Analysis of Dynamic Magnetic Resonance Elastography Data - Advance Image Processing in Magnetic Resonance Imaging - page 455

modulus estimations depends on the actual shear modulus and on the processing
algorithm used.

14.5.13 P HASE U NWRAPPING

Because shear waves attenuate quickly in certain tissues, large amplitudes near
the surface may be required to achieve sufficient amplitude in a deep region of
interest. Too much amplitude can cause phase wrap, i.e., large enough displace-
ments can cause accumulated phase shifts outside the range

, which are ambig-
uous. This sets an upper limit for the amplitude at which the tissue should be
driven. However, standard phase unwrapping algorithms [55] can be applied to
MRE data with good success, because the wrapped regions are usually fairly well
localized. The upper limit on amplitude can then be increased as long as the
phases can be reliably unwrapped. Alternatively, the increased amplitude can be
traded off for higher resolution by operation at a higher mechanical frequency.

±π

14.5.14 D IRECTIONAL F ILTERING

Most of the inversion algorithms described in the preceding text are derived from
the fundamental equations of motion and, in principle, correctly handle complex
wave fields with interference patterns due to reflection and refraction. However,
they tend to be sensitive to areas of low displacement amplitude (and hence low
SNR) that result from such situations. A spatiotemporal directional filter has been
described that can be applied as a preprocessing step to separate complex wave
fields into components propagating in different directions, each of which can be

analyzed separately [56] (see Subsection 6.1 ). Areas of low motion due to standing

waves or cancellation between interfering waves are minimized, and weighted
combinations of inversions from such directionally separated data sets signifi-
cantly improve reconstructions of shear moduli and attenuation.

14.6 RESULTS

To illustrate the different noise sensitivities, resolutions, and accuracies of the
various processing techniques, we present results on physical phantoms having
known parameters and ex vivo and in vivo results on both human and animal
tissues. Quantitative measurements of shear moduli with MRE have shown high
correlation with measurements using biomechanical testing devices [8,57,58].

14.6.1 P HANTOM O BJECT

Figure 14.3 illustrates a sample wave image from an agar gel phantom with four

stiff cylindrical inclusions (ranging from 5 to 25 mm in diameter) perpendicular
to the slice, acquired with mechanical vibrations of 100 Hz. The figure depicts
the out-of-plane displacement component, with the largest displacement being
approximately 10

m. The acoustic shear waves are introduced from the top of
the image and propagate downward, but they reflect off the cylinders and the

µ