True velocity estimation using the correlation technique [blood flow]

One of the most important biomedical applications of ultrasound is its use in the detection, measurement and mapping of blood flow. The correlation technique has been shown to give a better accuracy velocity estimation than the conventional frequency domain methods. This technique requires two consecutive echo signals in addition to the flow angle to produce the magnitude of the velocity vector based on transit-time calculations. The effect of the lateral beam pattern on the results has not been sufficiently treated in the literature. In this work, we present a new generalized formulation of the correlation technique that incorporates both axial and lateral beam characteristics. We show that the location of the correlation function peak given in the literature is a special case of this model when the field is a plane wave. Also, we show that for other practical beam forms, the lateral beam form introduces an angle-dependent bias to the axial velocity measurements obtained with the classical formula. By properly choosing the source aperture and excitation signal, we derive a formula for lateral displacement estimation from correlation peak locations and magnitudes. This displacement can be used directly to estimate the lateral velocity component and allow the calculation of the complete velocity vector