Optimising time-varying gradient orientation for microstructure sensitivity in diffusion-weighted MR

A review on investigation of the basic contrast mechanism underlying multidimensional diffusion MRI in assessment of neurological disorders

INTRODUCTION

Multidimensional diffusion MRI (MDD MRI) is a novel diffusion technique that uses advanced gradient waveforms for microstructural tissue characterization to provide information about average rate, anisotropy and orientation of the diffusion and to disentangle the signal fraction from specific cell types i.e., elongated cells, isotropic cells and free water.

AIM

To review the diagnostic potential of MDD MRI in the clinical setting for microstructural tissue characterization in patients with neurological disorders to aid in patient care and treatment.

METHOD

A scoping review on the clinical applications of MDD MRI was conducted from original articles published in PubMed and Scopus from 2015 to 2021 using the keywords "Multidimensional diffusion MRI" OR "diffusion tensor distribution" OR "Tensor-Valued Diffusion" OR "b-tensor encoding" OR "microscopic diffusion anisotropy" OR "microscopic anisotropy" OR "microscopic fractional anisotropy" OR "double diffusion encoding" OR "triple diffusion encoding" OR "double pulsed field gradients" OR "double wave vector" OR "correlation tensor imaging" AND "brain" OR "axons".

RESULTS

Initially 145 articles were screened and after applying inclusion and exclusion criteria, nine articles were included in the final analysis. In most of these studies, microscopic diffusion anisotropy within the lesion showed deviation from the normal-appearing tissue.

CONCLUSION

Multidimensional diffusion MRI can provide better quantification and visualization of tissue microstructure than conventional diffusion MRI and can be used in the clinical setting for diagnosis of neurological disorders.

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.

Task-driven assessment of experimental designs in diffusion MRI: A computational framework

This paper proposes a task-driven computational framework for assessing diffusion MRI experimental designs which, rather than relying on parameter-estimation metrics, directly measures quantitative task performance. Traditional computational experimental design (CED) methods may be ill-suited to experimental tasks, such as clinical classification, where outcome does not depend on parameter-estimation accuracy or precision alone. Current assessment metrics evaluate experiments' ability to faithfully recover microstructural parameters rather than their task performance. The method we propose addresses this shortcoming. For a given MRI experimental design (protocol, parameter-estimation method, model, etc.), experiments are simulated start-to-finish and task performance is computed from receiver operating characteristic (ROC) curves and associated summary metrics (e.g. area under the curve (AUC)). Two experiments were performed: first, a validation of the pipeline's task performance predictions against clinical results, comparing in-silico predictions to real-world ROC/AUC; and second, a demonstration of the pipeline's advantages over traditional CED approaches, using two simulated clinical classification tasks. Comparison with clinical datasets validates our method's predictions of (a) the qualitative form of ROC curves, (b) the relative task performance of different experimental designs, and (c) the absolute performance (AUC) of each experimental design. Furthermore, we show that our method outperforms traditional task-agnostic assessment methods, enabling improved, more useful experimental design. Our pipeline produces accurate, quantitative predictions of real-world task performance. Compared to current approaches, such task-driven assessment is more likely to identify experimental designs that perform well in practice. Our method is not limited to diffusion MRI; the pipeline generalises to any task-based quantitative MRI application, and provides the foundation for developing future task-driven end-to end CED frameworks.

Gradient waveform design for tensor-valued encoding in diffusion MRI

Diffusion encoding along multiple spatial directions per signal acquisition can be described in terms of a b-tensor. The benefit of tensor-valued diffusion encoding is that it unlocks the 'shape of the b-tensor' as a new encoding dimension. By modulating the b-tensor shape, we can control the sensitivity to microscopic diffusion anisotropy which can be used as a contrast mechanism; a feature that is inaccessible by conventional diffusion encoding. Since imaging methods based on tensor-valued diffusion encoding are finding an increasing number of applications we are prompted to highlight the challenge of designing the optimal gradient waveforms for any given application. In this review, we first establish the basic design objectives in creating field gradient waveforms for tensor-valued diffusion MRI. We also survey additional design considerations related to limitations imposed by hardware and physiology, potential confounding effects that cannot be captured by the b-tensor, and artifacts related to the diffusion encoding waveform. Throughout, we discuss the expected compromises and tradeoffs with an aim to establish a more complete understanding of gradient waveform design and its impact on accurate measurements and interpretations of data.

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.

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.

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

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

Anisotropic diffusion phantoms based on microcapillaries

Diffusion MRI is an efficient and widely used technique for the investigation of tissue structure and organisation in vivo. Multiple phenomenological and biophysical diffusion models are intensively exploited for the analysis of the diffusion experiments. However, the verification of the applied diffusion models remains challenging. In order to provide a "gold standard" and to assess the accuracy of the derived parameters and the limitations of the diffusion models, anisotropic diffusion phantoms with well known architecture are demanded. In the present work we built four anisotropic diffusion phantoms consisting of hollow microcapillaries with very small inner diameters of 5, 10 and 20μm and outer diameters of 90 and 150μm. For testing the suitability of these phantoms, we performed diffusion measurements on all of them and evaluated the resulting data with a set of popular diffusion models, such as diffusion tensor and diffusion kurtosis imaging, a two compartment model with intra- and extra-capillary water spaces using bi-exponential fitting, and time-dependent diffusion coefficients in Mitra's limit. The perspectives and limitations of these diffusion phantoms are presented and discussed.

Q-space trajectory imaging for multidimensional diffusion MRI of the human brain

This work describes a new diffusion MR framework for imaging and modeling of microstructure that we call q-space trajectory imaging (QTI). The QTI framework consists of two parts: encoding and modeling. First we propose q-space trajectory encoding, which uses time-varying gradients to probe a trajectory in q-space, in contrast to traditional pulsed field gradient sequences that attempt to probe a point in q-space. Then we propose a microstructure model, the diffusion tensor distribution (DTD) model, which takes advantage of additional information provided by QTI to estimate a distributional model over diffusion tensors. We show that the QTI framework enables microstructure modeling that is not possible with the traditional pulsed gradient encoding as introduced by Stejskal and Tanner. In our analysis of QTI, we find that the well-known scalar b-value naturally extends to a tensor-valued entity, i.e., a diffusion measurement tensor, which we call the b-tensor. We show that b-tensors of rank 2 or 3 enable estimation of the mean and covariance of the DTD model in terms of a second order tensor (the diffusion tensor) and a fourth order tensor. The QTI framework has been designed to improve discrimination of the sizes, shapes, and orientations of diffusion microenvironments within tissue. We derive rotationally invariant scalar quantities describing intuitive microstructural features including size, shape, and orientation coherence measures. To demonstrate the feasibility of QTI on a clinical scanner, we performed a small pilot study comparing a group of five healthy controls with five patients with schizophrenia. The parameter maps derived from QTI were compared between the groups, and 9 out of the 14 parameters investigated showed differences between groups. The ability to measure and model the distribution of diffusion tensors, rather than a quantity that has already been averaged within a voxel, has the potential to provide a powerful paradigm for the study of complex tissue architecture.

Model-based estimation of microscopic anisotropy using diffusion MRI: a simulation study

Non-invasive estimation of cell size and shape is a key challenge in diffusion MRI. This article presents a model-based approach that provides independent estimates of pore size and eccentricity from diffusion MRI data. The technique uses a geometric model of finite cylinders with gamma-distributed radii to represent pores of various sizes and elongations. We consider both macroscopically isotropic substrates and substrates of semi-coherently oriented anisotropic pores and we use Monte Carlo simulations to generate synthetic data. We compare the sensitivity of single and double diffusion encoding (SDE and DDE) sequences to the size distribution and eccentricity, and further analyse different protocols of DDE sequences with parallel and/or perpendicular pairs of gradients. We show that explicitly accounting for size distribution is necessary for accurate microstructural parameter estimates, and a model that assumes a single size yields biased eccentricity values. We also find that SDE sequences support estimates, although DDE sequences with mixed parallel and perpendicular gradients enhance accuracy. In the case of macroscopically anisotropic substrates, this model-based approach can be extended to a rotationally invariant framework to provide features of pore shape (specifically eccentricity) in the presence of size distribution and orientation dispersion.

A parametric finite element solution of the generalised Bloch-Torrey equation for arbitrary domains

Nuclear magnetic resonance (NMR) has proven of enormous value in the investigation of porous media. Its use allows to study pore size distributions, tortuosity, and permeability as a function of the relaxation time, diffusivity, and flow. This information plays an important role in plenty of applications, ranging from oil industry to medical diagnosis. A complete NMR analysis involves the solution of the Bloch-Torrey (BT) equation. However, solving this equation analytically becomes intractable for all but the simplest geometries. We present an efficient numerical framework for solving the complete BT equation in arbitrarily complex domains. In addition to the standard BT equation, the generalised BT formulation takes into account the flow and relaxation terms, allowing a better representation of the phenomena under scope. The presented framework is flexible enough to deal parametrically with any order of convergence in the spatial domain. The major advantage of such approach is to allow both faster computations and sensitivity analyses over realistic geometries. Moreover, we developed a second-order implicit scheme for the temporal discretisation with similar computational demands as the existing explicit methods. This represents a huge step forward for obtaining reliable results with few iterations. Comparisons with analytical solutions and real data show the flexibility and accuracy of the proposed methodology.

PGSE, OGSE, and sensitivity to axon diameter in diffusion MRI: Insight from a simulation study

Purpose

To identify optimal pulsed gradient spin‐echo (PGSE) and oscillating gradient spin‐echo (OGSE) sequence settings for maximizing sensitivity to axon diameter in idealized and practical conditions.

Methods

Simulations on a simple two‐compartment white matter model (with nonpermeable cylinders) are used to investigate a wide space of clinically plausible PGSE and OGSE sequence parameters with trapezoidal diffusion gradient waveforms. Signal sensitivity is measured as a derivative of the signal with respect to axon diameter. Models of parallel and dispersed fibers are investigated separately to represent idealized and practical conditions.

Results

Simulations show that, for the simple case of gradients perfectly perpendicular to straight parallel fibers, PGSE always gives maximum sensitivity. However, in real‐world scenarios where fibers have unknown and dispersed orientation, low‐frequency OGSE provides higher sensitivity. Maximum sensitivity results show that on current clinical scanners (G_max = 60 mT/m, signal to noise ratio (SNR) = 20) axon diameters below 6 µm are indistinguishable from zero. Scanners with stronger gradient systems such as the Massachusetts General Hospital (MGH) Connectom scanner (G_max = 300 mT/m) can extend this sensitivity limit down to 2–3 µm, probing a much greater proportion of the underlying axon diameter distribution.

Conclusion

Low‐frequency OGSE provides additional sensitivity to PGSE in practical situations. OGSE is particularly advantageous for systems with high performance gradients. Magn Reson Med 75:688–700, 2016. © 2015 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

The impact of gradient strength on in vivo diffusion MRI estimates of axon diameter

Diffusion magnetic resonance imaging (MRI) methods for axon diameter mapping benefit from higher maximum gradient strengths than are currently available on commercial human scanners. Using a dedicated high-gradient 3T human MRI scanner with a maximum gradient strength of 300 mT/m, we systematically studied the effect of gradient strength on in vivo axon diameter and density estimates in the human corpus callosum. Pulsed gradient spin echo experiments were performed in a single scan session lasting approximately 2h on each of three human subjects. The data were then divided into subsets with maximum gradient strengths of 77, 145, 212, and 293 mT/m and diffusion times encompassing short (16 and 25 ms) and long (60 and 94 ms) diffusion time regimes. A three-compartment model of intra-axonal diffusion, extra-axonal diffusion, and free diffusion in cerebrospinal fluid was fitted to the data using a Markov chain Monte Carlo approach. For the acquisition parameters, model, and fitting routine used in our study, it was found that higher maximum gradient strengths decreased the mean axon diameter estimates by two to three fold and decreased the uncertainty in axon diameter estimates by more than half across the corpus callosum. The exclusive use of longer diffusion times resulted in axon diameter estimates that were up to two times larger than those obtained with shorter diffusion times. Axon diameter and density maps appeared less noisy and showed improved contrast between different regions of the corpus callosum with higher maximum gradient strength. Known differences in axon diameter and density between the genu, body, and splenium of the corpus callosum were preserved and became more reproducible at higher maximum gradient strengths. Our results suggest that an optimal q-space sampling scheme for estimating in vivo axon diameters should incorporate the highest possible gradient strength. The improvement in axon diameter and density estimates that we demonstrate from increasing maximum gradient strength will inform protocol development and encourage the adoption of higher maximum gradient strengths for use in commercial human scanners.

A model for extra-axonal diffusion spectra with frequency-dependent restriction

PURPOSE

In the brain, there is growing interest in using the temporal diffusion spectrum to characterize axonal geometry in white matter because of the potential to be more sensitive to small pores compared to conventional time-dependent diffusion. However, analytical expressions for the diffusion spectrum of particles have only been derived for simple, restricting geometries such as cylinders, which are often used as a model for intra-axonal diffusion. The extra-axonal space is more complex, but the diffusion spectrum has largely not been modeled. We propose a model for the extra-axonal space, which can be used for interpretation of experimental data.

THEORY AND METHODS

An empirical model describing the extra-axonal space diffusion spectrum was compared with simulated spectra. Spectra were simulated using Monte Carlo methods for idealized, regularly and randomly packed axons over a wide range of packing densities and spatial scales. The model parameters are related to the microstructural properties of tortuosity, axonal radius, and separation for regularly packed axons and pore size for randomly packed axons.

RESULTS

Forward model predictions closely matched simulations. The model fitted the simulated spectra well and accurately estimated microstructural properties.

CONCLUSIONS

This simple model provides expressions that relate the diffusion spectrum to biologically relevant microstructural properties.

A pulse sequence optimization method for assessment of nucleus size in q-space analysis of idealized cells

To adjust pulse sequences that produce diffusion-weighted MRI signals for increased sensitivity to nucleus size, the impulse-propagator method in q-space is applied to a spherical geometry that would describe each member of a collection of cells and their nuclei, with several possible representations of the extracellular space. The method is extended to allow propagation between nucleus, cytoplasm, and extracellular space through semi-permeable membranes, using an approximate adjustment of intra-compartment propagators. Diffraction patterns are first calculated for the three compartments separately, for PGSE and OGSE pulse sequences, and verified by comparison with Monte Carlo simulations. The detailed patterns from the separate compartments determine the q value for maximum contrast in the total signal between large and small nuclei, an optimization that is not accurate in a Gaussian Phase Distribution (GPD) approximation. Then diffraction patterns are calculated for the case of linked compartments with semi-permeable membranes. The treatment of permeability adequately estimates pulse-sequence parameters for maximum contrast in calculated signal as nucleus size varies.

Measurement tensors in diffusion MRI: generalizing the concept of diffusion encoding

In traditional diffusion MRI, short pulsed field gradients (PFG) are used for the diffusion encoding. The standard Stejskal-Tanner sequence uses one single pair of such gradients, known as single-PFG (sPFG). In this work we describe how trajectories in q-space can be used for diffusion encoding. We discuss how such encoding enables the extension of the well-known scalar b-value to a tensor-valued entity we call the diffusion measurement tensor. The new measurements contain information about higher order diffusion propagator covariances not present in sPFG. As an example analysis, we use this new information to estimate a Gaussian distribution over diffusion tensors in each voxel, described by its mean (a diffusion tensor) and its covariance (a 4th order tensor).

Gaussian phase distribution approximations for oscillating gradient spin echo diffusion MRI

Oscillating gradients provide an optimal probe of small pore sizes in diffusion MRI. While sinusoidal oscillations have been popular for some time, recent work suggests additional benefits of square or trapezoidal oscillating waveforms. This paper presents analytical expressions of the free and restricted diffusion signal for trapezoidal and square oscillating gradient spin echo (OGSE) sequences using the Gaussian phase distribution (GPD) approximation and generalises existing similar expressions for sinusoidal OGSE. Accurate analytical models are necessary for exploitation of these pulse sequences in imaging studies, as they allow model fitting and parameter estimation in reasonable computation times. We evaluate the accuracy of the approximation against synthesised data from the Monte Carlo (MC) diffusion simulator in Camino and Callaghan's matrix method and we show that the accuracy of the approximation is within a few percent of the signal, while providing several orders of magnitude faster computation. Moreover, since the expressions for trapezoidal wave are complex, we test sine and square wave approximations to the trapezoidal OGSE signal. The best approximations depend on the gradient amplitude and the oscillation frequency and are accurate to within a few percent. Finally, we explore broader applications of trapezoidal OGSE, in particular for non-model based applications, such as apparent diffusion coefficient estimation, where only sinusoidal waveforms have been considered previously. We show that with the right apodisation, trapezoidal waves also have benefits by virtue of the higher diffusion weighting they provide compared to sinusoidal gradients.