Analysis of 2-d ultrasound cardiac strain imaging using joint probability density functions

Ultrasound frame rates play a key role for accurate cardiac deformation tracking. Insufficient frame rates lead to an increase in signal de-correlation artifacts resulting in erroneous displacement and strain estimation. Joint probability density distributions generated from estimated axial strain and its associated signal-to-noise ratio provide a useful approach to assess the minimum frame rate requirements. Previous reports have demonstrated that bi-modal distributions in the joint probability density indicate inaccurate strain estimation over a cardiac cycle. In this study, we utilize similar analysis to evaluate a 2-D multi-level displacement tracking and strain estimation algorithm for cardiac strain imaging. The effect of different frame rates, final kernel dimensions and a comparison of radio frequency and envelope based processing are evaluated using echo signals derived from a 3-D finite element cardiac model and five healthy volunteers. Cardiac simulation model analysis demonstrates that the minimum frame rates required to obtain accurate joint probability distributions for the signal-to-noise ratio and strain, for a final kernel dimension of 1 λ by 3 A-lines, was around 42 Hz for radio frequency signals. On the other hand, even a frame rate of 250 Hz with envelope signals did not replicate the ideal joint probability distribution. For the volunteer study, clinical data was acquired only at a 34 Hz frame rate, which appears to be sufficient for radio frequency analysis. We also show that an increase in the final kernel dimensions significantly affect the strain probability distribution and joint probability density function generated, with a smaller effect on the variation in the accumulated mean strain estimated over a cardiac cycle. Our results demonstrate that radio frequency frame rates currently achievable on clinical cardiac ultrasound systems are sufficient for accurate analysis of the strain probability distribution, when a multi-level 2-D algorithm and kernel dimensions on the order of 1 λ by 3 A-lines or smaller are utilized.