PREDICTING ARTERIAL FLOW AND PRESSURE DYNAMICS USING A 1D FLUID DYNAMICS MODEL WITH A VISCOELASTIC WALL

This paper combines a generalized viscoelastic model with a one-dimensional (1D) fluid dynamics model for the prediction of blood flow, pressure, and vessel area in systemic arteries. The 1D fluid dynamics model is derived from the Navier-Stokes equations for an incompressible Newtonian flow through a network of cylindrical vessels. This model predicts pressure and flow and is combined with a viscoelastic constitutive equation derived using the quasilinear viscoelasticity theory that relates pressure and vessel area. This formulation allows for inclusion of an elastic response as well as an appropriate creep function allowing for the description of the viscoelastic deformation of the arterial wall. Three constitutive models were investigated: a linear elastic model and two viscoelastic models. The Kelvin and sigmoidal viscoelastic models provide linear and nonlinear elastic responses, respectively. For the fluid domain, the model assumes that a given flow profile is prescribed at the inlet, that flow is conserved and pressure is continuous across vessel junctions, and that it incorporates a multiscale boundary condition (a three element Windkessel model) at each outlet. This outlet boundary condition allows prediction of the overall impact on the flow and pressure generated by the downstream vasculature. The coupled fluid structure interaction model is solved using a finite element method that is adapted to account for time history of the viscoelastic model. Results of this study demonstrate that incorporation of a viscoelastic wall model allows more physiologic prediction of arterial blood pressure and vessel deformation, which often is overestimated with the simple elastic wall models, while blood flow does not differ significantly between models.