Numerical Simulation of Angiogenesis and Intravascular Flow inside the Capillaries

Mathematical models of angiogenesis and fluid flow through the vasculature not only elucidate the development of networks but also the transportation of metabolites and therapeutic drugs to cells. In the present work, a meshless-based model is used to simulate sprouting angiogenesis in response to vascular endothelial growth factor (VEGF) concentrations. The model is combined with the Radial Point Interpolation Method (RPIM), being the area discretized considering an unorganized nodal cloud and a background mesh of integration points, without predefined relations. Results are calibrated with experiments, and the difference between the total capillary volume fractions assessed using both methodologies values smaller than 15% were obtained. Considering the structural adaptation of microvascular networks, the intravascular flow is formulated and the blood flux is calculated. Vessels wall shear stress that is induced by the flow during vascular growth, and intravascular pressure distribution and the flow flux are investigated. In summary, the network is able to meet the functional demands of tissue to generate a stimulated adaptive process.