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Blood flow in the arterial tree is essentially pulsatile. Time variation of the maximal velocity at certain points of the arterial tree may be obtained non-invasively, and used for tuning of 1D model parameters. In 1D models, it is convenient to assume a nearly flat velocity profile (blood flow rate is calculated as the product of maximal velocity and area) and Hagen-Poiuseuille friction model derived from a steady state flow condition. The goal of this paper is to estimate how good these two assumptions are. We use the measured maximal velocity and the Womersley quasi two dimensional (Q2D) solution of pulsatile flow in a rigid pipe [1] to define the velocity profile at the considered cross-section. From this velocity profile, we calculated the actual flow rate (or mean axial velocity) and wall shear stress. The proposed method for the calculation of the axial velocity using the measured maximal velocity requires the assumption of the Womersley number associated with the heart frequency. The discrepancy of maximal and mean axial velocity is high, as a consequence of which the estimation of blood flow rate using the maximal velocity is poor. The proposed method offers a good estimation of the mean velocity and wall shear stress.
Hemodynamics; Womersley solution; quasi two-dimensional model
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