Lagrangian deformation tracking for strain imaging

Lagrangian strain imaging requires knowledge of the prior state of the deformation at its very core and can be accomplished if all three components of the displacement vector field can be accurately estimated. However, most ultrasound imaging is still performed along two-dimensional imaging planes, with the feasibility of computing both in plane displacement vectors (axial and lateral) key to Lagrangian deformation tracking and accumulation. Higher frame-rates can mitigate some of the impacts of out-of-plane motion in the elevational direction. Our group has been engaged in developing algorithms for Lagrangian deformation tracking and strain tensor imaging for carotid, cardiac and liver ablation imaging over the last two decades. Our algorithms currently implemented on a graphics processing unit estimate both axial and lateral displacement vectors accurately and with high spatial resolution using radiofrequency (RF) echo signals. We utilize a coarse-to-fine multilevel strategy and sinc-interpolation to both interpolate RF data at the final processing level for improved lateral displacement vector estimation and for accurate and unbiased sub-sample displacement estimation.