This study analyzes neurodegenerative progression using longitudinal cognitive data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset. While conventional models describe progression as monotonic decline, we identify a two-stage structural process characterized by variance instability and directional collapse bias. We define structural persistence F(t) and derive a local decay rate λ(t) at the individual level. Across diagnostic groups (CN, SMC, EMCI, LMCI, AD), we observe: - A systematic increase in the variance of λ(t) prior to clinical conversion- A directional shift in asymmetry toward collapse-dominated dynamics- A statistically significant enrichment of variance peaks before conversion (66.8% vs random 64.0% ± 1.4%, Z = 2.07, p ≈ 0.019) These findings are consistent with early-warning signals observed in complex systems approaching critical transitions. We further propose a minimal structural interpretation using an asymmetric potential framework, providing a mechanistic link between instability and irreversible decline. This work provides a data-driven and structurally interpretable framework for understanding neurodegenerative dynamics, with potential applications in early prediction and longitudinal risk assessment.
Koji Okino (Fri,) studied this question.