  The intra-axonal water exchange time {\tau}i, a parameter associated with
axonal permeability, could be an important biomarker for understanding
demyelinating pathologies such as Multiple Sclerosis. Diffusion-Weighted MRI is
sensitive to changes in permeability, however, the parameter has remained
elusive due to the intractability of the mathematical models that incorporate
it. Machine learning based computational models can potentially be used to
estimate such parameters, and recently, a theoretical framework using a random
forest (RF) suggests this is a promising approach. In this study, we adopt such
an RF approach and experimentally investigate its suitability as a biomarker
for demyelinating pathologies through direct comparison with histology. For
this, we use an in-vivo cuprizone (CPZ) mouse model of demyelination with
available ex-vivo electron microscopy (EM) data. We test our model on
noise-free simulations and find very strong correlations between the predicted
and ground truth parameters. For realistic noise levels as in our in-vivo data,
the performance is affected, however, the parameters are still well estimated.
We apply our RF model on in-vivo data from 8 CPZ and 8 wild-type (WT) mice and
validate the RF estimates using histology. We find a strong correlation between
the in-vivo RF estimates of {\tau}i and the EM measurements of myelin thickness
({\rho_\tau}i = 0.82), and between RF estimates and EM measurements of
intra-axonal volume fraction ({\rho_f} = 0.98). When comparing {\tau}i in CPZ
and WT mice we find a statistically significant decrease in the corpus callosum
of the CPZ compared to the WT mice, in line with our expectations that {\tau}i
is lower in regions where the myelin sheath is damaged. Overall, these results
demonstrate the suitability of machine learning compartment models with
permeability as a potential biomarker for demyelinating pathologies.
