A mean blood velocity statistic for the Doppler signal from anarrow ultrasound beam

An easily calculable statistic proportional to the instantaneous spatial mean blood velocity through a vessel cross section is derived from Doppler power spectral estimates for the case where the Doppler beam is assumed to be of negligible thickness compared to the vessel diameter. This is an alternative statistic to that derived where uniform insonation is assumed, an assumption thought to be poorer in many real cases. The main requirement is that the velocity profile is monotonic increasing from the vessel wall to the vessel center. Errors in each statistic are compared for a variety of true beam dimensions, using a variety of velocity profiles, and the new statistic is shown to incur less error for Gaussian beam response profiles with a standard deviation less than 0.4 of the vessel radius, or for rectangular response profiles with a width less than 0.65 of the vessel diameter. If an estimate can be made of the true beam dimensions and vessel diameter, a weighted sum of the two statistics can give a more accurate estimate of mean velocity. The case of a beam displaced from the center of the vessel is also considered, and errors are found to be less than 4% for a displacement of 20% of the vessel radius