The inversion pulse

A diabatic inversion pulses are largely insensitive to B | inhom ogeneities and are, therefore, attractive for use in A SL experim ents in which uniform ly tagged regions are required. The quality of the inversion profile is also significantly im proved relative to a standard, sine (sinx/x) 180° inversion pulse. D eviations from the ideal, square profile, how ever, rem ain in the transition regions at the edges of the inversion band (see Sections 3.6.2.2 and 3.6.2.3 and the accom panying Fig. 3.13). The influence o f the relaxation tim es on the profile im perfections has been investigated and transverse relaxation was show n to be especially significant in defining the transition band (Frank,

1997). The application of shorter pulse durations with reduced R F am plitude was recom m ended. H ow ever, the transition region im perfections w ere not com pletely elim inated by this strategy and the slope at the edges of the profile was largely unaffected. In order to further im prove the inversion profile, a m odified adiabatic inversion pulse has been proposed (O rdidge, 1997). The frequency offset correction inversion (FO CI) pulse m akes use of a m agnified gradient to increase the degree of spatial localisation. The frequency sweep o f the adiabatic pulse brings successive spins across the plane o f the slice into resonance and subsequent inversion. The leading and trailing edges o f the pulse profile are thus defined at the beginning and end of the pulse application. T he F O C I pulse localisation gradient is increased and tem porally shaped during these phases o f the pulse and the spatial definition of the profile edges is thereby im proved. In general, the w aveform s describing the gradient, RF am plitude and frequency sw eep, G(t), B i(t) and Acû(t) respectively, are derived from the standard hyperbolic secant (HS) pulse, m ultiplied by a shaping function, A(t), so that, for exam ple, the follow ing relationship applies for the B| field

C h a p te r 3 P erfu sio n

(0 = (r) = A(f)BoSech(j8

[3.16] w here Bo is the m axim um intensity and p and |i are the adiabatic pulse param eters that define the truncation and the bandw idth of the pulse (truncation level = sech(pTp/2) w here Tp is the pulse duration; bandw idth[H z] = p | i / 7 i ) . The effective m agnetic field,

Beff, is m ultiplied by the same A(t) function and the adiabatic condition (Eq. [1.16]) is, thereby, satisfied to a greater extent than the standard HS pulse. The threshold RF am plitude is unchanged but the total pow er deposition is increased (Payne, 1997). In order to theoretically analyse the inversion profile o f the m odified pulses, a com puter sim ulation program was devised to num erically solve the Bloch equations that the adiabatic inversion describes. Several different forms for the A(t) function have been considered, and the so-called T-shape and C-shape pulse designs (O rdidge, 1997) have been im plem ented (Payne, 1997; Pell, 1998; Yongbi, 1998). No significant difference was found betw een the sim ulation profiles of these tw o designs and the T-shape pulse w ith a tetrahedral gradient w aveform was im plem ented for investigation in our laboratory (Fig. 3.11).

3 .6 .2 .] The optim isation pro ced u re

T he optim al design of the FO C I pulse with param eters described by Eq. [3.16], requires the appropriate choice of a num ber of the often interrelated param eters: p; p.; pulse bandw idth; pulse duration, Tp; m axim um B | intensity; m axim um of the A(t) function, denoted m ax[A (t)]; the fraction of A(t) over which the w aveform ram ps down, denoted ram p[A (t)]. T he sim ulation com puter program was em ployed in order to decide upon the optim al com bination of these param eters.

2 00 0 0 -| — HS — T-shape 10000 10 15 -10000 -20000 pulse tim e [ms] 300 250 200 150 100 50 10 pulse tim e [ms] 15 1 5 0 0 1 2 5 0 1000 7 5 0 5 0 0 J 10 1 5 pulse tim e [ms]

Fig. 3.11 Comparison o f frequency sweep, B, amplitude and gradient waveforms for the FOCI and standard HS pulses. Overlap o f the profiles is apparent in the central region where A (t)= l. Adiabatic pulse parameters were: (3 = 800s'% p = 10, pbw = 2546 Hz, Tp= 15 ms, max[A(t)] = 5, ramp[A(t)] = 40%. The maximum gradient o f our system is 1421 Hz/mm and, therefore, a plateau in the A(t) function is evident in these waveforms where the gradient output would otherwise exceed this limit.

C h a p te r 3 P e rfu sio n

T he follow ing conclusions were reached:

(1) A higher value o f |i improves the pulse profile (Payne, 1992) but, for a constant bandw idth, is accom panied by an increased level of pulse truncation (i.e. decreased P). Shorter bandwidths, therefore, limit the m axim al value of |1 that can be used. (2) A larger bandwidth (increased P or p.) reduces the num ber of spins in the transition

region of the pulse profile and is therefore beneficial. However, this is lim ited by gradient strength and eddy current considerations. An associated increase in the R F intensity is also required and this may conflict with the limits o f the RF am plifier. (3) The relaxation times, T | and T2, have a significant effect on the inversion profile. T |

relaxation results in a variation in the degree of inversion across the slice as the spins reach inversion; T% relaxation reduces the quality of the inversion band (see later in this section). These effects encourage the use of a shorter pulse duration (reduced time for T | relaxation) and minim al inversion pow er (reduced tim e for T2

relaxation as spins spend less tim e in transverse plane) (Frank, 1997).

(4) The overall sharpness of the FOCI pulse profile is im proved in the transition regions with an increase of either m ax[A(t)] or ram p[A(t)]. However, this is accom panied by an increase in the size of the ripples in the z-m agnetisation evident in this region and across the inverted area.

B ased on these considerations, optimal pulses were designed for a m inim um desired inversion slice thickness. In order to investigate the sensitivity of the FO C I pulse to the

relaxation time and off-resonance effects described by Frank et al. (Frank, 1997),

sim ulations were produced under a variety of conditions (Fig. 3.12).

The difference in the longitudinal m agnetisation, AM%, between the inversion profiles in the presence and absence of relaxation (defined by AMz = MJ^ideal) - M^{non-ideal)) is displayed for the inversion pulses shown in Fig. 3.11. An exaggerated scale is em ployed in Fig. 3.12 in order to display the effects of (a) T2 relaxation, (b) T | relaxation and (c)

B | am plitude. It can be seen that the relaxation-dependent characteristics o f the FO C I and standard HS pulses are very similar. The sim ilar threshold Bi characteristics required for inversion (indicated by Fig. 3.12(c)), are discussed in ref. (Payne, 1997).

(a) Ti relaxation ({T1J2}: {0.75s,0.75s}-{1 Os,0.75s}) 0.000 ■0.005 - ■0 0 1 0- ■0Æ1S -0.020 «

r

iG) for {Ti,T2}={10s,0.05Is}

L U -

1 ’ ;■ I ''" '

-0,00

distanc e [mm]

Fig. 3.12 Comparison of relaxation time and RF amplitude effects on the pulse profiles of the HS and FOCI pulses. An exaggerated ordinate scale is employed and the subtracted values (AM) are relative to the starting magnetisation, M^., of + 1. The simulated pulses parameters are as in Fig. 3.12 with an inversion slice thickness of 4 mm. The ideal relaxation time parameters are T,=T2=10 sec. For (a) the relaxation times are {T,,T2}= {0.75sec,0.75sec} and {10sec,0.75sec}; for (b), the corresponding times are {10sec,0.05sec} and { 10sec,10sec}; for (c), the corresponding values are { 10sec,0.05sec} in both, and B,=250 mG or 500 mO.

C h a p te r 3 P erfu sio n

3 .6 .2 .2 E xperim ental dem on stration I : P id se p rofile

In order to dem onstrate the benefits of the FOCI over the standard HS pulse, com puter sim ulations were obtained and com pared to experim ental profiles collected using an agar phantom on the 2.35T system The pulse param eters are described in the figure legend. The acquisition sequence was a standard spin-echo ID -FT with the readout gradient applied along the slice-selection axis. Results are displayed in Fig. 3.13 and com pared to the sim ulated profiles. A significant im provem ent in the pulse profile is apparent.

3 .6 .2 .3 E xperim ental dem on stration II : FAIR subtractions

T he effect o f the im proved inversion profile on the quality of the FA IR subtractions of static tissue was dem onstrated on the 2.35T system by acquiring selective and non- selective im ages at a num ber of inversion slice thicknesses and a uniform , cylindrical agar phantom . The pulse param eters were identical to those described for the previous experim ent and the nom inal slice thickness was 4 mm. The FA IR spin-echo EPI im aging sequence was em ployed as described in Section 4.4. The results are displayed in Fig. 3.14(a). It can be seen that the im proved pulse profile o f the F O C I pulse is reflected by the absence o f a system atic offset at shorter values o f the inversion slice thickness.

3 .6 .2 .3 E xperim ental dem on stration III : D eg ree o f inversion, Oo

T he com bined effect of the inversion and im aging pulses in FA IR is a convolution of the individual pulse profiles. The degree o f inversion in the case of the slice selective inversion recovery technique reflects the interaction of the profiles and was obtained by a 3-param eter fit at 12 inversion slice thicknesses between 4-10 m m (Fig. 3.14(b)). The data dem onstrate that for a tighter slice thickness ratio (STR), the FO C I pulse m aintains its value while the degree of inversion of the HS pulse decreases resulting in the system atic signal offset in the FA IR subtractions indicated in Fig. 3.14(a).

(a) S i m u l a t e d p r o f i l e s