Modelling the spatial dynamics of oncolytic virotherapy in the presence of virus-resistant tumour cells

Oncolytic virotherapy is a promising form of cancer treatment that uses native or genetically engineered viruses to target, infect and kill cancer cells. Unfortunately, this form of therapy is not effective in a substantial proportion of cancer patients, partly due to the occurrence of infection-resistant tumour cells. To shed new light on the mechanisms underlying therapeutic failure and to discover strategies that improve therapeutic efficacy we designed a cell-based model of viral infection. The model allows us to investigate the dynamics of infection-sensitive and infection-resistant cells in tumour tissue in presence of the virus. To reflect the importance of the spatial configuration of the tumour on the efficacy of virotherapy, we compare three variants of the model: two 2D models of a monolayer of tumour cells and a 3D model. In all model variants, we systematically investigate how the therapeutic outcome is affected by the properties of the virus (e.g. the rate of viral spread), the tumour (e.g. production rate of resistant cells, cost of resistance), the healthy stromal cells (e.g. degree of resistance to the virus) and the timing of treatment. We find that various therapeutic outcomes are possible when resistant cancer cells arise at low frequency in the tumour. These outcomes depend in an intricate but predictable way on the death rate of infected cells, where faster death leads to rapid virus clearance and cancer persistence. Our simulations reveal three different causes of therapy failure: rapid clearance of the virus, rapid selection of resistant cancer cells, and a low rate of viral spread due to the presence of infection-resistant healthy cells. Our models suggest that improved therapeutic efficacy can be achieved by sensitizing healthy stromal cells to infection, although this remedy has to be weighed against the toxicity induced in the healthy tissue.

Quantitative imaging and dynamics of tumor therapy with viruses

Cancer therapy remains challenging due to the myriad presentations of the disease and the vast genetic diversity of tumors that continuously evolve and often become resistant to therapy. Viruses can be engineered to specifically infect, replicate, and kill tumor cells (tumor virotherapy). Moreover, the viruses can be "armed" with therapeutic genes to enhance their oncolytic effect. Using viruses to treat cancer is exciting and novel and in principle can be used for a broad variety of tumors. However, the approach is distinctly different from other cancer therapies since success depends on establishment of an infection within the tumor and ongoing propagation of the oncolytic virus within the tumor itself. Therefore, the target itself amplifies the therapy. This introduces complex dynamics especially when the immune system is taken into consideration as well as the physical and other biological barriers to virus growth. Understanding these dynamics not only requires mathematical and computational models but also approaches for the noninvasive monitoring of the virus and tumor populations. In this perspective, we discuss strategies and current results to achieve this important goal of understanding these dynamics in pursuit of optimization of oncolytic virotherapy.

Analysis of a Multiple Delays Model for Treatment of Cancer with Oncolytic Virotherapy

Despite advanced discoveries in cancerology, conventional treatments by surgery, chemotherapy, or radiotherapy remain ineffective in some situations. Oncolytic virotherapy, i.e., the involvement of replicative viruses targeting specific tumor cells, opens new perspectives for better management of this disease. Certain viruses naturally have a preferential tropism for the tumor cells; others are genetically modifiable to present such properties, as the lytic cycle virus, which is a process that represents a vital role in oncolytic virotherapy. In the present paper, we present a mathematical model for the dynamics of oncolytic virotherapy that incorporates multiple time delays representing the multiple time periods of a lytic cycle. We compute the basic reproductive ratio R ₀, and we show that there exist a disease-free equilibrium point (DFE) and an endemic equilibrium point (DEE). By formulating suitable Lyapunov function, we prove that the disease-free equilibrium (DFE) is globally asymptotically stable if R ₀ < 1 and unstable otherwise. We also demonstrate that under additional conditions, the endemic equilibrium is stable. Also, a Hopf bifurcation analysis of our dynamic system is used to understand how solutions and their stability change as system parameters change in the case of a positive delay. To illustrate the effectiveness of our theoretical results, we give numerical simulations for several scenarios.

In vitro and in silico multidimensional modeling of oncolytic tumor virotherapy dynamics

Tumor therapy with replication competent viruses is an exciting approach to cancer eradication where viruses are engineered to specifically infect, replicate, spread and kill tumor cells. The outcome of tumor virotherapy is complex due to the variable interactions between the cancer cell and virus populations as well as the immune response. Oncolytic viruses are highly efficient in killing tumor cells in vitro, especially in a 2D monolayer of tumor cells, their efficiency is significantly lower in a 3D environment, both in vitro and in vivo. This indicates that the spatial dimension may have a major influence on the dynamics of virus spread. We study the dynamic behavior of a spatially explicit computational model of tumor and virus interactions using a combination of in vitro 2D and 3D experimental studies to inform the models. We determine the number of nearest neighbor tumor cells in 2D (median = 6) and 3D tumor spheroids (median = 16) and how this influences virus spread and the outcome of therapy. The parameter range leading to tumor eradication is small and even harder to achieve in 3D. The lower efficiency in 3D exists despite the presence of many more adjacent cells in the 3D environment that results in a shorter time to reach equilibrium. The mean field mathematical models generally used to describe tumor virotherapy appear to provide an overoptimistic view of the outcomes of therapy. Three dimensional space provides a significant barrier to efficient and complete virus spread within tumors and needs to be explicitly taken into account for virus optimization to achieve the desired outcome of therapy.

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.

Monitoring the initial delivery of an oncolytic measles virus encoding the human sodium iodide symporter to solid tumors using contrast-enhanced computed tomography

BACKGROUND

We aimed to determine the feasibility of monitoring viral delivery and initial distribution to solid tumors using iodinated contrast agent and micro-computed tomography (CT).

METHODS

Human BxPC-3 pancreatic tumor xenografts were established in nude mice. An oncolytic measles virus with an additional transcriptional unit encoding the sodium iodide symporter (NIS), as a reporter for viral infection, was mixed with a 1:10 dilution of Omnipaque 300 (GE Healthcare, Milwaukee, WI, USA) contrast agent and injected directly into tumors. Mice were imaged with micro-CT immediately before and after injection to determine the location of contrast agent/virus mixture. Mice were imaged again on day 3 after injection with micro-single-photon emission CT/CT to determine the location of NIS-mediated (99m) TcO(4) transport.

RESULTS

A 1:10 dilution of Omnipaque had no effect on viral infectivity or cell viability in vitro and was more than adequate for CT imaging of the intratumoral injectate distribution. The volume of tumor coverage with initial CT contrast agent and the 3-day postinfection measurement of virally infected tumor volume were significantly correlated. Additionally, regions of the tumor that did not receive contrast agent from the initial injection were largely devoid of viral infection at early time points.

CONCLUSIONS

Contrast-enhanced viral delivery enables a rapid and accurate prediction of the initial viral distribution within a solid tumor. This technique should enable real-time monitoring of viral propagation from initially infected tumor regions to adjacent tumor regions.

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.

How changes in cell mechanical properties induce cancerous behavior

Tumor growth and metastasis are ultimately mechanical processes involving cell migration and uncontrolled division. Using a 3D discrete model of cells, we show that increased compliance as observed for cancer cells causes them to grow at a much faster rate compared to surrounding healthy cells. We also show how changes in intercellular binding influence tumor malignancy and metastatic potential. These findings suggest that changes in the mechanical properties of cancer cells is the proximate cause of uncontrolled division and migration and various biochemical factors drive cancer progression via this mechanism.

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.

A mathematical model for cell cycle-specific cancer virotherapy

Oncolytic viruses preferentially infect and replicate in cancerous cells, leading to elimination of tumour populations, while sparing most healthy cells. Here, we study the cell cycle-specific activity of viruses such as vesicular stomatitis virus (VSV). In spite of its capacity as a robust cytolytic agent, VSV cannot effectively attack certain tumour cell types during the quiescent, or resting, phase of the cell cycle. In an effort to understand the interplay between the time course of the cell cycle and the specificity of VSV, we develop a mathematical model for cycle-specific virus therapeutics. We incorporate the minimum biologically required time spent in the non-quiescent cell cycle phases using systems of differential equations with incorporated time delays. Through analysis and simulation of the model, we describe how varying the minimum cycling time and the parameters that govern viral dynamics affect the stability of the cancer-free equilibrium, which represents therapeutic success.

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.