Analysis of Flow Pulse Propagation in Elastic Pipes for the Estimation of Arterial Stiffness

Abstract

Pulse Wave Velocity (PWV) in arteries is a valuable marker for the determination of the vessel stiffness, as it correlates with geometrical and biomechanical parameters of the artery wall. In addition, the PWV can be obtained non-invasively using Cardiac Magnetic Resonance Imaging. For straight vessels of constant diameter and thickness, the PWV is given by the Moens-Korteweg (M-K) equation, which indicates a direct proportionality between the square of the PWV and the elastic modulus of the wall material, its thickness and the inverse of the vessel diameter. In this work we performed three-dimensional simulations of flow pulses in straight elastic pipes and we compare the results with the M-K equation estimations. It was assumed that the flow is incompressible and the pipe wall has a linear elastic behaviour. A suitable absorbing boundary condition was designed in order to avoid wave reflections at the outflow border. The coupling between the fluid and structure solvers was carried out by a Dirichlet-to-Neumann strategy using the IQN-ILS (Interface Quasi-Newton with Inverse Jacobian from Least-Squares) method. The fluid transport properties and the mechanical properties of the pipe wall had physiologically realistic values similar to those found in the abdominal aorta, as well as the geometrical dimensions of the pipe. The PWV was computed as the distance between two transversal planes divided by the transit time for a given pressure (or velocity) amplitude level in both planes. Several configurations were analized, including variations in the elastic modulus of the wall tissue, wall thickness and initial pipe diameter. The results obtained for the PWV are in good agreement with the M-K prediction.