CATERPillar: A Flexible Framework for Generating White Matter Numerical Substrates with incorporated Glial Cells

Monte Carlo diffusion simulations in numerical substrates are valuable for exploring the sensitivity and specificity of the diffusion MRI (dMRI) signal to realistic cell microstructure features. A crucial component of such simulations is the use of numerical phantoms that accurately represent the target tissue, which is in this case, cerebral white matter (WM). This study introduces CATERPillar (Computational Axonal Threading Engine for Realistic Proliferation), a novel method that simulates the mechanic of axonal growth using overlapping spheres as elementary units. CATERPillar facilitates parallel axon development while preventing collisions, offering user control over key structural parameters such as cellular density, tortuosity, beading and myelination. Its uniqueness lies in its ability to generate not only realistic axonal structures but also realistic glial cells, enhancing the biological fidelity of simulations. We showed that our grown substrates feature distributions of key morphological parameters that agree with those from histological studies. The structural realism of the astrocytic components was quantitatively validated using Sholl analysis. Furthermore, the time-dependent diffusion in the extra- and intra-axonal compartments accurately reflected expected characteristics of short-range disorder, as predicted by theoretical models. CATERPillar is open source and can be used to (a) develop new acquisition schemes that sensitise the MRI signal to unique tissue microstructure features, (b) test the accuracy of a broad range of analytical models, and (c) build a set of substrates to train machine learning models on.