Mathematical Modelling of Tumour Dynamics in Hypoxic Environments

Maryam Alka

University of Birmingham

"Mathematical Modelling of Tumour Dynamics in Hypoxic Environments"

Understanding tumour dynamics under hypoxic conditions is critical for optimising cancer therapies, particularly with chemotherapeutic agents like Paclitaxel. This study presents a refined mathematical model of tumour growth that incorporates Paclitaxel effects and hypoxia-driven resistance using a system of nonlinear ordinary differential equations (ODEs). We employ the Metropolis-Hastings Markov Chain Monte Carlo (MH MCMC) algorithm for Bayesian inversion and parameter estimation, providing a probabilistic framework to capture uncertainties. Sensitivity analysis is conducted using the multiple shooting method, which enhances the stability and accuracy of local sensitivity estimates across time intervals. The simulation results demonstrate that cell viability is reduced under moderate hypoxia when treated with Paclitaxel, which is consistent with experimental data from HCC1806 breast cancer cell lines. This agreement between model predictions and experimental outcomes supports the model’s validity in capturing key biological mechanisms. Future work will extend the model using Physics-Informed Neural Networks (PINNs) to improve computational efficiency and explore advanced inverse problem-solving techniques for robust cancer treatment optimisation.

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