Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI

We develop a general analytical and numerical framework for estimating intra- and extra-neurite water fractions and diffusion coefficients, as well as neurite orientational dispersion, in each imaging voxel. By employing a set of rotational invariants and their expansion in the powers of diffusion weighting, we analytically uncover the nontrivial topology of the parameter estimation landscape, showing that multiple branches of parameters describe the measurement almost equally well, with only one of them corresponding to the biophysical reality. A comprehensive acquisition shows that the branch choice varies across the brain. Our framework reveals hidden degeneracies in MRI parameter estimation for neuronal tissue, provides microstructural and orientational maps in the whole brain without constraints or priors, and connects modern biophysical modeling with clinical MRI.Comment: 25 pages, 12 figures, elsarticle two-colum

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.Comment: 26 pages, 9 figures. Appearing in J. Magn. Reso

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

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

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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'

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

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

Double Diffusion Encoding Prevents Degeneracy in Parameter Estimation of Biophysical Models in Diffusion MRI

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, the general Standard Model has recently shown that model parameter estimation from dMRI data is ill-posed unless very strong magnetic gradients are used. We analyse 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) solves the ill-posedness and increases the accuracy of the parameter estimation. Methods: We analyse 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, which is enough to solve the degeneracy in the NODDIDA model parameter estimation.Comment: 22 pages, 7 figure