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Description
Mathematical models can be used to verify medical hypotheses and quantify the mechanisms of the progression of neurological pathologies like Alzheimer's disease. In this work, we are interested in elucidating the spread of misfolded tau protein, a critical hallmark of Alzheimer's disease, alongside amyloid $\beta$ protein, while taking the synergistic interaction between the two proteins into account \cite{Bianchi2024MCA}. We analyze a model consisting of a set of ordinary differential equations defined on brain networks derived from human connectomes, where brain regions are connected by edges representing fiber tracts. In particular, we consider several modeling choices, all employing network frameworks for protein evolution, differentiated by the network architecture and diffusion operators employed. By carefully comparing the model results against clinical tau concentration data \cite{Petersen2010N}, gathered through advanced multimodal analysis techniques, we can identify values for the parameters of the mathematical model such that it can reproduce the disease progression. Moreover, we show that certain models better replicate the protein's dynamics and that the mathematical setting must be chosen with great care if the comparison with clinical data is considered decisive \cite{Landi2026MBE}.
Bibliography
@article{Bianchi2024MCA,
author = {Bianchi, Stefano and Landi, Germana and Marella, Camilla and Tesi, Maria Carla and Testa, Claudia and on behalf of the Alzheimer's Disease Neuroimaging Initiative},
title = {A Network-Based Study of the Dynamics of {A$\beta$} and $\tau$ Proteins in {Alzheimer's} {Disease}},
journal = {Mathematical and Computational Applications},
volume = {29},
year = {2024},
number = {6},
doi = {https://doi.org/10.3390/mca29060113},
article-number = {113},
url = {https://www.mdpi.com/2297-8747/29/6/113},
issn = {2297-8747},
doi = {10.3390/mca29060113}
}
@article{Petersen2010N,
author = {Petersen, Ronald C. and Aisen, P. S. and Beckett, L. A. and Donohue, M. C. and Gamst, A. C. and Harvey, D. J. and Jack, C. R. and Jagust, W. J. and Shaw, L. M. and Toga, A. W. and Trojanowski, J. Q. and Weiner, M. W.},
title = {{Alzheimer's Disease Neuroimaging Initiative (ADNI)}: clinical characterization},
journal = {Neurology},
year = {2010},
month = {jan},
volume = {74},
number = {3},
pages = {201--209},
doi = {10.1212/WNL.0b013e3181cb3e25},
pmid = {20042704},
pmcid = {PMC2809036},
note = {Epub 2009 Dec 30 (https://adni.loni.usc.edu/) }
}
@article{Landi2026MBE,
title = {Spreading of pathological proteins through brain networks: A case study for Alzheimer's disease},
journal = {Mathematical Biosciences and Engineering},
volume = {23},
number = {3},
pages = {619-635},
year = {2026},
issn = {1551-0018},
doi = {10.3934/mbe.2026024},
url = {https://www.aimspress.com/article/doi/10.3934/mbe.2026024},
author = {Germana Landi and Arianna Scaravelli and Maria Carla Tesi and Claudia Testa},
keywords = {Alzheimer's disease, mathematical models on graphs, $ A\beta $ and $ \tau $ proteins, medical imaging, numerical simulations},
}
