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

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

Combined diffusion-relaxometry microstructure imaging: Current status and future prospects.

Microstructure imaging seeks to noninvasively measure and map microscopic tissue features by pairing mathematical modeling with tailored MRI protocols. This article reviews an emerging paradigm that has the potential to provide a more detailed assessment of tissue microstructure-combined diffusion-relaxometry imaging. Combined diffusion-relaxometry acquisitions vary multiple MR contrast encodings-such as b-value, gradient direction, inversion time, and echo time-in a multidimensional acquisition space. When paired with suitable analysis techniques, this enables quantification of correlations and coupling between multiple MR parameters-such as diffusivity, T1 , T2 , and T2∗ . This opens the possibility of disentangling multiple tissue compartments (within voxels) that are indistinguishable with single-contrast scans, enabling a new generation of microstructural maps with improved biological sensitivity and specificity.

Computing and visualising intra-voxel orientation-specific relaxation-diffusion features in the human brain.

Diffusion MRI techniques are used widely to study the characteristics of the human brain connectome in vivo. However, to resolve and characterise white matter (WM) fibres in heterogeneous MRI voxels remains a challenging problem typically approached with signal models that rely on prior information and constraints. We have recently introduced a 5D relaxation-diffusion correlation framework wherein multidimensional diffusion encoding strategies are used to acquire data at multiple echo-times to increase the amount of information encoded into the signal and ease the constraints needed for signal inversion. Nonparametric Monte Carlo inversion of the resulting datasets yields 5D relaxation-diffusion distributions where contributions from different sub-voxel tissue environments are separated with minimal assumptions on their microscopic properties. Here, we build on the 5D correlation approach to derive fibre-specific metrics that can be mapped throughout the imaged brain volume. Distribution components ascribed to fibrous tissues are resolved, and subsequently mapped to a dense mesh of overlapping orientation bins to define a smooth orientation distribution function (ODF). Moreover, relaxation and diffusion measures are correlated to each independent ODF coordinate, thereby allowing the estimation of orientation-specific relaxation rates and diffusivities. The proposed method is tested on a healthy volunteer, where the estimated ODFs were observed to capture major WM tracts, resolve fibre crossings, and, more importantly, inform on the relaxation and diffusion features along with distinct fibre bundles. If combined with fibre-tracking algorithms, the methodology presented in this work has potential for increasing the depth of characterisation of microstructural properties along individual WM pathways.

Diffusion tensor distribution imaging of an in vivo mouse brain at ultrahigh magnetic field by spatiotemporal encoding.

Diffusion tensor distribution (DTD) imaging builds on principles from diffusion, solid-state and low-field NMR spectroscopies, to quantify the contents of heterogeneous voxels as nonparametric distributions, with tensor "size", "shape" and orientation having direct relations to corresponding microstructural properties of biological tissues. The approach requires the acquisition of multiple images as a function of the magnitude, shape and direction of the diffusion-encoding gradients, leading to long acquisition times unless fast image read-out techniques like EPI are employed. While in previous in vivo human brain studies performed at 3 T this proved a viable option, porting these measurements to very high magnetic fields and/or to heterogeneous organs induces B0 - and B1 -inhomogeneity artifacts that challenge the limits of EPI. To overcome such challenges, we demonstrate here that high spatial resolution DTD of mouse brain can be carried out at 15.2 T with a surface-cryoprobe, by relying on SPatiotemporal ENcoding (SPEN) imaging sequences. These new acquisition and data-processing protocols are demonstrated with measurements on in vivo mouse brain, and validated with synthetic phantoms designed to mimic the diffusion properties of white matter, gray matter and cerebrospinal fluid. While still in need of full extensions to 3D mappings and of scanning additional animals to extract more general physiological conclusions, this work represents another step towards the model-free, noninvasive in vivo characterization of tissue microstructure and heterogeneity in animal models, at ≈0.1 mm resolutions.

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

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

Transferring principles of solid-state and Laplace NMR to the field of in vivo brain MRI.

Magnetic resonance imaging (MRI) is the primary method for noninvasive investigations of the human brain in health, disease, and development but yields data that are difficult to interpret whenever the millimeter-scale voxels contain multiple microscopic tissue environments with different chemical and structural properties. We propose a novel MRI framework to quantify the microscopic heterogeneity of the living human brain as spatially resolved five-dimensional relaxation-diffusion distributions by augmenting a conventional diffusion-weighted imaging sequence with signal encoding principles from multidimensional solid-state nuclear magnetic resonance (NMR) spectroscopy, relaxation-diffusion correlation methods from Laplace NMR of porous media, and Monte Carlo data inversion. The high dimensionality of the distribution space allows resolution of multiple microscopic environments within each heterogeneous voxel as well as their individual characterization with novel statistical measures that combine the chemical sensitivity of the relaxation rates with the link between microstructure and the anisotropic diffusivity of tissue water. The proposed framework is demonstrated on a healthy volunteer using both exhaustive and clinically viable acquisition protocols.

Multidimensional correlation of nuclear relaxation rates and diffusion tensors for model-free investigations of heterogeneous anisotropic porous materials.

Despite their widespread use in non-invasive studies of porous materials, conventional MRI methods yield ambiguous results for microscopically heterogeneous materials such as brain tissue. While the forward link between microstructure and MRI observables is well understood, the inverse problem of separating the signal contributions from different microscopic pores is notoriously difficult. Here, we introduce an experimental protocol where heterogeneity is resolved by establishing 6D correlations between the individual values of isotropic diffusivity, diffusion anisotropy, orientation of the diffusion tensor, and relaxation rates of distinct populations. Such procedure renders the acquired signal highly specific to the sample's microstructure, and allows characterization of the underlying pore space without prior assumptions on the number and nature of distinct microscopic environments. The experimental feasibility of the suggested method is demonstrated on a sample designed to mimic the properties of nerve tissue. If matched to the constraints of whole body scanners, this protocol could allow for the unconstrained determination of the different types of tissue that compose the living human brain.

Two-Dimensional Correlation of Isotropic and Directional Diffusion Using NMR.

Diffusion nuclear magnetic resonance (NMR) is a powerful technique for studying porous media, but yields ambiguous results when the sample comprises multiple regions with different pore sizes, shapes, and orientations. Inspired by solid-state NMR techniques for correlating isotropic and anisotropic chemical shifts, we propose a diffusion NMR method to resolve said ambiguity. Numerical data inversion relies on sparse representation of the data in a basis of radial and axial diffusivities. Experiments are performed on a composite sample with a cell suspension and a liquid crystal.

NMR molecular dynamics study of chromonic liquid crystals Edicol Sunset Yellow doped with salts.

We investigate the effect of monoatomic salts on the molecular dynamics in the nematic and isotropic phases formed by the chromonic liquid crystal Edicol Sunset Yellow. The study was carried out using proton nuclear magnetic resonance relaxometry. To analyse the effect of incorporation of additional sodium chloride or lithium chloride on the solutions' molecular dynamics, the spin-lattice relaxation time was measured for Larmor frequencies between 10 kHz and 100 MHz. In the nematic phase, the presence of additional sodium or lithium ions seems to contribute to an increase of the rotations/reorientations corr elation times in comparison with the mixture without extra ions. The collective motions detected by proton NMR relaxometry are associated with collective fluctuations of molecules within the stacks in the nematic phase and with order parameter fluctuations in the isotropic phase.