Assessment of blood volume flow in slightly curved arteries from a single velocity profile

Non-invasive estimation of arterial blood volume flow (BVF) has become a central issue in assessment of cardiovascular risk. Poiseuille and Womersley approaches are commonly used to assess the BVF from centerline velocity, but both methods neglect the influence of curvature. Based on the assumption that the velocity in curved tubes as function of the circumferential position for a given radial position can be approximated by a cosine, the BVF can also be estimated by averaging velocities at opposite radial positions, referred to as the cosine theta model (CTM). This study investigates the accuracy of BVF estimation in slightly curved arteries for BVF waveforms obtained in the brachial artery of 6 volunteers. Computational fluid dynamics simulations were used to compute the influence of curvature on velocity profiles. The BVF was then estimated from the simulation results with the CTM and methods based on Poiseuille, Womersley and using the center stream velocity and the velocity waveform at the position where the maximum velocity is observed, and compared to the prescribed BVF. The simulations show that the influence of curvature is strongest when the flow decelerates. For Poiseuille and Womersley, the time average BVF was underestimated by maximally 10.4% and 7.8% for a radius of curvature of 50 and 100 mm, respectively. The estimation error is lower for the CTM and equals 4.2% and 1.2% for a radius of curvature of 50 and 100mm, respectively. From this study, we can conclude that the velocity waveform at the position of the maximum rather than the center stream velocity waveform combined with the Womersley method should be chosen. The CTM improves current estimation techniques if in-vivo velocity distributions are available.