Particle Based Model of Tumor Progression Stimulated by the Process of Angiogenesis

Abstract

Abstract. We discuss a novel metaphor of tumor progression stimulated by the process of angiogenesis. The realistic 3-D dynamics of the entire system consisting of the tumor, tissue cells, blood vessels and blood flow can be reproduced by using interacting particles. The particles mimic the clusters of tumor cells. They interact with their closest neighbors via semi-harmonic forces simulating mechanical resistance of the cell walls and the external pressure. The particle dynamics is governed by both the Newtonian laws of motion and the rules of cell life-cycle. The particles replicate by a simple mechanism of division, similar to that of a single cell reproduction and die due to necrosis or apoptosis. We conclude that this concept can serve as a general framework for designing advanced multi-scale models of tumor dynamics. In respect to spatio-temporal scale, the interactions between particles can define e.g., cluster-to-cluster, cellto-cell, red blood cells and fluid particles interactions, cytokines motion, etc. Consequently, they influence the macroscopic dynamics of the particle ensembles in various sub-scales ranging from diffusion of cytokines, blood flow up to growth of tumor and vascular network expansion.

Nonlinear modelling of cancer: bridging the gap between cells and tumours

“…This approach is discussed in further detail below. Later, in the context of discrete cell-based systems, models of angiogenesis and vascular tumour growth were also implemented, see, for example, Gevertz and Torquato [238], Bartha and Rieger [50], Bauer et al [51] and Scislo and Dzwinel [547]. The effects of blood flow through the neovascular network on tumour growth were also recently considered in Alarcón et al [11], Bartha and Rieger (2006), Lee et al [330], Welter [548] and Owen et al [399] using cellular automaton models for tumour growth combined with dynamic network models for the vasculature.…”