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
imaging
1 in conjunction with an echo-planar gradient for readout
2,3
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 fitting
7
and 2D spectral fitting
8, 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
metabolites
10 on a Siemens 3T Trio scanner. Nine total data sets
were acquired using the following scan parameters: FOV = 16x16x12cm
3,
(k
x,k
y,k
z,t
2,t
1) =
(16,16,8,256,64), TE/TR = 30/1200ms, direct spectral bandwidth = 1190Hz and
indirect spectral bandwidth = 50Hz. Above, t
2 is the number of
points in the direct spectral dimension and t
1 is the number of
points in the indirect spectral dimension. The data were then non-uniformly
sampled along (k
y,k
z,t
1) according to an
exponentially weighted probability density function
11 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 T
1 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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