Biophysical model of white matter integrity across the lifespan: solving the differential equations of myelination and axonal degeneration
DOI:
https://doi.org/10.14295/bjs.v5i9.881Keywords:
white matter, lifespan brain charts, myelination, axonal degeneration, biophysical modelingAbstract
White matter integrity across the human lifespan follows characteristic nonlinear trajectories, with microstructural (fractional anisotropy) peaking near 24 years and macrostructural volume peaks near 34 years. Existing normative brain charts are purely statistical and lack mechanistic insight into the competing biological processes of myelination and axonal degeneration. Purpose: To develop and validate the first biophysically motivated ordinary differential equation (ODE) model of lifespan white matter integrity that explicitly captures the competition between constructive myelination and destructive degeneration. Methods: We formulated a system of ODEs with age‑dependent myelination rates (Gompertz decay) and cumulative damage terms. The model was calibrated to aggregated fractional anisotropy and volume trajectories from 35,120 diffusion MRI scans (ages 0–100 years) using Bayesian adaptive direct search and parametric bootstrap for uncertainty quantification. Sensitivity analysis, parameter identifiability assessment, and regional extensions to the corticospinal tract and cingulum bundle were performed. Findings: The model accurately reproduces empirical peak ages (24.1 years for microstructure, 33.8 years for macrostructure). Estimated parameters (α₀ = 0.15 yr⁻¹, βₘ = 0.008 yr⁻¹, γ = 0.02 yr⁻¹, αᵥ₀ = 0.10 yr⁻¹, βᵥ = 0.005 yr⁻¹) are biologically plausible. The novel myelination‑degeneration ratio detects the shift from net construction to net destruction before conventional z‑scores signal abnormality. Sensitivity analysis shows peak age is governed by early myelination parameters, while post‑peak decline is controlled by damage parameters. Conclusion: This biophysical framework transforms descriptive brain charts into a predictive, mechanistically grounded tool enabling hypothesis-driven simulations and early detection of pathological balance shifts. Recommendation: The open‑source software toolbox (Python/MATLAB) implementing normative centile scoring and the Myelination‑Degeneration Ratio should be validated in longitudinal cohorts for preclinical Alzheimer’s disease and other neurodegenerative conditions.
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