Image Processing Reference
In-Depth Information
muscle fibers [22,37]. The analysis algorithms presented earlier all assumed
tissues to be isotropic in order to reduce the large number of unknown parameters
to be estimated. Similar algorithms can be developed without this assumption or
by replacing it with a less-restrictive symmetry (e.g., transverse isotropy is prob-
ably the appropriate model for muscle fibers). Solving for the larger number of
unknowns may require larger data sets, probably from a wider variety of exper-
iments that excite different motions, and may be quite difficult. Sinkus et al. [33]
have proposed a technique that attempts to solve, in a limited way, for anisotropic
characteristics of tissue. They have applied this technique to the breast and suggest
that this can help differentiate between benign tissue, which appears isotropic,
and carcinoma, which appears to exhibit an increased degree of anisotropy.
14.5.11
H YPERELASTIC P ARAMETER D ETERMINATION
Tissues in general show nonlinear behavior, and the stress-strain curve for large
displacements can deviate considerably from a straight line. In MRE, the displace-
ments are usually small enough so behavior is linear, and the stiffness is represented
by the slope of the stress-strain curve at particular experimental conditions. How-
ever, the amount of compression applied to the tissue (by the mechanical driver to
couple it to the tissue or by other aspects of the experiment) can determine where
the stress-strain curve is being probed, and different experiments on the same tissue
can report different stiffness values. Samani et al. [54] modeled this behavior with
hyperelastic parameters and have proposed an inversion scheme that attempts to
recover these and use the entire stress-strain curve for material characterization.
14.5.12
S IGNAL - TO -N OISE C ONSIDERATIONS
It is important to understand whether there is sufficient signal in a given region
to yield an accurate stiffness estimate and what the uncertainty is in that estimate.
In MRE, “signal” means not only MR signal but, more importantly, that the
region is undergoing sufficient motion so that the induced phase shifts can be
detected and well quantified. A simple model of how noise in the MR acquisition
translates to noise in the phase difference or “wave” images can be derived. The
noise level in the standard MR magnitude image reconstructed from the MRE
acquisition can be determined from the background (after correction for the
effect of rectification). In areas of significant magnitude, this noise can be
considered to be Gaussian in both the real and imaginary components. Thus, it
forms a Gaussian cloud about the true magnitude and phase, and the uncertainty
in phase for a given noise level and magnitude can be calculated. In the wave
images, this uncertainty in phase is the noise, and the signal is the accumulated
phase shift due to motion. Local SNR in the wave images can thus be determined.
Higher SNR is obtained by (1) a larger underlying MR magnitude signal and
(2) a larger displacement amplitude, leading to a larger accumulated phase shift.
The effect of a given SNR in the wave images on the uncertainty of shear
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