Hierarchical Motion Estimation With Bayesian Regularization in Cardiac Elastography: Simulation and $In~ Vivo$ Validation

Cardiac elastography (CE) is an ultrasound-based technique utilizing radio-frequency (RF) signals for assessing global and regional myocardial function. In this work, a complete strain estimation pipeline for incorporating a Bayesian regularization-based hierarchical block-matching algorithm, with Lagrangian motion description and myocardial polar strain estimation is presented. The proposed regularization approach is validated using finite-element analysis (FEA) simulations of a canine cardiac deformation model that is incorporated into an ultrasound simulation program. Interframe displacements are initially estimated using a hierarchical motion estimation framework. Incremental displacements are then accumulated under a Lagrangian description of cardiac motion from end-diastole (ED) to end-systole (ES). In-plane Lagrangian finite strain tensors are then derived from the accumulated displacements. Cartesian to cardiac coordinate transformation is utilized to calculate radial and longitudinal strains for ease of interpretation. Benefits of regularization are demonstrated by comparing the same hierarchical block-matching algorithm with and without regularization. Application of Bayesian regularization in the canine FEA model provided improved ES radial and longitudinal strain estimation with statistically significant (p <; 0.001) error reduction of 48.88% and 50.16%, respectively. Bayesian regularization also improved the quality of temporal radial and longitudinal strain curves with error reductions of 78.38% and 86.67% (p <; 0.001), respectively. Qualitative and quantitative improvements were also visualized for in vivo results on a healthy murine model after Bayesian regularization. Radial strain elastographic signalto-noise ratio (SNRe) increased from 3.83 to 4.76 dB, while longitudinal strain SNRe increased from 2.29 to 4.58 dB with regularization.