Moving-boundary problems in blood flow

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A study of fluid-structure interaction between blood flow and compliant (elastic or viscoelastic) arteries is proposed. The underlying mathematical model couples the Navier-Stokes equations for an incompressible, viscous fluid with the structure equations describing vessel wall dynamics. The resulting moving-boundary problem has features of a mixed, hyperbolic-parabolic problem. An existence and uniqueness study of a reduced problem, and a novel scheme for efficient computation of the full problem, are proposed. A theoretical and computational study of Taylor dispersion in compliant tubes is also proposed. Results from this work are important for a study of intravascular nano-particle cancer drug delivery, and more generally, in the study of human cardiovascular function.Development of new mathematical and computational techniques to study blood flow in pulsating human arteries is proposed. The work is motivated by cardiovascular and oncological applications, and will proceed in collaboration with the Texas Medical Center in Houston.