Non-local multiscale approaches for tumour-oncolytic viruses interactions

Abstract

Oncolytic virus (OV) therapy is a promising treatment for cancer due to the OVs selective ability to infect and replicate inside cancer cells, thus killing them, without harming healthy cells. In this work, we present a new non-local multiscale moving boundary model for the spatio-temporal cancer-OV interactions. This model explores an important double feedback loop that links the macro-scale dynamics of cancer-virus interactions and the micro-scale dynamics of proteolytic activity taking place at the tumour interface. The cancer cell-cell and cell-matrix interactions are assumed to be nonlocal, while the cell-virus interactions are assumed local. With the help of this model we investigate computationally various cancer treatment scenarios involving oncolytic viruses (i.e., the effect of injecting the OV inside the tumour, or outside it). Moreover, we investigate the effect of different cell-cell and cell-matrix interaction strengths on the success of OV spreading throughout the tumour, and the effect of constant or density-dependent virus diffusion coefficients on viral spread.

A level-set approach for a multi-scale cancer invasion model

“…Using the scale separation, we explore the micro-dynamics within a cell-scale neighbourhood of each of the boundary points x ∈ ∂Ω(t) (i.e., at each point of the macroscopic interface) that is enabled by acorresponding εY micro-domain centred at x. In brief, adopting here a multiscale modelling perspective similar to the one proposed in [4,5,6,71,52,62,63,64,65,67,72,73], the coupling of two-scale dynamics of cancer invasion is captured as follows:…”

“…Schematic summary of our multiscale moving boundary modelling. The new model that we introduced here falls in the class of heterogeneous multiscale models that were developed over the past two decades not only for multiscale biological processes but also for other multiscale processes arising in material science or fluid-structure interactions [1,4,5,6,22,71,27,28,30,52,62,63,64,65,67,72,73]. Schematically, the two-scale dynamics of our cancer invasion model is coupled across the scales as depicted in Figure 2, and its progression can be summarised in the following three steps:…”

“…In this work we present a new formulation of the link that connects the two scales of the tumour dynamics that was considered in the initial multiscale moving boundary modelling approach presented in [73] as well as in the multiscale cancer invasion modelling developments that followed [4,5,6,71,52,62,63,64,65,67,72]. In particular, the movement of the tumor boundary is here defined by a velocity field instead of a displacement of the interface.…”

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

“…The great majority of these models are single-scale models, which focus on spatial tumour invasion [5,16,12], on tumour oncolytic therapies [11,14,13,17,21,28,42], or both [6,24,27,38,43]. More recently, various multi-scale mathematical models have been derived to reproduce and investigate biological processes that take place at different spatial scales [1,2,3,4,30,31,39,36]. For example, [39] introduced a multi-scale moving boundary model for cancer invasion, which focused on the local interactions between cancer cells and the ECM, via matrix degrading enzymes (MDEs) that act at the micro-scale level of the invading tumour boundary.…”

“…This study also considered a heterogeneous ECM population formed of fibres and non-fibrous sub-populations, and investigated the role of fibres (and their re-arrangement at macro-scale and micro-scale) in the evolution of a tumour population. Other local and nonlocal multiscale models were used in [3,4,1,2] to investigate the interactions between oncolytic viruses and cancer cells.…”