Angle-Independent Blood Volume Flow

Abstract

Standard ultrasound Doppler can estimate volume flow. However, the estimate depends on major assumptions, which include flow that has to be perfectly symmetric around the centerline of the vessel, a perfectly round vessel cross-section, and the Doppler measurements must be angle corrected. These restrictions make volume flow estimates problematic especially in environments where these assumptions do not hold, such as transjugular intrahepatic portosystemic shunts (TIPS) and umbilical cords. With the advent of 3D/4D ultrasound imaging, all of the limitations of ultrasound volume flow measurements can be overcome, potentially producing volume flow estimates that are as easy to obtain as standard color flow Doppler images, i.e. in real time. The method depends on the something called Gauss's theorem. This law states that volume flow is equal to the sum of all of the normal velocity vectors passing through any surface. Simply put, this sum, also known as the total flux, is just the sum of the local products of the velocity of the blood going perpendicularly through every individual element of a surface that cuts across a blood vessel This can be any continuous surface (often known as a C-surface or C-plane), it does not have to be a plane, and the method contains none of the assumptions required for standard volume flow measurement. Thus, this method is angle independent, flow profile independent, and vessel geometry independent. Hence, non-laminar flow profiles produced by the irregular TIPS stent walls or highly tortuous umbilical arteries and veins do not affect this method. We have tested this technique in simulations, phantoms, in in-vivo animal models, and human subjects. The method has proven to work well in all of these settings. In humans, linear regression of data from revised TIPS cases showed an inverse correlation between mean-normalized change in pre- and post-revision shunt volume flow and mean-normalized change in pre- and post-revision portosystemic pressure gradient (r2 = 0.71, P-value = 0.0044). Depth-corrected and weight normalized umbilical vein volume flow measurements in normal and pre-eclampsia subjects showed a statistically significant difference between groups (P = 0.035). Further, these measurements were highly reproducible in the mean estimate with an intra-subject relative standard error (RSE) of 12.1 ± 5.9 % and an intra-measurement RSE of 5.6 ± 1.9 %. This method is easy to perform, accurate, and reproducible. Using 2D ultrasound arrays, it can be in real-time. It could have a major impact on future flow analysis.