Optimal Experimental Design for Biophysical Modelling in Multidimensional Diffusion MRI

Computational models of biophysical tissue properties have been widely used in diffusion MRI (dMRI) research to elucidate the link between microstructural properties and MR signal formation. For brain tissue, the research community has developed the so-called Standard Model (SM) that has been widely used. However, in clinically applicable acquisition protocols, the inverse problem that recovers the SM parameters from a set of MR diffusion measurements using pairs of short pulsed field gradients was shown to be ill-posed. Multidimensional dMRI was shown to solve this problem by combining linear and planar tensor encoding data. Given sufficient measurements, multiple choices of b-tensor sets provide enough information to estimate all SM parameters. However, in the presence of noise, some sets will provide better results. In this work, we develop a framework for optimal experimental design of multidimensional dMRI sequences applicable to the SM. This framework is based on maximising the determinant of the Fisher information matrix, which is averaged over the full SM parameter space. This averaging provides a fairly objective information metric tailored for the expected signal but that only depends on the acquisition configuration. The optimisation of this metric can be further restricted to any subclass of desirable design constraints like, for instance, hardware-specific constraints. In this work, we compute the optimal acquisitions over the set of all b-tensors with fixed eigenvectors

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

Diffusion MRI for Well-posed and Optimal White Matter Microstructure Characterisation: Beyond Single Diffusion Encoding

The human brain hosts a colossal number of water molecules which are constantly moving due to Brownian motion. Their movement, random by nature, is restricted by the brain tissue walls. Magnetic Resonance Imaging (MRI) provides macroscopic measurements of the diffusion process in a non-invasive manner, i.e. diffusion MRI. Hidden in these measurements lies information about the underlying architecture. The ability to unravel tissue microstructure from the coarse-grained diffusion measurements is extremely valuable since this information is 2-3 orders of magnitude below typical MRI resolution. This makes diffusion MRI sensitive to pathological and developmental processes occurring at the mesoscopic scale, in the order of microns. Accessing this level of detail can lead to clinical biomarkers specific to early stages of neurodegenerative diseases or brain development. Computational models of biophysical tissue properties have been widely used in diffusion MRI research to elucidate the link between microstructural properties and MR signal formation. The potential increase in sensitivity and specificity in detecting brain microstructural changes is their major driving force. However, these models establish complex relationships between biophysical properties and the MR signal, making the inverse problem of recovering model parameters from noisy measurements ill-conditioned with conventional diffusion MRI acquisitions. This thesis explores ways to make diffusion MRI biophysical modelling more robust while maintaining time and hardware requirements that are feasible in clinical conditions. Firstly, we explore theoretically the benefits of incorporating functionally independent measurements, such as double diffusion encoding. Secondly, we propose an optimal experiment design framework that gives us, after exploring the whole multidimensional diffusion MRI measurement space, the acquisition that maximises accuracy and precision in the parameter estimation. Finally, we extract relevant information from histology images that can be used to feed or benchmark diffusion MRI models

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

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Probing brain microstructure with multidimensional diffusion MRI: Encoding, interpretation, and the role of exchange

Diffusion MRI (dMRI) is a non-invasive probe of human brain microstructure. It is a long-standing promise to use dMRI for ‘in vivo histology’ and estimate tissue quantities. However, this faces several challenges. First, the microstructure models used for dMRI data are based on assumptions that may cause erroneous interpretations. Also, probing neurites in gray matter assumes high microscopic diffusion anisotropy in both axons and dendrites, which is not supported by evidence. Furthermore, dMRI data analysis typically ignores diffusional exchange between microscopic environments. This thesis investigates and addresses these challenges using ‘multidimensional’ dMRI techniques that vary additional sequence encoding parameters to obtain new information on the tissue. In Paper I, we optimized an acquisition protocol for filter exchange imaging (FEXI). We found slow rates of diffusional exchange in normal brain tissue. In patients with gliomas and meningiomas, faster exchange was tentatively associated with higher tumor grade. In Paper II, we used tensor-valued diffusion encoding to test the NODDI microstructure model. The NODDI assumptions were contradicted by independent data and parameter estimates were found to be biased in normal brain and in gliomas. The CODIVIDE model combined data acquired with different b-tensor shapes to remove NODDI assumptions and reduce the susceptibility to bias. In Paper III, we used tensor-valued diffusion encoding with multiple echo times to investigate challenges in estimating neurite density. We found that microscopic anisotropy in the brain reflected axons but not dendrites. We could not separate the densities and T2 values of a two-component model in normal brain, but we did detect different component T2 values in white matter lesions. Microstructure models ranked regions from normal brain and white matter lesions inconsistently with respect to neurite density. In Paper IV, we optimized an acquisition protocol for tensor-valued diffusion encoding with multiple echo times. The data allowed removing all assumptions on diffusion and T2 relaxation from a two-component model. This increased the measurable parameters from two to six and reduced their susceptibility to bias. Data from the normal brain showed different component T2 values and contradicted common model assumptions. In Paper V, we used tensor-valued diffusion encoding in malformations of cortical development. Lesions that appeared gray matter-like in T1- and T2-weighted contrasts featured white matter-like regions with high microscopic diffusion anisotropy. We interpreted these regions as myelin-poor white matter with a high axonal content. By primarily reflecting axons and not dendrites or myelin, microscopic anisotropy may differentiate tissue where alterations to myelin confound conventional MRI contrasts. In Paper VI, we used SDE with multiple diffusion times in patients with acute ischemic stroke. Subacute lesions exhibited elevated diffusional exchange that predicted later infarction. MD reduction was partially reversible and did not predict infarction. Diffusional exchange may improve definition of ischemic core and identify additional patients for late revascularization

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.Comment: Invited review, submitted in May 2020 to the Journal of Neuroscience Methods. 46 pages, 9 figures, 35 equation

Diffusion-Weighted Imaging: Recent Advances and Applications

Quantitative diffusion imaging techniques enable the characterization of tissue microstructural properties of the human brain “in vivo”, and are widely used in neuroscientific and clinical contexts. In this review, we present the basic physical principles behind diffusion imaging and provide an overview of the current diffusion techniques, including standard and advanced techniques as well as their main clinical applications. Standard diffusion tensor imaging (DTI) offers sensitivity to changes in microstructure due to diseases and enables the characterization of single fiber distributions within a voxel as well as diffusion anisotropy. Nonetheless, its inability to represent complex intravoxel fiber topologies and the limited biological specificity of its metrics motivated the development of several advanced diffusion MRI techniques. For example, high-angular resolution diffusion imaging (HARDI) techniques enabled the characterization of fiber crossing areas and other complex fiber topologies in a single voxel and supported the development of higher-order signal representations aiming to decompose the diffusion MRI signal into distinct microstructure compartments. Biophysical models, often known by their acronym (e.g., CHARMED, WMTI, NODDI, DBSI, DIAMOND) contributed to capture the diffusion properties from each of such tissue compartments, enabling the computation of voxel-wise maps of axonal density and/or morphology that hold promise as clinically viable biomarkers in several neurological and neuroscientific applications; for example, to quantify tissue alterations due to disease or healthy processes. Current challenges and limitations of state-of-the-art models are discussed, including validation efforts. Finally, novel diffusion encoding approaches (e.g., b-tensor or double diffusion encoding) may increase the biological specificity of diffusion metrics towards intra-voxel diffusion heterogeneity in clinical settings, holding promise in neurological applications

Recommendations and guidelines from the ISMRM Diffusion Study Group for preclinical diffusion MRI: Part 1 -- In vivo small-animal imaging

The value of in vivo preclinical diffusion MRI (dMRI) is substantial. Small-animal dMRI has been used for methodological development and validation, characterizing the biological basis of diffusion phenomena, and comparative anatomy. Many of the influential works in this field were first performed in small animals or ex vivo samples. The steps from animal setup and monitoring, to acquisition, analysis, and interpretation are complex, with many decisions that may ultimately affect what questions can be answered using the data. This work aims to serve as a reference, presenting selected recommendations and guidelines from the diffusion community, on best practices for preclinical dMRI of in vivo animals. In each section, we also highlight areas for which no guidelines exist (and why), and where future work should focus. We first describe the value that small animal imaging adds to the field of dMRI, followed by general considerations and foundational knowledge that must be considered when designing experiments. We briefly describe differences in animal species and disease models and discuss how they are appropriate for different studies. We then give guidelines for in vivo acquisition protocols, including decisions on hardware, animal preparation, imaging sequences and data processing, including pre-processing, model-fitting, and tractography. Finally, we provide an online resource which lists publicly available preclinical dMRI datasets and software packages, to promote responsible and reproducible research. An overarching goal herein is to enhance the rigor and reproducibility of small animal dMRI acquisitions and analyses, and thereby advance biomedical knowledge.Comment: 69 pages, 6 figures, 1 tabl

SANDI: a compartment-based model for non-invasive apparent soma and neurite imaging by diffusion MRI

This work introduces a compartment-based model for apparent soma and neurite density imaging (SANDI) using non-invasive diffusion-weighted MRI (DW-MRI). The existing conjecture in brain microstructure imaging trough DW-MRI presents water diffusion in white (WM) and grey (GM) matter as restricted diffusion in neurites, modelled by infinite cylinders of null radius embedded in the hindered extra-neurite water. The extra-neurite pool in WM corresponds to water in the extra-axonal space, but in GM it combines water in the extra-cellular space with water in soma. While several studies showed that this microstructure model successfully describe DW-MRI data in WM and GM at b<3 ms/{\mum^2}, it has been also shown to fail in GM at high b values (b>>3 ms/{\mum^2}). Here we hypothesize that the unmodelled soma compartment may be responsible for this failure and propose SANDI as a new model of brain microstructure where soma (i.e. cell body of any brain cell type: from neuroglia to neurons) is explicitly included. We assess the effects of size and density of soma on the direction-averaged DW-MRI signal at high b values and the regime of validity of the model using numerical simulations and comparison with experimental data from mouse (bmax = 40 ms/{/mum^2}) and human (bmax = 10 ms/{\mum^2}) brain. We show that SANDI defines new contrasts representing new complementary information on the brain cyto- and myelo-architecture. Indeed, we show for the first-time maps from 25 healthy human subjects of MR soma and neurite signal fractions, that remarkably mirror contrasts of histological images of brain cyto- and myelo-architecture. Although still under validation, SANDI might provide new insight into tissue architecture by introducing a new set of biomarkers of potential great value for biomedical applications and pure neuroscience