Tau protein spreads through the brain along neural connections, and this spreading is thought to drive the progression of Alzheimer's disease. Computational models of the process fit clinical data and predict future atrophy patterns. But the models come in several variants — reaction-diffusion on continuous domains, network diffusion on discrete connectomes, Fisher-KPP equations with logistic growth — and the choice between them is usually treated as a modeling preference rather than an empirical question.
This paper shows the choice matters. Different PDE frameworks, fit to the same clinical data, give qualitatively different predictions for disease progression. Models that look similar in their mathematical structure — all involving some form of diffusion plus local reaction on a network — diverge when extrapolated beyond the fitting window. The interaction between tau and amyloid-beta, the other hallmark pathology, further amplifies the differences: models that agree on tau-only spreading disagree once amyloid modulation is included.
The practical implication is that model selection is not a technical detail but a scientific conclusion. The “best” model is the one that predicts data it wasn't fit to, and different frameworks excel in different regimes — early-stage spreading versus late-stage saturation, focal versus diffuse patterns.
The result is a caution against treating network-based disease models as interchangeable formalisms. The math is load-bearing. The diffusion operator, the reaction kinetics, the way the two pathologies interact — each shapes the prediction, and the shaping is measurable against clinical data. The model is not a container for the biology; it is a claim about the biology.