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

Oncolytic virotherapy for tumours following a Gompertz growth law

Oncolytic viruses are genetically engineered to treat growing tumours and represent a very promising therapeutic strategy. Using a Gompertz growth law, we discuss a model that captures the in vivo dynamics of a cancer under treatment with an oncolytic virus. With the aid of local stability analysis and bifurcation plots, the typical interactions between virus and tumour are investigated. The system shows a singular equilibrium and a number of nonlinear behaviours that have interesting biological consequences, such as long-period oscillations and bistable states where two different outcomes can occur depending on the initial conditions. Complete tumour eradication appears to be possible only for parameter combinations where viral characteristics match well with the tumour growth rate. Interestingly, the model shows that therapies with a high initial injection or involving a highly effective virus do not universally result in successful strategies for eradication. Further, the use of additional, “boosting” injection schedules does not always lead to complete eradication. Our framework, instead, suggests that low viral loads can be in some cases more effective than high loads, and that a less resilient virus can help avoid high amplitude oscillations between tumours and virus. Finally, the model points to a number of interesting findings regarding the role of oscillations and bistable states between a tumour and an oncolytic virus. Strategies for the elimination of such fluctuations depend strongly on the initial viral load and the combination of parameters describing the features of the tumour and virus.</p

Application of control theory in a delayed-infection and immune-evading oncolytic virotherapy

Oncolytic virotherapy is a promising cancer treatment that harnesses the power of viruses. Through genetic engineering, these viruses are cultivated to infect and destroy cancer cells. While this therapy has shown success in a range of clinical trials, an open problem in the field is to determine more effective perturbations of these viruses. In this work, we use a controlled therapy approach to determine the optimal treatment protocol for a delayed infection from an immune-evading, coated virus. We derive a system of partial differential equations to model the interaction between a growing tumour and this coated oncolytic virus. Using this system, we show that viruses with inhibited viral clearance and infectivity are more effective than uncoated viruses. We then consider a hierarchical level of coating that degrades over time and determine a nontrivial initial distribution of coating levels needed to produce the lowest tumour volume. Interestingly, we find that a bimodal mixture of thickly coated and thinly coated virus is necessary to achieve a minimum tumour size. Throughout this article we also consider the effects of immune clearance of the virus. We show how different immune responses instigate significantly different treatment outcomes.</p

The effect of chemotaxis on T-cell regulatory dynamics

Autoimmune diseases, such as Multiple Sclerosis, are often modelled through the dynamics of T-cell interactions. However, the spatial aspect of such diseases, and how dynamics may result in spatially heterogeneous outcomes, is often overlooked. We consider the effects of diffusion and chemotaxis on T-cell regulatory dynamics using a three-species model of effector and regulator T-cell populations, along with a chemical signalling agent. While diffusion alone cannot lead to instability and spatial patterning, the inclusion of chemotaxis can result in multiple forms of instability that produce highly complicated spatiotemporal behaviour. The parameter regimes in which different instabilities occur are determined through linear stability analysis and the full dynamics is explored through numerical simulation.</p

Engineering in Medicine to Address the Challenge of Cancer Drug Resistance: From Micro-and Nanotechnologies to Computational and Mathematical Modeling

Drug resistance has profoundly limited the success of cancer treatment, driving relapse, metastasis, and mortality. Nearly all anticancer drugs and even novel immunotherapies, which recalibrate the immune system for tumor recognition and destruction, have succumbed to resistance development. Engineers have emerged across mechanical, physical, chemical, mathematical, and biological disciplines to address the challenge of drug resistance using a combination of interdisciplinary tools and skill sets. This review explores the developing, complex, and under-recognized role of engineering in medicine to address the multitude of challenges in cancer drug resistance. Looking through the "lens"of intrinsic, extrinsic, and drug-induced resistance (also referred to as "tolerance"), we will discuss three specific areas where active innovation is driving novel treatment paradigms: (1) nanotechnology, which has revolutionized drug delivery in desmoplastic tissues, harnessing physiochemical characteristics to destroy tumors through photothermal therapy and rationally designed nanostructures to circumvent cancer immunotherapy failures, (2) bioengineered tumor models, which have benefitted from microfluidics and mechanical engineering, creating a paradigm shift in physiologically relevant environments to predict clinical refractoriness and enabling platforms for screening drug combinations to thwart resistance at the individual patient level, and (3) computational and mathematical modeling, which blends in silico simulations with molecular and evolutionary principles to map mutational patterns and model interactions between cells that promote resistance. On the basis that engineering in medicine has resulted in discoveries in resistance biology and successfully translated to clinical strategies that improve outcomes, we suggest the proliferation of multidisciplinary science that embraces engineering. </p

Treating cancerous cells with viruses: insights from a minimal model for oncolytic virotherapy

In recent years, interest in the capability of virus particles as a treatment for cancer has increased. In this work, we present a mathematical model embodying the interaction between tumour cells and virus particles engineered to infect and destroy cancerous tissue. To quantify the effectiveness of oncolytic virotherapy, we conduct a local stability analysis and bifurcation analysis of our model. In the absence of tumour growth or viral decay, the model predicts that oncolytic virotherapy will successfully eliminate the tumour cell population for a large proportion of initial conditions. In comparison, for growing tumours and decaying viral particles there are no stable equilibria in the model; however, oscillations emerge for certain regions in our parameter space. We investigate how the period and amplitude of oscillations depend on tumour growth and viral decay. We find that higher tumour replication rates result in longer periods between oscillations and lower amplitudes for uninfected tumour cells. From our analysis, we conclude that oncolytic viruses can reduce growing tumours into a stable oscillatory state, but are insufficient to completely eradicate them. We propose that it is only with the addition of other anti-cancer agents that tumour eradication may be achieved by oncolytic virus