We propose a new “Water-Only Look-Locker Inversion recovery” (WOLLI) sequence, based on MOLLI, that enables water-selective T1-mapping in an 8hb breath-hold at 3T. WOLLI uses a hypergeometric (HG) inversion pulse to selectively invert water with negligible effect on fat. To separate the steady-state fat and water signals, WOLLI adds one or more fat-inversions starting from the plateau of the water T1* recovery. WOLLI uses an extended Deichmann-Haase formula to correct for readout-induced saturation. We validated this approach by simulations, scans in a phantom containing 19 fat/water mixtures, and liver scans in 12 subjects (volunteers and liver disease patients).
MOLLI (Fig. 1a) uses “inversion epochs” containing a hyperbolic secant (HS) inversion pulse, followed by ECG-gated bSSFP readouts that sample the recovering magnetization in one breath-hold.10,11
The MOLLI HS pulse (Fig. 2a) inverts magnetization over γΔB0≈±500Hz, which means that fat (offset by 420Hz at 3T) is inverted too.12
We optimized a hypergeometric13 (HG) pulse (Fig. 2c) that has a similar duration, SAR and adiabatic onset to MOLLI's HS pulse. But the HG pulse is asymmetric, sharpening the transition-width between fat and water, enabling fat or water to be inverted selectively.
The complex-valued signal in a voxel containing water and fat (at fat fraction Ff) is
SSSFP=(1−Ff)×MSS,w(T1,w,T2,w,γΔB0−νw)+Ff×MSS,f(T1,f,T2,f,γΔB0−νf)[1]
where subscripts denote water and fat, and MSS is the bSSFP signal.
MOLLI analysis11 fits A, B, and T∗1 pixelwise to:
STI=A−Bexp(−TIT∗1)[2]
where TI is the inversion time, and T∗1 is an effective relaxation time. The Deichmann-Haase formula14 corrects T∗1 for readout-induced saturation:
TDH1=T∗1(B/A−1).[3]
Figure 2b shows the failure of MOLLI and Eqs [2-3] at high fat fractions. Both T∗1 and B/A are wrong.
Extending Eq. 2 to allow for selective inversion we write
STIk=Ak−Bkexp(−TIkT∗1,k);where Ak=αkMSSz,k, and Bk=Ak−αkM+z,k.[4]
TIk is the time since the most recent interruption of readouts for the kth pool; T∗1k is apparent relaxation time; Ak is the T∗1-recovery plateau signal; and Ak−Bk is the signal immediately after inversion. Note that this signal depends on the inversion efficiency (IEk=M+z,k/M−z,k) of the inversion pulse, and also on the longitudinal magnetization just before inversion M−z,k.
Providing the magnetization is at equilibrium before inversion (implicitly assumed in MOLLI), the Deichmann-Haase formula (Eq. 3)14,15 can be extended:
TDH1,k≈T∗1,k/(Ak/αM0,k)=T1,k(1−BplateaukAk)/IEk[5]
The inversion efficiency IEk is +1 for FA=0°, -1 for FA=180°.
Figure 2d shows that simply swapping HS (global) to HG (water-selective) inversion gives the correct T∗1w, but is insufficient to obtain T1w because Eq. 5 requires Aw, but the observed steady-state signal Aw+f≡Aw+Af comes from both water and fat.
To separate the water Aw and fat Af contributions to the plateau signal, we apply one or more fat-selective-inversion pulse(s) in the middle of a series of readouts at the water T∗1 plateau. The water signal stays unchanged. But the signal in the fat pool inverts to minus the plateau value, and so Af=BSSf/2, i.e. half the change in signal after fat-selective inversion. Hence Aw=Aw+f−Af, and is given by Eq. 5.
Matlab was used for simulations and data-processing.
Two WOLLI protocols were used in this study: WOLLI-7w1f, with one final image at the fat-null after fat-inversion; and WOLLI-7w3f, with three fat-inverted-images at different fat TIs, and we fit T∗1f in post-processing. We tested the sequence on a 3T Trio (Siemens), on a 19-vial fat-water phantom, and in vivo in the livers of 12 subjects (volunteers and liver disease patients).
We matched the T1 imaging parameters to a recent a clinical study1, i.e. ShMOLLI 5(1)1(1)1, with 35° FA, 2.51/1.05ms TR/TE, and 1.9x1.9x8.0mm3 voxel size. Reference T1 values were obtained by STEAM-IR single-voxel spectroscopy with TE=10ms, TM=7ms, and TR=2s.
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