Analysis of 2-D Ultrasound Cardiac Strain Imaging Using Joint Probability Density Functions

Abstract

Ultrasound frame rates play a key role for accurate cardiac deformation tracking. Insufficient frame rates lead to an increase in signal decorrelation 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 bimodal distributions in the joint probability density indicate inaccurate strain estimation over a cardiac cycle. In this study, we utilize similar analysis to evaluate a two-dimensional multi-level displacement tracking and strain estimation algorithm for cardiac strain imaging. The impact of different frame rates, final kernel dimensions, and a comparison of radiofrequency and envelope based processing are evaluated using echo signals derived from a three-dimensional finite element cardiac model and 5 healthy volunteers. Cardiac simulation model analysis demonstrate 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 radiofrequency signals. On the other hand, even a frame rate of 250Hz 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 radiofrequency analysis. We also show that an increase in the final kernel dimensions significantly impact the strain probability distribution and joint probability density function generated; with a smaller impact on the variation in the accumulated mean strain estimated over a cardiac cycle. Our results demonstrate that radiofrequency frame rates currently achievable on clinical cardiac ultrasound systems are sufficient for accurate analysis of the strain probability distribution, when a multi-level two-dimensional algorithm and kernel dimensions on the order of 1 λ by 3 A-lines or smaller are utilized.

Segmental Analysis of Cardiac Short-Axis Views Using Lagrangian Radial and Circumferential Strain

“…Interpolation errors incurred to generate a polar grid density similar to the original displacement field are significantly lower than errors incurred in the estimation of radial and circumferential strains using coordinate transformation from axial and lateral displacement vectors or strain tensors. We have also developed approaches for the 2D tracking of deformation for RF phased array data that have significantly improved spatial resolution, 34 which can be easily incorporated into the polar grid algorithm described in this paper.…”

“…B-mode images are derived from log-compressed and decimated envelope information derived from RF echo signals. 25-30 It has been previously demonstrated that strain estimated using RF signals provides a higher elastographic signal-to-noise ratio (SNR e ) 32,33 and significantly fewer strain artifacts 34 when compared with envelope and B-mode echo signals due to the additional phase information included in RF echo signals. These commercial algorithms track the movement of acoustic patterns or “speckle” on B-mode images, devoid of phase information reducing the accuracy and precision of the strain estimated.…”

Spatiotemporal Bayesian Regularization for Cardiac Strain Imaging: Simulation and In Vivo Results

“…To compare the algorithm performance in vivo , strain filters [ 67 ] were derived for the accumulated radial and longitudinal strains at all time points for each method by performing stochastic precision analysis [ 67 ]–[ 69 ]. First, local elastographic signal-to-noise (SNR e ) were computed as follows.…”

“…DISPLACEMENT ESTIMATION PARAMETERS FOR FEA SIMULATION AND IN VIVO STUDIES In vivo median filter axial kernel dimension was 7 pixelsstochastic precision analysis[67][68][69]. First, local elastographic signal-to-noise (SNR e ) were computed as follows.…”