The intra-axonal water exchange time (i) , a parameter associated with axonal permeability, could be an important biomarker for understanding and treating demyelinating pathologies such as Multiple Sclerosis. Diffusion-Weighted MRI (DW-MRI) is sensitive to changes in permeability; however, the parameter has so far remained elusive due to the lack of general biophysical models that incorporate it. Machine learning based computational models can potentially be used to estimate such parameters. Recently, for the first time, a theoretical framework using a random forest (RF) regressor suggests that this is a promising new approach for permeability estimation. In this study, we adopt such an approach and for the first time experimentally investigate it for demyelinating pathologies through direct comparison with histology. We construct a computational model using Monte Carlo simulations and an RF regressor in order to learn a mapping between features derived from DW-MRI signals and ground truth microstructure parameters. We test our model in simulations, and find strong correlations between the predicted and ground truth parameters (intra-axonal volume fraction f: R 2 = 0.99, i : R 2 = 0.84, intrinsic diffusivity d: R 2 = 0.99). We then apply the model in-vivo, on a controlled cuprizone (CPZ) mouse model of demyelination, comparing the results from two cohorts of mice, CPZ (N = 8) and healthy age-matched wild-type (WT, N = 8). We find that the RF model estimates sensible microstructure parameters for both groups, matching values found in literature. Furthermore, we perform histology for both groups using electron microscopy (EM), measuring the thickness of the myelin sheath as a surrogate for exchange time. Histology results show that our RF model estimates are very strongly correlated with the EM measurements (= 0.98 for f, = 0.82 for i). Finally, we find a statistically significant decrease in i in all three regions of the corpus callosum (splenium/genu/body) of the CPZ cohort (< i > = 310ms/330ms/350ms) compared to the WT group (< i > = 370ms/370ms/380ms). This is in line with our expectations that i is lower in regions where the myelin sheath is damaged, as axonal membranes become more permeable. Overall, these results demonstrate, for the first time experimentally and in vivo, that a computational model learned from simulations can reliably estimate microstructure parameters, including the axonal permeability .