Computational Study of Unsteady Viscous Flow in Flexible Vessels

In this paper, we investigate unsteady behavior of flexible vessels carrying a blood flow. Membrane model with constant tension for the vessel walls and incompressible newtonian fluid approximation for blood is adopted. Developed computational model is applied to simulate the coupled fluid-wall behavior in 2D collapsible channels and 3D collapsible tubes. INTRODUCTION Vessels carrying blood flow in a human body are known to be flexible tissues. Interaction of the internal blood flow with the vessel wall compliance, in addition to significant alteration of the fluid mechanical properties (such as shear and normal stresses) with respect to rigid wall cases, can also result in a variety of interesting mechanical phenomena, such as flow limitation, selfexciting oscillations (flutter), or tube collapse. These phenomena are especially pronounced at higher Reynolds number and thus are relevant to the medical condition of stenosis caused by atherosclerosis, which results in higher local flow rates and elevated risk of collapse manifestation. In the current paper, we investigate the flutter and collapse phenomena in application to 2D collapsible channels and 3D collapsible tubes. We model the elastic vessel wall as a biological membrane with the constant tension and no bending stiffness, supported by a common assumption of negligible bending stiffness in biological materials [1, 2]. We stress, however, that the tube law and the flow limitation regime depend strongly on the elasticity model. Thus, bending rigidity would act to reduce the wall collapse [3] and postpone the onset of divergence and flutter. ∗Address all correspondence to this author. E-mail:[email protected]. NUMERICAL METHOD Numerical method consists of an Arbitrary LagrangianEulerian (ALE) formulation of incompressible Navier-Stokes equations coupled to a simple constant-tension geometrically nonlinear elastic wall model by the kinematic and traction boundary conditions: