A theory to correct the systematic error caused by the imperfectly matched beam width to vessel diameter ratio on volumetric flow measurements using ultrasound techniques

Abstract

When a multigate procedure is used to measure volumetric flow in vessels, in addition to the flow rate result obtained from the conventional velocity profile method, a second result from an “average velocity profile method” can be obtained simultaneously. The latter method obtains the flow rate from the product of the average velocity across the profile and the cross-sectional area of the vessel. A theoretical model has been used to study the effect of the beam width to vessel diameter ratio (BWR) on these two results, as well as a third flow rate result obtained from the uniform insonation method. A theory has been established to correct the systematic error caused by the imperfectly matched BWR associated with each method. It uses a correction factor and the difference between the results from the average velocity profile method and the velocity profile method to compensate for the systematic error. The relationship between an optimal correction factor and the BWR under different flow conditions has been studied. The results using the correction therory in this model show that if the estimated BWR is within ±0.1 from the actual BWR value, the theoretical error in volumetric flow estimation can be limited to within 6.5% for the entire range of BWR.