Computational Neuroscience
Computational neuroscience combines mathematics, physics, biology, and computer science to understand the mechanisms underlying neural systems and neurodegenerative diseases. This area of research focuses on the mathematical modeling of Alzheimer's disease, neurodegeneration, biomarker interactions, and therapeutic intervention strategies.
These works integrate differential equation modeling, Bayesian inference, data-driven learning, and neural network approaches to study disease progression and therapeutic optimization. Special attention is given to amyloid-beta, phosphorylated tau proteins, cognitive decline dynamics, and mechanistic disease progression.
Methodology
- Ordinary and partial differential equation models
- Biomarker interaction modeling
- Bayesian parameter inference
- Physics-informed neural networks (PINNs)
- Optimal control theory for treatment strategies
- Clinical-data-driven computational simulations
Research Objectives
- Understanding progression of Alzheimer's disease
- Modeling tau and amyloid-beta interactions
- Predicting disease evolution using AI-assisted models
- Therapeutic optimization using control strategies
- Integrating mechanistic and data-driven approaches
Scientific Contributions
Recent studies investigate adaptive modeling approaches for anti-tau therapeutic interventions using Bayesian inference and physics-informed neural networks. The research demonstrates how data-driven methods can improve parameter estimation and uncertainty quantification while preserving mechanistic interpretability.
Selected References
1. Pal, S., & Melnik, R. (2025). Adaptive modelling of anti-tau treatments for neurodegenerative disorders based on the Bayesian approach with physics-informed neural networks. arXiv:2504.13438.
2. Pal, S., & Melnik, R. (2025). Nonequilibrium landscape of amyloid-beta and calcium ions in application to Alzheimer's disease. Physical Review E, 111, 014418.
3. Vyas, S., Golub, M.D., Sussillo, D., Shenoy, K.V. (2020). Computation Through Neural Population Dynamics. Annu Rev Neurosci., 43, 249-275.
3. Pal, S., & Melnik, R. (2025). Nonlocal Models in Biology and Life Sciences: Sources, Developments, and Applications. Physics of Life Reviews, 53, 24-75.