A coupled model of neovessel growth and matrix mechanics describes and predicts angiogenesis in vitro

During angiogenesis, sprouting microvessels interact with the extracellular matrix (ECM) by degrading and reorganizing the matrix, applying traction forces, and producing deformation. Morphometric features of the resulting microvascular network are affected by the interaction between the matrix and angiogenic microvessels. The objective of this study was to develop a continuous-discrete modeling approach to simulate mechanical interactions between growing neovessels and the deformation of the matrix in vitro. This was accomplished by coupling an existing angiogenesis growth model which uses properties of the ECM to regulate angiogenic growth with the nonlinear finite element software FEBio (http://www.febio.org). FEBio solves for the deformation and remodeling of the matrix caused by active stress generated by neovessel sprouts, and this deformation was used to update the ECM into the current configuration. After mesh resolution and parameter sensitivity studies, the model was used to accurately predict vascular alignment for various matrix boundary conditions. Alignment primarily arises passively as microvessels convect with the deformation of the matrix, but active alignment along collagen fibrils plays a role as well. Predictions of alignment were most sensitive to the range over which active stresses were applied and the viscoelastic time constant in the material model. The computational framework provides a flexible platform for interpreting in vitro investigations of vessel-matrix interactions, predicting new experiments, and simulating conditions that are outside current experimental capabilities.