Measurement of volumetric flow


Three-dimensional surface integration - A robust method for the measurement of volumetric flow

Oliver D. Kripfgans, Jonathan M. Rubin, Michael Richards,  J. Brian Fowlkes

Department of Radiology, University of Michigan, Ann Arbor, MI 48109-0553 USA


The purpose of this study was to evaluate whether 3-dimensional (3D) sonography can be used to measure volumetric flow without knowledge of vessel geometry, flow profile, or the angle between Doppler beam and actual flow.

Figure 1. Left: Traditional Color Flow and Doppler suffer from angle dependence. The measured flow profile narrows as the beam-to-tube angle approaches 90°(arrow) and the relative Doppler velocities fall into the wall filter. Note the increased (static) echogenicity inside the tube toward the right. It is a result of transducer array-to-tube alignment as well as a larger elevational slice thickness of the acoustic beam at this depth. Right: A constant depth geometry is the surface of a torus because the center of rotation for the axial-lateral and axial-elevational beams can differ. Doppler values from this constant depth surface are read to estimate volume flow.



A GE/Kretz Voluson 730 system (GE Healthcare, Milwaukee, WI) and RAB2-5 probe were used to acquire 3D Doppler measurements in a custom flow phantom (CIRS Inc., Norfolk, Virginia). Blood-mimicking fluid (Shelley Medical Imaging Technologies, London, Ontario, Canada) was circulated by a computer-controlled pump and provided a range of non-pulsatile flow velocities (2–15 mL/s). A 6-axis positioning system was used to position the ultrasound probe and subsequently maneuver it through a range of angles (40°–70° and 110°–140°) with respect to the tube (orthogonal to the tube being 90°). Volume data sets of approximately 50 mL were obtained spanning 29° lateral and 20° elevational angles encompassing the flow tube in a scanning time of less than 10 seconds.

Surface integration of velocity vectors is based on Gauss’ theorem, which relates the divergence of the quantity v in an enclosed volume V to the flux through the surface S covering V. In other words, a surface integral of v over the enclosing boundary S will yield the volume flow Q:

Power Doppler analysis was used to correct effects of partial voluming. Specifically, velocity data was spatially weighted by local power Doppler histogram information and then integrated across a plane that covers an area larger than the cross-section of the vessel as seen in Color Flow mode.

Power Doppler has been shown in the past to be appropriate for vessel delineation. Several tests were run under conditions of a set of known but variable flow rates and Doppler angles.


Using a single angle (110°) with respect to the flow tube, measured and actual volume flow rates were within the 95% confidence interval over the full range of flow rates. A maximum error of 20% and an average error of less than 10% were seen. At flow rates of 5 and 10 mL/s, the measured volume flow rates were all within ±15% of actual values for the range of angles tested and also stayed within the 95% confidence interval.


Direct comparisons of volume flow rates estimated with 3D sonography and known flow rates showed that 3D surface velocity integration has good accuracy. Subsequent comparisons under pulsatile and in vivo conditions will be needed to verify this performance for clinical applications.


Supported by the US National Institutes of Health via grant R01 HL67921 and by GE Healthcare.