Roberto Colotti^{1}, Jessica A.M. Bastiaansen^{1}, Patrick Omoumi^{1}, and Ruud B. van Heeswijk^{1,2}

The goal of this study was to develop an isotropic 3D lipid-insensitive T_{2}
mapping technique of knee cartilage. Therefore we combined an existing isotropic
3D T_{2}-prepared gradient-echo T_{2} mapping technique
(Iso3DGRE) with the novel lipid-insensitive binomial off-resonant RF excitation
(LIBRE) pulse. LIBRE pulse optimization was performed through numerical
simulations and verified in phantom experiments, yielding complete fat signal nulling
using a LIBRE pulse as short as 1 ms. T_{2} mapping of knee cartilage performed
in five healthy volunteers with LIBRE excitation allowed for improved cartilage
delineation and precise T_{2} values compared with normal excitation.

A novel water excitation method^{1}
that enables effective fat suppression at 3T was combined with a 0.6-mm isotropic
GRAPPA-accelerated three-dimensional T_{2}-prepared
gradient-echo (Iso3DGRE)^{2} T_{2} mapping technique. The lipid insensitive binomial
off-resonant radiofrequency (RF) excitation (LIBRE)^{1} pulse is composed of
two rectangular pulses that have an RF frequency offset (f_{RF}), duration (τ) and a LIBRE-defined
phase offset (φ=2πfτ). This variable parameter
space was exploited to achieve robust fat suppression with a total pulse
duration of 1ms (i.e. 2τ). If ∆f is the difference between f_{RF}
and the resonance frequency of fat (f_{fat}) at 3T, for small RF
excitation angles (α), the relation between ∆f and
τ can be described by:

$$∆f=\frac{1}{τ} \quad\quad\quad (Eq.1).$$

The
optimal f_{RF} (f_{RFopt}) can then be simply
calculated through Eq.1.

Bloch equation simulations were
performed in Matlab (The MathWorks) to determine the optimal α (α_{opt})
that resulted in simultaneous fat suppression and water excitation. Given
τ=0.5 ms, the transverse
magnetization M_{xy} was characterized as a function of tissue
frequency and α, following a T_{2} preparation module of 53ms and a LIBRE
excitation pulse.

The optimized LIBRE parameters f_{RFopt
}and α_{opt }were then verified in phantoms. All experiments were
performed on a 3T clinical system (Magnetom Prisma, Siemens) with a 15-channel Tx/Rx
knee coil. The phantom consisted of mixed solutions of agar (3-5% w/v) and
0.73µM NiCl_{2} and a tube of baby oil (Johnson and Johnson). The
signal-to-noise ratio (SNR) was approximated as the ratio between the signal in
a region of interest (ROI) and the standard deviation of the noise in an ROI
drawn outside the phantoms. The parameter f_{RFopt} was confirmed in
low-resolution LIBRE-Iso3DGRE scans by varying f_{RF} from 1500 to 1700Hz. The images acquired with a T_{2} preparation duration of 53ms were used
for analysis. To verify α_{opt}, phantoms were scanned with LIBRE-Iso3DGRE
with α varying from 5° to 40°. The images acquired with a T_{2}
preparation duration of 53ms were used to determine the SNR as a function of α in
the 4% agar phantom. The optimized LIBRE-Iso3DGRE protocol was then used to
acquire 4 input images (T_{2} preparation duration=0-23-38-53ms) to
generate a T_{2} map of the agar phantoms. The accuracy of the LIBRE-Iso3DGRE
T_{2} mapping technique was compared to the gold standard spin echo (SE)
(TR/TE=7000/6.8-15-30-60-120-250-400ms) with a linear regression and Bland-Altman
analysis.

Next, T_{2}
maps of the knee were acquired with LIBRE-Iso3DGRE and Iso3DGRE in five healthy volunteers (average
age 31.0±11.2 years and average weight 72.6±19.1kg). Six continuous
slices that covered the central region of the lateral and medial femorotibial
compartments were used for cartilage T_{2} quantification. Eight
cartilage sub-compartments were defined on the sagittal plane.

The precision was defined as inverse
of the relative standard deviation (the ratio of the standard deviation and the
average T_{2} value within the ROIs) and was compared between the two
techniques with a two-tailed Student’s t-test.

The theoretically optimal RF frequency offset (Eq.1) f_{RFopt} was
1560Hz and was confirmed in phantom experiments (Fig. 1a). The numerically optimal
excitation angle α_{opt} was 35° (Fig. 1b), which was similarly
confirmed in phantom experiments (Fig. 1c). These values yielded complete and robust
nulling of the fat signal using an excitation pulse of 1ms.

In the phantoms, LIBRE-Iso3DGRE T_{2} values agreed with the gold standard SE
values (y=0.93*x+0.11, R^{2}=0.99, P=0.0002). The almost direct
proportionality indicates that the slight underestimation can
potentially be corrected by using a scaling factor. The Bland-Altman analysis reported
a bias of -2.7ms with a 95% confidence interval of ±1.9ms (Fig. 2).

Averaged over all
volunteers and compartments, the LIBRE-Iso3DGRE T_{2} values (37.8±4.4ms) were
significantly higher than those determined with Iso3DGRE (34.1±5.5ms, P<0.0001), most
likely due to the slightly different relaxation mechanisms of the two
techniques.

In the healthy volunteers, LIBRE excitation completely avoided chemical
shift displacement (CSD) artifacts (Fig.3, 4), which resulted in more
conspicuous cartilage visualization as well as in a more precise T_{2}
estimation, as confirmed by a decrease in the relative T_{2} standard
deviation from 27.1±8.2% for Iso3DGRE to 21.2±6.0% for
LIBRE-Iso3DGRE (P<0.0001).

**[1]** JAM Bastiaansen et al. Flexible water excitation
for fat-free MRI at 3 Tesla using lipid insensitive binomial off-resonant RF
excitation (LIBRE) pulses. Magnetic Resonance in Medicine 2017, In Press

**[2]** R Colotti
et al. Isotropic Three-Dimensional T_{2} Mapping of Knee Cartilage:
Development and Validation. Journal of Magnetic Resonance Imaging 2017, In
Press.