Tracking large deformations in tissue using ultrasound can enable the reconstruction of nonlinear elastic parameters, but poses a challenge to displacement estimation algorithms. Such large deformations have to be broken up into steps, each of which contributes an estimation error to the final accumulated displacement map. The work reported here measured the error variance for single-step and accumulated displacement estimates using one-dimensional numerical simulations of ultrasound echo signals, subjected to tissue strain and electronic noise. The covariance between accumulation steps was also computed. These simulations show that errors due to electronic noise are negatively correlated between steps, and therefore accumulate slowly, while errors due to tissue deformation are positively correlated and accumulate quickly. For reasonably low electronic noise levels, the error variance in the accumulated displacement estimates is remarkably constant as a function of step size, but increases with the length of the tracking kernel.

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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 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 simulations, the work reported here measured error variance for single-step and accumulated displacement estimates using two-dimensional numerical simulations of ultrasound echo signals, subjected to both normal and axial shear strain as well as electronic noise. Previous results 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. A general comparison of tracking performance 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.

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We describe the beginnings of a multi-wavelength analysis of TeV blazars using observations from the WIYN 0.9m optical telescope, the VERITAS gamma-ray telescope, and the AMANDA/IceCube neutrino detector. Optical data were taken for Mrk 421, Mrk 501, and 1ES 1959+650 in coincidence with gamma-ray observations over a two-month period in Apr-June 2006. In the future we hope to use a statistical analysis of TeV flares in order to determine the significance of time-correlated neutrino detection with AMANDA/IceCube.