Robust strain rate estimation using two-dimensional cubic B-splines

In this study, the use of cubic B-splines for robust ultrasonic strain and strain rate estimation is demonstrated. To do this, radio-frequency data sets of cyclically compressed gelatine phantoms were acquired during M-mode imaging. Velocities were estimated by tracking temporally successive RF windows. Subsequently, a two-dimensional cubic smoothing B-spline was fitted through the velocity estimates for both depth and time. Strain rate could then be defined analytically as the cubic B-spline being the partial derivative of the velocity B-spline surface in the depth direction. Similarly, a strain B-spline surface could be defined as the analytical temporal integral of the strain rate B-spline. The method was shown to give accurate strain and strain rate estimates. Comparing this method to conventional processing, it was shown to produce less noisy strain rate and strain estimates.