Mathematical Modeling of Neurodegenerative Disease Progression

Mathematical modelling of neurodegenerative diseases seeks to characterise how pathological proteins misfold, aggregate and propagate through the brain’s intricate networks. By combining principles from reaction–diffusion theory, network science and kinetic equations, researchers construct predictive frameworks that capture both local enzymatic growth of aggregates and their global spread along white-matter tracts. Such models illuminate the temporal sequence of biomarker trajectories, explain regional vulnerability in disorders such as Alzheimer’s and Parkinson’s disease, and provide a quantitative basis for evaluating therapeutic strategies. Across different diseases, common elements emerge: templated growth of misfolded species, anisotropic transport governed by the connectome, and interactions among multiple protein species. These in silico approaches offer a powerful complement to imaging and fluid biomarkers, enabling scenario testing of clearance enhancement, seeding inhibition and spatially targeted interventions. Ultimately, they seek to establish prognostic timeframes of disease progression, guide clinical trial design and inform personalised treatment plans.

Research from Nature Portfolio

Recent studies have applied an epidemic spreading framework to in vivo imaging of tau pathology, demonstrating that a connectivity-based diffusion model accounts for up to 70 % of the spatial variance observed in tau-PET scans across the Alzheimer’s continuum. The model reproduces characteristic staging patterns even in the absence of significant amyloid burden, and reveals that regions with higher amyloid coincide with accelerated tau propagation. By calibrating transmission rates to individual imaging data, this approach offers a mechanistic link between structural connectomics and regional protein accumulation, and highlights potential targets for early intervention.

Mathematical Modeling of Neurodegenerative Disease Progression publication trend

The graph below shows the total number of articles in mathematical modeling of neurodegenerative disease progression across all publications each year (not limited to Nature Index journals).

Technical terms

Reaction–diffusion model: A framework coupling local biochemical reactions of protein misfolding with spatial diffusion along neural fibres.

Epidemic spreading model: A network-based approach that treats misfolded proteins as infectious agents propagating through the connectome.

Connectome: The comprehensive map of neural connections in the brain, often represented as a weighted graph of regions and fibre tracts.

Prion-like propagation: The process by which misfolded proteins template the conversion of native proteins and spread transneuronally.

Ordinary differential equation (ODE): A mathematical equation describing the rate of change of biomarker concentrations over time.

References

1. Spread of pathological tau proteins through communicating neurons in human Alzheimer’s disease. Nature Communications (2020).
2. Spatially-extended nucleation-aggregation-fragmentation models for the dynamics of prion-like neurodegenerative protein-spreading in the brain and its connectome. Journal of Theoretical Biology (2019).
3. A physics-based model explains the prion-like features of neurodegeneration in Alzheimer’s disease, Parkinson’s disease, and amyotrophic lateral sclerosis. Journal of the Mechanics and Physics of Solids (2019).
4. Computational Causal Modeling of the Dynamic Biomarker Cascade in Alzheimer’s Disease. Computational and Mathematical Methods in Medicine (2019).