Speaker
Description
This work presents a mathematical study of the progression of Alzheimer’s disease through a dynamical model based on ordinary differential equations. A detailed analysis is carried out on a biomarker cascade model which describes the sequential interaction between beta‑amyloid accumulation, tau hyperphosphorylation, neurodegeneration, and cognitive decline, in the line of the models introduced in \cite{Hao2022, Petrella2019}. A new causal model is proposed, introducing a time‑dependent growth rate for amyloid accumulation, providing greater flexibility to represent genetic factors, therapeutic interventions, and cognitive reserve. A theoretical analysis is developed, including analytical properties, equilibrium points, and stability of the resulting non‑autonomous system. Simulations show the model’s ability to fit diverse clinical patterns and highlight the usefulness of the model as a predictive tool and its potential for future personalized clinical applications based on real patient data.
Bibliography
@article{Hao2022,
title = {Optimal anti-amyloid-beta therapy for {A}lzheimer’s disease via a personalized mathematical model},
volume = {18},
ISSN = {1553-7358},
url = {http://dx.doi.org/10.1371/journal.pcbi.1010481},
DOI = {10.1371/journal.pcbi.1010481},
number = {9},
journal = {PLOS Computational Biology},
publisher = {Public Library of Science (PLoS)},
author = {Hao, Wenrui and Lenhart, Suzanne and Petrella, Jeffrey R.},
editor = {Jenner, Adrianne},
year = {2022},
month = sep,
pages = {e1010481}
}
@article{Petrella2019,
title = {Computational causal modeling of the dynamic biomarker cascade in {A}lzheimer’s disease},
volume = {2019},
ISSN = {1748-6718},
DOI = {10.1155/2019/6216530},
journal = {Computational and Mathematical Methods in Medicine},
publisher = {Hindawi Limited},
author = {Petrella, Jeffrey R. and Hao, Wenrui and Rao, Adithi and Doraiswamy, P. Murali},
year = {2019},
url={https://doi.org/10.1016/j.jalz.2016.04.008},
month = feb,
pages = {1–8}
}
