Division of Mathematics, University of Dundee, Dundee DD1 4HN, United Kingdom.
Laboratoire Mathematiques de Besançon, UMR-CNRS 6623, Université de Bourgogne Franche-Comté, 16 Route de Gray, Besançon, France.
Math Biosci Eng. 2021 Jun 11;18(5):5252-5284. doi: 10.3934/mbe.2021267.
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 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.
我们提出并研究了一种新的非局部多尺度运动边界数学模型，用于肿瘤和溶瘤病毒（OV）相互作用，同时考虑了癌症动力学的假设。这个时空模型关注两种可以被 OV 感染或保持未感染的癌细胞表型，它们可以响应细胞外基质（ECM）密度而移动或增殖。癌细胞之间、癌细胞与 ECM 之间以及细胞与 OV 之间的相互作用发生在宏观尺度上。在微观尺度上，我们专注于细胞与基质降解酶（MDE）之间的相互作用，这些相互作用会影响肿瘤边界的运动。借助这个多尺度模型，我们探讨了两种不同假设对肿瘤入侵模式的影响，这两种假设涉及细胞-细胞和细胞-基质相互作用。特别是，我们研究了当我们假设癌细胞通量是由于对细胞外基质（ECM）密度的局部平流或由于对细胞-ECM 粘附的非局部平流而产生时的模型动力学。我们还研究了主要移动和主要生长的癌细胞亚群之间的转换率的作用，以及病毒感染率和病毒复制率对整体肿瘤动力学的作用。
