The effect of arterial curvature on Doppler velocity blood flow waveform indices

Numerical simulations of pulsatile flow in curved arteries of various geometries are presented. Mean axial velocity profiles over one heart cycle provide the blood flow velocity waveforms from which Doppler ultrasound indices (DI) can be derived. Many studies make use of mathematical models to research these indices and often neglect the effects of curvature using straight tube models. The effect of curvature on the coronary, pulmonary, aortic-arch, femoral and umbilical artery axial flow velocity waveforms are presented. The simulations show that deviation from straight tube flow increases with increasing pressure and vessel diameter and with decreasing heart rate and radius of curvature. This is generalised and quantified by correlating the pulsatility Index with the modified unsteady Dean number (a/R) [ka/ων]², where a is the arterial radius, R is the radius of curvature, ν is the kinematic viscosity, k is the ratio of the peak to the mean of the applied pressure waveform and ω is the frequency. A cut off value of 1 for the modified unsteady Dean number marks the transition from the linear operating region of straight tube flow to the nonlinear operating region of curved tube flow