Linking microscopy to diffusion MRI with degenerate biophysical models: an application of the Bayesian EstimatioN of CHange (BENCH) framework

Biophysical modelling of diffusion MRI (dMRI) is used to non-invasively estimate microstructural features of tissue, particularly in the brain. However, meaningful description of tissue requires many unknown parameters, resulting in a model that is often ill-posed. The Bayesian EstimatioN of CHange (BENCH) framework was specifically designed to circumvent parameter fitting for ill-conditioned models when one is simply interested in interpreting signal changes related to some variable of interest. To understand the biological underpinning of some observed change in MR signal between different conditions, BENCH predicts which model parameter, or combination of parameters, best explains the observed change, without having to invert the model. BENCH has been previously used to identify which biophysical parameters could explain group-wise dMRI signal differences (e.g. patients vs. controls); here, we adapt BENCH to interpret dMRI signal changes related to continuous variables. We investigate how parameters from the dMRI standard model of white matter, with an additional sphere compartment to represent glial cell bodies, relate to tissue microstructure quantified from histology. We validate BENCH using synthetic dMRI data from numerical simulations. We then apply it to ex-vivo macaque brain data with dMRI and microscopy metrics of glial density, axonal density, and axonal dispersion in the same brain. We found that (i) increases in myelin density are primarily associated with an increased intra-axonal volume fraction and (ii) changes in the orientation dispersion derived from myelin microscopy are linked to variations in the orientation dispersion index. Finally, we found that the dMRI signal is sensitive to changes in glial cell soma in the WM, but that no parameter in the extended standard model was able to explain this observed signal change, suggesting model inadequacy.