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Updated: Jul 19, 2026

Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure
Published on: April 25, 2025
Measurement of volumetric flow
Oliver D Kripfgans1, Jonathan M Rubin, Anne L Hall
1Department of Radiology, University of Michigan, Kresge III, R3322, Ann Arbor, MI 48109-0553 USA. oliver.kripfgans@umich.edu
Objective:
The purpose of this study was to evaluate a 3-dimensional (3D) sonographic method for the measurement of volumetric flow under conditions of known flow rates and Doppler angles.
Methods:
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. Blood-mimicking fluid circulated by a computer-controlled pump provided a range of flow velocities (2-15 mL/s). A 6-axis positioning system maneuvered the ultrasound probe through a range of angles (40 degrees-70 degrees and 110 degrees -140 degrees) with respect to the tube (orthogonal to the tube being 90 degrees). Volume data sets were obtained spanning 29 degrees lateral and 20 degrees elevational angles encompassing the flow tube in a scanning time of less than 10 seconds. Power Doppler data were used to correct for partial volume effects.
Results:
Using a single angle (110 degrees) 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. 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.
Conclusions:
Direct comparisons of volume flow rates estimated with 3D sonography and known flow rates showed that the method has good accuracy. Subsequent comparisons under pulsatile and in vivo conditions will be needed to verify this performance for clinical applications.
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