Volumetric blood flow calculation using a narrow ultrasound beam

Spectral analysis of the Doppler signal from a negligibly thin ultrasound beam directed through the centre of the blood vessel can, for certain forms of velocity profile, produce a statistic deemed to be proportional to spatial mean blood velocity. A statistic recently derived for the case of an axisymmetric, monotonic velocity profile is generalised to the situation where the profile is axisymmetric and made up of a central monotonic section inside a region of reverse flow which is itself symmetric. Using the theory of oscillating flow in a rigid tube, instantaneous velocity profiles were derived for samples of actual cardiac cycles recorded from various arterial sites. In every case the profiles satisfied the assumptions for the statistic to be valid throughout considerable regions of each cycle. The resulting error in the use of the statistic to measure the volumetric flow in a cycle had a magnitude less than 0.01% for the carotid, radial and brachial artery recordings, was typically small and positive (+2.5%) for the common femoral artery, and was typically negative (0 to -8%) for the superficial femoral artery, with outlying value of -16%.