In vivo development of tissue engineered vascular grafts: a fluid-solid-growth model

Methods of tissue engineering continue to advance, and multiple clinical trials are underway evaluating tissue engineered vascular grafts (TEVGs). Whereas initial concerns focused on suture retention and burst pressure, there is now a pressing need to design grafts to have optimal performance, including an ability to grow and remodel in response to changing hemodynamic loads. Toward this end, there is similarly a need for computational methods that can describe and predict the evolution of TEVG geometry, composition, and material properties while accounting for changes in hemodynamics. Although the ultimate goal is a fluid-solid-growth (FSG) model incorporating fully 3D growth and remodeling and 3D hemodynamics, lower fidelity models having high computational efficiency promise to play important roles, especially in the design of candidate grafts. We introduce here an efficient FSG model of in vivo development of a TEVG based on two simplifying concepts: mechanobiologically equilibrated growth and remodeling of the graft and an embedded control volume analysis of the hemodynamics. Illustrative simulations for a model Fontan conduit reveal the utility of this approach, which promises to be particularly useful in initial design considerations involving formal methods of optimization which otherwise add considerably to the computational expense.