Digital Signal Processing Reference
In-Depth Information
cancer, respectively of the 300 total resonances, 273 were identified as spuri
ous by their zero amplitudes and the polezero coincidences, yielding the 27
genuine resonances.
11.3.1 Normal glandular prostate tissue: MR spectral data
reconstructed by FPT
For the normal glandular prostate the reconstructed data by the FPT (−) are
presented in Table 11.4 . The partial signal lengths shown are N P = 600 and
N P = 700.
We emphasize that all the input concentrations are given with at most
two decimals to preserve the accuracy of the corresponding data from Ref.
[443]. The concentrations reported here are set to match this latter input.
Nevertheless, all the reconstructed parameters are listed with 6 decimals.
At N P = 600 (upper panel (i)), 25 of the 27 resonances were identified.
Peak k = 11 (phosphocholine) at 3.230242 ppm and the component of the
taurine triplet at 3.250298 ppm (k = 13) were missing. Few of the spectral
parameters or concentrations were fully exact for any of the resonances. The
closest to being totally correct at N P = 600 were the spectral parameters
and computed concentrations for the peaks at the outermost regions of the
spectrum (k = 1−8 and k = 25−27). The reconstructed chemical shift,
Im(ν k ) and computed concentration for lactate at 1.330148 ppm were exact
at N P = 600, but the|d k
|was correct just to 4 of the 6 decimal places. The
last digit of the chemical shift and two digits for Im(ν k ) were not exact for
alanine, only two of the six decimal places were correct for the|d k
|and its
computed concentration was correct only to 1 decimal place at N P = 600. For
each of the doublets of doublets of citrate and for creatine the chemical shift,
Im(ν k ) and concentrations were exact, although the|d k
|were only correct
to 3 or 4 of the six decimal places at N P = 600. The computed concentration
for the polyamine resonance peak k = 8 was fully correct. Here, however, the
chemical shift, Im(ν k ) and |d k
| were correct to 5, 4 and 2 decimal places,
respectively at N P = 600.
For the region from 3.14 ppm to 3.65 ppm which has a greater spectral
density, none of the reconstructed spectral parameters of the identified reso
nances were fully exact at N P = 600. However, the computed concentrations
of choline, scylloinositol and the component within the myoinositol triplet
centered at 3.6555394 ppm were completely correct. At N P = 600 the chem
ical shift, Im(ν k ) and computed concentration of the myoinositol singlet at
4.070235 ppm were fully correct, but the|d k
|was not. Also, Re(ν k ) of the
lactate peak (k = 27) was correctly reconstructed to be 4.120142 ppm and the
computed concentration was correct, but for the Im(ν k ) and|d k
|the last one
and three decimal places, respectively were not exact at N P = 600. Although
most of the computed concentrations had the correct integer values, this was
not the case for GPC. The concentration of GPC was computed to be 5.83
M/g ww at N P = 600, rather than the correct concentration of 2.56 M/g
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