Statistical analysis and time correlation processes applied to velocity measurement (blood flow)

Abstract

A time description of pulsed Doppler signals backscattered by blood flow describes the pulse-Doppler effect on the successive echoes from a cloud of scatterers as a progressive translation in time due to the displacement of the scatterers along the ultrasound beam axis between two transmissions. However, a statistical analysis of the treatment provides a better description of this estimation process. In the general case where the velocity is neither axial nor uniform, the dispersion characteristics of the velocity distribution must be introduced. A description is given of the statistical averages naturally performed by the process in such cases. As a main result, the estimation of the local variance of the flow is also available. This variance has been estimated first with simulated signals for a validation of the theoretical description, then with in vivo data from pathological cases.