Computational modeling approaches to the dynamics of oncolytic viruses

Applications of Intravital Imaging in Cancer Immunotherapy

Currently, immunotherapy is one of the most effective treatment strategies for cancer. However, the efficacy of any specific anti-tumor immunotherapy can vary based on the dynamic characteristics of immune cells, such as their rate of migration and cell-to-cell interactions. Therefore, understanding the dynamics among cells involved in the immune response can inform the optimization and improvement of existing immunotherapy strategies. In vivo imaging technologies use optical microscopy techniques to visualize the movement and behavior of cells in vivo, including cells involved in the immune response, thereby showing great potential for application in the field of cancer immunotherapy. In this review, we briefly introduce the technical aspects required for in vivo imaging, such as fluorescent protein labeling, the construction of transgenic mice, and various window chamber models. Then, we discuss the elucidation of new phenomena and mechanisms relating to tumor immunotherapy that has been made possible by the application of in vivo imaging technology. Specifically, in vivo imaging has supported the characterization of the movement of T cells during immune checkpoint inhibitor therapy and the kinetic analysis of dendritic cell migration in tumor vaccine therapy. Finally, we provide a perspective on the challenges and future research directions for the use of in vivo imaging technology in cancer immunotherapy.

Agent-Based and Continuum Models for Spatial Dynamics of Infection by Oncolytic Viruses

The use of oncolytic viruses as cancer treatment has received considerable attention in recent years, however the spatial dynamics of this viral infection is still poorly understood. We present here a stochastic agent-based model describing infected and uninfected cells for solid tumours, which interact with viruses in the absence of an immune response. Two kinds of movement, namely undirected random and pressure-driven movements, are considered: the continuum limit of the models is derived and a systematic comparison between the systems of partial differential equations and the individual-based model, in one and two dimensions, is carried out. In the case of undirected movement, a good agreement between agent-based simulations and the numerical and well-known analytical results for the continuum model is possible. For pressure-driven motion, instead, we observe a wide parameter range in which the infection of the agents remains confined to the center of the tumour, even though the continuum model shows traveling waves of infection; outcomes appear to be more sensitive to stochasticity and uninfected regions appear harder to invade, giving rise to irregular, unpredictable growth patterns. Our results show that the presence of spatial constraints in tumours' microenvironments limiting free expansion has a very significant impact on virotherapy. Outcomes for these tumours suggest a notable increase in variability. All these aspects can have important effects when designing individually tailored therapies where virotherapy is included.

Mathematical Modeling of Oncolytic Virus Therapy Reveals Role of the Immune Response

Oncolytic adenoviruses (OAds) present a promising path for cancer treatment due to their selectivity in infecting and lysing tumor cells and their ability to stimulate the immune response. In this study, we use an ordinary differential equation (ODE) model of tumor growth inhibited by oncolytic virus activity to parameterize previous research on the effect of genetically re-engineered OAds in A549 lung cancer tumors in murine models. We find that the data are best fit by a model that accounts for an immune response, and that the immune response provides a mechanism for elimination of the tumor. We also find that parameter estimates for the most effective OAds share characteristics, most notably a high infection rate and low viral clearance rate, that might be potential reasons for these viruses' efficacy in delaying tumor growth. Further studies observing E1A and P19 recombined viruses in different tumor environments may further illuminate the extent of the effects of these genetic modifications.

Oncolytic virus treatment of human breast cancer cells: Modelling therapy efficacy

Oncolytic viruses are a promising new treatment for cancer, whereby viruses are engineered to selectively destroy cancer cells. Mathematical modelling of the dynamics of the virus-tumour system can be modelled to provide insight into the system outcomes under different treatment protocols. In this study key metrics of treatment efficacy were identified and the mathematical model used to develop a decision framework to assess different treatment protocols. The optimal treatment outcome is the interplay between the virus application protocol and the uncertainty about the tumour characteristics. The uncertainty in the model parameters decreases as more data is available for their inference - however to obtain more data more time is required and the tumour then grows in size. Thus, there is an inherent tension whether it is better to wait to know the characteristics of the tumour system better or immediately initiating treatment. It is shown that, for small tumours, parameter inference with limited data does not constrain the choice of treatment protocol and rather only influences longer term decisions.

Dynamic analysis of an age structure model for oncolytic virus therapy

Cancer is recognized as one of the serious diseases threatening human health. Oncolytic therapy is a safe and effective new cancer treatment method. Considering the limited ability of uninfected tumor cells to infect and the age of infected tumor cells have a significant effect on oncolytic therapy, an age-structured model of oncolytic therapy involving Holling-Ⅱ functional response is proposed to investigate the theoretical significance of oncolytic therapy. First, the existence and uniqueness of the solution is obtained. Furthermore, the stability of the system is confirmed. Then, the local stability and global stability of infection-free homeostasis are studied. The uniform persistence and local stability of the infected state are studied. The global stability of the infected state is proved by constructing the Lyapunov function. Finally, the theoretical results are verified by numerical simulation. The results show that when the tumor cells are at the appropriate age, injection of the right amount of oncolytic virus can achieve the purpose of tumor treatment.

Nonlocal multiscale modelling of tumour-oncolytic viruses interactions within a heterogeneous fibrous/non-fibrous extracellular matrix

In this study we investigate computationally tumour-oncolytic virus (OV) interactions that take place within a heterogeneous extracellular matrix (ECM). The ECM is viewed as a mixture of two constitutive phases, namely a fibre phase and a non-fibre phase. The multiscale mathematical model presented here focuses on the nonlocal cell-cell and cell-ECM interactions, and how these interactions might be impacted by the infection of cancer cells with the OV. At macroscale we track the kinetics of cancer cells, virus particles and the ECM. At microscale we track (i) the degradation of ECM by matrix degrading enzymes (MDEs) produced by cancer cells, which further influences the movement of tumour boundary; (ii) the re-arrangement of the microfibres that influences the re-arrangement of macrofibres (i.e., fibres at macroscale). With the help of this new multiscale model, we investigate two questions: (i) whether the infected cancer cell fluxes are the result of local or non-local advection in response to ECM density; and (ii) what is the effect of ECM fibres on the the spatial spread of oncolytic viruses and the outcome of oncolytic virotherapy.

Towards a Mathematical Model for the Viral Progression in the Pharynx

In this work, a comprehensive model for the viral progression in the pharynx has been developed. This one-dimension model considers both Fickian diffusion and convective flow coupled with chemical reactions, such as virus population growth, infected and uninfected cell accumulation as well as virus clearance. The effect of a sterilizing agent such as an alcoholic solution on the viral progression in the pharynx was taken into account and a parametric analysis for the effect of kinetic rate parameters on virus propagation was made. Moreover, different conditions caused by further medical treatment, such as a decrease in virus yield per infected cell, were examined. It is shown that the infection fails to establish by decreasing the virus yield per infected cell. It is believed that this work could be used to further investigate the medical treatment of viral progression in the pharynx.

A mathematical model of viral oncology as an immuno-oncology instigator

We develop and analyse a mathematical model of tumour-immune interaction that explicitly incorporates heterogeneity in tumour cell cycle duration by using a distributed delay differential equation. We derive a necessary and sufficient condition for local stability of the cancer-free equilibrium in which the amount of tumour-immune interaction completely characterizes disease progression. Consistent with the immunoediting hypothesis, we show that decreasing tumour-immune interaction leads to tumour expansion. Finally, by simulating the mathematical model, we show that the strength of tumour-immune interaction determines the long-term success or failure of viral therapy.

Oncolytic viruses encoding bispecific T cell engagers: a blueprint for emerging immunovirotherapies

Bispecific T cell engagers (BiTEs) are an innovative class of immunotherapeutics that redirect T cells to tumor surface antigens. While efficacious against certain hematological malignancies, limited bioavailability and severe toxicities have so far hampered broader clinical application, especially against solid tumors. Another emerging cancer immunotherapy are oncolytic viruses (OVs) which selectively infect and replicate in malignant cells, thereby mediating tumor vaccination effects. These oncotropic viruses can serve as vectors for tumor-targeted immunomodulation and synergize with other immunotherapies. In this article, we discuss the use of OVs to overcome challenges in BiTE therapy. We review the current state of the field, covering published preclinical studies as well as ongoing clinical investigations. We systematically introduce OV-BiTE vector design and characteristics as well as evidence for immune-stimulating and anti-tumor effects. Moreover, we address additional combination regimens, including CAR T cells and immune checkpoint inhibitors, and further strategies to modulate the tumor microenvironment using OV-BiTEs. The inherent complexity of these novel therapeutics highlights the importance of translational research including correlative studies in early-phase clinical trials. More broadly, OV-BiTEs can serve as a blueprint for diverse OV-based cancer immunotherapies.

Computational modelling of modern cancer immunotherapy

Modern cancer immunotherapy has revolutionised oncology and carries the potential to radically change the approach to cancer treatment. However, numerous questions remain to be answered to understand immunotherapy response better and further improve the benefit for future cancer patients. Computational models are promising tools that can contribute to accelerated immunotherapy research by providing new clues and hypotheses that could be tested in future trials, based on preceding simulations in addition to the empirical rationale. In this topical review, we briefly summarise the history of cancer immunotherapy, including computational modelling of traditional cancer immunotherapy, and comprehensively review computational models of modern cancer immunotherapy, such as immune checkpoint inhibitors (as monotherapy and combination treatment), co-stimulatory agonistic antibodies, bispecific antibodies, and chimeric antigen receptor T cells. The modelling approaches are classified into one of the following categories: data-driven top-down vs mechanistic bottom-up, simplistic vs detailed, continuous vs discrete, and hybrid. Several common modelling approaches are summarised, such as pharmacokinetic/pharmacodynamic models, Lotka-Volterra models, evolutionary game theory models, quantitative systems pharmacology models, spatio-temporal models, agent-based models, and logic-based models. Pros and cons of each modelling approach are critically discussed, particularly with the focus on the potential for successful translation into immuno-oncology research and routine clinical practice. Specific attention is paid to calibration and validation of each model, which is a necessary prerequisite for any successful model, and at the same time, one of the main obstacles. Lastly, we provide guidelines and suggestions for the future development of the field.

Parasite-Guest Infection Modeling: Social Science Applications

In this study we argue that parasite-host infections are a major research topic because of their implications for human health, agriculture and wildlife. The evolution of infection mechanisms is a research topic in areas such as virology and ecology. Mathematical modelling has been an essential tool to obtain a better systematic and quantitative understanding of the processes of parasitic infection that are difficult to discern through strictly experimental approaches. In this article we review recent attempts using mathematical models to discriminate and quantify these infection mechanisms. We also emphasize the challenges that these models could bring to new fields of study such as social sciences and economics.

Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment

Chemovirotherapy is a combination therapy with chemotherapy and oncolytic viruses. It is gaining more interest and attracting more attention in the clinical setting due to its effective therapy and potential synergistic interactions against cancer. In this paper, we develop and analyse a mathematical model in the form of parabolic non-linear partial differential equations to investigate the spatiotemporal dynamics of tumour cells under chemovirotherapy treatment. The proposed model consists of uninfected and infected tumour cells, a free virus, and a chemotherapeutic drug. The analysis of the model is carried out for both the temporal and spatiotemporal cases. Travelling wave solutions to the spatiotemporal model are used to determine the minimum wave speed of tumour invasion. A sensitivity analysis is performed on the model parameters to establish the key parameters that promote cancer remission during chemovirotherapy treatment. Model analysis of the temporal model suggests that virus burst size and virus infection rate determine the success of the virotherapy treatment, whereas travelling wave solutions to the spatiotemporal model show that tumour diffusivity and growth rate are critical during chemovirotherapy. Simulation results reveal that chemovirotherapy is more effective and a good alternative to either chemotherapy or virotherapy, which is in agreement with the recent experimental studies.

Fighting Cancer with Mathematics and Viruses

After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex antitumor effects, such as innate and adaptive immune responses and the destruction of tumor vasculature. With the availability of different vector platforms and the potential of both genetic engineering and combination regimens to enhance particular aspects of safety and efficacy, the identification of optimal treatments for patient subpopulations or even individual patients becomes a top priority. Mathematical modeling can provide support in this arena by making use of experimental and clinical data to generate hypotheses about the mechanisms underlying complex biology and, ultimately, predict optimal treatment protocols. Increasingly complex models can be applied to account for therapeutically relevant parameters such as components of the immune system. In this review, we describe current developments in oncolytic virotherapy and mathematical modeling to discuss the benefit of integrating different modeling approaches into biological and clinical experimentation. Conclusively, we propose a mutual combination of these research fields to increase the value of the preclinical development and the therapeutic efficacy of the resulting treatments.

A generic viral dynamic model to systematically characterize the interaction between oncolytic virus kinetics and tumor growth

Oncolytic viruses (OV) represent an encouraging new therapeutic concept for treatment of human cancers. OVs specifically replicate in tumor cells and initiate cell lysis whilst tumor cells act as endogenous bioreactors for virus amplification. This complex bidirectional interaction between tumor and oncolytic virus hampers the establishment of a straight dose-concentration-effect relation. We aimed to develop a generic mathematical pharmacokinetic/pharmacodynamics (PK/PD) model to characterize the relationship between tumor cell growth and kinetics of different OVs. U87 glioblastoma cell growth and titer of Newcastle disease virus (NDV), reovirus (RV) and parvovirus (PV) were systematically determined in vitro. PK/PD analyses were performed using non-linear mixed effects modeling. A viral dynamic model (VDM) with a common structure for the three different OVs was developed which simultaneously described tumor growth and virus replication. Virus specific parameters enabled a comparison of the kinetics and tumor killing efficacy of each OV. The long-term interactions of tumor cells with NDV and RV were simulated to predict tumor reoccurrence. Various treatment scenarios (single and multiple dosing with same OV, co-infection with different OVs and combination with hypothetical cytotoxic compounds) were simulated and ranked for efficacy using a newly developed treatment rating score. The developed VDM serves as flexible tool for the systematic cross-characterization of tumor-virus relationships and supports preselection of the most promising treatment regimens for follow-up in vivo analyses.