Inverting brain grey matter models with likelihoodfree inference: a tool for trustable cytoarchitecture measurements
Abstract
Effective characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in diffusion MRI (dMRI). Solving the problem of relating the dMRI signal with cytoarchitectural characteristics calls for the definition of a mathematical model that describes brain tissue via a handful of physiologicallyrelevant parameters and an algorithm for inverting the model. To address this issue, we propose a new forward model, specifically a new system of equations, requiring a few relatively sparse bshells. We then apply modern tools from Bayesian analysis known as likelihoodfree inference (LFI) to invert our proposed model. As opposed to other approaches from the literature, our algorithm yields not only an estimation of the parameter vector $\theta$ that best describes a given observed data point $x_0$, but also a full posterior distribution $p(\thetax_0)$ over the parameter space. This enables a richer description of the model inversion, providing indicators such as credible intervals for the estimated parameters and a complete characterization of the parameter regions where the model may present indeterminacies. We approximate the posterior distribution using deep neural density estimators, known as normalizing flows, and fit them using a set of repeated simulations from the forward model. We validate our approach on simulations using dmipy and then apply the whole pipeline on two publicly available datasets.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 DOI:
 10.48550/arXiv.2111.08693
 arXiv:
 arXiv:2111.08693
 Bibcode:
 2021arXiv211108693J
 Keywords:

 Quantitative Biology  Quantitative Methods;
 Computer Science  Machine Learning
 EPrint:
 Journal of Machine Learning for Biomedical Imaging, Melba editors, 2022, pp.127