Mathematical Models in Oncolytic Virotherapy and Immunology

In this thesis we build mathematical models to address fundamental questions in immunology and virotherapy. We begin with a study of T cell response to pathogens. Although the clonal expansion of T cells is well defined as a tightly regulated process, the mechanisms responsible for this control are not well understood. Guided by experimental data, we design a delay differential model to see if the CD4+ T cell response to infection is directly linked to antigen concentration. Our model successfully captures a series of experimental results, linking T cell expansion to antigen availability. Next, we turn our attention to virotherapy, a relatively novel form of cancer treatment. Introducing a spatial model, we investigate how enhancements in virus design could alter treatment outcome. Using bifurcation theory, we find that certain enhancements may cause undesirable effects in tumour dynamics, such as large oscillations. We then extend our virotherapy model to study a major barrier in the treatment of solid tumours: excess collagen, which is responsible for the lack of diffusion of oncolytic therapies. This investigation leads to a novel virus diffusion term that captures experimental observations. Importantly, we show that the classic diffusion equation, used in many virotherapy models, does not accurately capture the dispersion of virus in collagen-dense tumours, and this may ultimately result in inaccurate predictions of treatment outcome. Finally, we use our new virotherapy model to understand how different collagen-tumour configurations affect treatment outcome. We show that cell-collagen ratio, and gaps in the collagen surface need to be considered to better understand tumour response to treatment. The models developed in this thesis provide sound explanations to fundamental questions in immunology and virotherapy, highlighting key interactions that could significantly advance current therapies

Examining the efficacy of localised gemcitabine therapy for the treatment of pancreatic cancer using a hybrid agent-based model

The prognosis for pancreatic ductal adenocarcinoma (PDAC) patients has not significantly improved in the past 3 decades, highlighting the need for more effective treatment approaches. Poor patient outcomes and lack of response to therapy can be attributed, in part, to a lack of uptake of perfusion of systemically administered chemotherapeutic drugs into the tumour. Wet-spun alginate fibres loaded with the chemotherapeutic agent gemcitabine have been developed as a potential tool for overcoming the barriers in delivery of systemically administrated drugs to the PDAC tumour microenvironment by delivering high concentrations of drug to the tumour directly over an extended period. While exciting, the practicality, safety, and effectiveness of these devices in a clinical setting requires further investigation. Furthermore, an in-depth assessment of the drug-release rate from these devices needs to be undertaken to determine whether an optimal release profile exists. Using a hybrid computational model (agent-based model and partial differential equation system), we developed a simulation of pancreatic tumour growth and response to treatment with gemcitabine loaded alginate fibres. The model was calibrated using in vitro and in vivo data and simulated using a finite volume method discretisation. We then used the model to compare different intratumoural implantation protocols and gemcitabine-release rates. In our model, the primary driver of pancreatic tumour growth was the rate of tumour cell division. We were able to demonstrate that intratumoural placement of gemcitabine loaded fibres was more effective than peritumoural placement. Additionally, we quantified the efficacy of different release profiles from the implanted fibres that have not yet been tested experimentally. Altogether, the model developed here is a tool that can be used to investigate other drug delivery devices to improve the arsenal of treatments available for PDAC and other difficult-to-treat cancers in the future

Examining the efficacy of localised gemcitabine therapy for the treatment of pancreatic cancer using a hybrid agent-based model

The prognosis for pancreatic ductal adenocarcinoma (PDAC) patients has not significantly improved in the past 3 decades, highlighting the need for more effective treatment approaches. Poor patient outcomes and lack of response to therapy can be attributed, in part, to a lack of uptake of perfusion of systemically administered chemotherapeutic drugs into the tumour. Wetspun alginate fibres loaded with the chemotherapeutic agent gemcitabine have been developed as a potential tool for overcoming the barriers in delivery of systemically administrated drugs to the PDAC tumour microenvironment by delivering high concentrations of drug to the tumour directly over an extended period. While exciting, the practicality, safety, and effectiveness of these devices in a clinical setting requires further investigation. Furthermore, an indepth assessment of the drug-release rate from these devices needs to be undertaken to determine whether an optimal release profile exists. Using a hybrid computational model (agent-based model and partial differential equation system), we developed a simulation of pancreatic tumour growth and response to treatment with gemcitabine loaded alginate fibres. The model was calibrated using in vitro and in vivo data and simulated using a finite volume method discretisation. We then used the model to compare different intratumoural implantation protocols and gemcitabine-release rates. In our model, the primary driver of pancreatic tumour growth was the rate of tumour cell division. We were able to demonstrate that intratumoural placement of gemcitabine loaded fibres was more effective than peritumoural placement. Additionally, we quantified the efficacy of different release profiles from the implanted fibres that have not yet been tested experimentally. Altogether, the model developed here is a tool that can be used to investigate other drug delivery devices to improve the arsenal of treatments available for PDAC and other difficult-to-treat cancers in the future

Supplementary Tables and Figures.

Supplementary Tables and Figures that support results in the main text. Includes Tables A-E and Figs A-O. (DOCX)</p