Multiscale modelling of cancer response to oncolytic viral therapy

Modeling of oncolytic viruses in a heterogeneous cell population to predict spread into non-cancerous cells

New cancer treatment modalities that limit patient discomfort need to be developed. One possible new therapy is the use of oncolytic (cancer-killing) viruses. It is only recently that our ability to manipulate viral genomes has allowed us to consider deliberately infecting cancer patients with viruses. One key consideration is to ensure that the virus exclusively targets cancer cells and does not harm nearby non-cancerous cells. Here, we use a mathematical model of viral infection to determine the characteristics a virus would need to have in order to eradicate a tumor, but leave non-cancerous cells untouched. We conclude that the virus must differ in its ability to infect the two different cell types, with the infection rate of non-cancerous cells needing to be less than one hundredth of the infection rate of cancer cells. Differences in viral production rate or infectious cell death rate alone are not sufficient to protect non-cancerous cells.

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

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

Global boundedness of a higher-dimensional chemotaxis system on alopecia areata

This paper mainly focuses on the dynamics behavior of a three-component chemotaxis system on alopecia areata $ \begin{equation*} \left\{ \begin{array}{lll} u_t = \Delta{u}-\chi_1\nabla\cdot(u\nabla{w})+w-\mu_1u^2, &x\in\Omega, t>0, \\ v_t = \Delta{v}-\chi_2\nabla\cdot(v\nabla{w})+w+ruv-\mu_2v^2, &x\in \Omega, t>0, \\ w_t = \Delta{w}+u+v-w, &x\in \Omega, t>0, \\ \frac{\partial{u}}{\partial{\nu}} = \frac{\partial{v}}{\partial{\nu}} = \frac{\partial{w}}{\partial{\nu}} = 0, &x\in \partial \Omega, t>0, \\ u(x, 0) = u_0(x), \ v(x, 0) = v_0(x), \ w(x, 0) = w_0(x), &x\in \Omega, \ \end{array} \right. \end{equation*} $ where $ \Omega\subset\mathbb{R}^n $ $ (n \geq 4) $ is a bounded convex domain with smooth boundary $ \partial\Omega $, the parameters $ \chi_i $, $ \mu_i $ $ (i = 1, 2) $, and $ r $ are positive. We show that this system exists a globally bounded classical solution if $ \mu_i\; (i = 1, 2) $ is large enough. This result extends the corresponding results which were obtained by Lou and Tao (JDE, 2021) to the higher-dimensional case.

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

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

Electrical Stimulation for Immune Modulation in Cancer Treatments

Immunotherapy is becoming a very common treatment for cancer, using approaches like checkpoint inhibition, T cell transfer therapy, monoclonal antibodies and cancer vaccination. However, these approaches involve high doses of immune therapeutics with problematic side effects. A promising approach to reducing the dose of immunotherapeutic agents given to a cancer patient is to combine it with electrical stimulation, which can act in two ways; it can either modulate the immune system to produce the immune cytokines and agents in the patient's body or it can increase the cellular uptake of these immune agents via electroporation. Electrical stimulation in form of direct current has been shown to reduce tumor sizes in immune-competent mice while having no effect on tumor sizes in immune-deficient mice. Several studies have used nano-pulsed electrical stimulations to activate the immune system and drive it against tumor cells. This approach has been utilized for different types of cancers, like fibrosarcoma, hepatocellular carcinoma, human papillomavirus etc. Another common approach is to combine electrochemotherapy with immune modulation, either by inducing immunogenic cell death or injecting immunostimulants that increase the effectiveness of the treatments. Several therapies utilize electroporation to deliver immunostimulants (like genes encoded with cytokine producing sequences, cancer specific antigens or fragments of anti-tumor toxins) more effectively. Lastly, electrical stimulation of the vagus nerve can trigger production and activation of anti-tumor immune cells and immune reactions. Hence, the use of electrical stimulation to modulate the immune system in different ways can be a promising approach to treat cancer.

Non-local multiscale approach for the impact of go or grow hypothesis on tumour-viruses interactions

We propose and study computationally a novel non-local multiscale moving boundary mathematical model for tumour and oncolytic virus (OV) interactions when we consider the go or grow hypothesis for cancer dynamics. This spatio-temporal model focuses on two cancer cell phenotypes that can be infected with the OV or remain uninfected, and which can either move in response to the extracellular-matrix (ECM) density or proliferate. The interactions between cancer cells, those among cancer cells and ECM, and those among cells and OV occur at the macroscale. At the micro-scale, we focus on the interactions between cells and matrix degrading enzymes (MDEs) that impact the movement of tumour boundary. With the help of this multiscale model we explore the impact on tumour invasion patterns of two different assumptions that we consider in regard to cell-cell and cell-matrix interactions. In particular we investigate model dynamics when we assume that cancer cell fluxes are the result of local advection in response to the density of extracellular matrix (ECM), or of non-local advection in response to cell-ECM adhesion. We also investigate the role of the transition rates between mainly-moving and mainly-growing cancer cell sub-populations, as well as the role of virus infection rate and virus replication rate on the overall tumour dynamics.

Multidirectional Strategies for Targeted Delivery of Oncolytic Viruses by Tumor Infiltrating Immune Cells

Oncolytic virus (OV) immunotherapy has demonstrated to be a promising approach in cancer treatment due to tumor-specific oncolysis. However, their clinical use so far has been largely limited due to the lack of suitable delivery strategies with high efficacy. Direct 'intratumoral' injection is the way to cross the hurdles of systemic toxicity, while providing local effects. Progress in this field has enabled the development of alternative way using 'systemic' oncolytic virotherapy for producing better results. One major potential roadblock to systemic OV delivery is the low virus persistence in the face of hostile immune system. The delivery challenge is even greater when attempting to target the oncolytic viruses into the entire tumor mass, where not all tumor cells are equally exposed to exactly the same microenvironment. The microenvironment of many tumors is known to be massively infiltrated with various types of leucocytes in both primary and metastatic sites. Interestingly, this intratumoral immune cell heterogeneity exhibits a degree of organized distribution inside the tumor bed as evidenced, for example, by the hypoxic tumor microenviroment where predominantly recruits tumor-associated macrophages. Although in vivo OV delivery seems complicated and challenging, recent results are encouraging for decreasing the limitations of systemically administered oncolytic viruses and an improved efficiency of oncolytic viral therapy in targeting cancerous tissues in vitro. Here, we review the latest developments of carrier cell-based oncolytic virus delivery using tumor-infiltrating immune cells with a focus on the main features of each cellular vehicle.

Spatiotemporal dynamics of immunogenic tumors

A mathematical model, consisting of a system of two coupled reaction-diffusion partial differential equations describing the interaction between solid tumor and immune system (termed as effector cells), is proposed here. The main focus is on the analysis of the spatiotemporal dynamics of tumor cells and immune cells. The resulting system is analyzed and numerical simulations are presented. Different types of spatial patterns with respect to different initial conditions, and time are observed. Their analysis and mechanism of spatiotemporal pattern formation in immunogenic tumor are studied. Spatiotemporal perturbation around non-spatial steady state beyond the linear regime is obtained based on the analysis of higher-order perturbation terms.

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.