A common clinical practice during single-point Doppler analysis is to measure the centerline maximum velocity and to recover the time-averaged flow rate by exploiting an assumption on the shape of velocity profile ( a priori  formula), either a parabolic or a flat one. In a previous study, we proposed a new formula valid for the peak instant linking the maximum velocity and the flow rate by including a well-established dimensionless fluid-dynamics parameter (the Womersley number), in order to account for the hemodynamics conditions ( Womersley number-based  formula). Several  in silico  tests confirmed the reliability of the new formula. Nevertheless, an  in vivo  confirmation is missing limiting the clinical applicability of the formula. An experimental  in vivo  protocol using cine phase-contrast MRI (2-D PCMRI) technique has been designed and applied to ten healthy young volunteers in three different arterial districts: the abdominal aorta, the common carotid artery, and the brachial artery. Each PCMRI dataset has been used twice: 1) to compute the value of the blood flow rate used as a gold standard and 2) to estimate the flow rate by measuring directly the maximum velocity and the diameter (i.e., emulating the intravascular Doppler data acquisition) and by applying to these data the  a priori  and the  Womersley number-based  formulae. All the  in vivo  results have confirmed that the  Womersley number-based  formula provides better estimates of the flow rate at the peak instant with respect to the  a priori  formula. More precisely, mean performances of the  Womersley number-based  formula are about three times better than the  a priori  results in the abdominal aorta, five times better in the common carotid artery, and two times better in the brachial artery.
['R. Ponzini', 'Christian Vergara', 'Giovanna Rizzo', 'Alessandro Veneziani', 'Alberto Roghi', 'Angelo Vanzulli', 'Oberdan Parodi', 'Alberto Redaelli']
Womersley Number-Based Estimates of Blood Flow Rate in Doppler Analysis: In Vivo Validation by Means of Phase-Contrast MRI