Validation of a theoretical approach for estimation of velocity error of a vector Doppler system.

In arterial stenoses, where the flow velocity can be inclined significantly to the vessel axis, single beam Doppler systems give large errors in estimated maximum velocity. These errors can potentially be reduced by using a 2-beam system. The aim was the derivation and validation of simple equations for predicting the velocity estimation error of a 2-beam vector Doppler system. These were compared with results from a computer model of a linear array based system, and flow rig measurements using the same system. The effect of interbeam angle (IBA), flow rate, dwell time and beam-vessel angle (BVA) were investigated. Theoretically, the velocity fluctuations were expected to be approximately perpendicular to the beam bisector with the velocity magnitude and angle standard deviations proportional to (sin(BVA)/IBA)(Bandwidth/Dwelltime)(1/2) and (cos(BVA)/IBA)(Bandwidth/Dwelltime)(1/2) respectively. Using the 2-beam system we measured the frequency error for similar to 12degrees IBA, 10ms dwell time, 50cm/s Poiseuille flow, 70degrees BVA and vessel-centred 1.5mm sample volumes and then used the computer simulation to vary an four parameters about these settings. Experimentally, we found the velocity error was aligned at 730 to,the beam bisector with standard deviation of 21% of the mean magnitude, corresponding to an 11% mean frequency error. In the simulations the velocity magnitude and angle error scaled approximately as 1/IBA for IBA from 50 to 45degrees. The magnitude error scaled approximately as sin(BVA) from 350 to 85degrees and the angle error as cos(BVA) from 300 to 85degrees. Both magnitude and angle error fell approximately as the inverse root of the dwell time from 2ms to 19ms dwell time, the magnitude error rose approximately as the root and the angle fell as the inverse root of the flow rate from 10cm/s up to 95cm/s. None of the simulations showed a statistically significant bias for maximum velocity. The results showed the expected amplification of the single beam frequency fluctuation to give a much larger velocity error which is nearly perpendicular to the beam bisector and have verified the theoretical expressions derived for magnitude and angle errors.