The role of tissue microstructure and water exchange in biophysical modelling of diffusion in white matter

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.

Diffusion MRI with free gradient waveforms on a high-performance gradient system: Probing restriction and exchange in the human brain

The dependence of the diffusion MRI signal on the diffusion time carries signatures of restricted diffusion and exchange. Here we seek to highlight these signatures in the human brain by performing experiments using free gradient waveforms designed to be selectively sensitive to the two effects. We examine six healthy volunteers using both strong and ultra-strong gradients (80, 200 and 300 mT/m). In an experiment featuring a large set of 150 gradient waveforms with different sensitivities to restricted diffusion and exchange, our results reveal unique and different time-dependence signatures in grey and white matter. Grey matter was characterised by both restricted diffusion and exchange and white matter predominantly by restricted diffusion. Exchange in grey matter was at least twice as fast as in white matter, across all subjects and all gradient strengths. The cerebellar cortex featured relatively short exchange times (115 ms). Furthermore, we show that gradient waveforms with tailored designs can be used to map exchange in the human brain. We also assessed the feasibility of clinical applications of the method used in this work and found that the exchange-related contrast obtained with a 25-minute protocol at 300 mT/m was preserved in a 4-minute protocol at 300 mT/m and a 10-minute protocol at 80 mT/m. Our work underlines the utility of free waveforms for detecting time dependence signatures due to restricted diffusion and exchange in vivo, which may potentially serve as a tool for studying diseased tissue.

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.

Molecular Imaging with Aquaporin-Based Reporter Genes: Quantitative Considerations from Monte Carlo Diffusion Simulations

Aquaporins provide a unique approach for imaging genetic activity in deep tissues by increasing the rate of cellular water diffusion, which generates a magnetic resonance contrast. However, distinguishing aquaporin signals from the tissue background is challenging because water diffusion is influenced by structural factors, such as cell size and packing density. Here, we developed a Monte Carlo model to analyze how cell radius and intracellular volume fraction quantitatively affect aquaporin signals. We demonstrated that a differential imaging approach based on subtracting signals at two diffusion times can improve specificity by unambiguously isolating aquaporin signals from the tissue background. We further used Monte Carlo simulations to analyze the connection between diffusivity and the percentage of cells engineered to express aquaporin and established a mapping that accurately determined the volume fraction of aquaporin-expressing cells in mixed populations. The quantitative framework developed in this study will enable a broad range of applications in biomedical synthetic biology, requiring the use of aquaporins to noninvasively monitor the location and function of genetically engineered devices in live animals.

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.

Molecular imaging with aquaporin-based reporter genes: quantitative considerations from Monte Carlo diffusion simulations

Aquaporins provide a new class of genetic tools for imaging molecular activity in deep tissues by increasing the rate of cellular water diffusion, which generates magnetic resonance contrast. However, distinguishing aquaporin contrast from the tissue background is challenging because water diffusion is also influenced by structural factors such as cell size and packing density. Here, we developed and experimentally validated a Monte Carlo model to analyze how cell radius and intracellular volume fraction quantitatively affect aquaporin signals. We demonstrated that a differential imaging approach based on time-dependent changes in diffusivity can improve specificity by unambiguously isolating aquaporin-driven contrast from the tissue background. Finally, we used Monte Carlo simulations to analyze the connection between diffusivity and the percentage of cells engineered to express aquaporin, and established a simple mapping that accurately determined the volume fraction of aquaporin-expressing cells in mixed populations. This study creates a framework for broad applications of aquaporins, particularly in biomedicine and in vivo synthetic biology, where quantitative methods to measure the location and performance of genetic devices in whole vertebrates are necessary.

Diffusion MRI with free gradient waveforms on a high-performance gradient system: Probing restriction and exchange in the human brain

The dependence of the diffusion MRI signal on the diffusion time carries signatures of restricted diffusion and exchange. Here we seek to highlight these signatures in the human brain by performing experiments using free gradient waveforms that are selectively sensitive to the two effects. We examine six healthy volunteers using both strong and ultra-strong gradients (80, 200 and 300 mT/m). In an experiment featuring a large set of gradient waveforms with different sensitivities to restricted diffusion and exchange (150 samples), our results reveal unique time-dependence signatures in grey and white matter, where the former is characterised by both restricted diffusion and exchange and the latter predominantly exhibits restricted diffusion. Furthermore, we show that gradient waveforms with independently varying sensitivities to restricted diffusion and exchange can be used to map exchange in the human brain. We consistently find that exchange in grey matter is at least twice as fast as in white matter, across all subjects and all gradient strengths. The shortest exchange times observed in this study were in the cerebellar cortex (115 ms). We also assess the feasibility of future clinical applications of the method used in this work, where we find that the grey-white matter exchange contrast obtained with a 25-minute 300 mT/m protocol is preserved by a 4-minute 300 mT/m and a 10-minute 80 mT/m protocol. Our work underlines the utility of free waveforms for detecting time-dependence signatures due to restricted diffusion and exchange in vivo, which may potentially serve as a tool for studying diseased tissue.

Multi-readout DWI with a reduced FOV for studying the coupling between diffusion and T 2 * relaxation in the prostate

PURPOSE

To develop a DWI sequence with multiple readout echo-trains in a single shot (multi-readout DWI) over a reduced FOV, and to demonstrate its ability to achieve high data acquisition efficiency in the study of coupling between diffusion and relaxation in the human prostate.

METHODS

The proposed multi-readout DWI sequence plays out multiple EPI readout echo-trains after a Stejskal-Tanner diffusion preparation module. Each EPI readout echo-train corresponded to a distinct effective TE. To maintain a high spatial resolution with a relatively short echo-train for each readout, a 2D RF pulse was used to limit the FOV. Experiments were performed on the prostate of six healthy subjects to acquire a set of images with three b values (0, 500, and 1000 s/mm² ) and three TEs (63.0, 78.8, and 94.6 ms), producing three ADC maps at different TEs and three T 2 * $$ {T}_2^{\ast } $$ maps at different b values.

RESULTS

Multi-readout DWI enabled a threefold acceleration without compromising the spatial resolution when compared with a conventional single-readout sequence. Images with three b values and three TEs were obtained in 3 min 40 s with an adequate SNR (≥ 26.9). The ADC values (1.45 ± 0.13, 1.52 ± 0.14, and 1.58 ± 0.15  μm 2 / ms $$ {\upmu \mathrm{m}}^2/\mathrm{ms} $$ ; P < 0.01) exhibited an increasing trend as TEs increased (63.0 ms, 78.8 ms, and 94.6 ms), whereas T 2 * $$ {T}_2^{\ast } $$ values (74.78 ± 13.21, 63.21 ± 7.84, and 56.61 ± 5.05 ms; P < 0.01) decreases as the b values increased (0, 500, and 1000 s/mm² ).

CONCLUSION

The multi-readout DWI sequence over a reduced FOV provides a time-efficient technique to study the coupling between diffusion and relaxation times.

Tuned bipolar oscillating gradients for mapping frequency dispersion of diffusion kurtosis in the human brain

PURPOSE

Oscillating gradient spin-echo (OGSE) sequences have demonstrated an ability to probe time-dependent microstructural features, although they often suffer from low SNR due to increased TEs. In this work we introduce frequency-tuned bipolar (FTB) gradients as a variation of oscillating gradients with reduced TE and demonstrate their utility by mapping the frequency dispersion of kurtosis in human subjects.

METHODS

An FTB oscillating gradient waveform is presented that provides encoding of 1.5 net oscillation periods, thereby reducing the TE of the acquisition. Simulations were performed to determine an optimal protocol based on the SNR of kurtosis frequency dispersion-defined as the difference in kurtosis between pulsed and oscillating gradient acquisitions. Healthy human subjects were scanned at 7T using pulsed gradient and an optimized 23 Hz FTB protocol, which featured a maximum b-value of 2500 s/mm² . In addition, to directly compare existing methods, measurements using traditional cosine OGSE were also acquired.

RESULTS

FTB oscillating gradients demonstrated equivalent frequency-dependent diffusion measurements compared with cosine-modulated OGSE while enabling a significant reduction in TE. Optimization and in vivo results suggest that FTB gradients provide increased SNR of kurtosis dispersion maps compared with traditional cosine OGSE. The optimized FTB gradient protocol demonstrated consistent reductions in apparent kurtosis values and increased diffusivity in generated frequency dispersion maps.

CONCLUSIONS

This work presents an alternative to traditional cosine OGSE sequences, enabling more time-efficient acquisitions of frequency-dependent diffusion quantities as demonstrated through in vivo kurtosis frequency dispersion maps.

Comparison of two types of microscopic diffusion anisotropy in mouse brain

Two distinct types of microscopic diffusion anisotropy (MA) are compared in brain for both normal control and transgenic (3xTg-AD) mice, which develop Alzheimer's disease pathology. The first type of MA is the commonly used microscopic fractional anisotropy (μFA), and the second is a new MA measure referred to as μFA'. These two MA parameters have different symmetry properties that are central to their physical interpretations. Specifically, μFA is invariant with respect to local rotations of compartmental diffusion tensors while μFA' is invariant with respect to global diffusion tensor deformations. A key distinction between μFA and μFA' is that μFA is affected by the same type of orientationally coherent diffusion anisotropy as the conventional fractional anisotropy (FA) while μFA' is not. Furthermore, μFA can be viewed as having independent contributions from FA and μFA', as is quantified by an equation relating all three anisotropies. The normal control and transgenic mice are studied at ages ranging from 2 to 15 months, with double diffusion encoding MRI being used to estimate μFA and μFA'. μFA and μFA' are nearly identical in low FA brain regions, but they show notable differences when FA is large. In particular, μFA and FA are found to be strongly correlated in the fimbria, but μFA' and FA are not. In addition, both μFA and μFA' are seen to increase with age in the corpus callosum and external capsule, and modest differences between normal control and transgenic mice are observed for μFA and μFA' in the corpus callosum and for μFA in the fimbria. The triad of FA, μFA, and μFA' is proposed as a useful combination of parameters for assessing diffusion anisotropy in brain.

Diffusion MRI with pulsed and free gradient waveforms: Effects of restricted diffusion and exchange

Monitoring time dependence with diffusion MRI yields observables sensitive to compartment sizes (restricted diffusion) and membrane permeability (water exchange). However, restricted diffusion and exchange have opposite effects on the diffusion-weighted signal, which can lead to errors in parameter estimates. In this work, we propose a signal representation that incorporates the effects of both restricted diffusion and exchange up to second order in b-value and is compatible with gradient waveforms of arbitrary shape. The representation features mappings from a gradient waveform to two scalars that separately control the sensitivity to restriction and exchange. We demonstrate that these scalars span a two-dimensional space that can be used to choose waveforms that selectively probe restricted diffusion or exchange, eliminating the correlation between the two phenomena. We found that waveforms with specific but unconventional shapes provide an advantage over conventional pulsed and oscillating gradient acquisitions. We also show that parametrization of waveforms into a two-dimensional space can be used to understand protocols from other approaches that probe restricted diffusion and exchange. For example, we found that the variation of mixing time in filter-exchange imaging corresponds to variation of our exchange-weighting scalar at a fixed value of the restriction-weighting scalar. The proposed signal representation was evaluated using Monte Carlo simulations in identical parallel cylinders with hexagonal and random packing as well as parallel cylinders with gamma-distributed radii. Results showed that the approach is sensitive to sizes in the interval 4-12 μm and exchange rates in the simulated range of 0 to 20 s - 1 , but also that there is a sensitivity to the extracellular geometry. The presented theory constitutes a simple and intuitive description of how restricted diffusion and exchange influence the signal as well as a guide to protocol design capable of separating the two effects.

Reconstruction of ovine axonal cytoarchitecture enables more accurate models of brain biomechanics

There is an increased need and focus to understand how local brain microstructure affects the transport of drug molecules directly administered to the brain tissue, for example in convection-enhanced delivery procedures. This study reports a systematic attempt to characterize the cytoarchitecture of commissural, long association and projection fibres, namely the corpus callosum, the fornix and the corona radiata, with the specific aim to map different regions of the tissue and provide essential information for the development of accurate models of brain biomechanics. Ovine samples are imaged using scanning electron microscopy combined with focused ion beam milling to generate 3D volume reconstructions of the tissue at subcellular spatial resolution. Focus is placed on the characteristic cytological feature of the white matter: the axons and their alignment in the tissue. For each tract, a 3D reconstruction of relatively large volumes, including a significant number of axons, is performed and outer axonal ellipticity, outer axonal cross-sectional area and their relative perimeter are measured. The study of well-resolved microstructural features provides useful insight into the fibrous organization of the tissue, whose micromechanical behaviour is that of a composite material presenting elliptical tortuous tubular axonal structures embedded in the extra-cellular matrix. Drug flow can be captured through microstructurally-based models using 3D volumes, either reconstructed directly from images or generated in silico using parameters extracted from the database of images, leading to a workflow to enable physically-accurate simulations of drug delivery to the targeted tissue.

Imaging and reconstruction of sheep brain axonal cytoarchitecture provides insight for brain biomechanics models that simulate drug delivery and other biological processes governed by interstitial fluid flow and transport.

Clinical translation of quantitative magnetic resonance imaging biomarkers - An overview and gap analysis of current practice

PURPOSE

This overview of the current landscape of quantitative magnetic resonance imaging biomarkers (qMR IBs) aims to support the standardisation of academic IBs to assist their translation to clinical practice.

METHODS

We used three complementary approaches to investigate qMR IB use and quality management practices within the UK: 1) a literature search of qMR and quality management terms during 2011-2015 and 2016-2020; 2) a database search for clinical research studies using qMR IBs during 2016-2020; and 3) a survey to ascertain the current availability and quality management practices for clinical MRI scanners and associated equipment at research institutions across the UK.

RESULTS

The analysis showed increased use of all qMR methods between the periods 2011-2015 and 2016-2020 and diffusion-tensor MRI and volumetry to be popular methods. However, the "translation ratio" of journal articles to clinical research studies was higher for qMR methods that have evidence of clinical translation via a commercial route, such as fat fraction and T2 mapping. The number of journal articles citing quality management terms doubled between the periods 2011-2015 and 2016-2020; although, its proportion relative to all journal articles only increased by 3.0%. The survey suggested that quality assurance (QA) and quality control (QC) of data acquisition procedures are under-reported in the literature and that QA/QC of acquired data/data analysis are under-developed and lack consistency between institutions.

CONCLUSIONS

We summarise current attempts to standardise and translate qMR IBs, and conclude by outlining the ideal quality management practices and providing a gap analysis between current practice and a metrological standard.

Neurite Exchange Imaging (NEXI): A minimal model of diffusion in gray matter with inter-compartment water exchange

Biophysical models of diffusion in white matter have been center-stage over the past two decades and are essentially based on what is now commonly referred to as the "Standard Model" (SM) of non-exchanging anisotropic compartments with Gaussian diffusion. In this work, we focus on diffusion MRI in gray matter, which requires rethinking basic microstructure modeling blocks. In particular, at least three contributions beyond the SM need to be considered for gray matter: water exchange across the cell membrane - between neurites and the extracellular space; non-Gaussian diffusion along neuronal and glial processes - resulting from structural disorder; and signal contribution from soma. For the first contribution, we propose Neurite Exchange Imaging (NEXI) as an extension of the SM of diffusion, which builds on the anisotropic Kärger model of two exchanging compartments. Using datasets acquired at multiple diffusion weightings (b) and diffusion times (t) in the rat brain in vivo, we investigate the suitability of NEXI to describe the diffusion signal in the gray matter, compared to the other two possible contributions. Our results for the diffusion time window 20-45 ms show minimal diffusivity time-dependence and more pronounced kurtosis decay with time, which is well fit by the exchange model. Moreover, we observe lower signal for longer diffusion times at high b. In light of these observations, we identify exchange as the mechanism that best explains these signal signatures in both low-b and high-b regime, and thereby propose NEXI as the minimal model for gray matter microstructure mapping. We finally highlight multi-b multi-t acquisition protocols as being best suited to estimate NEXI model parameters reliably. Using this approach, we estimate the inter-compartment water exchange time to be 15 - 60 ms in the rat cortex and hippocampus in vivo, which is of the same order or shorter than the diffusion time in typical diffusion MRI acquisitions. This suggests water exchange as an essential component for interpreting diffusion MRI measurements in gray matter.

Diffusion tensor imaging in glioblastoma patients treated with volumetric modulated arc radiotherapy: a longitudinal study

BACKGROUND

Chemo- and radiotherapy (RT) is standard treatment for patients with high-grade glioma, but may cause side-effects on the patient's cognitive function.

AIM

Use of diffusion tensor imaging (DTI) to investigate the longitudinal changes in normal-appearing brain tissue in glioblastoma patients undergoing modern arc-based RT with volumetric modulated arc therapy (VMAT) or helical tomotherapy.

MATERIALS AND METHODS

The study included 27 patients newly diagnosed with glioblastoma and planned for VMAT or tomotherapy. All subjects underwent magnetic resonance imaging at the start of RT and at week 3, 6, 15, and 26. Fourteen subjects were additionally imaged at week 52. The DTI data were co-registered to the dose distribution maps. Longitudinal changes in fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RD), and axial diffusivity (AD) were assessed in the corpus callosum, the centrum semiovale, the hippocampus, and the amygdala.

RESULTS

Significant longitudinal changes in FA, MD, and RD were mainly found in the corpus callosum. In the other examined brain structures, only sparse and transient changes were seen. No consistent correlations were found between biodose, age, or gender and changes in DTI parameters.

CONCLUSION

Longitudinal changes in MD, FA, and RD were observed but only in a limited number of brain structures and the changes were smaller than expected from literature. The results suggest that modern, arc-based RT may have less negative effect on normal-appearing parts of the brain tissue up to 12 months after radiotherapy.

Diffusion time dependence, power-law scaling, and exchange in gray matter

Characterizing neural tissue microstructure is a critical goal for future neuroimaging. Diffusion MRI (dMRI) provides contrasts that reflect diffusing spins' interactions with myriad microstructural features of biological systems. However, the specificity of dMRI remains limited due to the ambiguity of its signals vis-à-vis the underlying microstructure. To improve specificity, biophysical models of white matter (WM) typically express dMRI signals according to the Standard Model (SM) and have more recently in gray matter (GM) taken spherical compartments into account (the SANDI model) in attempts to represent cell soma. The validity of the assumptions underlying these models, however, remains largely undetermined, especially in GM. To validate these assumptions experimentally, observing their unique, functional properties, such as the b-1/2 power-law associated with one-dimensional diffusion, has emerged as a fruitful strategy. The absence of this signature in GM, in turn, has been explained by neurite water exchange, non-linear morphology, and/or by obscuring soma signal contributions. Here, we present diffusion simulations in realistic neurons demonstrating that curvature and branching does not destroy the stick power-law behavior in impermeable neurites, but also that their signal is drowned by the soma signal under typical experimental conditions. Nevertheless, by studying the GM dMRI signal's behavior as a function of diffusion weighting as well as time, we identify an attainable experimental regime in which the neurite signal dominates. Furthermore, we find that exchange-driven time dependence produces a signal behavior opposite to that which would be expected from restricted diffusion, thereby providing a functional signature that disambiguates the two effects. We present data from dMRI experiments in ex vivo rat brain at ultrahigh field of 16.4T and observe a time dependence that is consistent with substantial exchange but also with a GM stick power-law. The first finding suggests significant water exchange between neurites and the extracellular space while the second suggests a small sub-population of impermeable neurites. To quantify these observations, we harness the Kärger exchange model and incorporate the corresponding signal time dependence in the SM and SANDI models.

Improved diffusion parameter estimation by incorporating T2 relaxation properties into the DKI-FWE model

The free water elimination (FWE) model and its kurtosis variant (DKI-FWE) can separate tissue and free water signal contributions, thus providing tissue-specific diffusional information. However, a downside of these models is that the associated parameter estimation problem is ill-conditioned, necessitating the use of advanced estimation techniques that can potentially bias the parameter estimates. In this work, we propose the T₂-DKI-FWE model that exploits the T₂ relaxation properties of both compartments, thereby better conditioning the parameter estimation problem and providing, at the same time, an additional potential biomarker (the T₂ of tissue). In our approach, the T₂ of tissue is estimated as an unknown parameter, whereas the T₂ of free water is assumed known a priori and fixed to a literature value (1573 ms). First, the error propagation of an erroneous assumption on the T₂ of free water is studied. Next, the improved conditioning of T₂-DKI-FWE compared to DKI-FWE is illustrated using the Cramér-Rao lower bound matrix. Finally, the performance of the T₂-DKI-FWE model is compared to that of the DKI-FWE and T₂-DKI models on both simulated and real datasets. The error due to a biased approximation of the T₂ of free water was found to be relatively small in various diffusion metrics and for a broad range of erroneous assumptions on its underlying ground truth value. Compared to DKI-FWE, using the T₂-DKI-FWE model is beneficial for the identifiability of the model parameters. Our results suggest that the T₂-DKI-FWE model can achieve precise and accurate diffusion parameter estimates, through effective reduction of free water partial volume effects and by using a standard nonlinear least squares approach. In conclusion, incorporating T₂ relaxation properties into the DKI-FWE model improves the conditioning of the model fitting, while only requiring an acquisition scheme with at least two different echo times.

Beyond Diffusion Tensor MRI Methods for Improved Characterization of the Brain after Ischemic Stroke: A Review

Ischemic stroke is a worldwide problem, with 15 million people experiencing a stroke annually. MR imaging is a valuable tool for understanding and assessing brain changes after stroke and predicting recovery. Of particular interest is the use of diffusion MR imaging in the nonacute stage 1-30 days poststroke. Thousands of articles have been published on the use of diffusion MR imaging in stroke, including several recent articles reviewing the use of DTI for stroke. The goal of this work was to survey and put into context the recent use of diffusion MR imaging methods beyond DTI, including diffusional kurtosis, generalized fractional anisotropy, spherical harmonics methods, and neurite orientation and dispersion models, in patients poststroke. Early studies report that these types of beyond-DTI methods outperform DTI metrics either in being more sensitive to poststroke changes or by better predicting outcome motor scores. More and larger studies are needed to confirm the improved prediction of stroke recovery with the beyond-DTI methods.

Disentangling the effects of restriction and exchange with diffusion exchange spectroscopy

Diffusion exchange spectroscopy (DEXSY) is a multidimensional NMR technique that can reveal how water molecules exchange between compartments within heterogeneous media, such as biological tissue. Data from DEXSY experiments is typically processed using numerical inverse Laplace transforms (ILTs) to produce a diffusion-diffusion spectrum. A tacit assumption of this ILT approach is that the signal behavior is Gaussian - i.e., the spin echo intensity decays exponentially with the degree of diffusion weighting. The assumptions that underlie Gaussian signal behavior may be violated, however, depending on the gradient strength applied and the sample under study. We argue that non-Gaussian signal behavior due to restrictions is to be expected in the study of biological tissue using diffusion NMR. Further, we argue that this signal behavior can produce confounding features in the diffusion-diffusion spectra obtained from numerical ILTs of DEXSY data - entangling the effects of restriction and exchange. Specifically, restricted signal behavior can result in broadening of peaks and in the appearance of illusory exchanging compartments with distributed diffusivities, which pearl into multiple peaks if not highly regularized. We demonstrate these effects on simulated data. That said, we suggest the use of features in the signal acquisition domain that can be used to rapidly probe exchange without employing an ILT. We also propose a means to characterize the non-Gaussian signal behavior due to restrictions within a sample using DEXSY measurements with a near zero mixing time or storage interval. We propose a combined acquisition scheme to independently characterize restriction and exchange with various DEXSY measurements, which we term Restriction and Exchange from Equally-weighted Double and Single Diffusion Encodings (REEDS-DE). We test this method on ex vivo neonatal mouse spinal cord - a sample consisting primarily of gray matter - using a low-field, static gradient NMR system. In sum, we highlight critical shortcomings of prevailing DEXSY analysis methods that conflate the effects of restriction and exchange, and suggest a viable experimental approach to disentangle them.

Neural networks for parameter estimation in microstructural MRI: Application to a diffusion-relaxation model of white matter

Specific features of white matter microstructure can be investigated by using biophysical models to interpret relaxation-diffusion MRI brain data. Although more intricate models have the potential to reveal more details of the tissue, they also incur time-consuming parameter estimation that may converge to inaccurate solutions due to a prevalence of local minima in a degenerate fitting landscape. Machine-learning fitting algorithms have been proposed to accelerate the parameter estimation and increase the robustness of the attained estimates. So far, learning-based fitting approaches have been restricted to microstructural models with a reduced number of independent model parameters where dense sets of training data are easy to generate. Moreover, the degree to which machine learning can alleviate the degeneracy problem is poorly understood. For conventional least-squares solvers, it has been shown that degeneracy can be avoided by acquisition with optimized relaxation-diffusion-correlation protocols that include tensor-valued diffusion encoding. Whether machine-learning techniques can offset these acquisition requirements remains to be tested. In this work, we employ artificial neural networks to vastly accelerate the parameter estimation for a recently introduced relaxation-diffusion model of white matter microstructure. We also develop strategies for assessing the accuracy and sensitivity of function fitting networks and use those strategies to explore the impact of the acquisition protocol. The developed learning-based fitting pipelines were tested on relaxation-diffusion data acquired with optimal and sub-optimal acquisition protocols. Networks trained with an optimized protocol were observed to provide accurate parameter estimates within short computational times. Comparing neural networks and least-squares solvers, we found the performance of the former to be less affected by sub-optimal protocols; however, model fitting networks were still susceptible to degeneracy issues and their use could not fully replace a careful design of the acquisition protocol.

Spatiotemporal characterisation of ischaemic lesions in transient stroke animal models using diffusion free water elimination and mapping MRI with echo time dependence

BACKGROUND AND PURPOSE

The excess fluid as a result of vasogenic oedema and the subsequent tissue cavitation obscure the microstructural characterisation of ischaemic tissue by conventional diffusion and relaxometry MRI. They lead to a pseudo-normalisation of the water diffusivity and transverse relaxation time maps in the subacute and chronic phases of stroke. Within the context of diffusion MRI, the free water elimination and mapping method (FWE) with echo time dependence has been proposed as a promising approach to measure the amount of free fluid in brain tissue robustly and to eliminate its biasing effect on other biomarkers. In this longitudinal study of transient middle cerebral artery occlusion (MCAo) in the rat brain, we investigated the use of FWE MRI with echo time dependence for the characterisation of the tissue microstructure and explored the potential of the free water fraction as a novel biomarker of ischaemic tissue condition.

METHODS

Adult rats received a transient MCAo. Diffusion- and transverse relaxation-weighted MRI experiments were performed longitudinally, pre-occlusion and on days 1, 3, 4, 5, 6, 7 and 10 after MCAo on four rats. Histology was performed for non-stroke and 1, 3 and 10 days after MCAo on three different rats at each time point.

RESULTS

The free water fraction was homogeneously increased in the ischaemic cortex one day after stroke. Between three and ten days after stroke, the core of the ischaemic tissue showed a progressive normalisation in the amount of free water, whereas the inner and outer border zones of the ischaemic cortex depicted a large, monotonous increase with time. The specific lesions in brain sections were verified by H&E and immunostaining. The tissue-specific diffusion and relaxometry MRI metrics in the ischaemic cortex were significantly different compared to their conventional counterpart.

CONCLUSIONS

Our results demonstrate that the free water fraction in FWE MRI with echo time dependence is a valuable biomarker, sensitive to the progressive degeneration in ischaemic tissue. We showed that part of the heterogeneity previously observed in conventional parameter maps can be accounted for by a heterogeneous distribution of free water in the tissue. Our results suggest that the temporal evolution of the free fluid fraction map at the core and inner border zone can be associated with the pathological changes linked to the evolution of vasogenic oedema. Namely, the homogeneous increase in free water one day after stroke and its tendency to normalise in the core of the ischaemic cortex starting three days after stroke, followed by a progressive increase in free water at the inner border zone from three to ten days after stroke. Finally, the monotonous increase in free fluid in the outer border zone of the cortex reflects the formation of fluid-filled cysts.

Axon diameter inferences in the human corpus callosum using oscillating gradient spin echo sequences

Previous methods used to infer axon diameter distributions using magnetic resonance imaging (MRI) primarily use single diffusion encoding sequences such as pulsed gradient spin echo (PGSE) and are thus sensitive to axons of diameters >5 μm. We applied oscillating gradient spin echo (OGSE) sequences to study human axons in the 1-2 μm range in the corpus callosum, which include the majority of axons constituting cortical connections. The ActiveAx model was applied to calculate the fitted mean effective diameter for axons (AxD) and was compared with values found using histology. Axon diameters from histological data were calculated using three different datasets; true diameters (minimum diameter), a combination of minimum and maximum diameters, and diameters measured across a consistent diffusion direction. The AxD estimates from MRI were 1.8 ± 0.1 μm to 2.34 ± 0.04 μm with an average of 2.0 ± 0.2 μm for the ActiveAx model. The histology AxD values were 1.43 ± 0.02 μm when using the true minimum axon diameters, 5.52 ± 0.02 μm when using the combination of minimum and maximum axon diameters, and 2.20 ± 0.02 μm when collecting measurements across a consistent diffusion direction. This experiment demonstrates the first known usage of OGSE to calculate axon diameters in the human corpus callosum on a 1-2 μm scale. The importance for the model to account for axonal orientation dispersion is indicated by histological results which more closely match the MRI model results depending on the direction of axon diameter measurements. These initial steps using this non-invasive imaging method can be applied to future methodology to develop in vivo axon diameter measurements in human brain tissue.

Ultrahigh-b diffusion-weighted imaging for quantitative evaluation of myelination in shiverer mouse spinal cord

PURPOSE

To perform a quantitative evaluation of myelination on WT and myelin-deficient (shiverer) mouse spinal cords using ultrahigh-b diffusion-weighted imaging (UHb-DWI).

METHODS

UHb-DWI of ex vivo on spinal cord specimens of two shiverer (C3HeB/FeJ-shiverer, homozygous genotype for MbP_shi ) and six WT (Black Six, C3HeB/FeJ) mice were acquired using 3D multishot diffusion-weighted stimulated-echo EPI, a homemade RF coil, and a small-bore 7T MRI system. Imaging was performed in transaxial plane with 75 × 75 μm² in-plane resolution, 1-mm-slice thickness, and radial DWI using b_max = 42,890 s/mm² . Histological evaluation was performed on upper thoracic sections using optical and transmission electron microscopy. Numerical Monte Carlo simulations (MCSs) of water diffusion were performed to facilitate interpretation of UHb-DWI signal-b curves.

RESULTS

The white matter ultrahigh-b radial DWI (UHb-rDWI) signal-b curves of WT mouse cords behaved biexponentially with high-b diffusion coefficient D_H < 0.020 × 10^-3 mm² /s. However, as expected with less myelination, the signal-b of shiverer mouse cords behaved monoexponentially with significantly greater D_H = 0.162 × 10^-3 , 0.142 × 10^-3 , and 0.164 × 10^-3 mm² /s at anterodorsal, posterodorsal, and lateral columns, respectively. The axial DWI signals of all mouse cords behaved monoexponentially with D = (0.718-1.124) × 10^-3 mm² /s. MCS suggests that these elevated D_H are mainly induced by increased water exchange at the myelin sheath. Microscopic results were consistent with the UHb-rDWI findings.

CONCLUSION

UHb-DWI provides quantitative differences in myelination of spinal cords from myelin-deficit shiverer and WT mice. UHb-DWI may become a powerful tool to evaluate myelination in demyelinating disease models that may translate to human diseases, including multiple sclerosis.

Diffusion MRI tractography for neurosurgery: the basics, current state, technical reliability and challenges

Diffusion magnetic resonance imaging (dMRI) tractography is currently the only imaging technique that allows for non-invasive delineation and visualisation of white matter (WM) tractsin vivo,prompting rapid advances in related fields of brain MRI research in recent years. One of its major clinical applications is for pre-surgical planning and intraoperative image guidance in neurosurgery, where knowledge about the location of WM tracts nearby the surgical target can be helpful to guide surgical resection and optimise post-surgical outcomes. Surgical injuries to these WM tracts can lead to permanent neurological and functional deficits, making the accuracy of tractography reconstructions paramount. The quality of dMRI tractography is influenced by many modifiable factors, ranging from MRI data acquisition through to the post-processing of tractography output, with the potential of error propagation based on decisions made at each and subsequent processing steps. Research over the last 25 years has significantly improved the anatomical accuracy of tractography. An updated review about tractography methodology in the context of neurosurgery is now timely given the thriving research activities in dMRI, to ensure more appropriate applications in the clinical neurosurgical realm. This article aims to review the dMRI physics, and tractography methodologies, highlighting recent advances to provide the key concepts of tractography-informed neurosurgery, with a focus on the general considerations, the current state of practice, technical challenges, potential advances, and future demands to this field.

Temporal Dynamics of Brain White Matter Plasticity in Sighted Subjects during Tactile Braille Learning: A Longitudinal Diffusion Tensor Imaging Study

The white matter (WM) architecture of the human brain changes in response to training, though fine-grained temporal characteristics of training-induced white matter plasticity remain unexplored. We investigated white matter microstructural changes using diffusion tensor imaging at five different time points in 26 sighted female adults during 8 months of training on tactile braille reading. Our results show that training-induced white matter plasticity occurs both within and beyond the trained sensory modality, as reflected by fractional anisotropy (FA) increases in somatosensory and visual cortex, respectively. The observed changes followed distinct time courses, with gradual linear FA increase along the training in the somatosensory cortex and sudden visual cortex cross-modal plasticity occurring after braille input became linguistically meaningful. WM changes observed in these areas returned to baseline after the cessation of learning in line with the supply-demand model of plasticity. These results also indicate that the temporal dynamics of microstructural plasticity in different cortical regions might be modulated by the nature of computational demands. We provide additional evidence that observed FA training-induced changes are behaviorally relevant to tactile reading. Together, these results demonstrate that WM plasticity is a highly dynamic process modulated by the introduction of novel experiences.SIGNIFICANCE STATEMENT Throughout the lifetime the human brain is shaped by various experiences. Training-induced reorganization in white matter (WM) microstructure has been reported, but we know little about its temporal dynamics. To fill this gap, we scanned sighted subjects five times during tactile braille reading training. We observed different dynamics of WM plasticity in the somatosensory and visual cortices implicated in braille reading. The former showed a continuous increase in WM tissue anisotropy along with tactile training, while microstructural changes in the latter were observed only after the participants learned to read braille words. Our results confirm the supply-demand model of brain plasticity and provide evidence that WM reorganization depends on distinct computational demands and functional roles of regions involved in the trained skill.

MESMERISED: Super-accelerating T1 relaxometry and diffusion MRI with STEAM at 7 T for quantitative multi-contrast and diffusion imaging

There is an increasing interest in quantitative imaging of T₁, T₂ and diffusion contrast in the brain due to greater robustness against bias fields and artifacts, as well as better biophysical interpretability in terms of microstructure. However, acquisition time constraints are a challenge, particularly when multiple quantitative contrasts are desired and when extensive sampling of diffusion directions, high b-values or long diffusion times are needed for multi-compartment microstructure modeling. Although ultra-high fields of 7 T and above have desirable properties for many MR modalities, the shortening T₂ and the high specific absorption rate (SAR) of inversion and refocusing pulses bring great challenges to quantitative T₁, T₂ and diffusion imaging. Here, we present the MESMERISED sequence (Multiplexed Echo Shifted Multiband Excited and Recalled Imaging of STEAM Encoded Diffusion). MESMERISED removes the dead time in Stimulated Echo Acquisition Mode (STEAM) imaging by an echo-shifting mechanism. The echo-shift (ES) factor is independent of multiband (MB) acceleration and allows for very high multiplicative (ESxMB) acceleration factors, particularly under moderate and long mixing times. This results in super-acceleration and high time efficiency at 7 T for quantitative T₁ and diffusion imaging, while also retaining the capacity to perform quantitative T₂ and B₁ mapping. We demonstrate the super-acceleration of MESMERISED for whole-brain T₁ relaxometry with total acceleration factors up to 36 at 1.8 mm isotropic resolution, and up to 54 at 1.25 mm resolution qT₁ imaging, corresponding to a 6x and 9x speedup, respectively, compared to MB-only accelerated acquisitions. We then demonstrate highly efficient diffusion MRI with high b-values and long diffusion times in two separate cases. First, we show that super-accelerated multi-shell diffusion acquisitions with 370 whole-brain diffusion volumes over 8 b-value shells up to b = 7000 s/mm² can be generated at 2 mm isotropic in under 8 minutes, a data rate of almost a volume per second, or at 1.8 mm isotropic in under 11 minutes, achieving up to 3.4x speedup compared to MB-only. A comparison of b = 7000 s/mm² MESMERISED against standard MB pulsed gradient spin echo (PGSE) diffusion imaging shows 70% higher SNR efficiency and greater effectiveness in supporting complex diffusion signal modeling. Second, we demonstrate time-efficient sampling of different diffusion times with 1.8 mm isotropic diffusion data acquired at four diffusion times up to 290 ms, which supports both Diffusion Tensor Imaging (DTI) and Diffusion Kurtosis Imaging (DKI) at each diffusion time. Finally, we demonstrate how adding quantitative T₂ and B₁⁺ mapping to super-accelerated qT₁ and diffusion imaging enables efficient quantitative multi-contrast mapping with the same MESMERISED sequence and the same readout train. MESMERISED extends possibilities to efficiently probe T₁, T₂ and diffusion contrast for multi-component modeling of tissue microstructure.

Recent Advances in Parameter Inference for Diffusion MRI Signal Models

In this paper, fundamentals and recent progress for obtaining biological features quantitatively by using diffusion MRI are reviewed. First, a brief description of diffusion MRI history, application, and development was presented. Then, well-known parametric models including diffusion tensor imaging (DTI), diffusional kurtosis imaging (DKI), and neurite orientation dispersion diffusion imaging (NODDI) are introduced with several classifications in various viewpoints with other modeling schemes. In addition, this review covers mathematical generalization and examples of methodologies for the model parameter inference from conventional fitting to recent machine learning approaches, which is called Q-space learning (QSL). Finally, future perspectives on diffusion MRI parameter inference are discussed with the aspects of imaging modeling and simulation.

Magic DIAMOND: Multi-fascicle diffusion compartment imaging with tensor distribution modeling and tensor-valued diffusion encoding

Diffusion tensor imaging provides increased sensitivity to microstructural tissue changes compared to conventional anatomical imaging but also presents limited specificity. To tackle this problem, the DIAMOND model subdivides the voxel content into diffusion compartments and draws from diffusion-weighted data to estimate compartmental non-central matrix-variate Gamma distributions of diffusion tensors. It models each sub-voxel fascicle separately, resolving crossing white-matter pathways and allowing for a fascicle-element (fixel) based analysis of microstructural features. Alternatively, specific features of the intra-voxel diffusion tensor distribution can be selectively measured using tensor-valued diffusion-weighted acquisition schemes. However, the impact of such schemes on estimating brain microstructural features has only been studied in a handful of parametric single-fascicle models. In this work, we derive a general Laplace transform for the non-central matrix-variate Gamma distribution, which enables the extension of DIAMOND to tensor-valued encoded data. We then evaluate this "Magic DIAMOND" model in silico and in vivo on various combinations of tensor-valued encoded data. Assessing uncertainty on parameter estimation via stratified bootstrap, we investigate both voxel-based and fixel-based metrics by carrying out multi-peak tractography. We demonstrate using in silico evaluations that tensor-valued diffusion encoding significantly improves Magic DIAMOND's accuracy. Most importantly, we show in vivo that our estimated metrics can be robustly mapped along tracks across regions of fiber crossing, which opens new perspectives for tractometry and microstructure mapping along specific white-matter tracts.

The sensitivity of diffusion MRI to microstructural properties and experimental factors

Diffusion MRI is a non-invasive technique to study brain microstructure. Differences in the microstructural properties of tissue, including size and anisotropy, can be represented in the signal if the appropriate method of acquisition is used. However, to depict the underlying properties, special care must be taken when designing the acquisition protocol as any changes in the procedure might impact on quantitative measurements. This work reviews state-of-the-art methods for studying brain microstructure using diffusion MRI and their sensitivity to microstructural differences and various experimental factors. Microstructural properties of the tissue at a micrometer scale can be linked to the diffusion signal at a millimeter-scale using modeling. In this paper, we first give an introduction to diffusion MRI and different encoding schemes. Then, signal representation-based methods and multi-compartment models are explained briefly. The sensitivity of the diffusion MRI signal to the microstructural components and the effects of curvedness of axonal trajectories on the diffusion signal are reviewed. Factors that impact on the quality (accuracy and precision) of derived metrics are then reviewed, including the impact of random noise, and variations in the acquisition parameters (i.e., number of sampled signals, b-value and number of acquisition shells). Finally, yet importantly, typical approaches to deal with experimental factors are depicted, including unbiased measures and harmonization. We conclude the review with some future directions and recommendations on this topic.

Studying pre-treatment and ketamine-induced changes in white matter microstructure in the context of ketamine's antidepressant effects

Ketamine is increasingly being used as a therapeutic for treatment-resistant depression (TRD), yet the effects of ketamine on the human brain remain largely unknown. This pilot study employed diffusion magnetic resonance imaging (dMRI) to examine relationships between ketamine treatment and white matter (WM) microstructure, with the aim of increasing the current understanding of ketamine's neural mechanisms of action in humans. Longitudinal dMRI data were acquired from 13 individuals with TRD two hours prior to (pre-infusion), and four hours following (post-infusion), an intravenous ketamine infusion. Free-water imaging was employed to quantify cerebrospinal fluid-corrected mean fractional anisotropy (FA) in 15 WM bundles pre- and post-infusion. Analyses revealed that higher pre-infusion FA in the left cingulum bundle and the left superior longitudinal fasciculus was associated with greater depression symptom improvement 24 h post-ketamine. Moreover, four hours after intravenous administration of ketamine, FA rapidly increased in numerous WM bundles in the brain; this increase was significantly associated with 24 h symptom improvement in select bundles. Overall, the results of this preliminary study suggest that WM properties, as measured by dMRI, may have a potential impact on clinical improvement following ketamine. Ketamine administration additionally appears to be associated with rapid WM diffusivity changes, suggestive of rapid changes in WM microstructure. This study thus points to pre-treatment WM structure as a potential factor associated with ketamine's clinical efficacy, and to post-treatment microstructural changes as a candidate neuroimaging marker of ketamine's cellular mechanisms.

Free-water DTI estimates from single b-value data might seem plausible but must be interpreted with care

PURPOSE

Free-water elimination DTI (FWE-DTI) has been used widely to distinguish increases of free-water partial-volume effects from tissue's diffusion in healthy aging and degenerative diseases. Because the FWE-DTI fitting is only well-posed for multishell acquisitions, a regularized gradient descent (RGD) method was proposed to enable application to single-shell data, more common in the clinic. However, the validity of the RGD method has been poorly assessed. This study aims to quantify the specificity of FWE-DTI procedures on single-shell and multishell data.

METHODS

Different FWE-DTI fitting procedures were tested on an open-source in vivo diffusion data set and single-shell and multishell synthetic signals, including the RGD and standard nonlinear least-squares methods. Single-voxel simulations were carried out to compare initialization approaches. A multivoxel phantom simulation was performed to evaluate the effect of spatial regularization when comparing between methods. To test the algorithms' specificity, phantoms with two different types of lesions were simulated: with altered mean diffusivity or with modified free water.

RESULTS

Plausible parameter maps were obtained with RGD from single-shell in vivo data. The plausibility of these maps was shown to be determined by the initialization. Tests with simulated lesions inserted into the in vivo data revealed that the RGD approach cannot distinguish free water from tissue mean-diffusivity alterations, contrarily to the nonlinear least-squares algorithm.

CONCLUSION

The RGD FWE-DTI method has limited specificity; thus, its results from single-shell data should be carefully interpreted. When possible, multishell acquisitions and the nonlinear least-squares approach should be preferred instead.

Accuracy and precision of statistical descriptors obtained from multidimensional diffusion signal inversion algorithms

In biological tissues, typical MRI voxels comprise multiple microscopic environments, the local organization of which can be captured by microscopic diffusion tensors. The measured diffusion MRI signal can, therefore, be written as the multidimensional Laplace transform of an intravoxel diffusion tensor distribution (DTD). Tensor-valued diffusion encoding schemes have been designed to probe specific features of the DTD, and several algorithms have been introduced to invert such data and estimate statistical descriptors of the DTD, such as the mean diffusivity, the variance of isotropic diffusivities, and the mean squared diffusion anisotropy. However, the accuracy and precision of these estimations have not been assessed systematically and compared across methods. In this article, we perform and compare such estimations in silico for a one-dimensional Gamma fit, a generalized two-term cumulant approach, and two-dimensional and four-dimensional Monte-Carlo-based inversion techniques, using a clinically feasible tensor-valued acquisition scheme. In particular, we compare their performance at different signal-to-noise ratios (SNRs) for voxel contents varying in terms of the aforementioned statistical descriptors, orientational order, and fractions of isotropic and anisotropic components. We find that all inversion techniques share similar precision (except for a lower precision of the two-dimensional Monte Carlo inversion) but differ in terms of accuracy. While the Gamma fit exhibits infinite-SNR biases when the signal deviates strongly from monoexponentiality and is unaffected by orientational order, the generalized cumulant approach shows infinite-SNR biases when this deviation originates from the variance in isotropic diffusivities or from the low orientational order of anisotropic diffusion components. The two-dimensional Monte Carlo inversion shows remarkable accuracy in all systems studied, given that the acquisition scheme possesses enough directions to yield a rotationally invariant powder average. The four-dimensional Monte Carlo inversion presents no infinite-SNR bias, but suffers significantly from noise in the data, while preserving good contrast in most systems investigated.

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

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

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 .

Challenges for biophysical modeling of microstructure

The biophysical modeling efforts in diffusion MRI have grown considerably over the past 25 years. In this review, we dwell on the various challenges along the journey of bringing a biophysical model from initial design to clinical implementation, identifying both hurdles that have been already overcome and outstanding issues. First, we describe the critical initial task of selecting which features of tissue microstructure can be estimated using a model and which acquisition protocol needs to be implemented to make the estimation possible. The model performance should necessarily be tested in realistic numerical simulations and in experimental data - adapting the fitting strategy accordingly, and parameter estimates should be validated against complementary techniques, when/if available. Secondly, the model performance and validity should be explored in pathological conditions, and, if appropriate, dedicated models for pathology should be developed. We build on examples from tumors, ischemia and demyelinating diseases. We then discuss the challenges associated with clinical translation and added value. Finally, we single out four major unresolved challenges that are related to: the availability of a microstructural ground truth, the validation of model parameters which cannot be accessed with complementary techniques, the development of a generalized standard model for any brain region and pathology, and the seamless communication between different parties involved in the development and application of biophysical models of diffusion.

Relating diffusion-weighted magnetic resonance imaging of brain white matter to cognitive processing-speed deficits in schizophrenia

Diffusion tensor imaging (DTI) and diffusion kurtosis imaging (DKI) analyses of diffusion-weighted magnetic resonance imaging (MRI) show that diffusional fractional anisotropy (FA) and kurtosis anisotropy (KA) of water inside brain white matter decrease for schizophrenic patients from that for healthy persons. DTI and DKI are statistical approaches and do not directly point to the underlying neurobiological reasons. In schizophrenia, it is believed that the demyelination of axons-microstructures that constitute the brain white matter-increases lateral diffusion of water and causes defective neural communications, resulting cognitive processing-speed deficits. Here, we use a simple but realistic neurobiological model for brain white matter and solve the Bloch-Torrey equation using numerical finite-element method to find out the underlying reasons of cognitive deficits in schizophrenia. FA and KA are calculated from computationally obtained diffusion-weighted MRI data after a Stejskal-Tanner gradient pulse sequence is applied to a periodic array of tubular axons with circular cross-sections. The calculated FA and KA decrease when the axon walls are more permeable to water, agree with the experimental findings, and correlate with the cognitive processing speeds of healthy persons and schizophrenic patients, and thus, help to understand the underlying reasons of cognitive processing-speed deficits in schizophrenia.

Dedicated diffusion phantoms for the investigation of free water elimination and mapping: insights into the influence of T2 relaxation properties

Conventional diffusion-weighted (DW) MRI suffers from free water contamination due to the finite voxel size. The most common case of free water contamination occurs with cerebrospinal fluid (CSF) in voxels located at the CSF-tissue interface, such as at the ventricles in the human brain. Another case refers to intra-tissue free water as in vasogenic oedema. In order to avoid the bias in diffusion metrics, several multi-compartment methods have been introduced, which explicitly model the presence of a free water compartment. However, fitting multi-compartment models in DW MRI represents a well known ill conditioned problem. Although during the last decade great effort has been devoted to mitigating this estimation problem, the research field remains active. The aim of this work is to introduce the design, characterise the NMR properties and demonstrate the use of two dedicated anisotropic diffusion fibre phantoms, useful for the study of free water elimination (FWE) and mapping models. In particular, we investigate the recently proposed FWE diffusion tensor imaging approach, which takes explicit account of differences in the transverse relaxation times between the free water and tissue compartments.

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.

Towards unconstrained compartment modeling in white matter using diffusion-relaxation MRI with tensor-valued diffusion encoding

PURPOSE

To optimize diffusion-relaxation MRI with tensor-valued diffusion encoding for precise estimation of compartment-specific fractions, diffusivities, and T₂ values within a two-compartment model of white matter, and to explore the approach in vivo.

METHODS

Sampling protocols featuring different b-values (b), b-tensor shapes (b_Δ ), and echo times (TE) were optimized using Cramér-Rao lower bounds (CRLB). Whole-brain data were acquired in children, adults, and elderly with white matter lesions. Compartment fractions, diffusivities, and T₂ values were estimated in a model featuring two microstructural compartments represented by a "stick" and a "zeppelin."

RESULTS

Precise parameter estimates were enabled by sampling protocols featuring seven or more "shells" with unique b/b_Δ /TE-combinations. Acquisition times were approximately 15 minutes. In white matter of adults, the "stick" compartment had a fraction of approximately 0.5 and, compared with the "zeppelin" compartment, featured lower isotropic diffusivities (0.6 vs. 1.3 μm² /ms) but higher T₂ values (85 vs. 65 ms). Children featured lower "stick" fractions (0.4). White matter lesions exhibited high "zeppelin" isotropic diffusivities (1.7 μm² /ms) and T₂ values (150 ms).

CONCLUSIONS

Diffusion-relaxation MRI with tensor-valued diffusion encoding expands the set of microstructure parameters that can be precisely estimated and therefore increases their specificity to biological quantities.

Diffusion-time dependence of diffusional kurtosis in the mouse brain

PURPOSE

To investigate diffusion-time dependency of diffusional kurtosis in the mouse brain using pulsed-gradient spin-echo (PGSE) and oscillating-gradient spin-echo (OGSE) sequences.

METHODS

3D PGSE and OGSE kurtosis tensor data were acquired from ex vivo brains of adult, cuprizone-treated, and age-matched control mice with diffusion-time (t_D ) ~ 20 ms and frequency (f) = 70 Hz, respectively. Further, 2D acquisitions were performed at multiple times/frequencies ranging from f = 140 Hz to t_D = 30 ms with b-values up to 4000 s/mm² . Monte Carlo simulations were used to investigate the coupled effects of varying restriction size and permeability on time/frequency-dependence of kurtosis with both diffusion-encoding schemes. Simulations and experiments were further performed to investigate the effect of varying number of cycles in OGSE waveforms.

RESULTS

Kurtosis and diffusivity maps exhibited significant region-specific changes with diffusion time/frequency across both gray and white matter areas. PGSE- and OGSE-based kurtosis maps showed reversed contrast between gray matter regions in the cerebellar and cerebral cortex. Localized time/frequency-dependent changes in kurtosis tensor metrics were found in the splenium of the corpus callosum in cuprizone-treated mouse brains, corresponding to regional demyelination seen with histological assessment. Monte Carlo simulations showed that kurtosis estimates with pulsed- and oscillating-gradient waveforms differ in their sensitivity to exchange. Both simulations and experiments showed dependence of kurtosis on number of cycles in OGSE waveforms for non-zero permeability.

CONCLUSION

The results show significant time/frequency-dependency of diffusional kurtosis in the mouse brain, which can provide sensitivity to probe intrinsic cellular heterogeneity and pathological alterations in gray and white matter.

Diffusion Kurtosis Imaging maps neural damage in the EAE model of multiple sclerosis

Diffusion kurtosis imaging (DKI) is an imaging modality that yields novel disease biomarkers and in combination with nervous tissue modeling, provides access to microstructural parameters. Recently, DKI and subsequent estimation of microstructural model parameters has been used for assessment of tissue changes in neurodegenerative diseases and associated animal models. In this study, mouse spinal cords from the experimental autoimmune encephalomyelitis (EAE) model of multiple sclerosis (MS) were investigated for the first time using DKI in combination with biophysical modeling to study the relationship between microstructural metrics and degree of animal dysfunction. Thirteen spinal cords were extracted from animals with varied grades of disability and scanned in a high-field MRI scanner along with five control specimen. Diffusion weighted data were acquired together with high resolution T₂* images. Diffusion data were fit to estimate diffusion and kurtosis tensors and white matter modeling parameters, which were all used for subsequent statistical analysis using a linear mixed effects model. T₂* images were used to delineate focal demyelination/inflammation. Our results reveal a strong relationship between disability and measured microstructural parameters in normal appearing white matter and gray matter. Relationships between disability and mean of the kurtosis tensor, radial kurtosis, radial diffusivity were similar to what has been found in other hypomyelinating MS models, and in patients. However, the changes in biophysical modeling parameters and in particular in extra-axonal axial diffusivity were clearly different from previous studies employing other animal models of MS. In conclusion, our data suggest that DKI and microstructural modeling can provide a unique contrast capable of detecting EAE-specific changes correlating with clinical disability.

Associations Between Diffusion Dynamics and Functional Outcome in Acute and Early Subacute Ischemic Stroke

PURPOSE

The current study aimed to investigate the associations between diffusion dynamics of ischemic lesions and clinical functional outcome of acute and early subacute stroke.

MATERIAL AND METHODS

A total of 80 patients with first ever infarcts in the territory of the middle cerebral artery underwent multi-b-values diffusion-weighted imaging and diffusion kurtosis imaging. Multiple diffusion parameters were generated in postprocessing using different diffusion models. Long-term functional outcome was evaluated with modified Rankin scale (mRS) at 6 months post-stroke. Good functional outcome was defined as mRS score ≤ 2 and poor functional outcome was defined as mRS score ≥ 3. Univariate analysis was used to compare the diffusion parameters and clinical features between patients with poor and good functional outcome. Significant parameters were further analyzed for correlations with functional outcome using partial correlation.

RESULTS

In univariate analyses, standard-b-values apparent diffusion coefficient (ADC_st) ratio and fractional anisotropy (FA) ratio of acute stroke, ADC_st ratio and mean kurtosis (MK) ratio of early subacute stroke were statistically different between patients with poor outcome and good outcome (P < 0.05). When the potential confounding factor of lesion volume was controlled, only FA ratio of acute stroke, ADC_st ratio and MK ratio of early subacute stroke remained correlated with the functional outcome (P < 0.05).

CONCLUSION

Diffusion dynamics are correlated with the clinical functional outcome of ischemic stroke. This correlation is independent of the effect of lesion volume and is specific to the time period between symptom onset and imaging. More effort is needed to further investigate the predictive value of diffusion-weighted imaging.

Optimization of data acquisition and analysis for fiber ball imaging

The inverse Funk transform of high angular resolution diffusion imaging (HARDI) data provides an estimate for the fiber orientation density function (fODF) in white matter (WM). Since the inverse Funk transform is a straightforward linear transformation, this technique, referred to as fiber ball imaging (FBI), offers a practical means of calculating the fODF that avoids the need for a response function or nonlinear numerical fitting. Nevertheless, the accuracy of FBI depends on both the choice of b-value and the number of diffusion-encoding directions used to acquire the HARDI data. To inform the design of optimal scan protocols for its implementation, FBI predictions are investigated here with in vivo data from healthy adult volunteers acquired at 3 T for b-values spanning 1000 to 10,000 s/mm², for diffusion-encoding directions varying in number from 30 to 256 and for TE ranging from 90 to 120 ms. Our results suggest b-values above 4000 s/mm² with at least 64 diffusion-encoding directions are adequate to achieve reasonable accuracy with FBI for calculating axon-specific diffusion measures and for performing WM fiber tractography (WMFT).

Searching for the neurite density with diffusion MRI: Challenges for biophysical modeling

In vivo mapping of the neurite density with diffusion MRI (dMRI) is a high but challenging aim. First, it is unknown whether all neurites exhibit completely anisotropic ("stick-like") diffusion. Second, the "density" of tissue components may be confounded by non-diffusion properties such as T2 relaxation. Third, the domain of validity for the estimated parameters to serve as indices of neurite density is incompletely explored. We investigated these challenges by acquiring data with "b-tensor encoding" and multiple echo times in brain regions with low orientation coherence and in white matter lesions. Results showed that microscopic anisotropy from b-tensor data is associated with myelinated axons but not with dendrites. Furthermore, b-tensor data together with data acquired for multiple echo times showed that unbiased density estimates in white matter lesions require data-driven estimates of compartment-specific T2 values. Finally, the "stick" fractions of different biophysical models could generally not serve as neurite density indices across the healthy brain and white matter lesions, where outcomes of comparisons depended on the choice of constraints. In particular, constraining compartment-specific T2 values was ambiguous in the healthy brain and had a large impact on estimated values. In summary, estimating neurite density generally requires accounting for different diffusion and/or T2 properties between axons and dendrites. Constrained "index" parameters could be valid within limited domains that should be delineated by future studies.

Monte Carlo Simulations of Water Exchange Through Myelin Wraps: Implications for Diffusion MRI

Diffusion magnetic resonance imaging (dMRI) yields parameters sensitive to brain tissue microstructure. A structurally important aspect of this microstructure is the myelin wrapping around the axons. This paper investigated the forward problem concerning whether water exchange via the spiraling structure of the myelin can meaningfully contribute to the signal in dMRI. Monte Carlo simulations were performed in a system with intra-axonal, myelin, and extra-axonal compartments. Diffusion in the myelin was simulated as a spiral wrapping the axon, with a custom number of wraps. Exchange (or intra-axonal residence) times were analyzed for various number of wraps and axon diameters. Pulsed gradient sequences were employed to simulate the dMRI signal, which was analyzed using different methods. Diffusional kurtosis imaging analysis yielded the radial diffusivity (RD) and radial kurtosis (RK), while the two-compartment Kärger model yielded estimates the intra-axonal volume fraction ( ν _ic ) and exchange time ( τ ). Results showed that τ was on the sub-second level for geometries with axon diameters below 1.0 μ m and less than eight wraps. Otherwise, exchange was negligible compared to typical experimental durations, with τ of seconds or longer. In situations where exchange influenced the signal, estimates of RK and ν _ic increased with the number of wraps, while RD decreased. τ estimates from simulated signals were in agreement with predicted ones. In conclusion, exchange through spiraling myelin permits sub-second τ for small diameters and low number of wraps. Such conditions may arise in the developing brain or in neurodegenerative disease, and thus the results could aid the interpretation of dMRI studies.

Diffusion MRI in the brain - Theory and concepts

Over the past two decades, diffusion MRI has become an essential tool in neuroimaging investigations. This is due to its sensitivity to the motion of water molecules as they diffuse through the microstructural environment, allowing diffusion MRI to be used as a 'probe' of tissue microstructure. Furthermore, this sensitivity is strongly direction-dependent, notably in brain white matter, due to the alignment of structures that restrict or hinder the motion of water molecules, notably axonal membranes. This provides a means of inferring the orientation of fibres in vivo, and by use of appropriate fibre-tracking algorithms, of delineating the path of white matter tracts in the brain. The ability to perform so-called tractography in humans in vivo non-invasively is unique to diffusion MRI, and is now used in applications such as neurosurgery planning and more broadly within investigations of brain connectomics. This review describes the theory and concepts of diffusion MRI and describes its most important areas of application in the brain, with a strong focus on tractography.

Imaging brain microstructure with diffusion MRI: practicality and applications

This article gives an overview of microstructure imaging of the brain with diffusion MRI and reviews the state of the art. The microstructure-imaging paradigm aims to estimate and map microscopic properties of tissue using a model that links these properties to the voxel scale MR signal. Imaging techniques of this type are just starting to make the transition from the technical research domain to wide application in biomedical studies. We focus here on the practicalities of both implementing such techniques and using them in applications. Specifically, the article summarizes the relevant aspects of brain microanatomy and the range of diffusion-weighted MR measurements that provide sensitivity to them. It then reviews the evolution of mathematical and computational models that relate the diffusion MR signal to brain tissue microstructure, as well as the expanding areas of application. Next we focus on practicalities of designing a working microstructure imaging technique: model selection, experiment design, parameter estimation, validation, and the pipeline of development of this class of technique. The article concludes with some future perspectives on opportunities in this topic and expectations on how the field will evolve in the short-to-medium term.

Review of diffusion MRI studies in chronic white matter diseases

Diffusion MRI studies characterizing the changes in white matter (WM) due to vascular cognitive impairment, which includes all forms of small vessel disease are reviewed. We reviewed the usefulness of diffusion methods in discriminating the affected WM regions and its relation to cognitive impairment. These studies were categorized based on the diffusion MRI techniques used. The most common method was the diffusion tensor imaging, whereas other methods included diffusion weighted imaging, diffusion kurtosis imaging, intravoxel incoherent motion, and studies based on diffusion tractography. The diffusion measures showed correlation with cognitive scores and disease progression, with mean diffusivity being the most robust parameter. Future studies should focus on incorporating multi-compartment and higher order diffusion models, which can handle the presence of multiple and crossing fibers inside a voxel.

Mean diffusivity related to collectivism among university students in Japan

Collectivism is an important factor for coping with stress in one’s social life. To date, no imaging studies have revealed a direct association between collectivism and white matter structure. Collectivism is positively related to independence, harm avoidance, rejection sensitivity, cooperativeness, external locus of control, and self-monitoring and negatively related to need for uniqueness. Accordingly, we hypothesised that the neural structures underpinning collectivism are those that are also involved with its relationship using magnetic resonance imaging (MRI). This study aimed to identify the brain structures associated with collectivism in healthy young adults (n = 797), using regional grey and white matter volume, fractional anisotropy, and mean diffusivity (MD) analyses of MRI data. Scores on the collectivism scale were positively associated with MD values in the bilateral dorsolateral prefrontal cortex, left orbitofrontal cortex, inferior frontal gyrus, right superior temporal gyrus, ventral posterior cingulate cortex, globus pallidus, and calcarine cortex using the threshold-free cluster enhancement method with family-wise errors corrected to P < 0.05 at the whole-brain level. No significant associations between were found collectivism and other measures. Thus, the present findings supported our hypothesis that the neural correlates of collectivism are situated in regions involved in its related factors.