Speaker
Description
Mathematical models can be used in order to verify medical hypotheses and quantify the mechanisms of the progression of neurological pathologies like Alzheimer's disease. Here we consider a model based on ordinary differential equations incorporating dynamics of toxic proteins like Amyloid $\beta$ species and tau tangles and describing their spread on a brain graph based on the human connectome, where brain regions are connected by edges representing fiber tracts.\cite{Bianchi2024MCA}
In order to solve the differential equation and compare the results with clinical data, Physics-Informed Neural Networks (PINNs\cite{Raissi2019CP}) can be leveraged. The deep-learning framework has shown to be powerful by combining previous physical knowledge with sparse or noisy data\cite{Zhang2024CMAME}, in this case tau concentrations inferred from PET scans of subjects with Alzheimer's disease \cite{Petersen2010N}. Choosing the best suited hyperparameters and the weights of the individual loss function terms is delicate, but even with a quite simple network architecture, results have been achieved that are comparable with those given by standard numerical methods in a steady-state setup.
Future applications and extensions of the approach will involve model parameters estimation by setting specific variables trainable within the PINN. Identifying the most suitable parameter values will allow further assessment of the model’s ability to reproduce observed patterns of pathology.
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{Raissi2019CP,
title = {Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations},
author = {Raissi, Maziar and Perdikaris, Paris and Karniadakis, George E.},
journal = {Journal of Computational Physics},
year = {2019},
volume = {378},
pages = {686--707},
doi = {10.1016/j.jcp.2018.10.045},
url = {https://doi.org/10.1016/j.jcp.2018.10.045}
}
@article{Zhang2024CMAME,
title = {Discovering a reaction–diffusion model for {Alzheimer’s} disease by
combining {PINNs} with symbolic regression},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {419},
pages = {116647},
year = {2024},
issn = {0045-7825},
doi = {https://doi.org/10.1016/j.cma.2023.116647},
url = {https://www.sciencedirect.com/science/article/pii/S0045782523007703},
author = {Zhen Zhang and Zongren Zou and Ellen Kuhl and George Em Karniadakis},
}
@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/) }
}
