The Role of the Innate Immune System in Oncolytic Virotherapy

A Mathematical Study of the Role of tBregs in Breast Cancer

A model for the mathematical study of immune response to breast cancer is proposed and studied, both analytically and numerically. It is a simplification of a complex one, recently introduced by two of the present authors. It serves for a compact study of the dynamical role in cancer promotion of a relatively recently described subgroup of regulatory B cells, which are evoked by the tumour.

Deterministic and stochastic modeling for PDGF-driven gliomas reveals a classification of gliomas

Motivated by our study of infiltrating dynamics of immune cells into tumors, we propose a stochastic model in terms of Ito stochastic differential equations to study how two parameters, the chemoattractant production rate and the chemotactic coefficient, influence immune cell migration and how these parameters distinguish two types of gliomas. We conduct a detailed analysis of the stochastic model and its deterministic counterpart. The deterministic model can differentiate two types of gliomas according to the range of the chemoattractant production rate as two equilibrium solutions, while the stochastic model also can differentiate two types of gliomas according to the ranges of the chemoattractant production rate and chemotactic coefficient with thresholds as one non-zero ergodic invariant measure and one weak persistent state when the noise intensities are small. When the noise intensities are large comparing with the chemotactic coefficient, there is only one type of glioma that corresponds to a non-zero ergodic invariant measure. Using our experimental data, numerical simulations are carried out to demonstrate properties of our models, and we give medical interpretations and implications for our analytical results and numerical simulations. This study also confirms some of our results about IDH gliomas.

Natural Killer Cells Recruitment in Oncolytic Virotherapy: A Mathematical Model

In this paper, we investigate how natural killer (NK) cell recruitment to the tumor microenvironment (TME) affects oncolytic virotherapy. NK cells play a major role against viral infections. They are, however, known to induce early viral clearance of oncolytic viruses, which hinders the overall efficacy of oncolytic virotherapy. Here, we formulate and analyze a simple mathematical model of the dynamics of the tumor, OV and NK cells using currently available preclinical information. The aim of this study is to characterize conditions under which the synergistic balance between OV-induced NK responses and required viral cytopathicity may or may not result in a successful treatment. In this study, we found that NK cell recruitment to the TME must take place neither too early nor too late in the course of OV infection so that treatment will be successful. NK cell responses are most influential at either early (partly because of rapid response of NK cells to viral infections or antigens) or later (partly because of antitumoral ability of NK cells) stages of oncolytic virotherapy. The model also predicts that: (a) an NK cell response augments oncolytic virotherapy only if viral cytopathicity is weak; (b) the recruitment of NK cells modulates tumor growth; and (c) the depletion of activated NK cells within the TME enhances the probability of tumor escape in oncolytic virotherapy. Taken together, our model results demonstrate that OV infection is crucial, not just to cytoreduce tumor burden, but also to induce the stronger NK cell response necessary to achieve complete or at least partial tumor remission. Furthermore, our modeling framework supports combination therapies involving NK cells and OV which are currently used in oncolytic immunovirotherapy to treat several cancer types.

Modeling dynamics of cancer radiovirotherapy

Advances in genetic engineering have paved the way for a new therapy for cancer, which is called virotherapy. This treatment uses genetically engineered viruses which selectively infect, replicate in, and destroy cancer cells without damaging normal cells. Furthermore, current research and clinical trials have indicated that these viruses can be delivered as single agents or in combination with other therapies. In this paper, we propose systems of ordinary differential equations for modeling the dynamics of aggressive tumor growth under radiovirotherapy treatment. We divide the treatment period into two phases; consequently, we present two mathematical models. First, we formulate the virotherapy model as Phase I of the treatment. Then we extend the model to include radiotherapy in combination with virotherapy as Phase II of the treatment. Comprehensive qualitative analyses of both models are conducted. Furthermore, numerical experiments are performed in order to support the analytical results. An analysis of the parameters is also carried out to investigate their effects on the outcome of the treatment. Overall, the analytical results reveal that radiovirotherapy is more effective than, and a good alternative to, virotherapy, as it is capable of eradicating tumors completely.

The role of viral infectivity in oncolytic virotherapy outcomes: A mathematical study

A model capturing the dynamics between virus and tumour cells in the context of oncolytic virotherapy is presented and analysed. The ability of the virus to be internalised by uninfected cells is described by an infectivity parameter, which is inferred from available experimental data. The parameter is also able to describe the effects of changes in the tumour environment that affect viral uptake from tumour cells. Results show that when a virus is inoculated inside a growing tumour, strategies for enhancing infectivity do not lead to a complete eradication of the tumour. Within typical times of experiments and treatments, we observe the onset of oscillations, which always prevent a full destruction of the tumour mass. These findings are in good agreement with available laboratory results. Further analysis shows why a fully successful therapy cannot exist for the proposed model and that care must be taken when designing and engineering viral vectors with enhanced features. In particular, bifurcation analysis reveals that creating longer lasting virus particles or using strategies for reducing infected cell lifespan can cause unexpected and unwanted surges in the overall tumour load over time. Our findings suggest that virotherapy alone seems unlikely to be effective in clinical settings unless adjuvant strategies are included.

Quantitative Systems Pharmacology Approaches for Immuno-Oncology: Adding Virtual Patients to the Development Paradigm

Drug development in oncology commonly exploits the tools of molecular biology to gain therapeutic benefit through reprograming of cellular responses. In immuno‐oncology (IO) the aim is to direct the patient’s own immune system to fight cancer. After remarkable successes of antibodies targeting PD1/PD‐L1 and CTLA4 receptors in targeted patient populations, the focus of further development has shifted toward combination therapies. However, the current drug‐development approach of exploiting a vast number of possible combination targets and dosing regimens has proven to be challenging and is arguably inefficient. In particular, the unprecedented number of clinical trials testing different combinations may no longer be sustainable by the population of available patients. Further development in IO requires a step change in selection and validation of candidate therapies to decrease development attrition rate and limit the number of clinical trials. Quantitative systems pharmacology (QSP) proposes to tackle this challenge through mechanistic modeling and simulation. Compounds’ pharmacokinetics, target binding, and mechanisms of action as well as existing knowledge on the underlying tumor and immune system biology are described by quantitative, dynamic models aiming to predict clinical results for novel combinations. Here, we review the current QSP approaches, the legacy of mathematical models available to quantitative clinical pharmacologists describing interaction between tumor and immune system, and the recent development of IO QSP platform models. We argue that QSP and virtual patients can be integrated as a new tool in existing IO drug development approaches to increase the efficiency and effectiveness of the search for novel combination therapies.

Basic stochastic model for tumor virotherapy

The complexity of oncolytic virotherapy arises from many factors. In this study, we incorporate environmental noise and stochastic effects to our basic deterministic model and propose a stochastic model for viral therapy in terms of Ito stochastic differential equations. We conduct a detailed analysis of the model using boundary methods. We find two combined parameters, one describes possibilities of eradicating tumors and one is an increasing function of the viral burst size, which serve as thresholds to classify asymptotical dynamics of the model solution paths. We show there are three ergodic invariant probability measures which correspond to equilibrium states of the deterministic model, and extra possibility to eradicate tumor due to strong variance of tumor growth rate and medium viral burst size. Numerical analysis demonstrates several typical solution paths with biological explanations. In addition, we provide some medical interpretations and implications.

Investigating Macrophages Plasticity Following Tumour-Immune Interactions During Oncolytic Therapies

Over the last few years, oncolytic virus therapy has been recognised as a promising approach in cancer treatment, due to the potential of these viruses to induce systemic anti-tumour immunity and selectively killing tumour cells. However, the effectiveness of these viruses depends significantly on their interactions with the host immune responses, both innate (e.g., macrophages, which accumulate in high numbers inside solid tumours) and adaptive (e.g., \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CD8}^{+}$$\end{document}CD8+ T cells). In this article, we consider a mathematical approach to investigate the possible outcomes of the complex interactions between two extreme types of macrophages (M1 and M2 cells), effector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CD8}^{+}$$\end{document}CD8+ T cells and an oncolytic Vesicular Stomatitis Virus (VSV), on the growth/elimination of B16F10 melanoma. We discuss, in terms of VSV, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CD8}^{+}$$\end{document}CD8+ and macrophages levels, two different types of immune responses which could ensure tumour control and eventual elimination. We show that both innate and adaptive anti-tumour immune responses, as well as the oncolytic virus, could be very important in delaying tumour relapse and eventually eliminating the tumour. Overall this study supports the use mathematical modelling to increase our understanding of the complex immune interaction following oncolytic virotherapies. However, the complexity of the model combined with a lack of sufficient data for model parametrisation has an impact on the possibility of making quantitative predictions.

Backward Hopf bifurcation in a mathematical model for oncolytic virotherapy with the infection delay and innate immune effects

In this paper, we consider a system of delay differential equations that models the oncolytic virotherapy on solid tumours with the delay of viral infection in the presence of the innate immune response. We conduct qualitative and numerical analysis, and provide possible medical implications for our results. The system has four equilibrium solutions. Fixed point analysis indicates that increasing the burst size and infection rate of the viruses has positive contribution to the therapy. However, increasing the immune killing infection rate, the immune stimulation rate, or the immune killing virus rate may lead the treatment failed. The viral infection time delay induces backward Hopf bifurcations, which means that the therapy may fail before time delay increases passing through a Hopf bifurcation. The parameter analysis also shows how saddle-node and Hopf bifurcations occur as viral burst size and other parameters vary, which yields further insights into the dynamics of the virotherapy.