Computational Systems Mechanobiology of Tumor-Induced Angiogenesis

Tumour-induced angiogenesis is affected by an interplay between different cell types, the mechanical stresses in the extracellular matrix (ECM), and the cell signalling networks. The morphology of the newly-created cells is highly dependent on the tip cells’ movements, yet the mechanical aspect of tip cell migration is not very well studied. The model developed here is one of the first phase-field models of angiogenesis incorporating the mechanics of the phenomenon. Besides, it is the only model to make a connection between the movement of the tip cell and the formation of matrix pathways in the extracellular matrix. Here, fracture formulas handle the modelling of the formation of matrix pathways. Furthermore, the model integrates the biochemical elements into the mechanical progression of the tip cells. This framework uses a set of equations to model different aspects of the phenomenon categorized into three modules; biomechanical, biochemical, and the vascular network module. The biomechanical module is simply a set of two partial differential equations (PDEs); the linear momentum balance equation and a phase-field equation for handling the two phases, the endothelial cells (ECs) and the ECM. We used an energy-based criterion for soft material for the fracture of the ECM. The biochemical module consists of four advection-diffusion-reaction equations, each of which is responsible for the concentration of one of the elements involved in the process namely: oxygen, TAF (tumour angiogenesis factor), MMP (matrix metalloproteinases), the ECM. The vascular network describes the movement of the tip cells and possible branching. This module uses a nonlinear equation solver and a stochastic function to find the location of the tip cell in each step. The results of this modelling approach conform with the results available from older computational models and experimental models