Speaker
Description
Angiogenesis is a hallmark of cancer wherein cancerous cells generate new vasculature to ensure that all cells continue to receive adequate nutrients as the tumour grows. Mathematical models exist for dynamics between tumour cells and vasculature, and a primary assumption in many of these models is that tumour carrying capacity is related to vasculature density \cite{H}. Although this is known to be true in a biological context \cite{L}, the precise relationship between vasculature density and tumour carrying capacity is not well defined, which makes the mathematical parameterization of this relationship difficult and subject to uncertainty. Here we employ Physics Informed Neural Networks (PINNs) to infer this critical parameter. PINNs incorporate domain-specific physical constraints to enhance the biological feasibility and predictive accuracy of mathematical models by integrating the models with empirical biological data \cite{R}. Inverse PINNs can be used to uncover unknown model parameters from sparse data. We employ an inverse PINN approach for parameter discovery, using clinical time series data, to quantify the relationship between vasculature density and solid tumour carrying capacity. We verify the predictive accuracy of our resulting model, and use in-silico data to explore implications for anti-angiogenic treatment protocols.
Bibliography
@article{H,
author = {Hahnfeldt, P. and Panigrahy, D. and Folkman, J. and Hlatky, L.},
title = {Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy},
journal = {Cancer Research},
volume = {59},
number = {19},
pages = {4770--4775},
year = {1999}
}
@article{L,
author = {Lugano, R. and Ramachandran, M. and Dimberg, A.},
title = {Tumor angiogenesis: causes, consequences, challenges and opportunities},
journal = {Cellular and Molecular Life Sciences},
year = {2020},
volume = {77},
number = {9},
pages = {1745--1770},
month = {May},
doi = {10.1007/s00018-019-03351-7},
pmid = {31690961},
pmcid = {PMC7190605}
}
@article{R,
author = {Raissi, M. and Perdikaris, P. and Karniadakis, G. E.},
title = {Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations},
journal = {Journal of Computational Physics},
year = {2019},
volume = {378},
pages = {686--707},
doi = {10.1016/j.jcp.2018.10.045}
}
