"Extreme Echoes" in FSE Sequences with Quadratically Incremented Phase (QUIP)
J. B. Murdoch1
1
Philips Medical Systems, Cleveland, Ohio, United States
Synopsis. “Non-CPMG” fast spin echo sequences in which the refocusing pulse phase increases quadratically can refocus both components of initial
transverse magnetization, even at reduced tip angles. Sequences with an even number (4-32) of pulses per phase cycle have been analyzed using
Mathematica – refocusing is nearly perfect at the end of each cycle for tip angles as low as ~110 degrees.
A quadratic increase in the phase of successive pulses (or more precisely, a linear increase in the pulse phase increment) is used for RF spoiling of
residual transverse coherences in fast steady-state imaging [1]: 0, φ, 3φ, 6φ, 10φ …. The same scheme can be used in “non-CPMG” fast spin echo
(FSE) sequences [2,3] to refocus both initial components of transverse magnetization: in-phase and out-of-phase with respect to the first refocusing
pulse. Moreover, successive echo amplitudes are better maintained with these sequences at reduced values of the refocusing tip angle α than with the
“traditional” CPMG approach [4], for which the pseudo-steady-state echo amplitude goes as v = sin(α/2) [5].
The properties of non-CPMG FSE sequences are examined in detail in Ref. 3; however, the focus (and refocus) there is on long cycle lengths – i.e.,
values of φ = (2πn / d ) chosen with d large and prime. Here we consider small, even values of d and the symmetric cycles of length 2d that they
spawn. The first several are as follows:
d=2
d=4
d=6
d=8
d=8
n=1 φ=180o
n=1 φ=90o
n=1 φ=60o
n=1 φ=45o
n=3 φ=135o
cycle = 0, 180, 180, 0 (i.e., MLEV-4 [6])
cycle = 0, 90, 270, 180, 180, 270, 90, 0
cycle = 0, 60, 180, 0, 240, 180, 180, 240, 0, 180, 60, 0
cycle = 0, 45, 135, 270, 90, 315, 225, 180, 180, 225, 315, 90, 270, 135, 45, 0
cycle = 0, 135, 45, 90, 270, 225, 315, 180, 180, 315, 225, 270, 90, 45, 135, 0
Analytic expressions for the resulting rotation matrices and magnetization distributions have been generated using Mathematica (Wolfram Research)
and the composite pulse formalism of Counsell et al. [7]. A striking feature of these cycles is that the corresponding propagator is very nearly unitary
(and hence good for decoupling too [8]). If the overall effect of the cycle is formulated as a rotation about an effective axis by an angle Ψ, then
cos(Ψ/2) = 1 – u2d + u2d cos(2dχ) ,
where u = cos(α/2) and χ is the rotation angle about the z-axis acquired for each isochromat between successive pulses. Initial-magnetization-to-finalecho components after one eight-pulse cycle for d=4 are as follows (with terms involving χ appropriately averaged away, as befits an echo):
MX
MY
M :
M :
X
Y
1 - 4 u8 + 8 u10 - 24 u12 + 32 u14 - 13 u16
1 - 4 u8 + 8 u10 - 8 u12 + 3 u16
MX
M
Y
or MY
M :
X
8 u10 – 16 u12 + 8 u14
[These expressions can be expanded in terms of v = sin(α/2) too, of course. If so, the effect of resonance offset ∆ω is easy to incorporate. If the
effective rotation axis for the pulse is tilted by an angle β(∆ω) away from the x-y plane, then merely replace v with v cos(β). Alternatively, the
magnetization can be written as a function of an effective rotation matrix element R33(∆ω).]
Echo intensities for this newly rechristened QUIP (QUadratically Incremented Phase) FSE sequence with φ = 135o and 16 pulses per cycle are
displayed below for three different values of α. The near-perfect regeneration of initial magnetization at the end of each cycle – a good place to
sample the center of k-space, naturally – is reminiscent of hyperechoes [9]. However, a bona fide 180o pulse is not required here. The persistence of
echo intensity at reduced tip angles (with reduced SAR) makes QUIP a good choice for 3T imaging.
References
1. Y. Zur et al., Magn. Reson. Med. 21, 251, 1991.
2. J.B. Murdoch, SMR 2nd Meeting, 1145, 1994.
3. P. Le Roux, J. Magn. Reson. 155, 278, 2002.
4. S. Meiboom et al., Rev. Sci. Instrum. 29, 688, 1958.
5. J. Hennig, Concepts Magn. Reson. 3, 125, 1991.
6. M.H. Levitt et al., J. Magn. Reson. 43, 502, 1981.
7. C. Counsell et al., J. Magn. Reson. 63, 133, 1985.
8. J.S. Waugh, J. Magn. Reson. 49, 517, 1982.
9. J. Hennig et al., Magn. Reson. Med. 46, 6, 2001.
Proc. Intl. Soc. Mag. Reson. Med. 11 (2003)
202