Angiogenesis Dynamics: A Computational Model of Intravascular Flow Within a Structural Adaptive Vascular Network

Understanding vascular development and the key factors involved in regulating angiogenesis-the growth of new blood vessels from pre-existing vasculature-is crucial for developing therapeutic approaches to promote wound healing. Computational techniques offer valuable insights into improving angiogenic strategies, leading to enhanced tissue regeneration and improved outcomes for chronic wound healing. While chorioallantoic membrane (CAM) models are widely used for examining fundamental mechanisms in vascular development, they lack quantification of essential parameters such as blood flow rate, intravascular pressure, and changes in vessel diameter.

To address this limitation, the current study develops a novel two-dimensional mathematical model of angiogenesis, integrating discrete and continuous modelling approaches to capture intricate cellular interactions and provide detailed information about the capillary network's structure. The proposed hybrid meshless-based model simulates sprouting angiogenesis using the in vivo CAM system.

The model successfully predicts the branching process with a total capillary volume fraction deviation of less than 15% compared to experimental data. Additionally, it implements blood flow through the capillary network and calculates the distribution of intravascular pressure and vessel wall shear stress. An adaptive network is introduced to consider capillary responses to hemodynamic and metabolic stimuli, reporting structural diameter changes across the generated vasculature network. The model demonstrates its robustness by verifying numerical outcomes, revealing statistically significant differences with deviations in key parameters, including diameter, wall shear stress (p < 0.05), circumferential wall stress, and metabolic stimuli (p < 0.01).

With its strong predictive capability in simulating intravascular flow and its ability to provide both quantitative and qualitative assessments, this research enhances our understanding of angiogenesis by introducing a biologically relevant network that addresses the functional demands of the tissue.