Qualitative and quantitative approaches to modelling tyrosine kinase inhibitor treatment and resistance in non-small cell lung cancer
Keywords: sensitivity analysis
identifiability analysis
drug resistance
stochastic modelling
tyrosine kinase inhibitors
mathematical modelling
mathematical oncology
Bayesian inference
non-small cell lung cancer
data fitting

Non-small cell lung cancer (NSCLC) affects 80-85% of lung cancer patients. Tyrosine kinase inhibitors (TKIs) are targeted therapies that bind to NSCLC cells with specific mutations and inhibit their growth. However, responses to these therapies generally fail due to the emergence of drug resistance and the onset of adverse events which can include; interstitial lung disease (ILD), edema, hypothyroidism, nausea and diarrhoea. Mathematical models can increase our understanding of the biological mechanisms that determine whether a tumour is likely to respond or become resistant to treatment. When combined with experimental studies, such models can provide mechanistic insight into factors which influence the evolution to resistance and how specific drugs act. They can also aid experimental design and generate testable hypotheses concerning, for example, optimal dose regimens, scheduling protocols and combination therapies. In this thesis, we develop mathematical models of tumour growth and treatment response, and use them to determine tumour-specific factors that influence drug resistance. Further, by combining the models with preclinical data, we infer the biological properties of different NSCLC cell lines and characterise their responses to different TKIs.
In the first part of the thesis, we develop a mathematical model that describes the dynamics of four cell populations that differ in their levels of resistance to two TKIs. The model accounts for mutations, competition for resources and cellular interactions and is formulated as a system of time-dependent, ordinary differential equations. We use the model to show how tumour responses to TKI combinations depend on the rates at which the tumour cells mutate and proliferate. We then reformulate the model to account for stochastic effects that encapsulate the random nature of mutation events that occur with low probabilities. We find considerable variation in the predictions generated by the deterministic and stochastic modelling frameworks, highlighting the need for careful consideration of the modelling approach when predicting drug resistance and treatment response.
The second part of the thesis focuses on integrating mathematical models with experimental data in order to uncover the mechanisms driving NSCLC cells’ responses to TKI treatment. We develop a suite of increasingly complex models that describe in vitro cell growth data. We use parameter estimation, information criteria/goodness-of-fit metrics and parameter identifiability analysis to investigate the identifiability of the model parameters given the preclinical data and to guide model selection. We extend the selected model to describe the response of NSCLC cells to TKI treatment. While this model is structurally identifiable, the existence of practically non-identifiable model parameters given the in vitro treatment data leads to uncertainty in the predictions of hidden variables. We use synthetic data to evaluate how experimental design (i.e. what variables are measured) affects certainty in parameter estimates and to generate hypotheses about the likely mechanisms of action of TKIs on NSCLC cells.
To summarise, in this thesis, we develop a series of mathematical models that increase our understanding of the biological mechanisms that drive the evolution to resistant tumours and determine tumour response to treatment. Our results highlight the benefit of theoretical approaches for distinguishing the growth dynamics of different NSCLC cell lines, providing mechanistic insight into the effects of different drugs on different cell lines and suggesting strategies for improving experimental design.