Dendritic atrophy and spine loss are hallmark pathologies in Alzheimer’s Disease (AD), typically interpreted as cumulative structural damage caused by amyloid toxicity or cytoskeletal breakdown. In this work, we propose an alternative physical etiology based on the Theory of Thermodynamic Branching. By modeling the neuron as an energy-optimizing transport network, we demonstrate that the complex dendritic arborization observed in healthy cortex (2. 4) is thermodynamically sustainable only under a high metabolic investment in signaling (0. 8). Using a biophysical simulation of mitochondrial dysfunction—a known precursor to AD pathology—we show that as available ATP declines, the thermodynamic attractor of the system shifts. The neuron is physically forced to abandon the "expensive" high-complexity regime and relax towards Murray's Law (3. 0), which minimizes volumetric maintenance costs at the expense of connectivity. Key Findings: Dendritic retraction is identified not as a stochastic degenerative process, but as a deterministic thermodynamic relaxation necessary for cell survival under hypometabolic conditions. The model quantitatively predicts the "thinning" and simplification of arbors observed in histological samples. This suggests that therapeutic strategies aiming to force dendritic regrowth without first restoring bioenergetic efficiency () may be thermodynamically unviable.
Riccardo Marchesi (Fri,) studied this question.