Three-dimensional Doppler velocimetry of flow jets

A closed-form solution is derived of the Doppler equation for the magnitude and angle to the three-dimensional velocity vector. The resultant solution is more general than previous formulations and, since it is based on multiple conventional transmit-receive Doppler probes, it can be readily applied by adapting existing Doppler units. Turntable experiments demonstrated that the three-dimensional angle-independent theory correctly predicted velocity within average 32% over a 26. degrees -range of Doppler angles. Experiments with a flow phantom showed general agreement with the angle-independent theory in the more demanding setting of an actual flow stream. Experiments utilizing a jet stream which modeled the clinically important conditions that exist in stenotic vessels, valvular abnormalities, and septal defects within 1.4-3.8% of the actual velocity, over an 18 degrees range of Doppler angles.>