Image Processing Reference
In-Depth Information
obtained at various phase offsets (typically 4 to 8) regularly spaced in a cycle,
which allows visualization of wave propagation as a cine loop. More importantly,
it allows extraction of the harmonic component at the frequency of interest, giving
the amplitude and the phase (relative to an arbitrary zero point) of the harmonic
displacement at each point in space [36]. This extraction also provides some
degree of noise reduction. The resulting complex displacement field is the input
to all the processing techniques described in the following text.
A single MRE acquisition is sensitized to motion in a single direction. How-
ever, the experiment can be repeated and the sensitization direction varied in
order to capture all three orthogonal components of displacement. Thus, MRE
can acquire full 3-D cyclic displacement information at MR pixel resolution
throughout a 3-D volume. In principle, this makes it feasible to estimate all
components of the strain tensor, making it possible to probe the anisotropic mechan-
ical properties of tissues [8,33,37]. This ability to capture full displacement infor-
mation and the freely oriented field of view unencumbered by any acoustic window
requirements represent the main advantages of MRE over ultrasound-based tech-
niques. Conversely, the much longer acquisition times required by MRE are its
single largest disadvantage.
MRE is highly sensitive only to motion that is precisely synchronized with
the sensitization gradients and is no more sensitive to physiologic motion than a
conventional gradient-echo sequence [38]. Sensitivity to nonsynchronous motion
can be further reduced by explicitly nulling the individual moments of the gradient
waveform. It is also possible to amplitude modulate the envelope of the motion-
encoding waveform to further increase its spectral selectivity [39].
In summary, MRE offers direct visualization and quantitative measurement of
tissue displacements, high sensitivity to very small motions, a field of view unen-
cumbered by acoustic window requirements, and the ability to obtain full 3-D
displacement information throughout a 3-D volume. As shown in the following
text, under some assumptions this allows direct local inversion of the data to recover
the elastic properties, with no need for boundary conditions or the estimation of a
stress field.
14.5
DATA PROCESSING
A variety of approaches can be used to invert the displacement data to recover
mechanical properties. These are characterized in the following text by the
assumptions or simplifications made in their derivations. Unlike many biomedical
inversions for which data are available only along a boundary, data in MRE are
available everywhere in a 3-D volume. In favorable situations, it is possible to
deduce quantitatively accurate values of properties such as the shear modulus. In
general, however, despite the richness of the data set and the variety of processing
techniques, it remains a challenge to extract accurate results from the intrinsically
noisy data in complex, heterogeneous objects.
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