Abstract
We derived the Cramér Rao lower bound for 2-D estimators employed in quasi-static
elastography. To illustrate the theory, we modeled the 2-D point spread function as
a sinc-modulated sine pulse in the axial direction and as a sinc function in the lateral
direction. We compared theoretical predictions of the variance incurred in displacements
and strains when quasi-static elastography was performed under varying conditions
(different scanning methods, different configuration of conventional linear array
imaging and different-size kernels) with those measured from simulated or experimentally
acquired data. We performed studies to illustrate the application of the derived expressions
when performing vascular elastography with plane wave and compounded plane wave imaging.
Standard deviations in lateral displacements were an order higher than those in axial.
Additionally, the derived expressions predicted that peak performance should occur
when 2% strain is applied, the same order of magnitude as observed in simulations
(1%) and experiments (1%–2%). We assessed how different configurations of conventional
linear array imaging (number of active reception and transmission elements) influenced
the quality of axial and lateral strain elastograms. The theoretical expressions predicted
that 2-D echo tracking should be performed with wide kernels, but the length of the
kernels should be selected using knowledge of the magnitude of the applied strain:
specifically, longer kernels for small strains (<5%) and shorter kernels for larger
strains. Although the general trends of theoretical predictions and experimental observations
were similar, biases incurred during beamforming and subsample displacement estimation
produced noticeable differences.
Key Words
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Article info
Publication history
Published online: June 26, 2017
Accepted:
May 21,
2017
Received in revised form:
April 6,
2017
Received:
November 9,
2016
Identification
Copyright
© 2017 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved.
