Constrained Mixtures Models for Blood Vessels

Research on growth and remodeling of blood vessels focuses on the characterization of the
mechanical behavior of arteries and of their response to altered chemo-mechanical environment
resembling either pathological situations, like hypertension, flow disturbances and Marfan
syndrome, or physiological development and aging
A microstructurally based constitutive models is proposed, accounting for the principal structural constituents of the arterial wall (collagen fibers, elastin and smooth muscles cells) and for
muscle activity. The theory of constrained mixtures is employed to relate the kinematics of the constituents to the motion of the vessel. The growth and remodeling formulation allows the single constituents to be continuously deposited and removed with rates that are function of the stress state of the vessel, of the stress rate over the cardiac cycle as well of the concentration of some chemical agents. The constituents are assumed to be deposited with different prestretches in the in-vivo configuration and this allows the evolution of the unloaded length during the growth and
remodeling process according to the deposition and removal of new constituents. Several results are presented concerning arterial response to quasi-static and dynamic perturbation of the
hemodynamics, aging, and development.