Cellular EXchange Imaging (CEXI): Evaluation of a diffusion model including water exchange in cells using numerical phantoms of permeable spheres

Purpose: Biophysical models of diffusion MRI have been developed to characterize microstructure in various tissues, but existing models are not suitable for tissue composed of permeable spherical cells. In this study we introduce Cellular Exchange Imaging (CEXI), a model tailored for permeable spherical cells, and compares its performance to a related Ball \& Sphere (BS) model that neglects permeability. Methods: We generated DW-MRI signals using Monte-Carlo simulations with a PGSE sequence in numerical substrates made of spherical cells and their extracellular space for a range of membrane permeability. From these signals, the properties of the substrates were inferred using both BS and CEXI models. Results: CEXI outperformed the impermeable model by providing more stable estimates cell size and intracellular volume fraction that were diffusion time-independent. Notably, CEXI accurately estimated the exchange time for low to moderate permeability levels previously reported in other studies ($\kappa<25\mu m/s$). However, in highly permeable substrates ($\kappa=50\mu m/s$), the estimated parameters were less stable, particularly the diffusion coefficients. Conclusion: This study highlights the importance of modeling the exchange time to accurately quantify microstructure properties in permeable cellular substrates. Future studies should evaluate CEXI in clinical applications such as lymph nodes, investigate exchange time as a potential biomarker of tumor severity, and develop more appropriate tissue models that account for anisotropic diffusion and highly permeable membranes.Comment: 7 figures, 2 tables, 21 pages, under revie

Learning Global Brain Microstructure Maps Using Trainable Sparse Encoders

underlying brain tissue microstructure. Currently, one of the promising methods for microstructure imaging is signal modelling using convex formulation, e.g. using the COMMIT framework. Despite the benefits introduced with such framework, an important limitation is the long convergence time, making the method unappealing for clinical applications. In order to address this limitation, we propose to use a neural network to learn the sparse representation of the data and perform an end-to-end reconstruction of the microstructure estimates directly from the diffusion-weighted data. Our results show that the neural network can accurately estimate the microstructure maps, 4 orders of magnitude faster than the convex formulation

The Microstructural Features of the Diffusion-Simulated Connectivity (DiSCo) Dataset

International audienceWe present a detailed description of the structural characteristics of the MICCAI 2021 Diffusion Simulated Connectivity (DiSCo) Challenge synthetic dataset. The DiSCo dataset are one of a kind numerical phantoms for the simulation of the diffusion-weighted images (DWIs) via Monte-Carlo diffusion simulations. The microscopic and macroscopic complexity of the synthetic substrates allows the evaluation of processing pipelines for the estimation of the quantitative structural connectivity. The diffusion-weighted signal in each voxel of the DWIs is obtained from Monte-Carlo simulations of particle dynamics within a substrate of an unprecedented size of 1 mm3, allowing for an image matrix size up to 40×40×40 voxels (isotropic voxel sizes of 25 μm). In this paper, we provide a characterization of the microstructural properties of the DiSCo dataset, which is composed of three numerical phantoms with comparable microstructure. We report the ground-truth tissue volume fractions (“intra-axonal”, “extra-axonal”, “myelin”), the fibre density, the bundle density and the fibre orientation distributions (FODs). We believe that this characterization will be beneficial for validating quantitative structural connectivity processing pipelines, and that could eventually find use in microstructural modelling based on machine learning approaches

The diffusion-simulated connectivity (DiSCo) dataset

International audienceThe methodological development in the mapping of the brain structural connectome from diffusion-weighted magnetic resonance imaging (DW-MRI) has raised many hopes in the neuroscientific community. Indeed, the knowledge of the connections between different brain regions is fundamental to study brain anatomy and function. The reliability of the structural connectome is therefore of paramount importance. In the search for accuracy, researchers have given particular attention to linking white matter tractography methods – used for estimating the connectome – with information about the microstructure of the nervous tissue. The creation and validation of methods in this context were hampered by a lack of practical numerical phantoms. To achieve this, we created a numerical phantom that mimics complex anatomical fibre pathway trajectories while also accounting for microstructural features such as axonal diameter distribution, myelin presence, and variable packing densities. The substrate has a micrometric resolution and an unprecedented size of 1 cubic millimetre to mimic an image acquisition matrix of voxels. DW-MRI images were obtained from Monte Carlo simulations of spin dynamics to enable the validation of quantitative tractography. The phantom is composed of 12,196 synthetic tubular fibres with diameters ranging from 1.4 µm to 4.2 µm, interconnecting sixteen regions of interest. The simulated images capture the microscopic properties of the tissue (e.g. fibre diameter, water diffusing within and around fibres, free water compartment), while also having desirable macroscopic properties resembling the anatomy, such as the smoothness of the fibre trajectories. While previous phantoms were used to validate either tractography or microstructure, this phantom can enable a better assessment of the connectome estimation’s reliability on the one side, and its adherence to the actual microstructure of the nervous tissue on the other

ActiveAx(ADD): Toward non-parametric and orientationally invariant axon diameter distribution mapping using PGSE

Purpose Non-invasive axon diameter distribution (ADD) mapping using diffusion MRI is an ill-posed problem. Current ADD mapping methods require knowledge of axon orientation before performing the acquisition. Instead, ActiveAx uses a 3D sampling scheme to estimate the orientation from the signal, providing orientationally invariant estimates. The mean diameter is estimated instead of the distribution for the solution to be tractable. Here, we propose an extension (ActiveAx(ADD)) that provides non-parametric and orientationally invariant estimates of the whole distribution. Theory The accelerated microstructure imaging with convex optimization (AMICO) framework accelerates mean diameter estimation using a linear formulation combined with Tikhonov regularization to stabilize the solution. Here, we implement a new formulation (ActiveAx(ADD)) that uses Laplacian regularization to provide robust estimates of the whole ADD. Methods The performance of ActiveAx(ADD) was evaluated using Monte Carlo simulations on synthetic white matter samples mimicking axon distributions reported in histological studies. Results ActiveAx(ADD) provided robust ADD reconstructions when considering the isolated intra-axonal signal. However, our formulation inherited some common microstructure imaging limitations. When accounting for the extra axonal compartment, estimated ADDs showed spurious peaks and increased variability because of the difficulty of disentangling intra and extra axonal contributions. Conclusion Laplacian regularization solves the ill-posedness regarding the intra axonal compartment. ActiveAx(ADD) can potentially provide non-parametric and orientationally invariant ADDs from isolated intra-axonal signals. However, further work is required before ActiveAx(ADD) can be applied to real data containing extra-axonal contributions, as disentangling the 2 compartment appears to be an overlooked challenge that affects microstructure imaging methods in general

A Signal Peak Separation Index for axisymmetric B-tensor encoding

Diffusion-weighted MRI (DW-MRI) has recently seen a rising interest in planar, spherical and general B-tensor encodings. Some of these sequences have aided traditional linear encoding in the estimation of white matter microstructural features, generally by making DW-MRI less sensitive to the orientation of axon fascicles in a voxel. However, less is known about their potential to make the signal more sensitive to fascicle orientation, especially in crossing-fascicle voxels. Although planar encoding has been commended for the resemblance of its signal with the voxel's orientation distribution function (ODF), linear encoding remains the near undisputed method of choice for orientation estimation. This paper presents a theoretical framework to gauge the sensitivity of axisymmetric B-tensors to fascicle orientations. A signal peak separation index (SPSI) is proposed, motivated by theoretical considerations on a simple multi-tensor model of fascicle crossing. Theory and simulations confirm the intuition that linear encoding, because it maximizes B-tensor anisotropy, possesses an intrinsic advantage over all other axisymmetric B-tensors. At identical SPSI however, oblate B-tensors yield higher signal and may be more robust to acquisition noise than their prolate counterparts. The proposed index relates the properties of the B-tensor to those of the tissue microstructure in a straightforward way and can thus guide the design of diffusion sequences for improved orientation estimation and tractography

An evolutionary framework for microstructure-sensitive generalized diffusion gradient waveforms

International audienceIn diffusion-weighted MRI, general gradient waveforms became of interest for their sensitivity to microstructure features of the brain white matter. However, the design of such waveforms remains an open problem. In this work, we propose a framework for generalized gradient waveform design with optimized sensitivity to selected microstruc-ture features. In particular, we present a rotation-invariant method based on a genetic algorithm to maximize the sensitivity of the signal to the intra-axonal volume fraction. The sensitivity is evaluated by computing a score based on the Fisher information matrix from Monte-Carlo simulations , which offer greater flexibility and realism than conventional analytical models. As proof of concept, we show that the optimized waveforms have higher scores than the conventional pulsed-field gradients experiments. Finally, the proposed framework can be generalized to optimize the waveforms for to any microstructure feature of interest

Robust Monte-Carlo Simulations in Diffusion-MRI: Effect of the Substrate Complexity and Parameter Choice on the Reproducibility of Results

Monte-Carlo Diffusion Simulations (MCDS) have been used extensively as a ground truth tool for the validation of microstructure models for Diffusion-Weighted MRI. However, methodological pitfalls in the design of the biomimicking geometrical configurations and the simulation parameters can lead to approximation biases. Such pitfalls affect the reliability of the estimated signal, as well as its validity and reproducibility as ground truth data. In this work, we first present a set of experiments in order to study three critical pitfalls encountered in the design of MCDS in the literature, namely, the number of simulated particles and time steps, simplifications in the intra-axonal substrate representation, and the impact of the substrate's size on the signal stemming from the extra-axonal space. The results obtained show important changes in the simulated signals and the recovered microstructure features when changes in those parameters are introduced. Thereupon, driven by our findings from the first studies, we outline a general framework able to generate complex substrates. We show the framework's capability to overcome the aforementioned simplifications by generating a complex crossing substrate, which preserves the volume in the crossing area and achieves a high packing density. The results presented in this work, along with the simulator developed, pave the way toward more realistic and reproducible Monte-Carlo simulations for Diffusion-Weighted MRI