A system dynamics model of brain plasticity under the influence of stress

Introduction: Brain plasticity under stress emerges from coupled neuroendocrine, neurotrophic, inflammatory, cognitive–emotional, recovery, and allostatic processes. We present an eight-state system-dynamics model that is explicitly mechanistic–phenomenological rather than being a first-principles or clinically calibrated model. The formulation addresses mathematical positivity, bounded interactions, local stability, initial-condition heterogeneity, reproducibility, and parameter uncertainty. Materials and methods: The dimensionless state variables are perceived stress S , hypothalamic–pituitary–adrenal (HPA) axis/cortisol activity H , neurotrophic support B , neuroinflammation I , effective plasticity P , cognitive–emotional function C , recovery resources R , and allostatic load A . Biological couplings are represented by bounded Michaelis–Menten/Hill functions. The positive orthant is proved forward-invariant and P is confined to [ 0 , P max ] . Simulations use Python 3.13.5 and SciPy 1.17.0, the adaptive Dormand–Prince eighth-order (DOP853) solver, relative tolerance 10 − 9 , absolute tolerance 10 − 11 , and daily output sampling. The day-40 intervention is implemented by exact piecewise integration. Local stability is evaluated from the Jacobian at equilibrium. Global sensitivity uses 1500 Latin-hypercube samples and partial rank correlation coefficients (PRCCs) across all 34 model parameters; 500 samples are also audited for local stability. Results: The model produces stable adaptive, chronic-stress, and post-intervention equilibria. Chronic forcing lowers B , P , C , and R while increasing S , H , I , and A . At day 100, P is 0.241 under chronic stress, 0.764 after stress reduction alone, 0.312 after recovery support alone, and 0.904 after the combined intervention. The full Jacobian is locally stable in the three reference equilibria; the seven-state feedback-subsystem spectral abscissae are − 0.129 , − 0.158 , and − 0.138 day −1 for control, chronic, and post-recovery conditions. Across the 500-sample stability audit, the feedback spectral abscissa remains negative ( − 0.190 to − 0.123 day −1 ). Plasticity at day 100 is most sensitive to HPA gain α H (PRCC = − 0.902 ), HPA clearance β H ( 0.895 ), plasticity formation α P