Towards predictive computational models of oncolytic virus therapy: basis for experimental validation and model selection

CAR T-cell and oncolytic virus dynamics and determinants of combination therapy success for glioblastoma

Glioblastoma is a highly aggressive and treatment-resistant primary brain cancer. While chimeric antigen receptor (CAR) T-cell therapy has demonstrated promising results in targeting these tumors, it has not yet been curative. An innovative approach to improve CAR T-cell efficacy is to combine them with other immune modulating therapies. In this study, we investigate in vitro combination of IL-13Rα2 targeted CAR T-cells with an oncolytic virus (OV) and study the complex interplay between tumor cells, CAR T-cells, and OV dynamics with a novel mathematical model. We fit the model to data collected from experiments with each therapy individually and in combination to reveal determinants of therapy synergy and improved efficacy. Our analysis reveals that the virus bursting size is a critical parameter in determining the net tumor infection rate and overall combination treatment efficacy. Moreover, the model predicts that administering the oncolytic virus simultaneously with, or prior to, CAR T-cells could maximize therapeutic efficacy.

Spatiotemporal spread of oncolytic virus in a heterogeneous cell population

Oncolytic (cancer-killing) virus treatment is a promising new therapy for cancer, with many viruses currently being tested for their ability to eradicate tumors. One of the major stumbling blocks to the development of this treatment modality has been preventing spread of the virus to non-cancerous cells. Our recent ability to manipulate RNA and DNA now allows for the possibility of creating designer viruses specifically targeted to cancer cells, thereby significantly reducing unwanted side effects in patients. In this study, we use a partial differential equation model to determine the characteristics of a virus needed to contain spread of an oncolytic virus within a spherical tumor and prevent it from spreading to non-cancerous cells outside the tumor. We find that oncolytic viruses that have different infection rates or different cell death rates in cancer and non-cancerous cells can be made to stay within the tumor. We find that there is a minimum difference in infection rates or cell death rates that will contain the virus and that this threshold value depends on the growth rate of the cancer. Identification of these types of thresholds can help researchers develop safer strains of oncolytic viruses allowing further development of this promising treatment.

A comparative analysis of 2D and 3D experimental data for the identification of the parameters of computational models

Computational models are becoming an increasingly valuable tool in biomedical research. Their accuracy and effectiveness, however, rely on the identification of suitable parameters and on appropriate validation of the in-silico framework. Both these steps are highly dependent on the experimental model used as a reference to acquire the data. Selecting the most appropriate experimental framework thus becomes key, together with the analysis of the effect of combining results from different experimental models, a common practice often necessary due to limited data availability. In this work, the same in-silico model of ovarian cancer cell growth and metastasis, was calibrated with datasets acquired from traditional 2D monolayers, 3D cell culture models or a combination of the two. The comparison between the parameters sets obtained in the different conditions, together with the corresponding simulated behaviours, is presented. It provides a framework for the study of the effect of the different experimental models on the development of computational systems. This work also provides a set of general guidelines for the comparative testing and selection of experimental models and protocols to be used for parameter optimization in computational models.

Slow-Fast Model and Therapy Optimization for Oncolytic Treatment of Tumors

The present work studies models of oncolytic virotherapy without space variable in which virus replication occurs at a faster time scale than tumor growth. We address the questions of the modeling of virus injection in this slow-fast system and of the optimal timing for different treatment strategies. To this aim, we first derive the asymptotic of a three-species slow-fast model and obtain a two-species dynamical system, where the variables are tumor cells and infected tumor cells. We fully characterize the behavior of this system depending on the various biological parameters. In the second part, we address the modeling of virus injection and its expression in the two-species system, where the amount of virus does not appear explicitly. We prove that the injection can be described by an instantaneous jump in the phase plane, where a certain amount of tumors cells are transformed instantly into infected tumor cells. This description allows discussing qualitatively the timing of different injections in the frame of successive treatment strategies. This work is illustrated by numerical simulations. The timing and amount of injected virus may have counterintuitive optimal values; nevertheless, the understanding is clear from the phase space analysis.

Bifurcation analysis of the cancer virotherapy system with time delay and diffusion

In this paper, we propose a cancer virotherapy model with virus lytic cycle and diffusion term. Spatiotemporal dynamic properties of the cancer virotherapy system are studied. First, by analyzing the roots distribution of the characteristic equation and transcendental equation, the conditions for the local stability of the constant equilibria of system are given. Second, we select delay as the bifurcation parameter, the existence conditions of Hopf bifurcation are given. By using the center manifold theory and normal form method of partial functional differential equation, the detailed formulae for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are given. Finally, some numerical simulations are given.

A combination therapy of oncolytic viruses and chimeric antigen receptor T cells: a mathematical model proof-of-concept

Combining chimeric antigen receptor T (CAR-T) cells with oncolytic viruses (OVs) has recently emerged as a promising treatment approach in preclinical studies that aim to alleviate some of the barriers faced by CAR-T cell therapy. In this study, we address by means of mathematical modeling the main question of whether a single dose or multiple sequential doses of CAR-T cells during the OVs therapy can have a synergetic effect on tumor reduction. To that end, we propose an ordinary differential equations-based model with virus-induced synergism to investigate potential effects of different regimes that could result in efficacious combination therapy against tumor cell populations. Model simulations show that, while the treatment with a single dose of CAR-T cells is inadequate to eliminate all tumor cells, combining the same dose with a single dose of OVs can successfully eliminate the tumor in the absence of virus-induced synergism. However, in the presence of virus-induced synergism, the same combination therapy fails to eliminate the tumor. Furthermore, it is shown that if the intensity of virus-induced synergy and/or virus oncolytic potency is high, then the induced CAR-T cell response can inhibit virus oncolysis. Additionally, the simulations show a more robust synergistic effect on tumor cell reduction when OVs and CAR-T cells are administered simultaneously compared to the combination treatment where CAR-T cells are administered first or after OV injection. Our findings suggest that the combination therapy of CAR-T cells and OVs seems unlikely to be effective if the virus-induced synergistic effects are included when genetically engineering oncolytic viral vectors.

Bistability in a model of tumor-immune system interactions with an oncolytic viral therapy

A mathematical model of tumor-immune system interactions with an oncolytic virus therapy for which the immune system plays a twofold role against cancer cells is derived. The immune cells can kill cancer cells but can also eliminate viruses from the therapy. In addition, immune cells can either be stimulated to proliferate or be impaired to reduce their growth by tumor cells. It is shown that if the tumor killing rate by immune cells is above a critical value, the tumor can be eradicated for all sizes, where the critical killing rate depends on whether the immune system is immunosuppressive or proliferative. For a reduced tumor killing rate with an immunosuppressive immune system, that bistability exists in a large parameter space follows from our numerical bifurcation study. Depending on the tumor size, the tumor can either be eradicated or be reduced to a size less than its carrying capacity. However, reducing the viral killing rate by immune cells always increases the effectiveness of the viral therapy. This reduction may be achieved by manipulating certain genes of viruses via genetic engineering or by chemical modification of viral coat proteins to avoid detection by the immune cells.

Computational tools for assessing gene therapy under branching process models of mutation

Multitype branching processes are ideal for studying the population dynamics of stem cell populations undergoing mutation accumulation over the years following transplant. In such stochastic models, several quantities are of clinical interest as insertional mutagenesis carries the potential threat of leukemogenesis following gene therapy with autologous stem cell transplantation. In this paper, we develop a three-type branching process model describing accumulations of mutations in a population of stem cells distinguished by their ability for long-term self-renewal. Our outcome of interest is the appearance of a double-mutant cell, which carries a high potential for leukemic transformation. In our model, a single-hit mutation carries a slight proliferative advantage over a wild-type stem cells. We compute marginalized transition probabilities that allow us to capture important quantitative aspects of our model, including the probability of observing a double-hit mutant and relevant moments of a single-hit mutation population over time. We thoroughly explore the model behavior numerically, varying birth rates across the initial sizes and populations of wild type stem cells and single-hit mutants, and compare the probability of observing a double-hit mutant under these conditions. We find that increasing the number of single-mutants over wild-type particles initially present has a large effect on the occurrence of a double-mutant, and that it is relatively safe for single-mutants to be quite proliferative, provided the lentiviral gene addition avoids creating single mutants in the original insertion process. Our approach is broadly applicable to an important set of questions in cancer modeling and other population processes involving multiple stages, compartments, or types.

An Agent-Based Model of Combination Oncolytic Viral Therapy and Anti-PD-1 Immunotherapy Reveals the Importance of Spatial Location When Treating Glioblastoma

Simple Summary

A combination of oncolytic viral therapy and immunotherapy provides an alternative option to the standard of care for treating the lethal brain tumor glioblastoma (GBM). Although this combination therapy shows promise, there are many unknown questions regarding how the tumor landscape and spatial dosing strategies impact the effectiveness of the treatment. Our study aims to shed light on these questions using a novel spatially explicit computational model of GBM response to treatment. Our results suggest that oncolytic viral dosing in the location of highest tumor cell density leads to substantial tumor size reduction over viral dosing in the center of the tumor. These results can help to inform future clinical trials and more effective treatment strategies for oncolytic viral therapy in GBM patients.

Abstract

Oncolytic viral therapies and immunotherapies are of growing clinical interest due to their selectivity for tumor cells over healthy cells and their immunostimulatory properties. These treatment modalities provide promising alternatives to the standard of care, particularly for cancers with poor prognoses, such as the lethal brain tumor glioblastoma (GBM). However, uncertainty remains regarding optimal dosing strategies, including how the spatial location of viral doses impacts therapeutic efficacy and tumor landscape characteristics that are most conducive to producing an effective immune response. We develop a three-dimensional agent-based model (ABM) of GBM undergoing treatment with a combination of an oncolytic Herpes Simplex Virus and an anti-PD-1 immunotherapy. We use a mechanistic approach to model the interactions between distinct populations of immune cells, incorporating both innate and adaptive immune responses to oncolytic viral therapy and including a mechanism of adaptive immune suppression via the PD-1/PD-L1 checkpoint pathway. We utilize the spatially explicit nature of the ABM to determine optimal viral dosing in both the temporal and spatial contexts. After proposing an adaptive viral dosing strategy that chooses to dose sites at the location of highest tumor cell density, we find that, in most cases, this adaptive strategy produces a more effective treatment outcome than repeatedly dosing in the center of the tumor.

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.

The Impact of Social and Behavioral Factors on Reproducibility in Terrestrial Vertebrate Models

The use of animal models remains critical in preclinical and translational research. The reliability of the animal models and aspects of their validity is likely key to effective translation of findings to medicine. However, despite considerable uniformity in animal models brought about by control of genetics, there remain a number of social as well as innate and acquired behavioral characteristics of laboratory animals that may impact on research outcomes. These include the effects of strain and genetics, age and development, sex, personality and affective states, and social factors largely brought about by housing and husbandry. In addition, aspects of the testing environment may also influence research findings. A number of considerations resulting from the animals' innate and acquired behavioral characteristics as well as their social structures are described. Suggestions for minimizing the impact of these factors on research are provided.

Modeling Oncolytic Viral Therapy, Immune Checkpoint Inhibition, and the Complex Dynamics of Innate and Adaptive Immunity in Glioblastoma Treatment

Oncolytic viruses are of growing interest to cancer researchers and clinicians, due to their selectivity for tumor cells over healthy cells and their immunostimulatory properties. The immune response to an oncolytic virus plays a critical role in treatment efficacy. However, uncertainty remains regarding the circumstances under which the immune system either assists in eliminating tumor cells or inhibits treatment via rapid viral clearance, leading to the cessation of the immune response. In this work, we develop an ordinary differential equation model of treatment for a lethal brain tumor, glioblastoma, using an oncolytic Herpes Simplex Virus. We use a mechanistic approach to model the interactions between distinct populations of immune cells, incorporating both innate and adaptive immune responses to oncolytic viral therapy (OVT), and including a mechanism of adaptive immune suppression via the PD-1/PD-L1 checkpoint pathway. We focus on the tradeoff between viral clearance by innate immune cells and the innate immune cell-mediated recruitment of antiviral and antitumor adaptive immune cells. Our model suggests that when a tumor is treated with OVT alone, the innate immune cells' ability to clear the virus quickly after administration has a much larger impact on the treatment outcome than the adaptive immune cells' antitumor activity. Even in a highly antigenic tumor with a strong innate immune response, the faster recruitment of antitumor adaptive immune cells is not sufficient to offset the rapid viral clearance. This motivates our subsequent incorporation of an immunotherapy that inhibits the PD-1/PD-L1 checkpoint pathway by blocking PD-1, which we combine with OVT within the model. The combination therapy is most effective for a highly antigenic tumor or for intermediate levels of innate immune localization. Extreme levels of innate immune cell activity either clear the virus too quickly or fail to activate a sufficiently strong adaptive response, yielding ineffective combination therapy of GBM. Hence, we show that the innate and adaptive immune interactions significantly influence treatment response and that combining OVT with an immune checkpoint inhibitor expands the range of immune conditions that allow for tumor size reduction or clearance.

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.

Spatial Model for Oncolytic Virotherapy with Lytic Cycle Delay

We formulate a mathematical model of functional partial differential equations for oncolytic virotherapy which incorporates virus diffusivity, tumor cell diffusion, and the viral lytic cycle based on a basic oncolytic virus dynamics model. We conduct a detailed analysis for the dynamics of the model and carry out numerical simulations to demonstrate our analytic results. Particularly, we establish the positive invariant domain for the [Formula: see text] limit set of the system and show that the model has three spatially homogenous equilibriums solutions. We prove that the spatially uniform virus-free steady state is globally asymptotically stable for any viral lytic period delay and diffusion coefficients of tumor cells and viruses when the viral burst size is smaller than a critical value. We obtain the conditions, for example the ratio of virus diffusion coefficient to that of tumor cells is greater than a value and the viral lytic cycle, is greater than a critical value, under which the spatially uniform positive steady state is locally asymptotically stable. We also obtain conditions under which the system undergoes Hopf bifurcations, and stable periodic solutions occur. We point out medical implications of our results which are difficult to obtain from models without combining diffusive properties of viruses and tumor cells with viral lytic cycles.

Developing a Minimally Structured Mathematical Model of Cancer Treatment with Oncolytic Viruses and Dendritic Cell Injections

Mathematical models of biological systems must strike a balance between being sufficiently complex to capture important biological features, while being simple enough that they remain tractable through analysis or simulation. In this work, we rigorously explore how to balance these competing interests when modeling murine melanoma treatment with oncolytic viruses and dendritic cell injections. Previously, we developed a system of six ordinary differential equations containing fourteen parameters that well describes experimental data on the efficacy of these treatments. Here, we explore whether this previously developed model is the minimal model needed to accurately describe the data. Using a variety of techniques, including sensitivity analyses and a parameter sloppiness analysis, we find that our model can be reduced by one variable and three parameters and still give excellent fits to the data. We also argue that our model is not too simple to capture the dynamics of the data, and that the original and minimal models make similar predictions about the efficacy and robustness of protocols not considered in experiments. Reducing the model to its minimal form allows us to increase the tractability of the system in the face of parametric uncertainty.

Modelling heterogeneity in viral-tumour dynamics: The effects of gene-attenuation on viral characteristics

The use of viruses as a cancer treatment is becoming increasingly more robust; however, there is still a long way to go before a completely successful treatment is formulated. One major challenge in the field is to select which virus, out of a burgeoning number of oncolytic viruses and engineered derivatives, can maximise both treatment spread and anticancer cytotoxicity. To assist in solving this problem, an in-depth understanding of the virus-tumour interaction is crucial. In this article, we present a novel integro-differential system with distributed delays embodying the dynamics of an oncolytic adenovirus with a fixed population of tumour cells in vitro, allowing for heterogeneity to exist in the virus and cell populations. The parameters of the model are optimised in a hierarchical manner, the purpose of which is not to obtain a perfect representation of the data. Instead, we place our parameter values in the correct region of the parameter space. Due to the sparse nature of the data it is not possible to obtain the parameter values with any certainty, but rather we demonstrate the suitability of the model. Using our model we quantify how modifications to the viral genome alter the viral characteristics, specifically how the attenuation of the E1B 19 and E1B 55 gene affect the system performance, and identify the dominant processes altered by the mutations. From our analysis, we conclude that the deletion of the E1B 55 gene significantly reduces the replication rate of the virus in comparison to the deletion of the E1B 19 gene. We also found that the deletion of both the E1B 19 and E1B 55 genes resulted in a long delay in the average replication start time of the virus. This leads us to propose the use of E1B 19 gene-attenuated adenovirus for cancer therapy, as opposed to E1B 55 gene-attenuated adenoviruses.

Imaging, Tracking and Computational Analyses of Virus Entry and Egress with the Cytoskeleton

Viruses have a dual nature: particles are “passive substances” lacking chemical energy transformation, whereas infected cells are “active substances” turning-over energy. How passive viral substances convert to active substances, comprising viral replication and assembly compartments has been of intense interest to virologists, cell and molecular biologists and immunologists. Infection starts with virus entry into a susceptible cell and delivers the viral genome to the replication site. This is a multi-step process, and involves the cytoskeleton and associated motor proteins. Likewise, the egress of progeny virus particles from the replication site to the extracellular space is enhanced by the cytoskeleton and associated motor proteins. This overcomes the limitation of thermal diffusion, and transports virions and virion components, often in association with cellular organelles. This review explores how the analysis of viral trajectories informs about mechanisms of infection. We discuss the methodology enabling researchers to visualize single virions in cells by fluorescence imaging and tracking. Virus visualization and tracking are increasingly enhanced by computational analyses of virus trajectories as well as in silico modeling. Combined approaches reveal previously unrecognized features of virus-infected cells. Using select examples of complementary methodology, we highlight the role of actin filaments and microtubules, and their associated motors in virus infections. In-depth studies of single virion dynamics at high temporal and spatial resolutions thereby provide deep insight into virus infection processes, and are a basis for uncovering underlying mechanisms of how cells function.

The Role of the Innate Immune System in Oncolytic Virotherapy

The complexity of the immune responses is a major challenge in current virotherapy. This study incorporates the innate immune response into our basic model for virotherapy and investigates how the innate immunity affects the outcome of virotherapy. The viral therapeutic dynamics is largely determined by the viral burst size, relative innate immune killing rate, and relative innate immunity decay rate. The innate immunity may complicate virotherapy in the way of creating more equilibria when the viral burst size is not too big, while the dynamics is similar to the system without innate immunity when the viral burst size is big.

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.

Oncolytic potency and reduced virus tumor-specificity in oncolytic virotherapy. A mathematical modelling approach

In the present paper, we address by means of mathematical modeling the following main question: How can oncolytic virus infection of some normal cells in the vicinity of tumor cells enhance oncolytic virotherapy? We formulate a mathematical model describing the interactions between the oncolytic virus, the tumor cells, the normal cells, and the antitumoral and antiviral immune responses. The model consists of a system of delay differential equations with one (discrete) delay. We derive the model's basic reproductive number within tumor and normal cell populations and use their ratio as a metric for virus tumor-specificity. Numerical simulations are performed for different values of the basic reproduction numbers and their ratios to investigate potential trade-offs between tumor reduction and normal cells losses. A fundamental feature unravelled by the model simulations is its great sensitivity to parameters that account for most variation in the early or late stages of oncolytic virotherapy. From a clinical point of view, our findings indicate that designing an oncolytic virus that is not 100% tumor-specific can increase virus particles, which in turn, can further infect tumor cells. Moreover, our findings indicate that when infected tissues can be regenerated, oncolytic viral infection of normal cells could improve cancer treatment.

Hybrid multiscale modeling and prediction of cancer cell behavior

Background

Understanding cancer development crossing several spatial-temporal scales is of great practical significance to better understand and treat cancers. It is difficult to tackle this challenge with pure biological means. Moreover, hybrid modeling techniques have been proposed that combine the advantages of the continuum and the discrete methods to model multiscale problems.

Methods

In light of these problems, we have proposed a new hybrid vascular model to facilitate the multiscale modeling and simulation of cancer development with respect to the agent-based, cellular automata and machine learning methods. The purpose of this simulation is to create a dataset that can be used for prediction of cell phenotypes. By using a proposed Q-learning based on SVR-NSGA-II method, the cells have the capability to predict their phenotypes autonomously that is, to act on its own without external direction in response to situations it encounters.

Results

Computational simulations of the model were performed in order to analyze its performance. The most striking feature of our results is that each cell can select its phenotype at each time step according to its condition. We provide evidence that the prediction of cell phenotypes is reliable.

Conclusion

Our proposed model, which we term a hybrid multiscale modeling of cancer cell behavior, has the potential to combine the best features of both continuum and discrete models. The in silico results indicate that the 3D model can represent key features of cancer growth, angiogenesis, and its related micro-environment and show that the findings are in good agreement with biological tumor behavior. To the best of our knowledge, this paper is the first hybrid vascular multiscale modeling of cancer cell behavior that has the capability to predict cell phenotypes individually by a self-generated dataset.

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.

Computational modeling approaches to the dynamics of oncolytic viruses

Replicating oncolytic viruses represent a promising treatment approach against cancer, specifically targeting the tumor cells. Significant progress has been made through experimental and clinical studies. Besides these approaches, however, mathematical models can be useful when analyzing the dynamics of virus spread through tumors, because the interactions between a growing tumor and a replicating virus are complex and nonlinear, making them difficult to understand by experimentation alone. Mathematical models have provided significant biological insight into the field of virus dynamics, and similar approaches can be adopted to study oncolytic viruses. The review discusses this approach and highlights some of the challenges that need to be overcome in order to build mathematical and computation models that are clinically predictive. WIREs Syst Biol Med 2016, 8:242-252. doi: 10.1002/wsbm.1332 For further resources related to this article, please visit the WIREs website.

Differences in predictions of ODE models of tumor growth: a cautionary example

BACKGROUND

While mathematical models are often used to predict progression of cancer and treatment outcomes, there is still uncertainty over how to best model tumor growth. Seven ordinary differential equation (ODE) models of tumor growth (exponential, Mendelsohn, logistic, linear, surface, Gompertz, and Bertalanffy) have been proposed, but there is no clear guidance on how to choose the most appropriate model for a particular cancer.

METHODS

We examined all seven of the previously proposed ODE models in the presence and absence of chemotherapy. We derived equations for the maximum tumor size, doubling time, and the minimum amount of chemotherapy needed to suppress the tumor and used a sample data set to compare how these quantities differ based on choice of growth model.

RESULTS

We find that there is a 12-fold difference in predicting doubling times and a 6-fold difference in the predicted amount of chemotherapy needed for suppression depending on which growth model was used.

CONCLUSION

Our results highlight the need for careful consideration of model assumptions when developing mathematical models for use in cancer treatment planning.

Infectio: a Generic Framework for Computational Simulation of Virus Transmission between Cells

Infectio presents a generalized platform to analyze virus infection spread between cells. It allows the simulation of plaque phenotypes from image-based assays. Viral plaques are the result of virus spreading from primary infected cells to neighboring cells. This is a complex process and involves neighborhood effects at cell-cell contact sites or fluid dynamics in the extracellular medium. Infectio differentiates between two major modes of virus transmission between cells, allowing in silico testing of hypotheses about spreading mechanisms of any virus which can be grown in cell cultures, based on experimentally measured parameters, such as infection intensity or cell killing. The results of these tests can be compared with experimental data and allow interpretations with regard to biophysical mechanisms. Infectio also facilitates characterizations of the mode of action of therapeutic agents, such as oncolytic viruses or other infectious or cytotoxic agents.

Viruses spread between cells, tissues, and organisms by cell-free and cell-cell mechanisms, depending on the cell type, the nature of the virus, or the phase of the infection cycle. The mode of viral transmission has a large impact on disease development, the outcome of antiviral therapies or the efficacy of gene therapy protocols. The transmission mode of viruses can be addressed in tissue culture systems using live-cell imaging. Yet even in relatively simple cell cultures, the mechanisms of viral transmission are difficult to distinguish. Here we present a cross-platform software framework called “Infectio,” which is capable of simulating transmission phenotypes in tissue culture of virtually any virus. Infectio can estimate interdependent biological parameters, for example for vaccinia virus infection, and differentiate between cell-cell and cell-free virus spreading. Infectio assists in elucidating virus transmission mechanisms, a feature useful for designing strategies of perturbing or enhancing viral transmission. The complexity of the Infectio software is low compared to that of other software commonly used to quantitate features of cell biological images, which yields stable and relatively error-free output from Infectio. The software is open source (GPLv3 license), and operates on the major platforms (Windows, Mac, and Linux). The complete source code can be downloaded from http://infectio.github.io/index.html.

IMPORTANCE Infectio presents a generalized platform to analyze virus infection spread between cells. It allows the simulation of plaque phenotypes from image-based assays. Viral plaques are the result of virus spreading from primary infected cells to neighboring cells. This is a complex process and involves neighborhood effects at cell-cell contact sites or fluid dynamics in the extracellular medium. Infectio differentiates between two major modes of virus transmission between cells, allowing in silico testing of hypotheses about spreading mechanisms of any virus which can be grown in cell cultures, based on experimentally measured parameters, such as infection intensity or cell killing. The results of these tests can be compared with experimental data and allow interpretations with regard to biophysical mechanisms. Infectio also facilitates characterizations of the mode of action of therapeutic agents, such as oncolytic viruses or other infectious or cytotoxic agents.

Perfusion Pressure Is a Critical Determinant of the Intratumoral Extravasation of Oncolytic Viruses

Antitumor efficacy of oncolytic virotherapy is determined by the density and distribution of infectious centers within the tumor, which may be heavily influenced by the permeability and blood flow in tumor microvessels. Here, we investigated whether systemic perfusion pressure, a key driver of tumor blood flow, could influence the intratumoral extravasation of systemically administered oncolytic vesicular stomatitis virus (VSV) in myeloma tumor-bearing mice. Exercise was used to increase mean arterial pressure, and general anesthesia to decrease it. A recombinant VSV expressing the sodium iodide symporter (NIS), which concentrates radiotracers at sites of infection, was administered intravenously to exercising or anesthetized mice, and nuclear NIS reporter gene imaging was used to noninvasively track the density and spatial distribution of intratumoral infectious centers. Anesthesia resulted in decreased intratumoral infection density, while exercise increased the density and uniformity of infectious centers. Perfusion state also had a significant impact on the antitumor efficacy of the VSV therapy. In conclusion, quantitative dynamic radiohistologic imaging was used to noninvasively interrogate delivery of oncolytic virotherapy, highlighting the critical importance of perfusion pressure as a driver of intratumoral delivery and efficacy of oncolytic viruses.

Treatment strategies for combining immunostimulatory oncolytic virus therapeutics with dendritic cell injections

Oncolytic viruses (OVs) are used to treat cancer, as they selectively replicate inside of and lyse tumor cells. The efficacy of this process is limited and new OVs are being designed to mediate tumor cell release of cytokines and co-stimulatory molecules, which attract cytotoxic T cells to target tumor cells, thus increasing the tumor-killing effects of OVs. To further promote treatment efficacy, OVs can be combined with other treatments, such as was done by Huang et al., who showed that combining OV injections with dendritic cell (DC) injections was a more effective treatment than either treatment alone. To further investigate this combination, we built a mathematical model consisting of a system of ordinary differential equations and fit the model to the hierarchical data provided from Huang et al. We used the model to determine the effect of varying doses of OV and DC injections and to test alternative treatment strategies. We found that the DC dose given in Huang et al. was near a bifurcation point and that a slightly larger dose could cause complete eradication of the tumor. Further, the model results suggest that it is more effective to treat a tumor with immunostimulatory oncolytic viruses first and then follow-up with a sequence of DCs than to alternate OV and DC injections. This protocol, which was not considered in the experiments of Huang et al., allows the infection to initially thrive before the immune response is enhanced. Taken together, our work shows how the ordering, temporal spacing, and dosage of OV and DC can be chosen to maximize efficacy and to potentially eliminate tumors altogether.

Quantitative impact of immunomodulation versus oncolysis with cytokine-expressing virus therapeutics

The past century's description of oncolytic virotherapy as a cancer treatment involving specially-engineered viruses that exploit immune deficiencies to selectively lyse cancer cells is no longer adequate. Some of the most promising therapeutic candidates are now being engineered to produce immunostimulatory factors, such as cytokines and co-stimulatory molecules, which, in addition to viral oncolysis, initiate a cytotoxic immune attack against the tumor. This study addresses the combined effects of viral oncolysis and T-cell-mediated oncolysis. We employ a mathematical model of virotherapy that induces release of cytokine IL-12 and co-stimulatory molecule 4-1BB ligand. We found that the model closely matches previously published data, and while viral oncolysis is fundamental in reducing tumor burden, increased stimulation of cytotoxic T cells leads to a short-term reduction in tumor size, but a faster relapse. In addition, we found that combinations of specialist viruses that express either IL-12 or 4-1BBL might initially act more potently against tumors than a generalist virus that simultaneously expresses both, but the advantage is likely not large enough to replace treatment using the generalist virus. Finally, according to our model and its current assumptions, virotherapy appears to be optimizable through targeted design and treatment combinations to substantially improve therapeutic outcomes.

Modeling T cell responses to antigenic challenge

T cell responses are a crucial part of the adaptive immune system in the fight against infections. This article discusses the use of mathematical models for understanding the dynamics of cytotoxic T lymphocyte (CTL) responses against viral infections. Complementing experimental research, mathematical models have been very useful for exploring new hypotheses, interpreting experimental data, and for defining what needs to be measured to improve understanding. This review will start with minimally parameterized models of CTL responses, which have generated some valuable insights into basic dynamics and correlates of control. Subsequently, more biological complexity is incorporated into this modeling framework, examining different mechanisms of CTL expansion, different effector activities, and the influence of T cell help. Models and results are discussed in the context of data from specific infections.

On the laws of virus spread through cell populations

The dynamics of viral infections have been investigated extensively, often with a combination of experimental and mathematical approaches. Mathematical descriptions of virus spread through cell populations are well established in the literature and have yielded important insights, yet the formulation of certain fundamental aspects of virus dynamics models remains uncertain and untested. Here, we investigate the process of infection and, in particular, the effect of varying the target cell population size on the number of productively infected cells generated. Using an in vitro single-round HIV-1 infection system, we find that the established modeling framework cannot accurately fit the data. If the model is fit to data with the lowest number of cells and is used to predict data generated with larger cell populations, the model significantly overestimates the number of productively infected cells generated. Interestingly, this deviation becomes stronger under experimental conditions that promote mixing of cells and viruses. The reason for the deviation is that the standard model makes certain oversimplifying assumptions about the fate of viruses that fail to find a cell in their immediate proximity. We derive from stochastic processes a different model that assumes simultaneous access of the virus to multiple target cells. In this scenario, if no cell is available to the virus at its location, it has a chance to interact with other cells, a process that can be promoted by mixing of the populations. This model can accurately fit the experimental data and suggests a new interpretation of mass action in virus dynamics models.

IMPORTANCE

Understanding the principles of virus growth through cell populations is of fundamental importance to virology. It helps us make informed decisions about intervention strategies aimed at preventing virus growth, such as drug treatment or vaccination approaches, e.g., in HIV infection, yet considerable uncertainty remains in this respect. An important variable in this context is the number of susceptible cells available for virus replication. How does the number of susceptible cells influence the growth potential of the virus? Besides the importance of such information for clinical responses, a thorough understanding of this is also important for the prediction of virus levels in patients and the estimation of crucial patient parameters through the use of mathematical models. This paper investigates the relationship between target cell availability and the virus growth potential with a combination of experimental and mathematical approaches and provides significant new insights.

Modeling oncolytic virotherapy: is complete tumor-tropism too much of a good thing?

The specific targeting of tumor cells by replication-competent oncolytic viruses is considered indispensable for realizing the potential of oncolytic virotherapy. Yet off-target infections by oncolytic viruses may increase virus production, further reducing tumor load. This ability may be critical when tumor-cell scarcity or the onset of an adaptive immune response constrain viral anti-tumoral efficacy. Here we develop a mathematical framework for assessing whether oncolytic viruses with reduced tumor-specificity can more effectively eliminate tumors while keeping losses to normal cell populations low. We find viruses that infect some normal cells can potentially balance the competing goals of tumor elimination and minimizing the effects on normal cell populations. Particularly when infected tissues can be regenerated, moderating rather than completely eliminating the ability of oncolytic viruses to infect and lyse normal cells could improve cancer treatment, with potentially fewer side-effects than conventional treatments such as chemotherapy.

Mathematical model for radial expansion and conflation of intratumoral infectious centers predicts curative oncolytic virotherapy parameters

Simple, inductive mathematical models of oncolytic virotherapy are needed to guide protocol design and improve treatment outcomes. Analysis of plasmacytomas regressing after a single intravenous dose of oncolytic vesicular stomatitis virus in myeloma animal models revealed that intratumoral virus spread was spatially constrained, occurring almost exclusively through radial expansion of randomly distributed infectious centers. From these experimental observations we developed a simple model to calculate the probability of survival for any cell within a treated tumor. The model predicted that small changes to the density of initially infected cells or to the average maximum radius of infected centers would have a major impact on treatment outcome, and this was confirmed experimentally. The new model provides a useful and flexible tool for virotherapy protocol optimization.

Evolutionary dynamics of giant viruses and their virophages

Giant viruses contain large genomes, encode many proteins atypical for viruses, replicate in large viral factories, and tend to infect protists. The giant virus replication factories can in turn be infected by so called virophages, which are smaller viruses that negatively impact giant virus replication. An example is Mimiviruses that infect the protist Acanthamoeba and that are themselves infected by the virophage Sputnik. This study examines the evolutionary dynamics of this system, using mathematical models. While the models suggest that the virophage population will evolve to increasing degrees of giant virus inhibition, it further suggests that this renders the virophage population prone to extinction due to dynamic instabilities over wide parameter ranges. Implications and conditions required to avoid extinction are discussed. Another interesting result is that virophage presence can fundamentally alter the evolutionary course of the giant virus. While the giant virus is predicted to evolve toward increasing its basic reproductive ratio in the absence of the virophage, the opposite is true in its presence. Therefore, virophages can not only benefit the host population directly by inhibiting the giant viruses but also indirectly by causing giant viruses to evolve toward weaker phenotypes. Experimental tests for this model are suggested.

Activation of intestinal peroxisome proliferator-activated receptor-α increases high-density lipoprotein production

AIMS

Peroxisome proliferator-activated receptor (PPAR)-α is a transcription factor controlling lipid metabolism in liver, heart, muscle, and macrophages. Peroxisome proliferator-activated receptor-α activation increases plasma HDL cholesterol and exerts hypotriglyceridaemic actions via the liver. However, the intestine expresses PPAR-α, produces HDL and chylomicrons, and is exposed to diet-derived PPAR-α ligands. Therefore, we examined the effects of PPAR-α activation on intestinal lipid and lipoprotein metabolism.

METHODS AND RESULTS

The impact of PPAR-α activation was evaluated in term of HDL-related gene expression in mice, ex vivo in human jejunal biopsies and in Caco-2/TC7 cells. Apolipoprotein-AI/HDL secretion, cholesterol esterification, and trafficking were also studied in vitro. In parallel to improving plasma lipid profiles and increasing liver and intestinal expression of fatty acid oxidation genes, treatment with the dual PPAR-α/δ ligand GFT505 resulted in a more pronounced increase in plasma HDL compared with fenofibrate in mice. GFT505, but not fenofibrate, increased the expression of HDL production genes such as apolipoprotein-AI and ATP-binding cassette A1 transporter in murine intestines. A similar increase was observed upon PPAR-α activation of human biopsies and Caco-2/TC7 cells. Additionally, HDL secretion by Caco-2/TC7 cells increased. Moreover, PPAR-α activation decreased the cholesterol esterification capacity of Caco-2/TC7 cells, modified cholesterol trafficking, and reduced apolipoprotein-B secretion.

CONCLUSION

Peroxisome proliferator-activated receptor-α activation reduces cholesterol esterification, suppresses chylomicron, and increases HDL secretion by enterocytes. These results identify the intestine as a target organ of PPAR-α ligands with entero-hepatic tropism to reduce atherogenic dyslipidaemia.

Optimization and preclinical design of genetically engineered viruses for human oncolytic therapy

INTRODUCTION

Oncolytic viruses (OVs) occupy a strategic niche in the dynamic era of biological and gene therapy of human cancers. However, the use of OVs is the subject of close scrutiny due to impediments such as the insufficiency of patient generalizations posed by heterogeneous tumor responses to treatment, inherent or potentially lethal viral pathogenicities, unanticipated host- or immune-related adverse effects, and the emergence of virus-resistant cancer cells. These challenges can be overcome by the design and development of more definitive (optimized, targeted, and individualized) cancer virotherapeutics.

AREAS COVERED

The translation of current knowledge and recent innovations into rational treatment prospects hinges on an iterative loop of variables pertaining to genetically engineered viral oncolytic efficacy and safety profiles, mechanism-of-action data, potencies of synergistic oncolytic viral combinations with conventional tumor, immuno-, chemo-, and radiation treatment modalities, optimization of the probabilities of treatment successes in heterogeneous (virus-sensitive and -resistant) tumor cell populations by mathematical modeling, and lessons learned from preclinical studies and human clinical trials.

EXPERT OPINION

In recent years, it has become increasingly clear that proof-of-principle is critical for the preclinical optimization of oncolytic viruses to target heterogeneous forms of cancer and to prioritize current concerns related to the efficacy and safety of oncolytic virotherapy.

Complex spatial dynamics of oncolytic viruses in vitro: mathematical and experimental approaches

Oncolytic viruses replicate selectively in tumor cells and can serve as targeted treatment agents. While promising results have been observed in clinical trials, consistent success of therapy remains elusive. The dynamics of virus spread through tumor cell populations has been studied both experimentally and computationally. However, a basic understanding of the principles underlying virus spread in spatially structured target cell populations has yet to be obtained. This paper studies such dynamics, using a newly constructed recombinant adenovirus type-5 (Ad5) that expresses enhanced jellyfish green fluorescent protein (EGFP), AdEGFPuci, and grows on human 293 embryonic kidney epithelial cells, allowing us to track cell numbers and spatial patterns over time. The cells are arranged in a two-dimensional setting and allow virus spread to occur only to target cells within the local neighborhood. Despite the simplicity of the setup, complex dynamics are observed. Experiments gave rise to three spatial patterns that we call "hollow ring structure", "filled ring structure", and "disperse pattern". An agent-based, stochastic computational model is used to simulate and interpret the experiments. The model can reproduce the experimentally observed patterns, and identifies key parameters that determine which pattern of virus growth arises. The model is further used to study the long-term outcome of the dynamics for the different growth patterns, and to investigate conditions under which the virus population eliminates the target cells. We find that both the filled ring structure and disperse pattern of initial expansion are indicative of treatment failure, where target cells persist in the long run. The hollow ring structure is associated with either target cell extinction or low-level persistence, both of which can be viewed as treatment success. Interestingly, it is found that equilibrium properties of ordinary differential equations describing the dynamics in local neighborhoods in the agent-based model can predict the outcome of the spatial virus-cell dynamics, which has important practical implications. This analysis provides a first step towards understanding spatial oncolytic virus dynamics, upon which more detailed investigations and further complexity can be built.

Isolation of more potent oncolytic paramyxovirus by bioselection

Newcastle disease virus (NDV) is an oncolytic paramyxovirus with a nonsegmented single-stranded RNA genome. In this report, a recombinant oncolytic NDV was passaged in human tumor xenografts and reisolated and characterized after two rounds of bioselection. Several isolates could be recovered that differed from the parental virus with respect to virus spread in tumor cells and the ability to form syncytia in human tumor cells. Three isolates were identified that demonstrated superior oncolytic potency compared with the parental virus as measured by increased oncolytic potency in confluent tumor cell monolayers, in tumor cell spheroids and in a mouse xenograft tumor model. The surface proteins F and HN were sequence analyzed and characterized for fusogenicity. The present study demonstrates that in vivo NDV bioselection can enable the isolation of novel, oncolytic NDV and thus represents a powerful methodology for the development of highly potent oncolytic viruses.

Early infection and spread of a conditionally replicating adenovirus under conditions of plaque formation

Conditionally-replicating adenoviruses (CRAds) and other oncolytic viruses replicate selectively in tumor cells, presenting a potential cancer treatment approach. To optimize application of these viruses, understanding of early spread of these viruses in target cells is important. Here we used a recombinant adenovirus expressing enhanced jellyfish green fluorescent protein (EGFP) in place of the EIA and EIB genes (AdEGFPuci). Infection of susceptible cells (AD-293) under plaque formation conditions (MOI<<1) on gridded culture dishes and daily monitoring allowed visualization of initially infected cells, as well as spread to neighboring cells. We determined key parameters of early infection, including the rate and efficiency of spread from the initially infected cell to other cells. It was noteworthy that a minority of initially infected cells ultimately resulted in plaques. The approaches elucidated here will be useful for determining early infection parameters for CRAds of therapeutic interest.

Questing for an optimal, universal viral agent for oncolytic virotherapy

One of the most promising strategies to treat cancer is attacking it with viruses designed to exploit specific altered pathways. Here, the effects of oncolytic virotherapy on tumors having compact, papillary, and disconnected morphologies are investigated through computer simulations of a multiscale model coupling macroscopic reaction-diffusion equations for the nutrients with microscopic stochastic rules for the actions of individual cells and viruses. The interaction among viruses and tumor cells involves cell infection, intracellular virus replication, and the release of new viruses in the tissue after cell lysis. The evolution over time of both the viral load and cancer cell population, as well as the probabilities for tumor eradication, were evaluated for a range of multiplicities of infection, viral entries, and burst sizes. It was found that in immunosuppressed hosts, the antitumor efficacy of a virus is primarily determined by its entry efficiency, its replicative capacity within the tumor, and its ability to spread over the tissue. However, the optimal traits for oncolytic viruses depend critically on the tumor growth dynamics and do not necessarily include rapid replication, cytolysis, or spreading, currently assumed as necessary conditions for a successful therapeutic outcome. Our findings have potential implications on the design of new vectors for the viral therapy of cancer.

Dynamics of melanoma tumor therapy with vesicular stomatitis virus: explaining the variability in outcomes using mathematical modeling

Tumor selective, replication competent viruses are being tested for cancer gene therapy. This approach introduces a new therapeutic paradigm due to potential replication of the therapeutic agent and induction of a tumor-specific immune response. However, the experimental outcomes are quite variable, even when studies utilize highly inbred strains of mice and the same cell line and virus. Recognizing that virotherapy is an exercise in population dynamics, we utilize mathematical modeling to understand the variable outcomes observed when B16ova malignant melanoma tumors are treated with vesicular stomatitis virus in syngeneic, fully immunocompetent mice. We show how variability in the initial tumor size and the actual amount of virus delivered to the tumor have critical roles on the outcome of therapy. Virotherapy works best when tumors are small, and a robust innate immune response can lead to superior tumor control. Strategies that reduce tumor burden without suppressing the immune response and methods that maximize the amount of virus delivered to the tumor should optimize tumor control in this model system.

The replicability of oncolytic virus: defining conditions in tumor virotherapy

The replicability of an oncolytic virus is measured by its burst size. The burst size is the number of new viruses coming out from a lysis of an infected tumor cell. Some clinical evidences show that the burst size of an oncolytic virus is a defining parameter for the success of virotherapy. This article analyzes a basic mathematical model that includes burst size for oncolytic virotherapy. The analysis of the model shows that there are two threshold values of the burst size: below the first threshold, the tumor always grows to its maximum (carrying capacity) size; while passing this threshold, there is a locally stable positive equilibrium solution appearing through transcritical bifurcation; while at or above the second threshold, there exits one or three families of periodic solutions arising from Hopf bifurcations. The study suggests that the tumor load can drop to a undetectable level either during the oscillation or when the burst size is large enough.

ODE models for oncolytic virus dynamics

Replicating oncolytic viruses are able to infect and lyse cancer cells and spread through the tumor, while leaving normal cells largely unharmed. This makes them potentially useful in cancer therapy, and a variety of viruses have shown promising results in clinical trials. Nevertheless, consistent success remains elusive and the correlates of success have been the subject of investigation, both from an experimental and a mathematical point of view. Mathematical modeling of oncolytic virus therapy is often limited by the fact that the predicted dynamics depend strongly on particular mathematical terms in the model, the nature of which remains uncertain. We aim to address this issue in the context of ODE modeling, by formulating a general computational framework that is independent of particular mathematical expressions. By analyzing this framework, we find some new insights into the conditions for successful virus therapy. We find that depending on our assumptions about the virus spread, there can be two distinct types of dynamics. In models of the first type (the "fast spread" models), we predict that the viruses can eliminate the tumor if the viral replication rate is sufficiently high. The second type of models is characterized by a suboptimal spread (the "slow spread" models). For such models, the simulated treatment may fail, even for very high viral replication rates. Our methodology can be used to study the dynamics of many biological systems, and thus has implications beyond the study of virus therapy of cancers.

Mathematical modeling as a tool for planning anticancer therapy

We review a large volume of literature concerning mathematical models of cancer therapy, oriented towards optimization of treatment protocols. The review, although partly idiosyncratic, covers such major areas of therapy optimization as phase-specific chemotherapy, antiangiogenic therapy and therapy under drug resistance. We start from early cell cycle progression models, very simple but admitting explicit mathematical solutions, based on methods of control theory. We continue with more complex models involving evolution of drug resistance and pharmacokinetic and pharmacodynamic effects. Then, we consider two more recent areas: angiogenesis of tumors and molecular signaling within and among cells. We discuss biological background and mathematical techniques of this field, which has a large although only partly realized potential for contributing to cancer treatment.