise estimation of the effective MR radius is observed in the test-retest analysis, but it is shown that the performance can be improved fourfold using a customized along-tract analysis.

Beyond the diffusion standard model in fixed rat spinal cord with combined linear and planar encoding

Information about tissue on the microscopic and mesoscopic scales can be accessed by modelling diffusion MRI signals, with the aim of extracting microstructure-specific biomarkers. The standard model (SM) of diffusion, currently the most broadly adopted microstructural model, describes diffusion in white matter (WM) tissues by two Gaussian components, one of which has zero radial diffusivity, to represent diffusion in intra- and extra-axonal water, respectively. Here, we reappraise these SM assumptions by collecting comprehensive double diffusion encoded (DDE) MRI data with both linear and planar encodings, which was recently shown to substantially enhance the ability to estimate SM parameters. We find however, that the SM is unable to account for data recorded in fixed rat spinal cord at an ultrahigh field of 16.4 T, suggesting that its underlying assumptions are violated in our experimental data. We offer three model extensions to mitigate this problem: first, we generalize the SM to accommodate finite radii (axons) by releasing the constraint of zero radial diffusivity in the intra-axonal compartment. Second, we include intracompartmental kurtosis to account for non-Gaussian behaviour. Third, we introduce an additional (third) compartment. The ability of these models to account for our experimental data are compared based on parameter feasibility and Bayesian information criterion. Our analysis identifies the three-compartment description as the optimal model. The third compartment exhibits slow diffusion with a minor but non-negligible signal fraction (∼12%). We demonstrate how failure to take the presence of such a compartment into account severely misguides inferences about WM microstructure. Our findings bear significance for microstructural modelling at large and can impact the interpretation of biomarkers extracted from the standard model of diffusion.

Axon morphology is modulated by the local environment and impacts the noninvasive investigation of its structure-function relationship

Axonal conduction velocity, which ensures efficient function of the brain network, is related to axon diameter. Noninvasive, in vivo axon diameter estimates can be made with diffusion magnetic resonance imaging, but the technique requires three-dimensional (3D) validation. Here, high-resolution, 3D synchrotron X-ray nano-holotomography images of white matter samples from the corpus callosum of a monkey brain reveal that blood vessels, cells, and vacuoles affect axonal diameter and trajectory. Within single axons, we find that the variation in diameter and conduction velocity correlates with the mean diameter, contesting the value of precise diameter determination in larger axons. These complex 3D axon morphologies drive previously reported 2D trends in axon diameter and g-ratio. Furthermore, we find that these morphologies bias the estimates of axon diameter with diffusion magnetic resonance imaging and, ultimately, impact the investigation and formulation of the axon structure-function relationship.

Multiparametric MRI in the Diagnosis of Prostate Cancer: Physical Foundations, Limitations, and Prospective Advances of Diffusion-Weighted MRI

BACKGROUND

 Diffusion-weighted imaging (DWI) is an essential component of the multiparametric MRI exam for the diagnosis and assessment of prostate cancer (PCa). Over the last two decades, various models have been developed to quantitatively correlate the DWI signal with microstructural characteristics of prostate tissue. The simplest approach (ADC: apparent diffusion coefficient) - currently established as the clinical standard - describes monoexponential decay of the DWI signal. While numerous studies have shown an inverse correlation of ADC values with the Gleason score, the ADC model lacks specificity and is based on water diffusion dynamics that are not true in human tissue. This article aims to explain the biophysical limitations of the standard DWI model and to discuss the potential of more complex, advanced DWI models.

METHODS

 This article is a review based on a selective literature review.

RESULTS

 Four phenomenological DWI models are introduced: diffusion tensor imaging, intravoxel incoherent motion, biexponential model, and diffusion kurtosis imaging. Their parameters may potentially improve PCa diagnostics but show varying degrees of statistical significance with respect to the detection and characterization of PCa in current studies. Phenomenological model parameters lack specificity, which has motivated the development of more descriptive tissue models that directly relate microstructural features to the DWI signal. Finally, we present two of such structural models, i. e. the VERDICT (Vascular, Extracellular, and Restricted Diffusion for Cytometry in Tumors) and RSI (Restriction Spectrum Imaging) model. Both have shown promising results in initial studies regarding the characterization and prognosis of PCa.

CONCLUSION

 Recent developments in DWI techniques promise increasing accuracy and more specific statements about microstructural changes of PCa. However, further studies are necessary to establish a standardized DWI protocol for the diagnosis of PCa.

KEY POINTS

  · DWI is paramount to the mpMRI exam for the diagnosis of PCa.. · Though of clinical value, the ADC model lacks specificity and oversimplifies tissue complexities.. · Advanced phenomenological and structural models have been developed to describe the DWI signal.. · Phenomenological models may improve diagnostics but show inconsistent results regarding PCa assessment.. · Structural models have demonstrated promising results in initial studies regarding PCa characterization..

CITATION FORMAT

· Wichtmann BD, Zöllner FG, Attenberger UI et al. Multiparametric MRI in the Diagnosis of Prostate Cancer: Physical Foundations, Limitations, and Prospective Advances of Diffusion-Weighted MRI. Fortschr Röntgenstr 2021; 193: 399 - 409.

A simple estimate of axon size with diffusion MRI

Noninvasive estimation of mean axon diameter presents a new opportunity to explore white matter plasticity, development, and pathology. Several diffusion-weighted MRI (DW-MRI) methods have been proposed to measure the average axon diameter in white matter, but they typically require many diffusion encoding measurements and complicated mathematical models to fit the signal to multiple tissue compartments, including intra- and extra-axonal spaces. Here, Monte Carlo simulations uncovered a straightforward DW-MRI metric of axon diameter: the change in radial apparent diffusion coefficient estimated at different effective diffusion times, ΔD_⊥. Simulations indicated that this metric increases monotonically within a relevant range of effective mean axon diameter while being insensitive to changes in extra-axonal volume fraction, axon diameter distribution, g-ratio, and influence of myelin water. Also, a monotonic relationship was found to exist for signals coming from both intra- and extra-axonal compartments. The slope in ΔD_⊥ with effective axon diameter increased with the difference in diffusion time of both oscillating and pulsed gradient diffusion sequences.

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.

Machine learning based white matter models with permeability: An experimental study in cuprizone treated in-vivo mouse model of axonal demyelination

The intra-axonal water exchange time (τ_i), a parameter associated with axonal permeability, could be an important biomarker for understanding and treating demyelinating pathologies such as Multiple Sclerosis. Diffusion-Weighted MRI (DW-MRI) is sensitive to changes in permeability; however, the parameter has so far remained elusive due to the lack of general biophysical models that incorporate it. Machine learning based computational models can potentially be used to estimate such parameters. Recently, for the first time, a theoretical framework using a random forest (RF) regressor suggests that this is a promising new approach for permeability estimation. In this study, we adopt such an approach and for the first time experimentally investigate it for demyelinating pathologies through direct comparison with histology. We construct a computational model using Monte Carlo simulations and an RF regressor in order to learn a mapping between features derived from DW-MRI signals and ground truth microstructure parameters. We test our model in simulations, and find strong correlations between the predicted and ground truth parameters (intra-axonal volume fraction f: R² =0.99, τ_i: R² =0.84, intrinsic diffusivity d: R² =0.99). We then apply the model in-vivo, on a controlled cuprizone (CPZ) mouse model of demyelination, comparing the results from two cohorts of mice, CPZ (N=8) and healthy age-matched wild-type (WT, N=8). We find that the RF model estimates sensible microstructure parameters for both groups, matching values found in literature. Furthermore, we perform histology for both groups using electron microscopy (EM), measuring the thickness of the myelin sheath as a surrogate for exchange time. Histology results show that our RF model estimates are very strongly correlated with the EM measurements (ρ = 0.98 for f, ρ = 0.82 for τ_i). Finally, we find a statistically significant decrease in τ_i in all three regions of the corpus callosum (splenium/genu/body) of the CPZ cohort (<τ_i>=310ms/330ms/350ms) compared to the WT group (<τ_i>=370ms/370ms/380ms). This is in line with our expectations that τ_i is lower in regions where the myelin sheath is damaged, as axonal membranes become more permeable. Overall, these results demonstrate, for the first time experimentally and in vivo, that a computational model learned from simulations can reliably estimate microstructure parameters, including the axonal permeability .

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.

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.

Direction-averaged diffusion-weighted MRI signal using different axisymmetric B-tensor encoding schemes

Purpose

It has been shown, theoretically and in vivo, that using the Stejskal‐Tanner pulsed‐gradient, or linear tensor encoding (LTE), and in tissue exhibiting a “stick‐like” diffusion geometry, the direction‐averaged diffusion‐weighted MRI signal at high b‐values ( 7000<b<10000s/mm2) follows a power‐law, decaying as 1/b. It has also been shown, theoretically, that for planar tensor encoding (PTE), the direction‐averaged diffusion‐weighted MRI signal decays as 1/b. We aimed to confirm this theoretical prediction in vivo. We then considered the direction‐averaged signal for arbitrary b‐tensor shapes and different tissue substrates to look for other conditions under which a power‐law exists.

Methods

We considered the signal decay for high b‐values for encoding geometries ranging from 2‐dimensional PTE, through isotropic or spherical tensor encoding to LTE. When a power‐law behavior was suggested, this was tested using in silico simulations and, when appropriate, in vivo using ultra‐strong (300 mT/m) gradients.

Results

Our in vivo results confirmed the predicted 1/b power law for PTE. Moreover, our analysis showed that using an axisymmetric b‐tensor a power‐law only exists under very specific conditions: (a) “stick‐like” tissue geometry and purely LTE or purely PTE waveforms; and (b) "pancake‐like" tissue geometry and a purely LTE waveform.

Conclusions

A complete analysis of the power‐law dependencies of the diffusion‐weighted signal at high b‐values has been performed. Only three specific forms of encoding result in a power‐law dependency, pure linear and pure PTE when the tissue geometry is “stick‐like” and pure LTE when the tissue geometry is "pancake‐like". The different exponents of these encodings could be used to provide independent validation of the presence of different tissue geometries in vivo.

Nonivasive quantification of axon radii using diffusion MRI

Axon caliber plays a crucial role in determining conduction velocity and, consequently, in the timing and synchronization of neural activation. Noninvasive measurement of axon radii could have significant impact on the understanding of healthy and diseased neural processes. Until now, accurate axon radius mapping has eluded in vivo neuroimaging, mainly due to a lack of sensitivity of the MRI signal to micron-sized axons. Here, we show how - when confounding factors such as extra-axonal water and axonal orientation dispersion are eliminated - heavily diffusion-weighted MRI signals become sensitive to axon radii. However, diffusion MRI is only capable of estimating a single metric, the effective radius, representing the entire axon radius distribution within a voxel that emphasizes the larger axons. Our findings, both in rodents and humans, enable noninvasive mapping of critical information on axon radii, as well as resolve the long-standing debate on whether axon radii can be quantified.

Estimating axon conduction velocity in vivo from microstructural MRI

The conduction velocity (CV) of action potentials along axons is a key neurophysiological property central to neural communication. The ability to estimate CV in humans in vivo from non-invasive MRI methods would therefore represent a significant advance in neuroscience. However, there are two major challenges that this paper aims to address: (1) Much of the complexity of the neurophysiology of action potentials cannot be captured with currently available MRI techniques. Therefore, we seek to establish the variability in CV that can be captured when predicting CV purely from parameters that have been reported to be estimatable from MRI: inner axon diameter (AD) and g-ratio. (2) errors inherent in existing MRI-based biophysical models of tissue will propagate through to estimates of CV, the extent to which is currently unknown. Issue (1) is investigated by performing a sensitivity analysis on a comprehensive model of axon electrophysiology and determining the relative sensitivity to various morphological and electrical parameters. The investigations suggest that 85% of the variance in CV is accounted for by variation in AD and g-ratio. The observed dependency of CV on AD and g-ratio is well characterised by the previously reported model by Rushton. Issue (2) is investigated through simulation of diffusion and relaxometry MRI data for a range of axon morphologies, applying models of restricted diffusion and relaxation processes to derive estimates of axon volume fraction (AVF), AD and g-ratio and estimating CV from the derived parameters. The results show that errors in the AVF have the biggest detrimental impact on estimates of CV, particularly for sparse fibre populations (AVF<0.3). For our equipment set-up and acquisition protocol, CV estimates are most accurate (below 5% error) where AVF is above 0.3, g-ratio is between 0.6 and 0.85 and AD is high (above 4μm). CV estimates are robust to errors in g-ratio estimation but are highly sensitive to errors in AD estimation, particularly where ADs are small. We additionally show CV estimates in human corpus callosum in a small number of subjects. In conclusion, we demonstrate accurate CV estimates are possible in regions of the brain where AD is sufficiently large. Problems with estimating ADs for smaller axons presents a problem for estimating CV across the whole CNS and should be the focus of further study.

Multishell diffusion imaging reveals sex-specific trajectories of early white matter degeneration in normal aging

During aging, human white matter (WM) is subject to dynamic structural changes which have a deep impact on healthy and pathological evolution of the brain through the lifespan; characterizing this pattern is of key importance for understanding brain development, maturation, and aging as well as for studying its pathological alterations. Diffusion magnetic resonance imaging (MRI) can provide a quantitative assessment of the white-matter microstructural organization that characterizes these trajectories. Here, we use both conventional and advanced diffusion MRI in a cohort of 91 individuals (age range: 13-62 years) to study region- and sex-specific features of WM microstructural integrity in healthy aging. We focus on the age at which microstructural imaging parameters invert their development trend as the time point which marks the onset of microstructural decline in WM. Importantly, our results indicate that age-related brain changes begin earlier in males than females and affect more frontal regions-in accordance with evolutionary theories and numerous evidences across non-MRI domains. Advanced diffusion MRI reveals age-related WM modification patterns which cannot be detected using conventional diffusion tensor imaging.

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.

Probing Surface-to-Volume Ratio of an Anisotropic Medium by Diffusion NMR with General Gradient Encoding

Since the seminal paper by Mitra et al., diffusion MR has been widely used in order to estimate surface-to-volume ratios. In this paper, we generalize Mitra's formula for arbitrary diffusion encoding waveforms, including recently developed q-space trajectory encoding sequences. We show that the surface-to-volume ratio can be significantly misestimated using the original Mitra's formula without taking into account the applied gradient profile. In order to obtain more accurate estimation in anisotropic samples, we propose an efficient and robust optimization algorithm to design diffusion gradient waveforms with prescribed features. Our results are supported by Monte Carlo simulations.

The Dmipy Toolbox: Diffusion MRI Multi-Compartment Modeling and Microstructure Recovery Made Easy

Non-invasive estimation of brain microstructure features using diffusion MRI (dMRI)—known as Microstructure Imaging—has become an increasingly diverse and complicated field over the last decades. Multi-compartment (MC)-models, representing the measured diffusion signal as a linear combination of signal models of distinct tissue types, have been developed in many forms to estimate these features. However, a generalized implementation of MC-modeling as a whole, providing deeper insights in its capabilities, remains missing. To address this fact, we present Diffusion Microstructure Imaging in Python (Dmipy), an open-source toolbox implementing PGSE-based MC-modeling in its most general form. Dmipy allows on-the-fly implementation, signal modeling, and optimization of any user-defined MC-model, for any PGSE acquisition scheme. Dmipy follows a “building block”-based philosophy to Microstructure Imaging, meaning MC-models are modularly constructed to include any number and type of tissue models, allowing simultaneous representation of a tissue's diffusivity, orientation, volume fractions, axon orientation dispersion, and axon diameter distribution. In particular, Dmipy is geared toward facilitating reproducible, reliable MC-modeling pipelines, often allowing the whole process from model construction to parameter map recovery in fewer than 10 lines of code. To demonstrate Dmipy's ease of use and potential, we implement a wide range of well-known MC-models, including IVIM, AxCaliber, NODDI(x), Bingham-NODDI, the spherical mean-based SMT and MC-MDI, and spherical convolution-based single- and multi-tissue CSD. By allowing parameter cascading between MC-models, Dmipy also facilitates implementation of advanced approaches like CSD with voxel-varying kernels and single-shell 3-tissue CSD. By providing a well-tested, user-friendly toolbox that simplifies the interaction with the otherwise complicated field of dMRI-based Microstructure Imaging, Dmipy contributes to more reproducible, high-quality research.

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.

Resolving degeneracy in diffusion MRI biophysical model parameter estimation using double diffusion encoding

PURPOSE

Biophysical tissue models are increasingly used in the interpretation of diffusion MRI (dMRI) data, with the potential to provide specific biomarkers of brain microstructural changes. However, it has been shown recently that, in the general Standard Model, parameter estimation from dMRI data is ill-conditioned even when very high b-values are applied. We analyze this issue for the Neurite Orientation Dispersion and Density Imaging with Diffusivity Assessment (NODDIDA) model and demonstrate that its extension from single diffusion encoding (SDE) to double diffusion encoding (DDE) resolves the ill-posedness for intermediate diffusion weightings, producing an increase in accuracy and precision of the parameter estimation.

METHODS

We analyze theoretically the cumulant expansion up to fourth order in b of SDE and DDE signals. Additionally, we perform in silico experiments to compare SDE and DDE capabilities under similar noise conditions.

RESULTS

We prove analytically that DDE provides invariant information non-accessible from SDE, which makes the NODDIDA parameter estimation injective. The in silico experiments show that DDE reduces the bias and mean square error of the estimation along the whole feasible region of 5D model parameter space.

CONCLUSIONS

DDE adds additional information for estimating the model parameters, unexplored by SDE. We show, as an example, that this is sufficient to solve the previously reported degeneracies in the NODDIDA model parameter estimation.

Multidimensional diffusion MRI with spectrally modulated gradients reveals unprecedented microstructural detail

Characterization of porous media is essential in a wide range of biomedical and industrial applications. Microstructural features can be probed non-invasively by diffusion magnetic resonance imaging (dMRI). However, diffusion encoding in conventional dMRI may yield similar signatures for very different microstructures, which represents a significant limitation for disentangling individual microstructural features in heterogeneous materials. To solve this problem, we propose an augmented multidimensional diffusion encoding (MDE) framework, which unlocks a novel encoding dimension to assess time-dependent diffusion specific to structures with different microscopic anisotropies. Our approach relies on spectral analysis of complex but experimentally efficient MDE waveforms. Two independent contrasts to differentiate features such as cell shape and size can be generated directly by signal subtraction from only three types of measurements. Analytical calculations and simulations support our experimental observations. Proof-of-concept experiments were applied on samples with known and distinctly different microstructures. We further demonstrate substantially different contrasts in different tissue types of a post mortem brain. Our simultaneous assessment of restriction size and shape may be instrumental in studies of a wide range of porous materials, enable new insights into the microstructure of biological tissues or be of great value in diagnostics.

Age-related alterations in axonal microstructure in the corpus callosum measured by high-gradient diffusion MRI

Cerebral white matter exhibits age-related degenerative changes during the course of normal aging, including decreases in axon density and alterations in axonal structure. Noninvasive approaches to measure these microstructural alterations throughout the lifespan would be invaluable for understanding the substrate and regional variability of age-related white matter degeneration. Recent advances in diffusion magnetic resonance imaging (MRI) have leveraged high gradient strengths to increase sensitivity toward axonal size and density in the living human brain. Here, we examined the relationship between age and indices of axon diameter and packing density using high-gradient strength diffusion MRI in 36 healthy adults (aged 22-72) in well-defined central white matter tracts in the brain. A recently validated method for inferring the effective axonal compartment size and packing density from diffusion MRI measurements acquired with 300 mT/m maximum gradient strength was applied to the in vivo human brain to obtain indices of axon diameter and density in the corpus callosum, its sub-regions, and adjacent anterior and posterior fibers in the forceps minor and forceps major. The relationships between the axonal metrics, corpus callosum area and regional gray matter volume were also explored. Results revealed a significant increase in axon diameter index with advancing age in the whole corpus callosum. Similar analyses in sub-regions of the corpus callosum showed that age-related alterations in axon diameter index and axon density were most pronounced in the genu of the corpus callosum and relatively absent in the splenium, in keeping with findings from previous histological studies. The significance of these correlations was mirrored in the forceps minor and forceps major, consistent with previously reported decreases in FA in the forceps minor but not in the forceps major with age. Alterations in the axonal imaging metrics paralleled decreases in corpus callosum area and regional gray matter volume with age. Among older adults, results from cognitive testing suggested an association between larger effective compartment size in the corpus callosum, particularly within the genu of the corpus callosum, and lower scores on the Montreal Cognitive Assessment, largely driven by deficits in short-term memory. The current study suggests that high-gradient diffusion MRI may be sensitive to the axonal substrate of age-related white matter degeneration reflected in traditional DTI metrics and provides further evidence for regionally selective alterations in white matter microstructure with advancing age.

Microscopic anisotropy misestimation in spherical-mean single diffusion encoding MRI

Purpose

Microscopic fractional anisotropy (µFA) can disentangle microstructural information from orientation dispersion. While double diffusion encoding (DDE) MRI methods are widely used to extract accurate µFA, it has only recently been proposed that powder‐averaged single diffusion encoding (SDE) signals, when coupled with the diffusion standard model (SM) and a set of constraints, could be used for µFA estimation. This study aims to evaluate µFA as derived from the spherical mean technique (SMT) set of constraints, as well as more generally for powder‐averaged SM signals.

Methods

SDE experiments were performed at 16.4 T on an ex vivo mouse brain (Δ/δ = 12/1.5 ms). The µFA maps obtained from powder‐averaged SDE signals were then compared to maps obtained from DDE‐MRI experiments (Δ/τ/δ = 12/12/1.5 ms), which allow a model‐free estimation of µFA. Theory and simulations that consider different types of heterogeneity are presented for corroborating the experimental findings.

Results

µFA, as well as other estimates derived from powder‐averaged SDE signals produced large deviations from the ground truth in both gray and white matter. Simulations revealed that these misestimations are likely a consequence of factors not considered by the underlying microstructural models (such as intercomponent and intracompartmental kurtosis).

Conclusion

Powder‐averaged SMT and (2‐component) SM are unable to accurately report µFA and other microstructural parameters in ex vivo tissues. Improper model assumptions and constraints can significantly compromise parameter specificity. Further developments and validations are required prior to implementation of these models in clinical or preclinical research.

Towards microstructure fingerprinting: Estimation of tissue properties from a dictionary of Monte Carlo diffusion MRI simulations

Many closed-form analytical models have been proposed to relate the diffusion-weighted magnetic resonance imaging (DW-MRI) signal to microstructural features of white matter tissues. These models generally make assumptions about the tissue and the diffusion processes which often depart from the biophysical reality, limiting their reliability and interpretability in practice. Monte Carlo simulations of the random walk of water molecules are widely recognized to provide near groundtruth for DW-MRI signals. However, they have mostly been limited to the validation of simpler models rather than used for the estimation of microstructural properties. This work proposes a general framework which leverages Monte Carlo simulations for the estimation of physically interpretable microstructural parameters, both in single and in crossing fascicles of axons. Monte Carlo simulations of DW-MRI signals, or fingerprints, are pre-computed for a large collection of microstructural configurations. At every voxel, the microstructural parameters are estimated by optimizing a sparse combination of these fingerprints. Extensive synthetic experiments showed that our approach achieves accurate and robust estimates in the presence of noise and uncertainties over fixed or input parameters. In an in vivo rat model of spinal cord injury, our approach provided microstructural parameters that showed better correspondence with histology than five closed-form models of the diffusion signal: MMWMD, NODDI, DIAMOND, WMTI and MAPL. On whole-brain in vivo data from the human connectome project (HCP), our method exhibited spatial distributions of apparent axonal radius and axonal density indices in keeping with ex vivo studies. This work paves the way for microstructure fingerprinting with Monte Carlo simulations used directly at the modeling stage and not only as a validation tool.

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.

On the scaling behavior of water diffusion in human brain white matter

Development of therapies for neurological disorders depends on our ability to non-invasively diagnose and monitor the progression of underlying pathologies at the cellular level. Physics and physiology limit the resolution of human MRI to be orders of magnitude coarser than cell dimensions. Here we identify and quantify the MRI signal coming from within micrometer-thin axons in human white matter tracts in vivo, by utilizing the sensitivity of diffusion MRI to Brownian motion of water molecules restricted by cell walls. We study a specific power-law scaling of the diffusion MRI signal with the diffusion weighting, predicted for water confined to narrow axons, and quantify axonal water fraction and orientation dispersion.