Angel Torrado-Carvajal^{1}, Daniel S Albrecht^{1}, Ovidiu C Andronesi^{1}, Eva-Maria Ratai^{1}, Vitaly Napadow^{1}, and Marco L Loggia^{1}

Chemical Shift Imaging (CSI) allows for the quantification of brain metabolite concentrations across multiple voxels/slices. However, issues with model fit (e.g., suboptimal standard deviation, line width/full width at half-maximum, and/or signal-to-noise ratio) can result in the significant loss of usable voxels. Here, we show that an image restoration method called “inpainting” can be successfully used to restore poorly fitted CSI voxels. This method exhibits superior performance (lowest root-mean-square errors) compared to more traditional methods. Inpainting and similar techniques can prove particularly useful as a means of minimizing voxel loss in group voxelwise analyses in standard space.

Datasets: 18 healthy controls underwent MR
imaging in a 3T Siemens TIM Trio scanner using an 8-channel head and neck coil.
MR imaging included an anatomical T1-weighted volume (MEMPRAGE;
TR/TE1/TE2/TE3/TE4=2530/1.64/3.5/5.36/7.22ms, flip angle=7º, voxel
size=1x1x1mm, acquisition matrix=280x280x208), and chemical shift imaging data
(CSI, using LASER excitation and stack-of-spiral 3D k-space encoding;
TR/TE=1500/30ms, voxel size=10x10x10mm)^{2}.

LCModel
Fitting: Metabolites
from CSI data were fitted with LCModel^{3} and metabolic maps were
constructed using MINC/FSL/Matlab tools.

Image
Inpainting: Image
inpainting, commonly used in art restoration, is a technique used to change an
image in a non-detectable form. For the purpose of its application to brain
imaging, we have assessed an implementation based on a penalized least squares
method that allows restoring missing data by means of the discrete cosine
transform^{4}. This method is sometimes also called “fill in”, because it
consists of filling in regions presenting problems with the information of the
surrounding (either local or non-local) areas.

Multivariate
Interpolation Methods: As
comparators, we have also used three different multivariate interpolation
methods commonly used in medical imaging: nearest neighbor, trilinear and
tricubic interpolation. Nearest neighbor interpolation is a simple method that
replaces the value of the poorly-fitted voxel with that of the closest neighboring
voxel. Trilinear interpolation estimates missing values by fitting f(x)=a_{x1}x+a_{y1}y+a_{z1}z+a_{0}.
Tricubic interpolation estimates missing values by fitting f(x)=a_{x3}x^{3}+a_{y3}y^{3}+a_{z3}z^{3}+a_{x2}x^{2}+a_{y2}y^{2}+a_{z2}z^{2}+a_{x1}x+a_{y1}y+a_{z1}z+a_{0},
where a_{x3}, a_{y3}, a_{z3}, a_{x2}, a_{y2},
a_{z2}, a_{x1}, a_{y1}, a_{z1} and a_{0}
are the coefficients of the polynomial, and x, y, and z correspond to points in
the space.

Analysis: High-resolution T1-weighted images and N-acetylaspartate (NAA) CSI images (which did not have a significant amount of poorly-fitted voxels) were corrupted to lose a fixed percentage of random voxels, from a 5% to 95% (in steps of 5%). Quantitative performance of the different methods was assessed by comparing the root mean square error (RMSE) computed between ground truth images and interpolated/inpainted images, using a repeated measures analysis of the variance (ANOVA).

1. Bertalmio M, Sapiro G, Caselles V, Ballester C. Image inpainting. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, New Orleans, LA, USA – July 23-28, 2000, 2000;417-424. ACM Press/Addison-Wesley Publishing Co.

2. Andronesi OC, Gagoski BA, Sorensen AG. Neurologic 3D MR spectroscopic imaging with low-power adiabatic pulses and fast spiral acquisition. Radiology, 2012;262(2):647-661.

3. Provencher SW. Estimation of metabolite concentrations from localized in vivo proton NMR spectra. Magn Reson Med, 1993;30(6):672-679.

4. Garcia D. Robust smoothing of gridded data in one and higher dimensions with missing values. Comput Stat Data An, 2010;54(4):1167-1178.