Prior Knowledge Fitting (ProFit) of Non-uniformly Sampled 5D Echo Planar Spectroscopic Imaging Data : Effect of Acceleration on Concentrations and  Cramer Rao Lower Bounds
Zohaib Iqbal1 and M. Albert Thomas1

1Radiological Sciences, University of California - Los Angeles, Los Angeles, CA, United States

Synopsis

The five dimensional echo planar spectroscopic imaging (5D EP-JRESI) sequence uses an echo planar readout, non-uniform sampling (NUS), and compressed sensing reconstruction to obtain two dimensional spectra from three spatial dimensions. However, the effects of NUS and reconstruction on quantitation results and fit quality parameters, such as the Cramer Rao Lower Bound (CRLB), are unknown. This study uses the new Prior knowledge Fitting (ProFit) algorithm to fit the 5D EP-JRESI results acquired using retrospective as well as prospective NUS. Comparison to the full data demonstrates that the 5D EP-JRESI method can sample 8-times faster while retaining accurate metabolite ratios and CRLB values.

Purpose

Quantifying metabolite concentrations using in vivo 1H MRS provides valuable information on the physiological condition of different tissues. Chemical shift imaging1 in conjunction with an echo-planar gradient for readout2,3 allows for metabolic evaluation across multiple spatial locations. One dimensional (1D) spectra suffer from severe spectral overlap, and therefore it is beneficial to spread the signal over a second spectral dimension (2D). The five dimensional echo planar spectroscopic imaging sequence (5D EP-JRESI)4 incorporates an echo planar readout in addition to a 2D spectral acquisition, yielding 2D spectra from three spatial dimensions. The method also utilizes non-uniform sampling and compressed sensing (CS)5 reconstruction to achieve further acceleration. However, the effects of the non-linear reconstruction algorithm on quantitation are unknown. The Cramer Rao Lower Bound (CRLB)6 has been used to assess reliability of fitting for both 1D spectral fitting7 and 2D spectral fitting8, but this value is dependent on noise levels which are affected by the non-linear reconstruction. Using the improved Prior Knowledge Fitting algorithm (ProFit)9, the effects of non-uniform sampling and non-linear reconstruction on metabolite concentrations and CRLB values were investigated using retrospective analysis of in vitro data.

Methods

The fully sampled 5D EP-JRESI sequence was used to scan a gray matter phantom with physiological concentrations of several metabolites10 on a Siemens 3T Trio scanner. Nine total data sets were acquired using the following scan parameters: FOV = 16x16x12cm3, (kx,ky,kz,t2,t1) = (16,16,8,256,64), TE/TR = 30/1200ms, direct spectral bandwidth = 1190Hz and indirect spectral bandwidth = 50Hz. Above, t2 is the number of points in the direct spectral dimension and t1 is the number of points in the indirect spectral dimension. The data were then non-uniformly sampled along (ky,kz,t1) according to an exponentially weighted probability density function11 to one-fourth the total points (4x), one-eighth the total points (8x), one-twelfth the total points (12x), and one-sixteenth the total points (16x). The data were reconstructed using $$\min_{u} TV(u) \quad \text{s.t. } \|R\mathcal{F}u - f\|_2^2 < \sigma^2$$ where u is the reconstructed 5D data, TV is total variation, R is the sampling mask, $$$\mathcal{F}$$$ is the Fourier transformation along the non-uniformly sampled dimensions, f is the sampled data, and $$$\sigma$$$ is an estimate of the noise variance. A total of 72 voxels from the nine scans were quantified using ProFit for the full, 4x, 8x, 12x, and 16x measurements. The prior knowledge included: NAA, NAAG, GABA, Asp, PCh, GPC, Ch, Cr, Glu, Gln, mI, Pe, Gsh, and Tau. Fit quality and CRLB values were assessed qualitatively, and metabolite concentrations were compared quantitatively to the full data using a Student’s t-test. Additionally, a prospective 8x in vitro measurement was acquired and compared with the retrospective 8x results.

Results

Figure 1 shows that ProFit excelled at fitting the voxels, even from the 16x measurements. Residuals remained low for all voxels fit, and were similar to the residual seen in Figure 1. In general, as the number of sampled points decreased, the CRLB mean and standard deviation increased. However, the CRLB values are still classified as acceptable (<30%), which can be seen in Figure 2. As seen from Figure 3, some metabolite concentrations were significantly different (p<0.05 from Student’s t-test) when compared to the fully sampled data. This was the case for tNAA (12x, 16x), mI (12x), Gsh (16x), Pe (16x), and Tau (8x, 12x, 16x). Figure 4 shows the comparison between the retrospective and prospective 8x NUS results. The prospective results were taken from four central voxels fit with ProFit.

Discussion and Conclusion

It is clear that non-uniform sampling and non-linear reconstruction using TV affect the quantitation results of metabolites at sampling rates of 12x and 16x. All of the major metabolites and most of the lower concentration metabolites were stable at the sampling rate of 8x, suggesting that this is the limit for retaining quantitative accuracy. ProFit overestimated and underestimated several metabolites when compared to the actual concentration, which may be a result of using a very short TR for acquisition. Severe T1 weighting can greatly affect quantitation results. However, ProFit results are very consistent and reproducible, as seen by the small error bars for most metabolites. Future studies will focus on fitting 8x 5D EP-JRESI in vivo results using this method.

Acknowledgements

NIH R21 Grant (NS080649-02)

References

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Figures

Figure 1. The results of fitting a voxel from a reconstructed 16x scan using ProFit are shown above. The residual is minimal for the 2D spectral region. Contour levels are the same for the three windows.

Figure 2. A bar graph showing the effects of non-uniform sampling and reconstruction using TV on CRLB values can be seen. For most major (A) and lower concentration (B) metabolites, CRLBs have higher means and standard deviations as fewer points are sampled.

Figure 3. The major (A) and minor (B) metabolite concentrations with respect to Cr3.0 can be seen. An asterisk (*) indicates a significant difference (p<0.05) when compared to the fully sampled data (Full). True (Expected) metabolite concentrations are also shown.

Figure 4. A comparison between the 8x NUS retrospective (black) and prospective (gray) results can be seen.



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