Multiscale modelling of cancer response to oncolytic viral therapy

Abstract

Oncolytic viruses (OV) are viruses that can replicate selectively within cancer cells and destroy them. While the past few decades have seen significant progress related to the use of these viruses in clinical contexts, the success of oncolytic therapies is dampened by the complex spatial tumour-OV interactions. In this work, we present a novel multiscale moving boundary modelling for the tumour-OV interactions, which is based on coupled systems of partial differential equations both at macro-scale (tissue-scale) and at micro-scale (cell-scale) that are connected through a double feedback link. At the macro-scale, we account for the coupled dynamics of uninfected cancer cells, OV-infected cancer cells, extracellular matrix (ECM) and oncolytic viruses. At the same time, at the micro scale, we focus on essential dynamics of urokinase plasminogen activator (uPA) system which is one of the important proteolytic systems responsible for the degradation of the ECM, with notable influence in cancer invasion. While sourced by the cancer cells that arrive during their macro-dynamics within the outer proliferating rim of the tumour, the uPA micro-dynamics is crucial in determining the movement of the macro-scale tumour boundary (both in terms of direction and displacement magnitude). In this investigation, we consider three scenarios for the macro-scale tumour-OV interactions. While assuming the usual context of reaction-diffusion-taxis coupled PDEs, the three macro-dynamics scenarios gradually explore the influence of the ECM taxis over the tumour-OV interaction, in the form of haptotaxis of both uninfected and infected cells populations as well as the indirect ECM taxis for the oncolytic virus. Finally, the complex tumour-OV interactions is investigated numerically through the development a new multiscale moving boundary computational framework. While further investigation is needed to validate the findings of our modelling, for the parameter regimes that we considered, our numerical simulations indicate that the viral therapy leads to control and decrease of the overall cancer expansion and in certain cases this can result even in the elimination of the tumour.

Non-local multiscale approaches for tumour-oncolytic viruses interactions

“…Building on the multiscale moving boundary model for cancer invasion introduced in [50] and the multiscale model of cancer response to OV proposed in [3], in this work we address the multiscale nature of tumour-OV interactions through a new non-local modelling approach. This modelling captures the complex tumour-virus-ECM dynamics by exploring the genuine multiscale character of this interaction.…”

“…The last two decades have seen the development of various mathematical models for multiscale cancer dynamics [1,34,39,48,49,50]. Nevertheless, there are not many multiscale mathematical models for oncolytic viral therapies and tumour-viral interactions; among the very few multiscale models we mention those in [3,4,37,38]. These models focus on local cancer cell dynamics and local interactions between cells, ECM and viruses.…”

“…In this study we develop further the multi-scale approach for modelling cancer-OV interactions introduced in [3,4], and consider non-local cell-cell and cell-matrix interactions for cancer dynamics. We are particularly interested in investigating the role of cell-cell and cell-matrix adhesion on cancer cell movement and degradation of ECM -since this further impacts the spread of OVs.…”

“…Simulations of system(3) investigating the role of density-dependent viral diffusion D v (c) coefficient (given by eq. (2.12) with α v = 0.1).…”

Numerical simulation for a class of predator–prey system with homogeneous Neumann boundary condition based on a sinc function interpolation method

“…When studying the spatial distribution structure and maintaining biodiversity [6,7] of predators and prey populations, the reaction diffusion system [8][9][10][11][12][13] can more accurately describe the interaction between predators and preys. In the PPS, spatial diffusion is reflected in the predator's efforts to catch up with the prey, and the prey's efforts to escape the predator's pursuit.…”