Directed Laplacian from tracer polarity for connectome models of neurodegenerative spread, with a nonlocal-versus-local correction and clearance as a conditional future aim

Abstract

Dated research note. The claim is that the next network-diffusion model for prion-like pathology spread on a primate connectome should be a directed graph Laplacian whose edge polarity is taken from tract-tracing data rather than from diffusion MRI, with separate anterograde and retrograde operators and their ratio left free: diffusion MRI supplies fibre orientation but no polarity, so directional models built from it alone are directional in name only, and a seed region with no streamlines in a tractography-derived connectome cannot be seeded where an experiment seeded it. Two secondary points are recorded: (1) a streamline- or tracer-weighted graph Laplacian is a nonlocal operator and is therefore not the coarse-grained limit of a voxelwise anisotropic diffusion model, which is local; for trans-synaptic spread the nonlocal graph is the more faithful representation and the local tensor model is the glioma-migration picture imported into a setting where it does not apply; (2) a spatially varying clearance sink derived from an independent perivascular-flow measurement is a legitimate future term, conditional on per-animal diffusion MRI and a species-validated index, and is not a candidate for datasets that cannot already identify a scalar clearance rate. The note gives minimal and stronger tests, a test that would retire the idea, and an ordered list of candidate models. Files are restricted; the Markdown note and its OpenTimestamps proof (Bitcoin block 970887) are deposited to fix the date.