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Modeling viscoelastic behavior of arterial walls and their interaction with pulsatile blood flow

By Sun Čica Čanić, Josip Tamba Ča, Giovanna Guidoboni, Andro Mikeli Ć, Craig J. Hartley and Doreen Rosenstrauch


Abstract. Fluid-structure interaction describing wave propagation in arteries driven by the pulsatile blood flow is a complex problem. Whenever possible, simplified models are called for. One-dimensional models are typically used in arterial sections that can be approximated by the cylindrical geometry allowing axially symmetric flows. Although a good first approximation to the underlying problem, the one-dimensional model suffers from several drawbacks: the model is not closed (an ad hoc velocity profile needs to be prescribed to obtain a closed system) and the model equations are quasi-linear hyperbolic (oversimplifying the viscous fluid dissipation), typically producing shock wave solutions not observed in healthy humans. In this manuscript we derived a simple, closed reduced model that accounts for the viscous fluid dissipation to the leading order. The resulting fluid-structure interaction system is of hyperbolic-parabolic type. Arterial walls were modeled by a novel, linearly viscoelastic cylindrical Koiter shell model and the flow of blood by the incompressible, viscous Navier–Stokes equations. Kelvin–Voigt-type viscoelasticity was used to capture the hysteresis behavior observed in the measurements of the arterial stress-strain response. Using the a priori estimates obtained from an energy inequality, together with the asymptotic analysis and ideas from homogenization theory for porous media flows, we derived an effective model whic

Year: 2006
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