Antoine Klauser^{1}, Frédéric Grouiller^{2}, Sebastien Courvoisier^{1}, and Francois Lazeyras^{1}

High-resolution
T_{1}
maps are measured over the whole human brain with proton FID-MRSI with incremental flip-angles. MRSI datasets with multiple flip-angles
are reconstructed simultaneously through a low-rank-total generalized
variation model and T_{1}
values
are determined by fit of the steady state magnetization with B_{1}
inhomogeneity correction. Twofold
compressed-sensing
acceleration enables acquisition of a single flip-angle in 5
min
and resulting in acquisition of 3 flip-angles in 15 min.
Precise
determination of T_{1}
would
enables
an accurate correction of
signal
loss and might provide important information on brain
micro-structure.

**Introduction**

**Method**

*Sequence*

A
2D-FID-MRSI sequence including WET^{4}
water suppression was implemented (Fig.1). Echo-time was 1.1ms
and the FID signal was acquired with 1024 points at 4kHz leading to a TR of 344ms.

*Experiment*

Healthy
volunteer brain data were acquired at 3T (Siemens/Erlangen/Germany)
with 64-channel receiver head coil.
Three successive acquisitions of 2D-FID-MRSI with FA = 20, 40 and 60
degree were planned on a 210x180 mm2
FOV with 4 mm in-plane resolution and a 10 mm thick slice. A B_{1}-map
was acquired for FA correction during T_{1}
fitting. *Low-rank approximation*

MRSI dataset
are generally assumed to be partially separable^{8}.
This concept has been extended to include multiple FA in the MRSI
dataset and to assume that the whole dataset is partially separable
into a finite number of spatial components and time-FA components.
This low-rank approximation for the reconstructed MRSI dataset $$$\rho^\alpha({\bf r },t)$$$ at
spatial coordinate $$$\bf{r}$$$
at
time $$$t$$$ and FA index $$$\alpha$$$
reads:

$$\rho^\alpha({\bf r},t)=\sum_{c=1}^{N_C}U_c({\bf r})V^\alpha_c(t)$$

*Low-Rank
TGV Reconstruction*
After
removal of the remaining water signal with HSVD

$${\bf U}({\bf r}),{\bf V}^\alpha(t)=\arg\min_{{\bf U},{\bf V}}\:\:\left\| S^\alpha({\bf k},t)-\mathcal{FSB}\{{\bf U}({\bf r}){\bf V}^\alpha(t)\}\right\|^2_2+\:\lambda\:TGV^2({\bf U}({\bf r}))$$

where $$$\mathcal{B}$$$,
is the *B _{0}*
inhomogeneity operator, $$$\mathcal{S}$$$,
the coil-sensitivity profiles, $$$\mathcal{F}$$$,
the Fourier encoding and $$$\lambda$$$ the regularization parameter (Fig.2).
Compressed-sensing
acceleration
scheme was implemented

*
Quantification
and T _{1}
fitting*

The reconstructed
MRSI datasets were quantified using LCModel^{11}
for
each FA individually. The
resulting concentration map for metabolite $$$m$$$ and FA $$$\phi_\alpha$$$
is assumed to follow the steady-state
magnetization
signal amplitude^{12}:

$$M^m(\phi_\alpha,{\bf r})=M^{m}_{0}({\bf r})\frac{\sin(\phi_\alpha B_1({\bf r}))\left(1-e^{-TR/T_1^m({\bf r})}\right)}{1-e^{-TR/T_1^m({\bf r})}\cos(\phi_\alpha B_1({\bf r}))}$$

At
each voxel, the longitudinal relaxation time, $$$
T_{1}^{m}({\bf r})$$$,
and
the T_{1}-corrected
concentration, $$$ M_{0}^{m}({\bf r})$$$,
were estimated with a non-linear least-square fit. FA $$$\phi_\alpha$$$
is corrected
for B_{1}
field
inhomogeneity by the normalized factor $$$B_1({\bf r})$$$
from the measured B_{1}-map.

**Discussion**

[1] Brief, E. E., Whittall, K. P., Li, D. K. B., & MacKay, A. (2003). ProtonT1 relaxation times of cerebral metabolites differ within and between regions of normal human brain. NMR in Biomedicine, 16(8), 503–509.

[2] Ethofer, T., Mader, I., Seeger, U., Helms, G., Erb, M., Grodd, W., … Klose, U. (2003). Comparison of longitudinal metabolite relaxation times in different regions of the human brain at 1.5 and 3 Tesla. MRM, 50(6), 1296–1301. Figure 1: FID-MRSI sequence with varying flip-angle and sparse random k-space sampling.

[3] Nassirpour, S., Chang, P., Henning, A. (2017). High and ultra-high resolution metabolite mapping of the human brain using 1H FID MRSI at 9.4T. NeuroImage

[4] Ogg, R. J., Kingsley, P. B., & Taylor, J. S. (1994). WET, a T1- and B1-insensitive water-suppression method for in vivo localized 1H NMR spectroscopy. Journal of Magnetic Resonance. Series B.

[5] Barkhuijsen, H., de Beer, R., & van Ormondt, D. (1987). Improved algorithm for noniterative time-domain model fitting to exponentially damped magnetic resonance signals. Journal of Magnetic Resonance (1969), 73(3), 553–557.

[6] Bilgic, B., Gagoski, B., Kok, T. and Adalsteinsson, E. (2013) Magn Reson Med 69, 1501-1511

[7] Klauser, A., Van De Ville, D. ,Lazeyras, F. . Low-Rank TGV Reconstruction of High-Resolution 1H-FID-MRSI of Whole Brain Slices. (2017) ISMRM 25th Annual Meeting, preceeding #5517

[8] Nguyen, H.M., Peng, X., Do, M.N. and Liang, Z. (2013). Denoising MR spectroscopic imaging data with low-rank approximations. IEEE Trans Biomed Eng 60, 78-89.

[9] Kasten, J., Lazeyras, F., & Van De Ville, D. (2013). Data-Driven MRSI Spectral Localization Via Low-Rank Component Analysis. Medical Imaging, IEEE Transactions on, 32(10), 1853–1863.

[10] Liang, D., Liu, B., Wang, J., & Ying, L. (2009). Accelerating SENSE using compressed sensing. Magnetic Resonance in Medicine, 62(6), 1574–84. https://doi.org/10.1002/mrm.22161

[11] Provencher, S.W. (1993). Estimation of metabolite concentrations from localized in vivo proton NMR spectra. Magn Reson Med 30, 672-679.

[12] de Graaf, R. A. (2007). In Vivo NMR Spectroscopy: Principles and Techniques: 2nd Edition. In Vivo NMR Spectroscopy: Principles and Techniques: 2nd Edition.

2D-FID-MRSI sequence with
varying flip-angle and sparse random k-space sampling.

The multi-flip-angle MRSI data are
reconstructed simultaneously with a low-rank TGV model preceeded by
water and lipid suppression. The reconstructed MRSI dataset is then
quantified by LCModel individually for each flip-angle.

Illustration of the T_{1}
map fitting for total creatine metabolite. The
reconstructed and quantified metabolite map at multiple flip-angle
are used to fit the metabolite T_{1} value and the
T_{1}-corrected value in each voxel. The normalized B_{1}
field map is used to correct the flip-angle for B_{1}
inhomogeneity.

High-resolution T_{1}
maps of metabolites: NAA + NAAG (tNAA), GPC+PCh (choline), glutamate +
glutamine (Glx) and myo-inositol (Ins) and the corresponding
T_{1}-corrected concentration maps.