Speakers
Description
Mathematical modelling is an important tool for understanding a complex pathology such as Alzheimers disease (AD). Quantitative models enable to formalize hypotheses about key factors such as the dynamics of proteins ($A\beta$ and $\tau$) and inflammation, providing insights difficult to obtain through experiments alone. To this purpose many different and possibly complementary approaches can be adopted. The aim of this proposal is to favour interaction between researchers using different mathematical and computational tools to study similar issues. To model the spread of proteins, a very convenient mathematical setting is given by networks, in particular by connectomes, which are weighted graphs constructed from clinical data \cite{ber,bre}. By integrating data from neuroimaging, computational models can help elucidate disease progression patterns across brain networks \cite{lan}. Mechanistic models also support the identification of critical transition points in the preclinical phase of AD, improving early detection strategies \cite{far}. Interesting results have also been obtained with analytical methods from semigroups theory and homogenisation \cite{fra}. Overall, mathematical modelling provides a rigorous framework to integrate multi-scale AD data, generate testable predictions, and ultimately accelerate the development of effective clinical, possibly personalized strategies. They therefore represent a major challenge nowadays in a cutting-edge research area.
Bibliography
@article{bre,
title = {A network aggregation model for {amyloid-$\beta$} dynamics and treatment of {Alzheimer}’s diseases at the brain scale},
volume = {90},
issn = {0303-6812, 1432-1416},
url = {https://link.springer.com/10.1007/s00285-024-02179-5},
doi = {10.1007/s00285-024-02179-5},
abstract = {},
language = {en},
number = {2},
urldate = {2026-01-19},
journal = {Journal of Mathematical Biology},
author = {Brennan, Georgia S. and Goriely, Alain},
month = feb,
year = {2025},
pages = {22},
}
@article{far,
title = {Mechanistic multiscale modelling of energy metabolism in human astrocytes reveals the impact of morphology changes in {Alzheimer}’s {Disease}},
volume = {19},
issn = {1553-7358},
url = {https://dx.plos.org/10.1371/journal.pcbi.1011464},
doi = {10.1371/journal.pcbi.1011464},
abstract = {},
language = {en},
number = {9},
urldate = {2026-01-20},
journal = {PLOS Computational Biology},
author = {Farina, Sofia and Voorsluijs, Valerie and Fixemer, Sonja and Bouvier, David S. and Claus, Susanne and Ellisman, Mark H. and Bordas, Stephane P. A. and Skupin, Alexander},
editor = {Berry, Hugues},
month = sep,
year = {2023},
pages = {e1011464},
}
@article{fra,
title = {Homogenization of {Smoluchowski}-type equations with transmission boundary conditions},
volume = {24},
copyright = {http://creativecommons.org/licenses/by/4.0},
issn = {2169-0375},
url = {https://www.degruyter.com/document/doi/10.1515/ans-2023-0143/html},
doi = {10.1515/ans-2023-0143},
abstract = {},
language = {en},
number = {4},
urldate = {2026-01-20},
journal = {Advanced Nonlinear Studies},
author = {Franchi, Bruno and Lorenzani, Silvia},
month = oct,
year = {2024},
pages = {952--991},
}
@article{ber,
title = {The role of {A$\beta$} and {Tau} proteins in {Alzheimer}’s disease: a mathematical model on graphs},
volume = {87},
issn = {0303-6812, 1432-1416},
shorttitle = {The role of {A}\$\${\textbackslash}beta \$\$ and {Tau} proteins in {Alzheimer}’s disease},
url = {https://link.springer.com/10.1007/s00285-023-01985-7},
doi = {10.1007/s00285-023-01985-7},
abstract = {},
language = {en},
number = {3},
urldate = {2026-01-20},
journal = {Journal of Mathematical Biology},
author = {Bertsch, Michiel and Franchi, Bruno and Tesi, Maria Carla and Tora, Veronica},
month = sep,
year = {2023},
pages = {49},
}
@article{lan,
title = {Spreading of pathological proteins through brain networks: A case study for {Alzheimer}’s disease},
volume = {xx},
issn = {1551-0018, 1547-1063},
url = {accepted for publication},
doi = {10.3934/mbe.2026xxx},
language = {en},
number = {xx},
urldate = {2026-01-20},
journal = {To appear in Mathematical Biosciences and Engineering},
author = {Landi, Germana and Scaravelli, Arianna and Tesi, Maria Carla and Testa, Claudia},
month = jan,
year = {2026},
pages = {18},
}
