Modelling of Tumour-induced Angiogenesis

Controlled by extracellular signals, tumour-induced angiogenesis is a crucial step in the development of tumours. Among the many cell signals already identified, the VEGF and Notch signalling pathways play a critical role in controlling endothelial cells (ECs) during angiogenesis. Although this regulatory mechanism has become a current research focus in biology, its computational modelling is still rare. We focus on developing a computational model to simulate the VEGF and Notch signalling regulatory mechanism to perceive the micro procedure of angiogenesis in silico and fill the gap between biology and computer engineering. We first developed a mathematical model with nonlinear partial differential equations (PDEs) to describe the migration of endothelial tip cells during tumour-induced angiogenesis. The simulation results show that both chemotaxis and haptotaxis have impacts on the migration of ECs in velocity and density, and the impacts depend on the gradient and direction of tumour angiogenenic factor (TAF), and fibronectin, implying a possible malignant mechanism for some subgroups of tumour. We then developed the model further to simulate the regression, recurrence or clearance of tumours due to tumour cytotoxic factors, including the immune system and drugs delivered through the vessels formed during angiogenesis, providing a broader understanding of tumours. Based on the PDE model which provided parameters of continuum mathematical model, we finally developed an enzymatic catalysed regulating model in the form of ordinary differential equations (ODEs) with agent-based modelling (ABM) using Java and MATLAB languages, to visually realise the sprouting regulated by VEGF and Notch signalling during angiogenesis. The simulation describes the process of how an endothelial stalk cell becomes an endothelial tip cell, and sprouts under the influence of VEGF and Notch signalling, revealing the relationship between sprouting and branching. As the simulation results are consistent with reported in vitro and in vivo assays, the study bridges angiogenesis research and computer modelling from the dynamic regulatory mechanism perspective, offering a huge leap over previous studies in computationally simulating tumour-induced angiogenesis. It is hoped that the results will assist researchers in both the experimental and theoretical angiogenesis communities to improve understanding of the complexity and identify the fundamental principles of angiogenesis, whilst also using modelling approaches that will enrich knowledge for computational scientists in this field