Low-rank based compartmentalized reconstruction algorithm for high resolution MRSI without lipid suppression methods

Ipshita Bhattacharya^{1} and Mathews Jacob^{1}

Spectral leakage from extracranial lipids, whose concentrations are several folds higher than that of the metabolites, causes severe artifacts in MR spectroscopic imaging (MRSI). The effects of spectral leakage are even more aggravated at low resolution due to truncation artifacts. Several methods used for lipid suppression like outer volume suppression, inversion recovery, selective excitation, long echo times etc[1,2,3], result either in signal loss or in partial brain coverage. Improved k-space coverage reduces lipid leakage [4], but at the cost of deteriorated metabolite SNR and increased scan time.

In this work we introduce a novel compartmental low rank algorithm for high resolution MR spectroscopic reconstruction for lipid unsuppressed data. We use the spiral data acquisition scheme introduced in [5], to achieve high spatial resolution MRSI, in a reasonable scan time and with minimal SNR loss. We model the field inhomogeneity compensated data as the sum of two low-rank subspaces for metabolites and lipids which are mutually orthogonal.Experimental results demonstrate the performance of the proposed algorithm with and without the use of lipid suppression methods.

Variable density multi-shot spirals were used to obtain matrix
sixe of 128x128 with the center k-space region of 32x32 averaged 12 times. This
achieves an in-plane spatial resolution of upto 1.8x1.8 mm^{2} at a
scan time of 7.2 mins/slice with TR=1.5 ms. A separate water reference data is
acquired in 2.4 mins/slice(TR=0.5 secs) and was processed using [6] to obtain high
resolution B_{0 }map and lipid and brain masks that characterize
the spatial compartments.
The field inhomogeneity corrected spatio-temporal data is
modeled as the sum of low-rank compartments belonging to metabolites ($$$ X_{M} $$$)
and lipids ($$$ X_{L} $$$) respectively;
$$$ X(r,t) =
X_{M}(r,t)+X_{L}(r,t) $$$ . These
compartments are assumed to be low rank and their spatial support is given by
the metabolite and lipid masks. Using a single low-rank subspace to model the
entire dataset is not effective because, the massive dynamic range between
lipids and metabolites results in the subspace being dominated by the lipid basis
functions. We exploit the orthogonality between metabolites and lipids as
established in [7] to minimize lipid leakage artifacts. This enables us to
recover the subspaces without imposing any prior knowledge of the spectral
support. The recovery is formulated as the optimization problem,

$$ f(X) = \arg\min_{X_{M},X_{L}} \|\mathcal{A}X-b\|+\lambda_{1}\|X_{M}\|_{p}+\lambda_{2}\|X_{L}\|_{p} $$

$$ \text{for} \ p \leq 1 \ \text{such that} \ X_{M} \perp X_{L} $$

where $$$\mathcal{A}$$$ is the forward model accounting for the non-uniform Fourier transform, field inhomogeneity, and coil sensitivity encoding and $$$b$$$ is the measured data. Water is removed as a pre-processing step using HSVD [8]. Equation (2) is solved using iterative reweighted least square algorithm [9].

This work has some conceptual similarities to [10,11]. However what distinguishes the proposed method is the absence of specialized data acquisition and processing steps for estimating the metabolite and lipid basis functions that explicitly account for the spectral support. The subspaces for metabolites and lipids are automatically estimated from the measured data. Hence the proposed method is not sensitive to line broadening of lipids and metabolites; and robust to deviation from known spectral location which may occur in practical applications with large field variations near the skull. Also in addition these methods employ outer volume suppression or long echo times.

[1] Chu, A., Alger, J. R., Moore, G. J., & Posse, S. (2003). Proton echo-planar spectroscopic imaging with highly effective outer volume suppression using combined presaturation and spatially selective echo dephasing. Magnetic resonance in medicine, 49(5), 817-821.

[2] Bydder, G. M., & Young, I. R. (1985). MR imaging: clinical use of the inversion recovery sequence. Journal of computer assisted tomography, 9(4), 659-675.

[3] Bottomley, P. A. (1987). Spatial localization in NMR spectroscopy in vivo. Annals of the New York Academy of Sciences, 508(1), 333-348.

[4] Ebel, A., & Maudsley, A. A. (2003). Improved spectral quality for 3D MR spectroscopic imaging using a high spatial resolution acquisition strategy. Magnetic resonance imaging, 21(2), 113-120.

[5] Bhattacharya I. , Jacob M.(2015). High Resolution 1H MRSI without lipid suppression at short echo times using variable density spirals;in Proc of ISMRM 2015, #2017.

[6] Cui, C., Wu, X., Newell, J. D., & Jacob, M. (2015). Fat water decomposition using globally optimal surface estimation (GOOSE) algorithm. Magnetic Resonance in Medicine, 73(3), 1289-1299.

[7] Bilgic, B., Gagoski, B., Kok, T., & Adalsteinsson, E. (2013). Lipid suppression in CSI with spatial priors and highly undersampled peripheral k-space. Magnetic Resonance in Medicine, 69(6), 1501-1511.

[8] 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.

[9] Fornasier, M., Rauhut, H., & Ward, R. (2011). Low-rank matrix recovery via iteratively reweighted least squares minimization. SIAM Journal on Optimization, 21(4), 1614-1640.

[10] Lam, F., & Liang, Z. P. (2014). A subspace approach to high-resolution spectroscopic imaging. Magnetic Resonance in Medicine, 71(4), 1349-1357.

[11] Ma, C., Lam, F., Johnson, C. L., & Liang, Z. P. (2015). Removal of nuisance signals from limited and sparse 1H MRSI data using a union-of-subspaces model. Magnetic Resonance in Medicine.

Fig(1) : NAA maps for (a)lipid suppressed data and (b) lipid
unsuppressed data. IFFT reconstruction shows lipid leakage artifacts even with
lipid suppression .Proposed method retains high resolution details and
eliminates lipid leakage artifacts.

Fig(2) : Spectra at
different pixels(see (a)) for (b) lipid suppressed data and (c) lipid
unsuppressed data. The spectra from IFFT reconstruction (blue) are noisy and
show heavy lipid leakage especially in case of lipid unsuppressed data whereas
the spectra from proposed method(red) are denoised and devoid of lipid leakage.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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