Orientation-Dispersed Apparent Axon Diameter via Multi-Stage Spherical Mean Optimization

The estimation of the apparent axon diameter (AAD) via diffusion MRI is affected by the incoherent alignment of single axons around its axon bundle direction, also known as orientational dispersion. The simultaneous estimation of AAD and dispersion is challenging and requires the optimization of many parameters at the same time. We propose to reduce the complexity of the estimation with an multi-stage approach, inspired to alternate convex search, that separates the estimation problem into simpler ones, thus avoiding the estimation of all the relevant model parameters at once. The method is composed of three optimization stages that are iterated, where we separately estimate the volume fractions, diffusivities, dispersion, and mean AAD, using a Cylinder and Zeppelin model. First, we use multi-shell data to estimate the undispersed axon micro-environment’s signal fractions and diffusivities using the spherical mean technique; then, to account for dispersion, we use the obtained micro-environment parameters to estimate a Watson axon orientation distribution; finally, we use data acquired perpendicularly to the axon bundle direction to estimate the mean AAD and updated signal fractions, while fixing the previously estimated diffusivity and dispersion parameters. We use the estimated mean AAD to initiate the following iteration. We show that our approach converges to good estimates while being more efficient than optimizing all model parameters at once. We apply our method to ex-vivo spinal cord data, showing that including dispersion effects results in mean apparent axon diameter estimates that are closer to their measured histological values

Dmipy, a Diffusion Microstructure Imaging toolbox in Python to improve research reproducibility

International audienceNon-invasive estimation of brain white matter microstructure features using diffusion MRI - otherwise known as Microstructure Imaging - has become an increasingly diverse and complicated field over the last decade. Multi-compartment-based models have been a popular approach to estimate these features. In this work, we present Diffusion Microstructure Imaging in Python (Dmipy), a diffusion MRI toolbox which allows accessing any multi-compartment-based model and robustly estimates these important features from single-shell, multi-shell, and multi-diffusion time, and multi-TE data. Dmipy follows a building block-based philosophy to microstructure imaging, meaning a multi-compartment model can be constructed and fitted to dMRI data using any combination of underlying tissue models, axon dispersion-or diameter distributions, and optimization algorithms using less than 10 lines of code, thus helps improve research reproducibility. In describing the toolbox, we show how Dmipy enables to easily design microstructure models and offers to the users the freedom to choose among different optimization strategies.We finally present three advanced examples of highly complex modeling approaches which are made easy using Dmipy