City Research Online

Abstract

Mathematical Modelling of Adaptive Cancer Therapy

Maximum tolerated dose (MTD) chemotherapy has long been the standard of care for cancer treatment. An MTD protocol will rapidly deplete the population of treatment sensitive cells in the tumour, leaving only treatment-resistant cells behind, which will then grow without inhibition. A proposed alternative, called adaptive therapy (AT), aims to maintain a constant, high tumour burden, in a bid to leverage the evolutionary dynamics present in the tumour microenvironment to the patient’s advantage. Building on previous works, in collaboration with experimental biologists, we conduct a combined mathematical and experimental analysis of cancer adaptive therapy with epidermal growth factor receptor tyrosine kinase inhibitors. We present an analysis of both in-vitro cell assays and in-vivo mice experiments with PC-9 non-small cell lung cancer under treatment with erlotinib and osimertinib. From this analysis, we use a hierarchical Bayesian inference framework to parameterise an ODE model which we use to both explain phenomena and test hypotheses resulting from our data analysis. Combining this with analytical and numerical techniques which tell us the nature of the interaction between the cancer cells in vitro, we propose an adaptive therapy treatment protocol which should outperform a standard MTD protocol in terms of survival time. We use reproducible techniques to quantify model parameters and describe the nature of competition between these cells, informing future clinical trials based on these models.

Mathematical Modelling of Bipolar Androgen Therapy

Androgen deprivation therapy (ADT) has long been the standard of care for treatment of advanced and metastatic prostate cancer. The aim of ADT is to deprive the hormone-dependent cancer cells of testosterone, inhibiting their proliferative capabilities or killing them outright. However, the cancer will eventually adapt to its new environment, reducing the efficacy of androgen ablation. When the disease progresses despite continued ADT, we refer to it as castrate-resistant prostate cancer (CRPC).

The proposed method for Bipolar Androgen therapy, or BAT, involves cycling between near-castrate levels of testosterone seen during ADT and supraphysiologic testosterone levels achieved via an intramuscular testosterone injection. This injection of large amounts of testosterone has been shown to inhibit the growth of castrate-resistant prostate cancer cells by overloading their androgen receptors, and has been shown to restore sensitivity to ADT. As of yet, no mathematical models have been designed which try to describe this treatment. As such, we present an ODE model with minimal assumptions which aims to describe the BAT treatment protocols seen in the literature. By simplifying this model to a to make it more analytically tractable, we investigate the key facets of the treatment. We present a means to find the optimal treatment in a model where therapies alternate, and build upon this result to suggest a protocol for scheduling BAT which improves upon the protocol consistently seen in literature, supporting these claims with simulations.

Bayesian Modelling of Cancer Incidence Rates

Recent reports show that cancer incidence in adults under the age of 50 are increasing. Many different factors have been considered as potential drivers for these increases. It is possible, however, that processes such as screening for cancers such as breast or colorectal cancers, could be the driving force behind this increase in rate.

In order to investigate this, we adapt the hierarchical Bayesian inference workflow used for our investigations on adaptive therapy to study DEVCAN (probability of Developing or Dying of Cancer) statistics pulled from the US SEER ( Surveillance, Epidemiology and End Results) data for cancer incidence. We used our inference workflow to fit two different Weibull-type models to this pan-cancer data set. The first model tests whether or not a true increase in incidence is occurring; the second fixes the incidence rate and tests whether or not the increased incidence can be explained by a decrease in detection lag time; the third tests both simultaneously to see which of the two might have a greater influence on results when both parameters governing these different factors are allowed to vary. We then test individual cancers to examine whether the trends in the pan-cancer data hold up for individual cases. We find that although both models do fit pan-cancer data, which would suggest that either hypothesis could explain the increase in incidence, the model fails to properly fit the data for individual cancers, suggesting that these Weibull type models may be too simple to capture the trends in these cases.

Altogether, we present in this thesis a methodological framework for analysing an array of different cancer data sets and treatment strategies. We use statistical and theoretical modelling to propose novel treatment strategies for both adaptive therapy and bipolar androgen therapy. We demonstrate the versatility of our hierarchical bayesian modelling framework by using it to parameterise models which aim to describe phenomena seen in in vitro and in vivo experimental cancer data, as well as test hypotheses which can explain trends in cancer incidence data by using our framework to parameterise simple models which validate these hypotheses.

Publication Type:	Thesis (Doctoral)
Subjects:	H Social Sciences > HA Statistics Q Science > QA Mathematics R Medicine > RC Internal medicine > RC0254 Neoplasms. Tumors. Oncology (including Cancer)
Departments:	School of Science & Technology > Department of Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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