Flowchart of the coupling between angiogenic growth and matrix deformation in AngioFE. First, the growth model (angio3d) calculates a growth step in the current extracellular matrix field (top). Next, local stresses are generated at the position of neovessel sprouts to represent cell-generated traction and remodeling (right). FEBio is then used to calculate for the deformation that results from the cell-generated stress (bottom). The kinematics predicted from FEBio are then used to update vessels and the extracellular matrix field into the new configuration (left). This involves displacing microvessels, re-orienting collagen fibrils, and updating matrix density. The next growth step occurs in this new extracellular field, causing growing neovessels to receive dynamic feedback based on the deformation of the matrix.

Angiogenic growth was simulated using a discrete growth model which used local information about extracellular matrix fibril orientation and density to regulate growth. This image is from a simulation of angiogenic microvessels growing in a randomly oriented fibril field at Day 6.

Simulation of a rectangular vascularized collagen gel with the long-axis (x-axis) constrained with 1/8th symmetry applied. Initial microvessel fragments at Day 0 are shown above, and the new vascular network at Day 6 is shown below. Stresses within the matrix generated by neovessel sprouts causes the matrix to deform, and this deformation is used to update microvessel position and extracellular matrix fibril orientation and density. As a result, these simulations include growth that responds to dynamic kinematic feedback during matrix deformation.