Two-dimensional simulations of displacement accumulation incorporating shear strain

Using ultrasound images to track large tissue deformations usually requires breaking up the deformation into steps and then summing the resulting displacement estimates. The accumulated displacement estimation error therefore depends not only on the error in each step but also on the statistical relationships between estimation steps. These relationships have not been thoroughly studied. Building on previous work with one-dimensional (1-D) simulations, the work reported here measured error variance for single-step and accumulated displacement estimates using two-dimensional (2-D) numerical simulations of ultrasound echo signals, subjected to both normal and axial shear strain as well as electronic noise. Previous results from 1-D simulations were confirmed, showing that errors due to electronic noise are negatively correlated between steps and accumulate slowly, while errors due to strain are positively correlated and accumulate quickly. These properties hold for both normal and axial shear strain. An analysis of 2-D kernel size for tissue under normal and axial shear strain was also performed. Under axial shear strain, error variance tends to increase with larger lateral kernel sizes but decrease for larger axial kernel sizes; the opposite relationship holds under normal strain. A combination of these two types of strain limits the practical kernel size in both dimensions.