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Optimized, unequal pulse spacing in multiple echo sequences improves refocusing in magnetic resonance
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Image of FIG. 1.
FIG. 1.

(a) Generic multiple echo sequence. All pulses are pulses with the same phase; the position of the pulse is and the delay just before the pulse is . (b) Static resonance frequency variations are rotated by the pulses, giving a toggling frame Hamiltonian proportional to [in this case, is proportional to the modulation function ]. As long as , the effect cancels since averages to zero. (c) A time-varying frequency fluctuation is altered by the pulse sequence but in general, is not averaged to zero even though is unchanged. The UDD sequence in Fig. 2 does the best possible job of canceling extremely low-frequency fluctuations.

Image of FIG. 2.
FIG. 2.

16-pulse CPMG, UDD, and anti-UDD pulse sequences. For example, for an 80 ms total echo time, the CPMG sequence has a uniform delay between the pulses of 2.5 ms, except for the first and last delays, which are 1.25 ms each. The delays in the UDD sequence are 0.681, 2.02, 3.2902, 4.4483, 5.455, 6.2759, 6.883, 7.2558, 7.3814, 7.2558, 6.883, 6.2759, 5.455, 4.4483, 3.2902, 2.02, and. 681 ms. The anti-UDD sequence (see text) is a control sequence with the same delays as the UDD sequence, arranged in different orders.

Image of FIG. 3.
FIG. 3.

(a) The pulse spacing in an -pulse UDD sequence suppresses the effects of resonance frequency fluctuations at low frequency, making the first derivatives around vanish. This figure compares the even derivatives of the 16-pulse version to a CPMG sequence (which has a nonvanishing second derivative). Odd derivatives vanish for both. (b) Explicit comparison of the efficiency of frequency fluctuations (for example, from diffusion in a structured sample with susceptibility differences) in causing dephasing. This is proportional to the power spectrum of the modulation function created by the pulse train. This figure compares a 16-pulse UDD sequence and a 16-pulse CPMG sequence of the same duration. Note that for low-frequency modulation, UDD vastly outperforms CPMG in inhibiting relaxation.

Image of FIG. 4.
FIG. 4.

Spin echo image of the postmortem mouse used in the experiments in Fig. 5. Arrows indicate locations in the mouse where there is excess free water since the mouse was frozen and thawed. The boxes in red show the ROIs used for the analysis of signal strength in Table I.

Image of FIG. 5.
FIG. 5.

Comparison of the UDD, CPMG, and anti-UDD pulse sequences on the postmortem mouse in Fig. 4. The effect of the UDD sequence is most apparent at the longer echo times, with larger numbers of pulses.

Image of FIG. 6.
FIG. 6.

Left: map on a postmortem mouse (different from the one in Figs. 4 and 5) obtained by fitting spin echo data from 10 to 160 ms. Right: difference image between eight-pulse UDD and eight-pulse CPMG (sequence length 80 ms). Regions with moderate benefit more from the UDD sequence than do the long regions.

Image of FIG. 7.
FIG. 7.

In vivo axial images of tumor tissue obtained with eight-pulse UDD and CPMG sequences and with a spin echo sequence (120 ms total echo time). The tumor tissue appears highly inhomogeneous with several necrotic areas with a higher signal intensity. Differences between UDD, CPMG, and spin echo are typically ±25%.


Generic image for table
Table I.

Comparison of the signal strength from the UDD, anti-UDD, and CPMG sequences. Free water and tissue ROIs were selected, as shown in Fig. 4. Note that at the longer echo times with 16 pulses, the CPMG sequence refocuses the free water very well, while the UDD sequence has significantly improved signal-to-noise ratio in the tissue ROI. In addition, the anti-UDD sequence significantly underperforms both the UDD and CPMG sequence in the tissue ROI for the 16-pulse sequence with .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Optimized, unequal pulse spacing in multiple echo sequences improves refocusing in magnetic resonance