Implicit neural representations for accurate estimation of the standard model of white matter

To extract biologically interpretable information, a common approach is to fit a microstructural tissue model to a set of signals acquired with different dMRI acquisition settings (Alexander et al., 2019; Lampinen et al., 2023; Jelescu et al., 2020). In the absence of diffusion time dependence, these typically include different combinations of gradient strengths (commonly quantified by the b-value), directions (b-vector), and B-tensor shape (Westin et al., 2014). Microstructural parameters estimated by these models - including compartmental signal fractions and diffusivities - have shown to be sensitive to changes in brain structure due to diseases like multiple sclerosis (Alotaibi et al., 2021), Alzheimer's disease (Parker et al., 2018) and Parkinson's disease (Kim et al., 2016), and can provide a more fundamental understanding of tissue microstructure in both healthy and pathological tissues (Zhang et al., 2012). The Standard Model of white matter (SM) (Novikov et al., 2019) describes the signal arising from white matter by a kernel consisting of three compartments (intra-axonal, extra-axonal, and free water (occasionally omitted)) convolved with a fiber orientation distribution (FOD) (Tournier et al., 2007b). Compartmental signal fractions and diffusivities can be estimated, alongside the parameters that describe the FOD (usually in the form of a spherical harmonics (SH) series). Nevertheless, the high-dimensional parameter space of the SM complicates the estimation of its parameters, potentially leading to low accuracy, precision, and degeneracy of estimates (Jelescu et al., 2016).