  In the approaches to elastography, two mathematical operations have been
frequently applied to improve the final estimate of shear wave speed and shear
modulus of tissues. The vector curl operator can separate out the transverse
component of a complicated displacement field, and directional filters can
separate distinct orientations of wave propagation. However, there are
practical limitations that can prevent the intended improvement in elastography
estimates. Some simple configurations of wavefields relevant to elastography
are examined against theoretical models within the semi-infinite elastic medium
and guided waves in a bounded medium. The Miller-Pursey solutions in simplified
form are examined for the semi-infinite medium and the Lamb wave symmetric form
is considered for the guided wave structure. In both cases, wave combinations
along with practical limits on the imaging plane can prevent the curl and
directional filter operations from directly providing an improved measure of
shear wave speed and shear modulus. Additional limits on signal-to-noise and
the support of filters also restrict the applica-bility of these strategies for
improving elastographic measures. Practical implementations of shear wave
excitations applied to the body and to bounded structures within the body can
involve waves that are not easily resolved by the vector curl operator and
directional filters. These limits may be overcome by more advanced strategies
or simple improvements in baseline parameters including the size of the region
of interest and the number of shear waves propagated within.

Medical Physics;Image and Video Processing