Spatial quadrature: a novel technique for multi-dimensional velocity estimation

Conventional ultrasonic motion or flow velocity estimation is limited to the axial velocity component. I present a novel technique, called “spatial quadrature”, for the simultaneous estimation of axial and lateral velocity components. This technique utilizes even and odd spatial weightings of the point spread function which have a quadrature relationship. These weightings produce modulation in the received echo which can be decoded to quantify lateral motion. This technique is conceptually related to both the multiple beam and spectral broadening paradigms for the estimation of the lateral velocity component. However, it also has unique characteristics which overcome some of the limitations of these previously described techniques. This estimator can be implemented for two-dimensional velocity estimation with a conventional transducer array and any medical ultrasound scanner, preferably one with parallel receive processing. The technique can also be extended to three-dimensional velocity estimation given an appropriate 2-D transducer and scanner. I present space and frequency domain descriptions of this estimator in the context of a brief overview of 2-D flow estimation methods, including analyses characterizing the performance envelope of this estimator. I also present the results of phantom studies using a clinical scanner which demonstrate this technique in two dimensions. I also discuss the application of this technique in CW and PW regimes