MRI Measurement of Heart Wall Motion - Advance Image Processing in Magnetic Resonance Imaging - page 354

relaxation and has a phase modulated by the spatial position x . The third com-
ponent has a phase modulated by x X , i.e., a complex sinusoid that varies

approximately twice as fast as the initial tag frequency. These three signal com-
ponents give rise to spectral peaks in k-space at 0, k e and 2 k e , respectively.
As in previous DENSE implementations [36,37], the tag gradient k e can be
chosen high enough (greater than 0.25 cycles per pixel) so that the third spectral

+

peak is shifted above the maximum frequency sampled ( Figure 10.12 ). (Note that

the spatial frequencies above twice the sampling frequency are removed with an
analog low-pass filter before the signal is sampled, so that the higher spatial
frequencies will not be aliased into the digitized signal.)
The second term, arising due to T1 relaxation, has a phase modulated by k e ⋅

x .
This term cannot be pushed out of the readout window because large values of k e
result in unacceptable signal loss due to myocardial strain. Instead, the CSPAMM
technique can be used to subtract out the relaxed component. As in CSPAMM
HARP, two data sets are acquired, in which the second RF pulse in the 1-1 SPAMM
encoding is 90 in the second set. Subtraction of these two

images reinforces the first term and cancels out the second term [38].

+ 90 in the first set and −

10.6.3 K INEMATICS

Analysis of DENSE images can be performed in the same way as for HARP
(Subsection 10.4.2). Spatial derivatives of phase can be used to calculate the
Eulerian strain at each time frame. For reconstruction of displacements greater
than

/k e pixels, a phase unwrapping procedure must be used. A 3-D analysis
can be performed using the procedure outlined in Subsection 10.2.5, in which n
is a unit vector in the direction of the encode gradient g and the displacements
u are directly obtained from the (unwrapped) DENSE phase.

π

10.7 DIFFUSION

The MRI signal can also be made sensitive to diffusion, primarily due to the
incoherent motion of water within the tissue [39]. In the heart, diffusion tensor
imaging can be used to determine the direction of maximum diffusivity, which
corresponds to the eigenvector of the maximum eigenvalue of the diffusion tensor
[40]. This is typically aligned in the direction of the muscle cells [41]. The second
and third eigenvectors can give information on the layered structure of the myo-
cytes [42]. It is interesting to note that the pulse sequence for diffusion-weighted

imaging is the same as shown in Figure 10.9 . In the case of diffusion imaging,

any incoherent motion between the two gradients results in a diminished echo
magnitude (due to partial dephasing within a voxel that is not refocused by the

decode gradient). The stimulated echo version is shown in Figure 10.11 . This

sequence has been used to measure diffusion in the beating heart [42]. Thus,
DENSE imaging is intrinsically diffusion weighted. As shown in the preceding
text, DENSE is also strain weighted, because any strain within the tissue will
also cause loss in signal. This was exploited by Osman et al. [43], who used the