Fundamentals of diffusion MRI physics

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

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

In vivo mapping of cellular resolution neuropathology in brain ischemia with diffusion MRI

Noninvasive mapping of cellular pathology can provide critical diagnostic and prognostic information. Recent advances in diffusion magnetic resonance imaging enabled in vivo examination of tissue microstructures well beyond the imaging resolution. Here, we proposed to use diffusion time-dependent diffusion kurtosis imaging (tDKI) to simultaneously assess cellular morphology and transmembrane permeability in hypoxic-ischemic (HI) brain injury. Through numerical simulations and organoid imaging, we demonstrated the feasibility of capturing effective size and permeability changes using tDKI. In vivo MRI of HI-injured mouse brains detected a shift of the tDKI peak to longer diffusion times, suggesting swelling of the cellular processes. Furthermore, we observed a faster decrease of the tDKI tail, reflecting increased transmembrane permeability associated with up-regulated water exchange or necrosis. Such information, unavailable from a single diffusion time, can predict salvageable tissues. Preliminary applications of tDKI in patients with ischemic stroke suggested increased transmembrane permeability in stroke regions, illustrating tDKI's potential for detecting pathological changes in the clinics.

CMRsim-A python package for cardiovascular MR simulations incorporating complex motion and flow

PURPOSE

To present an open-source MR simulation framework that facilitates the incorporation of complex motion and flow for studying cardiovascular MR (CMR) acquisition and reconstruction.

METHODS

CMRsim is a Python package that allows simulation of CMR images using dynamic digital phantoms with complex motion as input. Two simulation paradigms are available, namely, numerical and analytical solutions to the Bloch equations, using a common motion representation. Competitive simulation speeds are achieved using TensorFlow for GPU acceleration. To demonstrate the capability of the package, one introductory and two advanced CMR simulation experiments are presented. The latter showcase phase-contrast imaging of turbulent flow downstream of a stenotic section and cardiac diffusion tensor imaging on a contracting left ventricle. Additionally, extensive documentation and example resources are provided.

RESULTS

The Bloch simulation with turbulent flow using approximately 1.5 million particles and a sequence duration of 710 ms for each of the seven different velocity encodings took a total of 29 min on a NVIDIA Titan RTX GPU. The results show characteristic phase contrast and magnitude modulation present in real data. The analytical simulation of cardiac diffusion tensor imaging with bulk-motion phase sensitivity took approximately 10 s per diffusion-weighted image, including preparation and loading steps. The results exhibit the expected alteration of diffusion metrics due to strain.

CONCLUSION

CMRsim is the first simulation framework that allows one to feasibly incorporate complex motion, including turbulent flow, to systematically study advanced CMR acquisition and reconstruction approaches. The open-source package features modularity and transparency, facilitating maintainability and extensibility in support of reproducible research.

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

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

In vivo Mapping of Cellular Resolution Neuropathology in Brain Ischemia by Diffusion MRI

Non-invasive mapping of cellular pathology can provide critical diagnostic and prognostic information. Recent developments in diffusion MRI have produced new tools for examining tissue microstructure at a level well below the imaging resolution. Here, we report the use of diffusion time ( t )-dependent diffusion kurtosis imaging ( t DKI) to simultaneously assess the morphology and transmembrane permeability of cells and their processes in the context of pathological changes in hypoxic-ischemic brain (HI) injury. Through Monte Carlo simulations and cell culture organoid imaging, we demonstrate feasibility in measuring effective size and permeability changes based on the peak and tail of t DKI curves. In a mouse model of HI, in vivo imaging at 11.7T detects a marked shift of the t DKI peak to longer t in brain edema, suggesting swelling and beading associated with the astrocytic processes and neuronal neurites. Furthermore, we observed a faster decrease of the t DKI tail in injured brain regions, reflecting increased membrane permeability that was associated with upregulated water exchange upon astrocyte activation at acute stage as well as necrosis with disrupted membrane integrity at subacute stage. Such information, unavailable with conventional diffusion MRI at a single t, can predict salvageable tissues. For a proof-of-concept, t DKI at 3T on an ischemic stroke patient suggested increased membrane permeability in the stroke region. This work therefore demonstrates the potential of t DKI for in vivo detection of the pathological changes in microstructural morphology and transmembrane permeability after ischemic injury using a clinically translatable protocol.

Profiling specific cell populations within the inflammatory tumor microenvironment by oscillating-gradient diffusion-weighted MRI

BACKGROUND

The inflammatory tumor microenvironment (TME) is formed by various immune cells, being closely associated with tumorigenesis. Especially, the interaction between tumor-infiltrating T-cells and macrophages has a crucial impact on tumor progression and metastatic spread. The purpose of this study was to investigate whether oscillating-gradient diffusion-weighted MRI (OGSE-DWI) enables a cell size-based discrimination between different cell populations of the TME.

METHODS

Sine-shaped OGSE-DWI was combined with the Imaging Microstructural Parameters Using Limited Spectrally Edited Diffusion (IMPULSED) approach to measure microscale diffusion distances, here relating to cell sizes. The accuracy of IMPULSED-derived cell radii was evaluated using in vitro spheroid models, consisting of either pure cancer cells, macrophages, or T-cells. Subsequently, in vivo experiments aimed to assess changes within the TME and its specific immune cell composition in syngeneic murine breast cancer models with divergent degrees of malignancy (4T1, 67NR) during tumor progression, clodronate liposome-mediated depletion of macrophages, and immune checkpoint inhibitor (ICI) treatment. Ex vivo analysis of IMPULSED-derived cell radii was conducted by immunohistochemical wheat germ agglutinin staining of cell membranes, while intratumoral immune cell composition was analyzed by CD3 and F4/80 co-staining.

RESULTS

OGSE-DWI detected mean cell radii of 8.8±1.3 µm for 4T1, 8.2±1.4 µm for 67NR, 13.0±1.7 for macrophage, and 3.8±1.8 µm for T-cell spheroids. While T-cell infiltration during progression of 4T1 tumors was observed by decreasing mean cell radii from 9.7±1.0 to 5.0±1.5 µm, increasing amount of intratumoral macrophages during progression of 67NR tumors resulted in increasing mean cell radii from 8.9±1.2 to 12.5±1.1 µm. After macrophage depletion, mean cell radii decreased from 6.3±1.7 to 4.4±0.5 µm. T-cell infiltration after ICI treatment was captured by decreasing mean cell radii in both tumor models, with more pronounced effects in the 67NR tumor model.

CONCLUSIONS

OGSE-DWI provides a versatile tool for non-invasive profiling of the inflammatory TME by assessing the dominating cell type T-cells or macrophages.

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.

Transport in the Brain Extracellular Space: Diffusion, but Which Kind?

The mechanisms of transport of substances in the brain parenchyma have been a hot topic in scientific discussion in the past decade. This discussion was triggered by the proposed glymphatic hypothesis, which assumes a directed flow of cerebral fluid within the parenchyma, in contrast to the previous notion that diffusion is the main mechanism. However, when discussing the issue of “diffusion or non-diffusion”, much less attention was given to the question that diffusion itself can have a different character. In our opinion, some of the recently published results do not fit into the traditional understanding of diffusion. In this regard, we outline the relevant new theoretical approaches on transport processes in complex random media such as concepts of diffusive diffusivity and time-dependent homogenization, which expands the understanding of the forms of transport of substances based on diffusion.

Reproducibility of the Standard Model of diffusion in white matter on clinical MRI systems

Estimating intra- and extra-axonal microstructure parameters, such as volume fractions and diffusivities, has been one of the major efforts in brain microstructure imaging with MRI. The Standard Model (SM) of diffusion in white matter has unified various modeling approaches based on impermeable narrow cylinders embedded in locally anisotropic extra-axonal space. However, estimating the SM parameters from a set of conventional diffusion MRI (dMRI) measurements is ill-conditioned. Multidimensional dMRI helps resolve the estimation degeneracies, but there remains a need for clinically feasible acquisitions that yield robust parameter maps. Here we find optimal multidimensional protocols by minimizing the mean-squared error of machine learning-based SM parameter estimates for two 3T scanners with corresponding gradient strengths of 40and80mT/m. We assess intra-scanner and inter-scanner repeatability for 15-minute optimal protocols by scanning 20 healthy volunteers twice on both scanners. The coefficients of variation all SM parameters except free water fraction are ≲10% voxelwise and 1-4% for their region-averaged values. As the achieved SM reproducibility outcomes are similar to those of conventional diffusion tensor imaging, our results enable robust in vivo mapping of white matter microstructure in neuroscience research and in the clinic.

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.

Advanced Diffusion MR Imaging for Multiple Sclerosis in the Brain and Spinal Cord

Diffusion tensor imaging (DTI) has been established its usefulness in evaluating normal-appearing white matter (NAWM) and other lesions that are difficult to evaluate with routine clinical MRI in the evaluation of the brain and spinal cord lesions in multiple sclerosis (MS), a demyelinating disease. With the recent advances in the software and hardware of MRI systems, increasingly complex and sophisticated MRI and analysis methods, such as q-space imaging, diffusional kurtosis imaging, neurite orientation dispersion and density imaging, white matter tract integrity, and multiple diffusion encoding, referred to as advanced diffusion MRI, have been proposed. These are capable of capturing in vivo microstructural changes in the brain and spinal cord in normal and pathological states in greater detail than DTI.

This paper reviews the current status of recent advanced diffusion MRI for assessing MS in vivo as part of an issue celebrating two decades of magnetic resonance in medical sciences (MRMS), an official journal of the Japanese Society of Magnetic Resonance in Medicine.

Anomalous diffusion, aging, and nonergodicity of scaled Brownian motion with fractional Gaussian noise: overview of related experimental observations and models

How does a systematic time-dependence of the diffusion coefficient $D (t)$ affect the ergodic and statistical characteristics of fractional Brownian motion (FBM)? Here, we examine how the behavior of the...

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

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

On the down-sampling of diffusion MRI data along the angular dimension

BACKGROUND

It has been established that the diffusion gradient directions in diffusion MRI should be uniformly distributed in 3D spherical space, so that orientation-dependent diffusion properties (e.g., fractional anisotropy or FA) can be properly quantified. Sometimes the acquired data need to be down-sampled along the angular dimension before computing diffusion properties (e.g., to exclude data points corrupted by motion artifact; to harmonize data obtained with different protocols). It is important to quantitatively assess the impact of data down-sampling on measurement of diffusion properties.

MATERIALS AND METHODS

Here we report 1) a numerical procedure for down-sampling diffusion MRI (e.g., for data harmonization), and 2) a spatial uniformity index of diffusion directions, aiming to predict the quality of the chosen down-sampling schemes (e.g., from data harmonization; or rejection of motion corrupted data points). We quantitatively evaluated human diffusion MRI data, which were down-sampled from 64 or 60 diffusion gradient directions to 30 directions, in terms of their 1) FA value accuracy (using fully-sampled data as the ground truth), 2) FA fitting residuals, and 3) spatial uniformity indices.

RESULTS

Our experimental data show that the proposed spatial uniformity index is correlated with errors in FA obtained from down-sampled diffusion MRI data. The FA fitting residuals that are typically used to assess diffusion MRI quality are not correlated with either FA errors or spatial uniformity index.

CONCLUSIONS

These results suggest that the spatial uniformity index could be more valuable in assessing quality of down-sampled diffusion MRI data, as compared with FA fitting residual measures. We expect that our implemented software procedure should prove valuable for 1) guiding data harmonization for multi-site diffusion MRI studies, and 2) assessing the impact of rejecting motion corrupted data points on the accuracy of diffusion measures.

Microstructural features assessment of different waterlogged wood species by NMR diffusion validated with complementary techniques

Wood is a hygroscopic, multi-scale and anisotropic natural material composed of pores with different size and differently oriented. In particular, archaeologically excavated wood generally is waterlogged wood with very high moisture content (400%-800%) that need to have a rapid investigation at the microstructural level to obtain the best treatment with preservative agents. Time-dependent diffusion coefficient D(t) quantified by Pulse Field Gradient (PFG) Nuclear Magnetic Resonance (NMR) techniques provides useful information about complex porous media, such as the tortuosity (τ) describing pore connectivity and fluid transport through media, the average-pore size, the anisotropic degree (a_n). However, diffusion NMR is intrinsically limited since it is an indirect measure of medium microstructure and relies on inferences from models and estimation of relevant diffusion parameters. Therefore, it is necessary to validate the information obtained from NMR diffusion parameters through complementary investigations. In this work, the structures of five waterlogged wood species were studied by PFG of absorbed water. D(t) and τ of water diffusing along and perpendicular to vessels/tracheids main axes together with relaxation times and a_n were quantified. From these parameters, the pore sizes distribution and the wood microstructure characterization were obtained. Results among wood species were compared, validated and integrated by micro-imaging NMR (μ-MRI), environmental-scanning electron-microscope (ESEM) images, wood dry density and imbibition times measurement of all woods. The work suggests that a_n vs τ rather than the estimated pore size diversifies and characterize the different wood species. As a consequence diffusion-anisotropy vs tortuosity could be an alternative method to characterize and differentiate wood species of waterlogged wood when high resolution images (μ-MRI and ESEM) are not available. Moreover, the combined use of D(t) and micro-MRI expands the scale of dimensions observable by NMR covering all the interesting length scales of wood.

Travelling Waves Approach in a Parabolic Coupled System for Modelling the Behaviour of Substances in a Fuel Tank

The aim of this work was to provide a formulation of a non-linear diffusion model with forced convection in the form of a reaction–absorption system. The model was studied with analytical and numerical approaches in the frame of the parabolic operators theory. In addition, the solutions are applied to a gas interaction phenomenon with the intention of producing an inerted ullage in an Airbus A320 aircraft centre fuel tank. We made use of the travelling wave (TW) solutions approach to study the existence of solutions, stability and the precise evolution of profiles. The application exercise sought to answer a key question for aerospace sciences which can be formulated as the time required to ensure an aircraft fuel tank is safe (inerted) to prevent explosion due to the presence of oxygen in the tank ullage.

DiSpect: Displacement spectrum imaging of flow and tissue perfusion using spin-labeling and stimulated echoes

PURPOSE

We propose a new method, displacement spectrum (DiSpect) imaging, for probing in vivo complex tissue dynamics such as motion, flow, diffusion, and perfusion. Based on stimulated echoes and image phase, our flexible approach enables observations of the spin dynamics over short (milliseconds) to long (seconds) evolution times.

METHODS

The DiSpect method is a Fourier-encoded variant of displacement encoding with stimulated echoes, which encodes bulk displacement of spins that occurs between tagging and imaging in the image phase. However, this method fails to capture partial volume effects as well as blood flow. The DiSpect variant mitigates this by performing multiple scans with increasing displacement-encoding steps. Fourier analysis can then resolve the multidimensional spectrum of displacements that spins exhibit over the mixing time. In addition, repeated imaging following tagging can capture dynamic displacement spectra with increasing mixing times.

RESULTS

We demonstrate properties of DiSpect MRI using flow phantom experiments as well as in vivo brain scans. Specifically, the ability of DiSpect to perform retrospective vessel-selective perfusion imaging at multiple mixing times is highlighted.

CONCLUSION

The DiSpect variant is a new tool in the arsenal of MRI techniques for probing complex tissue dynamics. The flexibility and the rich information it provides open the possibility of alternative ways to quantitatively measure numerous complex spin dynamics, such as flow and perfusion within a single exam.

Technical Basics of Diffusion-Weighted Imaging

Diffusion-weighted images provide a unique contrast that shows the ability to assess tissue structure and condition on a micrometer scale. Notably, these equations are necessary to understand diffusion MR imaging as a theory but not for real imaging, particularly in clinical practice. The diffusion phenomenon can be observed only through MR measurements. One of the emerging fields of diffusion MRI is to probe the tissue microstructure by altering the diffusion time t, the time interval over which spin displacements are sampled. However, the diffusion time is, in a sense, more important than the b-value for diffusion-weighted images and their quantitative metrics.

Sensitivity analysis of effective transverse shear viscoelastic and diffusional properties of myelinated white matter

Motivated by the need to interpret the results from a combined use of in vivo brain Magnetic Resonance Elastography (MRE) and Diffusion Tensor Imaging (DTI), we developed a computational framework to study the sensitivity of single-frequency MRE and DTI metrics to white matter microstructure and cell-level mechanical and diffusional properties. White matter was modeled as a triphasic unidirectional composite, consisting of parallel cylindrical inclusions (axons) surrounded by sheaths (myelin), and embedded in a matrix (glial cells plus extracellular matrix). Only 2D mechanics and diffusion in the transverse plane (perpendicular to the axon direction) was considered, and homogenized (effective) properties were derived for a periodic domain containing a single axon. The numerical solutions of the MRE problem were performed with ABAQUS and by employing a sophisticated boundary-conforming grid generation scheme. Based on the linear viscoelastic response to harmonic shear excitation and steady-state diffusion in the transverse plane, a systematic sensitivity analysis of MRE metrics (effective transverse shear storage and loss moduli) and DTI metric (effective radial diffusivity) was performed for a wide range of microstructural and intrinsic (phase-based) physical properties. The microstructural properties considered were fiber volume fraction, and the myelin sheath/axon diameter ratio. The MRE and DTI metrics are very sensitive to the fiber volume fraction, and the intrinsic viscoelastic moduli of the glial phase. The MRE metrics are nonlinear functions of the fiber volume fraction, but the effective diffusion coefficient varies linearly with it. Finally, the transverse metrics of both MRE and DTI are insensitive to the axon diameter in steady state. Our results are consistent with the limited anisotropic MRE and co-registered DTI measurements, mainly in the corpus callosum, available in the literature. We conclude that isotropic MRE and DTI constitutive models are good approximations for myelinated white matter in the transverse plane. The unidirectional composite model presented here is used for the first time to model harmonic shear stress under MRE-relevant frequency on the cell level. This model can be extended to 3D in order to inform the solution of the inverse problem in MRE, establish the biological basis of MRE metrics, and integrate MRE/DTI with other modalities towards increasing the specificity of neuroimaging.

Feasibility of generalised diffusion kurtosis imaging approach for brain glioma grading

Purpose

An accurate differentiation of brain glioma grade constitutes an important clinical issue. Powerful non-invasive approach based on diffusion MRI has already demonstrated its feasibility in glioma grade stratification. However, the conventional diffusion tensor (DTI) and kurtosis imaging (DKI) demonstrated moderate sensitivity and performance in glioma grading. In the present work, we apply generalised DKI (gDKI) approach in order to assess its diagnostic accuracy and potential application in glioma grading.

Methods

Diffusion scalar metrics were obtained from 50 patients with different glioma grades confirmed by histological tests following biopsy or surgery. All patients were divided into two groups with low- and high-grade gliomas as grade II versus grades III and IV, respectively. For a comparison, trained radiologists segmented the brain tissue into three regions with solid tumour, oedema, and normal appearing white matter. For each region, we estimated the conventional and gDKI metrics including DTI maps.

Results

We found high correlations between DKI and gDKI metrics in high-grade glioma. Further, gDKI metrics enabled introduction of a complementary measure for glioma differentiation based on correlations between the conventional and generalised approaches. Both conventional and generalised DKI metrics showed quantitative maps of tumour heterogeneity and oedema behaviour. gDKI approach demonstrated largely similar sensitivity and specificity in low-high glioma differentiation as in the case of conventional DKI method.

Conclusion

The generalised diffusion kurtosis imaging enables differentiation of low- and high-grade gliomas at the same level as the conventional DKI. Additionally, gDKI exhibited higher sensitivity to tumour heterogeneity and tissue contrast between tumour and healthy tissue and, thus, may contribute as a complementary source of information on tumour differentiation.

Realistic Microstructure Simulator (RMS): Monte Carlo simulations of diffusion in three-dimensional cell segmentations of microscopy images

BACKGROUND

Monte Carlo simulations of diffusion are commonly used as a model validation tool as they are especially suitable for generating the diffusion MRI signal in complicated tissue microgeometries.

NEW METHOD

Here we describe the details of implementing Monte Carlo simulations in three-dimensional (3d) voxelized segmentations of cells in microscopy images. Using the concept of the corner reflector, we largely reduce the computational load of simulating diffusion within and exchange between multiple cells. Precision is further achieved by GPU-based parallel computations.

RESULTS

Our simulation of diffusion in white matter axons segmented from a mouse brain demonstrates its value in validating biophysical models. Furthermore, we provide the theoretical background for implementing a discretized diffusion process, and consider the finite-step effects of the particle-membrane reflection and permeation events, needed for efficient simulation of interactions with irregular boundaries, spatially variable diffusion coefficient, and exchange.

COMPARISON WITH EXISTING METHODS

To our knowledge, this is the first Monte Carlo pipeline for MR signal simulations in a substrate composed of numerous realistic cells, accounting for their permeable and irregularly-shaped membranes.

CONCLUSIONS

The proposed RMS pipeline makes it possible to achieve fast and accurate simulations of diffusion in realistic tissue microgeometry, as well as the interplay with other MR contrasts. Presently, RMS focuses on simulations of diffusion, exchange, and T₁ and T₂ NMR relaxation in static tissues, with a possibility to straightforwardly account for susceptibility-induced T₂^* effects and flow.

Diffusion MRI simulation of realistic neurons with SpinDoctor and the Neuron Module

The diffusion MRI signal arising from neurons can be numerically simulated by solving the Bloch-Torrey partial differential equation. In this paper we present the Neuron Module that we implemented within the Matlab-based diffusion MRI simulation toolbox SpinDoctor. SpinDoctor uses finite element discretization and adaptive time integration to solve the Bloch-Torrey partial differential equation for general diffusion-encoding sequences, at multiple b-values and in multiple diffusion directions. In order to facilitate the diffusion MRI simulation of realistic neurons by the research community, we constructed finite element meshes for a group of 36 pyramidal neurons and a group of 29 spindle neurons whose morphological descriptions were found in the publicly available neuron repository NeuroMorpho.Org. These finite elements meshes range from having 15,163 nodes to 622,553 nodes. We also broke the neurons into the soma and dendrite branches and created finite elements meshes for these cell components. Through the Neuron Module, these neuron and cell components finite element meshes can be seamlessly coupled with the functionalities of SpinDoctor to provide the diffusion MRI signal attributable to spins inside neurons. We make these meshes and the source code of the Neuron Module available to the public as an open-source package. To illustrate some potential uses of the Neuron Module, we show numerical examples of the simulated diffusion MRI signals in multiple diffusion directions from whole neurons as well as from the soma and dendrite branches, and include a comparison of the high b-value behavior between dendrite branches and whole neurons. In addition, we demonstrate that the neuron meshes can be used to perform Monte-Carlo diffusion MRI simulations as well. We show that at equivalent accuracy, if only one gradient direction needs to be simulated, SpinDoctor is faster than a GPU implementation of Monte-Carlo, but if many gradient directions need to be simulated, there is a break-even point when the GPU implementation of Monte-Carlo becomes faster than SpinDoctor. Furthermore, we numerically compute the eigenfunctions and the eigenvalues of the Bloch-Torrey and the Laplace operators on the neuron geometries using a finite elements discretization, in order to give guidance in the choice of the space and time discretization parameters for both finite elements and Monte-Carlo approaches. Finally, we perform a statistical study on the set of 65 neurons to test some candidate biomakers that can potentially indicate the soma size. This preliminary study exemplifies the possible research that can be conducted using the Neuron Module.

The localization regime in a nutshell

High diffusion-sensitizing magnetic field gradients have been more and more often applied nowadays to achieve a better characterization of the microstructure. As the resulting spin-echo signal significantly deviates from the conventional Gaussian form, various models have been employed to interpret these deviations and to relate them with the microstructural properties of a sample. In this paper, we argue that the non-Gaussian behavior of the signal is a generic universal feature of the Bloch-Torrey equation. We provide a simple yet rigorous description of the localization regime emerging at high extended gradients and identify its origin as a symmetry breaking at the reflecting boundary. We compare the consequent non-Gaussian signal decay to other diffusion NMR regimes such as slow-diffusion, motional-narrowing and diffusion-diffraction regimes. We emphasize limitations of conventional perturbative techniques and advocate for non-perturbative approaches which may pave a way to new imaging modalities in this field.

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.

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.

Lattice Boltzmann method for simulation of diffusion magnetic resonance imaging physics in multiphase tissue models

We report an implementation of the lattice Boltzmann method (LBM) to integrate the Bloch-Torrey equation, which describes the evolution of the transverse magnetization vector and the fate of the signal of diffusion magnetic resonance imaging (dMRI). Motivated by the need to interpret dMRI experiments in biological tissues, and to offset the small time-step limitation of classical LBM, a hybrid LBM scheme is introduced and implemented to solve the Bloch-Torrey equation. A membrane boundary condition is presented which is able to accurately represent the effects of thin curvilinear membranes typically found in biological tissues. As implemented, the hybrid LBM scheme accommodates piece-wise uniform transport, dMRI parameters, periodic and mirroring outer boundary conditions, and finite membrane permeabilities on non-boundary-conforming inner boundaries. By comparing with analytical solutions of limiting cases, we demonstrate that the hybrid LBM scheme is more accurate than the classical LBM scheme. The proposed explicit LBM scheme maintains second-order spatial accuracy, stability, and first-order temporal accuracy for a wide range of parameters. The parallel implementation of the hybrid LBM code in a multi-CPU computer system, as well as on GPUs, is straightforward and efficient. Along with offering certain advantages over finite element or Monte Carlo schemes, the proposed hybrid LBM constitutes a flexible scheme that can by easily adapted to model more complex interfacial conditions and physics in heterogeneous multiphase tissue models and to accommodate sophisticated dMRI sequences.

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.

A time-dependent diffusion MRI signature of axon caliber variations and beading

MRI provides a unique non-invasive window into the brain, yet is limited to millimeter resolution, orders of magnitude coarser than cell dimensions. Here, we show that diffusion MRI is sensitive to the micrometer-scale variations in axon caliber or pathological beading, by identifying a signature power-law diffusion time-dependence of the along-fiber diffusion coefficient. We observe this signature in human brain white matter and identify its origins by Monte Carlo simulations in realistic substrates from 3-dimensional electron microscopy of mouse corpus callosum. Simulations reveal that the time-dependence originates from axon caliber variation, rather than from mitochondria or axonal undulations. We report a decreased amplitude of time-dependence in multiple sclerosis lesions, illustrating the potential sensitivity of our method to axonal beading in a plethora of neurodegenerative disorders. This specificity to microstructure offers an exciting possibility of bridging across scales to image cellular-level pathology with a clinically feasible MRI technique.

Quantitative imaging for radiotherapy purposes

Quantitative imaging biomarkers show great potential for use in radiotherapy. Quantitative images based on microscopic tissue properties and tissue function can be used to improve contouring of the radiotherapy targets. Furthermore, quantitative imaging biomarkers might be used to predict treatment response for several treatment regimens and hence be used as a tool for treatment stratification, either to determine which treatment modality is most promising or to determine patient-specific radiation dose. Finally, patient-specific radiation doses can be further tailored to a tissue/voxel specific radiation dose when quantitative imaging is used for dose painting. In this review, published standards, guidelines and recommendations on quantitative imaging assessment using CT, PET and MRI are discussed. Furthermore, critical issues regarding the use of quantitative imaging for radiation oncology purposes and resultant pending research topics are identified.

Time-dependent diffusion MRI as a probe of microstructural changes in a mouse model of Duchenne muscular dystrophy

Dystrophic muscles show a high variability of fibre sizes and altered sarcolemmal integrity, which are typically assessed by histology. Time-dependent diffusion MRI is sensitive to tissue microstructure and its investigation through age-related changes in dystrophic and healthy muscles may help the understanding of the onset and progression of Duchenne muscular dystrophy (DMD). We investigated the capability of time-dependent diffusion MRI to quantify age and disease-related changes in hind-limb muscle microstructure between dystrophic (mdx) and wild-type (WT) mice of three age groups (7.5, 22 and 44 weeks). Diffusion time-dependent apparent diffusion coefficients (ADCs) of the gastrocnemius and tibialis anterior muscles were determined versus age and diffusion-gradient orientation at six diffusion times (Δ; range: 25-350 ms). Mean muscle ADCs were compared between groups and ages, and correlated with T₂ , using Student's t test, one-way analysis of variance and Pearson correlation, respectively. Muscle fibre sizes and sarcolemmal integrity were evaluated by histology and compared with diffusion measurements. Hind-limb muscle ADC showed characteristic restricted diffusion behaviour in both mdx and WT animals with decreasing ADC values at longer Δ. Significant differences in ADC were observed at long Δ values (≥ 250 ms; p < 0.05, comparison between groups; p < 0.01, comparison between ages) with ADC increased by 5-15% in dystrophic muscles, indicative of reduced diffusion restriction. No significant correlation was found between T₂ and ADC. Additionally, muscle fibre size distributions showed higher variability and lower mean fibre size in mdx than WT animals (p < 0.001). The extensive Evans Blue Dye uptake shown in dystrophic muscles revealed substantial sarcolemmal damage, suggesting diffusion measurements as more consistent with altered permeability rather than changes in muscle fibre sizes. This study shows the potential of diffusion MRI to non-invasively discriminate between dystrophic and healthy muscles with enhanced sensitivity when using long Δ.

Motion and eddy current-induced signal dephasing in in vivo cardiac DTI

PURPOSE

To address motion in cardiac DWI, stimulated-echo acquisition mode (STEAM) and second-order motion-compensated spin-echo (SE) sequences have been proposed. Despite applying motion-compensation strategies, residual motion can cause misleading signal attenuation. The purpose of this study is to estimate the motion-induced error in both sequences by analysis of image phase.

METHODS

Diffusion-weighted motion-compensated SE sequences and STEAM imaging was applied in vivo with diffusion encoding along 3 orthogonal directions. A b-value range of 100 to 600 s/mm² and trigger delays of 25%, 50%, and 75% of end systole and middiastole were used. Eddy-current contributions were obtained from phantom measurements. After computation of motion-induced phase maps, the amount of signal dephasing was computed from phase gradients, and the resulting errors in diffusion tensor parameters were calculated.

RESULTS

Motion-induced dephasing from the STEAM sequence showed less dependency on the b-value and no dependency on the heart phase, whereas SE imaging performed best at 75% end systole followed by 50% end systole and middiastole. For a typical experimental setting, errors of 3.3%/3.0% mean diffusivity, 4.9%/4.8% fractional anisotropy, 2.9º/3.2º helix angulation, 0.8º/0.7º transverse angulation, and 9.9º/10.0º sheet angulation (SE/STEAM) were calculated.

CONCLUSION

Image phase contains valuable information regarding uncompensated motion and eddy currents in cardiac DTI. Although the trigger delay window for SE is narrower compared with the STEAM-based approach, imaging in both systole and diastole is feasible and both sequences perform similarly if the trigger delays are selected carefully with SE.

Performance of Diffusion Kurtosis Imaging Versus Diffusion Tensor Imaging in Discriminating Between Benign Tissue, Low and High Gleason Grade Prostate Cancer

RATIONALE AND OBJECTIVES

To investigate the performance of diffusion kurtosis imaging (DKI) and diffusion tensor imaging (DTI) in discriminating benign tissue, low- and high-grade prostate adenocarcinoma (PCa).

MATERIALS AND METHODS

Forty-eight patients with biopsy-proven PCa of different Gleason grade (GG), who provided written informed consent, were enrolled. All subjects underwent 3T DWI examinations by using b values 0, 500, 1000, 1500, 2000, and 2500 s/mm² and six gradient directions. Mean diffusivity, fractional anisotropy (FA), apparent kurtosis (K), apparent kurtosis-derived diffusivity (D), and proxy fractional kurtosis anisotropy (KFA) maps were obtained. Regions of interest were selected in PCa, in the contralateral benign zone, and in the peritumoral area. Histogram analysis was performed by measuring mean, 10th, 25th, and 90th (p90) percentile of the whole-lesion volume. Kruskal-Wallis test with Bonferroni correction was used to assess significant differences between different regions of interest. The correlation between diffusion metrics and GG and between DKI and DTI parameters was evaluated with Pearson's test. ROC curve analysis was carried out to analyze the ability of histogram variables to differentiate low- and high-GG PCa.

RESULTS

All metrics significantly discriminated PCa from benign and from peritumoral tissue (except for K, KFA_p90, and FA). K_p90 showed the highest correlation with GG and the best diagnostic ability (area under the curve = 0.84) in discriminating low- from high-risk PCa.

CONCLUSION

Compared to DTI, DKI provides complementary and additional information about prostate cancer tissue, resulting more sensitive to PCa-derived modifications and more accurate in discriminating low- and high-risk PCa.

Tensor-valued diffusion MRI in under 3 minutes: an initial survey of microscopic anisotropy and tissue heterogeneity in intracranial tumors

PURPOSE

To evaluate the feasibility of a 3-minutes protocol for assessment of the microscopic anisotropy and tissue heterogeneity based on tensor-valued diffusion MRI in a wide range of intracranial tumors.

METHODS

B-tensor encoding was performed in 42 patients with intracranial tumors (gliomas, meningiomas, adenomas, and metastases). Microscopic anisotropy and tissue heterogeneity were evaluated by estimating the anisotropic kurtosis (MK_A ) and isotropic kurtosis (MK_I ), respectively. An extensive imaging protocol was compared with a 3-minutes protocol.

RESULTS

The fast imaging protocol yielded parameters with characteristics in terms of bias and precision similar to the full protocol. Glioblastomas had lower microscopic anisotropy than meningiomas (MK_A = 0.29 ± 0.06 vs. 0.45 ± 0.08, P = 0.003). Metastases had higher tissue heterogeneity (MK_I = 0.57 ± 0.07) than both the glioblastomas (0.44 ± 0.06, P < 0.001) and meningiomas (0.46 ± 0.06, P = 0.03).

CONCLUSION

Evaluation of the microscopic anisotropy and tissue heterogeneity in intracranial tumor patients is feasible in clinically relevant times frames.

Localization regime in diffusion NMR: Theory and experiments

In this work we investigate the emergence of the localization regime for diffusion NMR in various geometries: inside slabs, inside cylinders and outside rods arranged on a square array. At high gradients, the transverse magnetization is strongly attenuated in the bulk, whereas the macroscopic signal is formed by the remaining magnetization localized near boundaries of the sample. As a consequence, the signal is particularly sensitive to the microstructure. The theoretical analysis relies on recent mathematical advances on the study of the Bloch-Torrey equation. Experiments were conducted with hyperpolarized xenon-129 gas in 3D-printed phantoms and show an excellent agreement with numerical simulations and theoretical predictions. Our mathematical arguments and experimental evidence indicate that the localization regime with a stretched-exponential decay of the macroscopic signal is a generic feature of diffusion NMR that can be observed at moderately high gradients in most NMR scanners.

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.

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.

Motion-Induced Signal Loss in In Vivo Cardiac Diffusion-Weighted Imaging

LEVEL OF EVIDENCE

5 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2020;51:319-320.

Effects of nongaussian diffusion on "isotropic diffusion" measurements: An ex-vivo microimaging and simulation study

Designing novel diffusion-weighted pulse sequences to probe tissue microstructure beyond the conventional Stejskal-Tanner family is currently of broad interest. One such technique, multidimensional diffusion MRI, has been recently proposed to afford model-free decomposition of diffusion signal kurtosis into terms originating from either ensemble variance of isotropic diffusivity or microscopic diffusion anisotropy. This ability rests on the assumption that diffusion can be described as a sum of multiple Gaussian compartments, but this is often not strictly fulfilled. The effects of nongaussian diffusion on single shot isotropic diffusion sequences were first considered in detail by de Swiet and Mitra in 1996. They showed theoretically that anisotropic compartments lead to anisotropic time dependence of the diffusion tensors, which causes the measured isotropic diffusivity to depend on gradient frame orientation. Here we show how such deviations from the multiple Gaussian compartments assumption conflates orientation dispersion with ensemble variance in isotropic diffusivity. Second, we consider additional contributions to the apparent variance in isotropic diffusivity arising due to intracompartmental kurtosis. These will likewise depend on gradient frame orientation. We illustrate the potential importance of these confounds with analytical expressions, numerical simulations in simple model geometries, and microimaging experiments in fixed spinal cord using isotropic diffusion encoding waveforms with 7.5 ms duration and 3000 mT/m maximum amplitude.

Age-related microstructural and physiological changes in normal brain measured by MRI γ-metrics derived from anomalous diffusion signal representation

Nowadays, increasing longevity associated with declining cerebral nervous system functions, suggests the need for continued development of new imaging contrast mechanisms to support the differential diagnosis of age-related decline. In our previous papers, we developed a new imaging contrast metrics derived from anomalous diffusion signal representation and obtained from diffusion-weighted (DW) data collected by varying diffusion gradient strengths. Recently, we highlighted that the new metrics, named γ-metrics, depended on the local inhomogeneity due to differences in magnetic susceptibility between tissues and diffusion compartments in young healthy subjects, thus providing information about myelin orientation and iron content within cerebral regions. The major structural modifications occurring in brain aging are myelinated fibers damage in nerve fibers and iron accumulation in gray matter nuclei. Therefore, we investigated the potential of γ-metrics in relation to other conventional diffusion metrics such as DTI, DKI and NODDI in detecting age-related structural changes in white matter (WM) and subcortical gray matter (scGM). DW-images were acquired in 32 healthy subjects, adults and elderly (age range 20-77 years) using 3.0T and 12 b-values up to 5000 s/mm². Association between diffusion metrics and subjects' age was assessed using linear regression. A decline in mean γ (Mγ) in the scGM and a complementary increase in radial γ (γ_⊥) in frontal WM, genu of corpus callosum and anterior corona radiata with advancing age were found. We suggested that the increase in γ⊥ might reflect declined myelin density, and Mγ decrease might mirror iron accumulation. An increase in D_// and a decrease in the orientation dispersion index (ODI) were associated with axonal loss in the pyramidal tracts, while their inverted trends within the thalamus were thought to be linked to reduced architectural complexity of nerve fibers. γ-metrics together with conventional diffusion-metrics can more comprehensively characterize the complex mechanisms underlining age-related changes than conventional diffusion techniques alone.

Evaluation of the accuracy and precision of the diffusion parameter EStImation with Gibbs and NoisE removal pipeline

This work evaluates the accuracy and precision of the Diffusion parameter EStImation with Gibbs and NoisE Removal (DESIGNER) pipeline, developed to identify and minimize common sources of methodological variability including: thermal noise, Gibbs ringing artifacts, Rician bias, EPI and eddy current induced spatial distortions, and motion-related artifacts. Following this processing pipeline, iterative parameter estimation techniques were used to derive diffusion parameters of interest based on the diffusion tensor and kurtosis tensor. We evaluated accuracy using a software phantom based on 36 diffusion datasets from the Human Connectome project and tested the precision by analyzing data from 30 healthy volunteers scanned three times within one week. Preprocessing with both DESIGNER or a standard pipeline based on smoothing (instead of noise removal) improved parameter precision by up to a factor of 2 compared to preprocessing with motion correction alone. When evaluating accuracy, we report average decreases in bias (deviation from simulated parameters) over all included regions for fractional anisotropy, mean diffusivity, mean kurtosis, and axonal water fraction of 9.7%, 8.7%, 4.2%, and 7.6% using DESIGNER compared to the standard pipeline, demonstrating that preprocessing with DESIGNER improves accuracy compared to other processing methods.

Isotropically weighted intravoxel incoherent motion brain imaging at 7T

Perfusion magnetic resonance imaging (MRI) is a promising non-invasive technique providing insights regarding the brain's microvascular architecture in vivo. The scalar perfusion metrics can be used for quantitative diagnostics of various brain abnormalities, in particular, in the stroke cases and tumours. However, conventional MRI-based perfusion approaches such as dynamic contrast-enhanced perfusion imaging or arterial spin labelling have a few weaknesses, for instance, contrast agent deposition, low signal-to-noise ratio, limited temporal and spatial resolution, and specific absorption rate constraints. As an alternative, the intravoxel incoherent motion (IVIM) approach exploits an extension of diffusion MRI in order to estimate perfusion parameters in the human brain. Application of IVIM imaging at ultra-high field MRI might employ the advantage of a higher signal-to-noise ratio, and thereby the use of higher spatial and temporal resolutions. In the present work, we demonstrate an application of recently developed isotropic diffusion weighted sequences to the evaluation of IVIM parameters at an ultra-high 7T field. The used sequence exhibits high immunity to image degrading factors and allows one to acquire the data in a fast and efficient way. Utilising the bi-exponential fitting model of the signal attenuation, we performed an extensive analysis of the IVIM scalar metrics obtained by a isotropic diffusion weighted sequence in vivo and compared results with a conventional pulsed gradient sequence at 7T. In order to evaluate a possible metric bias originating from blood flows, we additionally used a truncated b-value protocol (b-values from 100 to 200 s/mm² with the step 20 s/mm²) accompanied to the full range (b-values from 0 to 200 s/mm²). The IVIM scalar metrics have been assessed and analysed together with a large and middle vessel density atlas of the human brain. We found that the diffusion coefficients and perfusion fractions of the voxels consisting of large and middle vessels have higher values in contrast to other tissues. Additionally, we did not find a strong dependence of the IVIM metrics on the density values of the vessel atlas. Perspectives and limitations of the developed isotropic diffusion weighted perfusion are presented and discussed.

Transverse NMR relaxation in biological tissues

Transverse NMR relaxation is a fundamental physical phenomenon underpinning a wide range of MRI-based techniques, essential for non-invasive studies in biology, physiology and neuroscience, as well as in diagnostic imaging. Biophysically, transverse relaxation originates from a number of distinct scales - molecular (nanometers), cellular (micrometers), and macroscopic (millimeter-level MRI resolution). Here we review the contributions to the observed relaxation from each of these scales, with the main focus on the cellular level of tissue organization, commensurate with the diffusion length of spin-carrying molecules. We discuss how the interplay between diffusion and spin dephasing in a spatially heterogeneous tissue environment leads to a non-monoexponential time-dependent transverse relaxation signal that contains important biophysical information about tissue microstructure.

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.

The Kärger vs bi-exponential model: Theoretical insights and experimental validations

We revise three common models accounting for water exchange in pulsed-gradient spin-echo measurements: a bi-exponential model with time-dependent water fractions, the Kärger model, and a modified Kärger model designed for restricted diffusion, e.g. inside cells. The three models are compared and applied to experimental data from yeast cell suspensions. The Kärger model and the modified Kärger model yield very close results and accurately fit the data. The bi-exponential model, although less rigorous, has a natural physical interpretation and suggests a new experimental modality to estimate the water exchange time.