2012 Proceedings - International Tissue Elasticity Conference

057 THE ACCUMULATION OF DISPLACEMENT ESTIMATION ERROR OVER LARGE
DEFORMATIONS.
Matthew A. Bayer 1 , Timothy J. Hall 1 .
1 University of Wisconsin–Madison, Madison, WI, USA.
Background: Elastography usually aims to measure the stiffness of tissue, but the elastic nonlinearity
may also be a useful diagnostic parameter. Reconstructions of the nonlinearity require displacement
estimation over large deformations which must be broken up into steps and accumulated into a final
displacement map. Each step contributes an estimation error in the final result. Such a multi–step
approach has been used and investigated previously, but previous studies have usually used it as a
heuristic in experiment [1], assumed consecutive estimates are independent [2] or were not able to
characterize the error properties in detail [3].
Aims: To characterize the error variance of large–deformation accumulated displacement estimates and
the covariance between their steps using simulated signals and tracking.
Methods: One–dimensional radiofrequency echo signals were simulated by convolving dense, randomly
placed point scatterers with a windowed cosine pulse function. Uncorrelated noise with the same power
spectrum as the signal was added to simulate the electronic noise of the system. A total of 20%
compressive strain was applied to the scatterers in 180 steps, with a new convolution and noise
realization applied at each step. Displacements were estimated by finding the peak of the normalized
cross–correlation between signal kernels over a displacement range of one wavelength. Error variances
were then measured as a function of stain step size for both single–step and multi–step estimates. The
covariance between steps of the accumulated sequences was also measured. All computations were
performed in Matlab (The MathWorks Inc., Natick, MA, USA).
Results: Analysis of the covariance between estimation steps shows that errors due to electronic noise
are partially anti–correlated and, therefore, tend to cancel out and accumulate slowly. Furthermore,
errors due to tissue strain are highly correlated, which together with the single–step dependence on
strain, has the effect that accumulated strain–induced error is relatively insensitive to step size, at least
for smaller kernels. Tracking kernel length still has a strong effect on the accumulated error. Figure 1a
shows the surprisingly weak effects of signal–to–noise ratio (SNR) and step size for a single kernel length,
while Figure 1b shows the effects of kernel length for a single SNR.
Figure 1: Accumulated variance as a
function of strain step
size, for varying SNR (a),
and kernel sizes (b). Note
the different y–axis scales.
Conclusions: These results show that covariance between estimation steps must be considered for a
proper analysis of accumulated displacement estimation error. They should also provide guidance for
producing more accurate accumulated displacement maps for elastic nonlinearity reconstruction. The
simplifying assumptions of our simulations (one–dimensional, uniaxial and uniform strain) may limit
their validity when applied to tissue, but they provide a useful and suggestive starting point for more
complex experiments.
Acknowledgements: NIH grants R01CA140271 and T32CA009206.
References:
[1] O’Donnell M, Skovoroda AR, et al.: Internal Displacement and Strain Imaging using Ultrasonic Speckle Tracking.
IEEE Trans Ultrason Ferroelectr Freq Control, 41(3), pp. 314–325, 1994.
[2] Varghese T, Ophir J: Performance Optimization in Elastography: Multicompression with Temporal Stretching.
Ultrasonic Imaging, 18(3), pp. 193–214, 1996.
[3] Du H, Liu J, Pellot–Barakat C: Noise Minimization by Multi–Compression Approach in Elasticity Imaging. Proc
IEEE Ultrasonics Symp, pp. 32–35, 2004.
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