Validating the standard model of diffusion MRI in white matter with numerical substrates

The non-invasive estimation of intra- and extracellular microstructural parameters using biophysical models has been a major focus in brain microstructure imaging with MRI. The Standard Model (SM) of diffusion in white matter (WM) provides a unifying framework for various modelling approaches, representing axons as impermeable sticks embedded within a locally anisotropic extra-axonal space. However, the SM relies on simplifying assumptions that may not hold in realistic WM tissue, as they do not take into account axonal undulations, beading, the presence of glial cells, or membrane permeability. In this work, we investigate how SM parameter estimates, derived using the Standard Model Imaging (SMI) framework, behave when the model is applied to realistic numerical WM substrates generated by the CATERPillar tool. Specifically, we vary (i) axonal morphological features such as beading and undulations, (ii) axonal packing density, (iii) orientation dispersion, (iv) membrane permeability of axons and astrocytes separately, (v) myelin volume fraction, and (vi) diffusion time. In each part of the analysis, different noise levels are introduced. Our findings enable users to identify potential biases introduced by varying conditions and to adjust their interpretations accordingly.