Applications of Mathematical Modelling in Oncolytic Virotherapy and Immunotherapy

Cancer is a devastating disease that touches almost everyone and finding effective treatments presents a highly complex problem, requiring extensive multidisciplinary research. Mathematical modelling can provide insight into both cancer formation and treatment. A range of techniques are developed in this thesis to investigate two promising therapies: oncolytic virotherapy, and combined oncolytic virotherapy and immunotherapy. Oncolytic virotherapy endeavours to eradicate cancer cells by exploiting the aptitude of virus-induced cell death. Building on this premise, combined oncolytic virotherapy and immunotherapy aims to harness and stimulate the immune system's inherent ability to recognise and destroy cancerous cells. Using deterministic and agent-based mathematical modelling, perturbations of treatment characteristics are investigated and optimal treatment protocols are suggested. An integro differential equation with distributed parameters is developed to characterise the function of the E1B genes in an oncolytic adenovirus. Subsequently, by using a bifurcation analysis of a coupled-system of ordinary differential equations for oncolytic virotherapy, regions of bistability are discovered, where increased injections can result in either tumour eradication or tumour stabilisation. Through an extensive hierarchical optimisation to multiple data sets, drawn from in vitro and in vivo modelling, gel-release of a combined oncolytic virotherapy and immunotherapy treatment is optimised. Additionally, using an agent-based modelling approach, delayed-infection of an intratumourally administered virus is shown to be able to reduce tumour burden. This thesis develops new mathematical models that can be applied to a range of cancer therapies and suggests engineered treatment designs that can significantly advance current therapies and improve treatments

Smoothing in linear multicompartment biological processes subject to stochastic input

Many physical and biological systems rely on the progression of material through multiple independent stages. In viral replication, for example, virions enter a cell to undergo a complex process comprising several disparate stages before the eventual accumulation and release of replicated virions. While such systems may have some control over the internal dynamics that make up this progression, a challenge for many is to regulate behavior under what are often highly variable external environments acting as system inputs. In this work, we study a simple analog of this problem through a linear multicompartment model subject to a stochastic input in the form of a mean-reverting Ornstein-Uhlenbeck process, a type of Gaussian process. By expressing the system as a multidimensional Gaussian process, we derive several closed-form analytical results relating to the covariances and autocorrelations of the system, quantifying the smoothing effect discrete compartments afford multicompartment systems. Semianalytical results demonstrate that feedback and feedforward loops can enhance system robustness, and simulation results probe the intractable problem of the first passage time distribution, which has specific relevance to eventual cell lysis in the viral replication cycle. Finally, we demonstrate that the smoothing seen in the process is a consequence of the discreteness of the system, and does not manifest in systems with continuous transport. While we make progress through analysis of a simple linear problem, many of our insights are applicable more generally, and our work enables future analysis into multicompartment processes subject to stochastic inputs

Smoothing in linear multicompartment biological processes subject to stochastic input

Many physical and biological systems rely on the progression of material through multiple independent stages. In viral replication, for example, virions enter a cell to undergo a complex process comprising several disparate stages before the eventual accumulation and release of replicated virions. While such systems may have some control over the internal dynamics that make up this progression, a challenge for many is to regulate behaviour under what are often highly variable external environments acting as system inputs. In this work, we study a simple analogue of this problem through a linear multicompartment model subject to a stochastic input in the form of a mean-reverting Ornstein-Uhlenbeck process, a type of Gaussian process. By expressing the system as a multidimensional Gaussian process, we derive several closed-form analytical results relating to the covariances and autocorrelations of the system, quantifying the smoothing effect discrete compartments afford multicompartment systems. Semi-analytical results demonstrate that feedback and feedforward loops can enhance system robustness, and simulation results probe the intractable problem of the first passage time distribution, which has specific relevance to eventual cell lysis in the viral replication cycle. Finally, we demonstrate that the smoothing seen in the process is a consequence of the discreteness of the system, and does not manifest in an equivalent continuum limit description. While we make progress through analysis of a simple linear problem, many of our insights are applicable more generally, and our work enables future analysis into multicompartment processes subject to stochastic inputs

Mathematical modelling of the interaction between cancer cells and an oncolytic virus: insights into the effects of treatment protocols

Oncolytic virotherapy is an experimental cancer treatment that uses genetically engineered viruses to target and kill cancer cells. One major limitation of this treatment is that virus particles are rapidly cleared by the immune system, preventing them from arriving at the tumour site. To improve virus survival and infectivity modified virus particles with the polymer polyethylene glycol (PEG) and the monoclonal antibody herceptin. While PEG modification appeared to improve plasma retention and initial infectivity it also increased the virus particle arrival time. We derive a mathematical model that describes the interaction between tumour cells and an oncolytic virus. We tune our model to represent the experimental data by Kim et al. (2011) and obtain optimised parameters. Our model provides a platform from which predictions may be made about the response of cancer growth to other treatment protocols beyond those in the experiments. Through model simulations we find that the treatment protocol affects the outcome dramatically. We quantify the effects of dosage strategy as a function of tumour cell replication and tumour carrying capacity on the outcome of oncolytic virotherapy as a treatment. The relative significance of the modification of the virus and the crucial role it plays in optimising treatment efficacy is explored.Comment: 15 pages, 6 figure

Efficient inference and identifiability analysis for differential equation models with random parameters

Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data. Therefore, methods for exploring the identifiability of models that explicitly incorporate heterogeneity through variability in model parameters are relatively underdeveloped. We develop a new likelihood-based framework, based on moment matching, for inference and identifiability analysis of differential equation models that capture biological heterogeneity through parameters that vary according to probability distributions. As our novel method is based on an approximate likelihood function, it is highly flexible; we demonstrate identifiability analysis using both a frequentist approach based on profile likelihood, and a Bayesian approach based on Markov-chain Monte Carlo. Through three case studies, we demonstrate our method by providing a didactic guide to inference and identifiability analysis of hyperparameters that relate to the statistical moments of model parameters from independent observed data. Our approach has a computational cost comparable to analysis of models that neglect heterogeneity, a significant improvement over many existing alternatives. We demonstrate how analysis of random parameter models can aid better understanding of the sources of heterogeneity from biological data.Comment: Minor changes to text. Additional results in supplementary material. Additional statistics regarding results given in main and supplementary materia

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

Optimising Hydrogel Release Profiles for Viro-Immunotherapy Using Oncolytic Adenovirus Expressing IL-12 and GM-CSF with Immature Dendritic Cells

Sustained-release delivery systems, such as hydrogels, significantly improve cancer therapies by extending the treatment efficacy and avoiding excess wash-out. Combined virotherapy and immunotherapy (viro-immunotherapy) is naturally improved by these sustained-release systems, as it relies on the continual stimulation of the antitumour immune response. In this article, we consider a previously developed viro-immunotherapy treatment where oncolytic viruses that are genetically engineered to infect and lyse cancer cells are loaded onto hydrogels with immature dendritic cells (DCs). The time-dependent release of virus and immune cells results in a prolonged cancer cell killing from both the virus and activated immune cells. Although effective, a major challenge is optimising the release profile of the virus and immature DCs from the gel so as to obtain a minimum tumour size. Using a system of ordinary differential equations calibrated to experimental results, we undertake a novel numerical investigation of different gel-release profiles to determine the optimal release profile for this viro-immunotherapy. Using a data-calibrated mathematical model, we show that if the virus is released rapidly within the first few days and the DCs are released for two weeks, the tumour burden can be significantly decreased. We then find the true optimal gel-release kinetics using a genetic algorithm and suggest that complex profiles present unnecessary risk and that a simple linear-release model is optimal. In this work, insight is provided into a fundamental problem in the growing field of sustained-delivery systems using mathematical modelling and analysis

Translational approaches to treating dynamical diseases through in silico clinical trials

The primary goal of drug developers is to establish efficient and effective therapeutic protocols. Multifactorial pathologies, including dynamical diseases and complex disorders, can be difficult to treat, given the high degree of inter- and intra-patient variability and nonlinear physiological relationships. Quantitative approaches combining mechanistic disease modeling and computational strategies are increasingly leveraged to rationalize pre-clinical and clinical studies and to establish effective treatment strategies. The development of clinical trials has led to new computational methods that allow for large clinical data sets to be combined with pharmacokinetic and pharmacodynamic models of diseases. Here, we discuss recent progress using in silico clinical trials to explore treatments for a variety of complex diseases, ultimately demonstrating the immense utility of quantitative methods in drug development and medicine. </p