Computational fluid dynamics-based estimation of blood flow rate in Doppler analysis: in vivo validation by means of Phase Contrast Magnetic Resonance Imaging

We carry out an in vivo validation of a new method for estimating blood flow rate from the maximum velocity, as it is usually done in single-wire Doppler catheter measurements. A common practice is to measure the centerline velocity and to recover the flow rate (a-priori approach) by exploiting an assumption on the shape of velocity profile, either a parabolic or a flat one. Our method proposes a new formula valid for the peak instant linking the maximum velocity and the flow rate including the Womersley number, in order to account in a more accurate way the haemodynamics conditions (Womersley-based approach). In vivo validation of the Womersley-based approach is performed. An experimental protocol using cine Phase Contrast MRI (2D 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. 2) To estimate the flow rate using information only on the maximum velocity and on the diameter value (i.e. emulating the intravascular Doppler data acquisition) by using the a priori and the Womersley-based approaches. All the in vivo results concerning the three arterial districts allow to state that the Womersley-based approach provides better estimates of the flow rate at the peak instant with the respect to the a-priori approach. These results might have relevant clinical implication, for example in Coronary Flow Reserve determination.