Digital Signal Processing Reference
In-Depth Information
On the absorption component shape spectrum, the two polyamine peaks
centered at 3.10 ppm and 3.14 ppm are broad, large and clearly distinguished.
However, on the total shape spectrum for the glandular prostate, there is only
a possible leftward shoulder at around 3.14 ppm which might suggest a second
polyamine component.
The spectra from normal glandular and normal stromal prostate differ strik
ingly. The intensity of most of the spectral structures is lower for stromal tis
sue. The doublets of citrate doublets are clearly smaller, and the polyamines
are di cult to detect for stromal prostate tissue. The creatine peak at 3.04
ppm is the most prominent after lactate at 1.33 ppm. The myoinositol triplet
centered around 3.55 ppm is also smaller in the stromal prostate compared to
the normal glandular tissue.
For the case of prostate cancer, the lactate peaks at 1.33 ppm and 4.12 ppm
are larger than for the two normal prostate tissues. The choline components
at 3.21 ppm to 3.24 ppm (i.e., total choline) are altogether more abundant
than creatine at 3.04 ppm. The spectrum for the malignant prostate is most
sharply distinguished from that of normal glandular prostate, particularly in
that for prostate cancer the citrate doublet peaks and the two polyamine
resonances are much smaller than the components of choline.
The converged Padereconstructed absorption component and total shape
spectra for the normal glandular prostate (top panels (i)), normal stromal
prostate (middle panel (ii)) and malignant prostate data (bottom panel (iii))
within the zoomed region from 2.40 ppm to 3.70 ppm using the partial length
N P = 800 are shown in Figs. 11.12 and 11.13 , respectively.
In these figures, the component spectra clearly delineate the phosphocholine
and glycerophosphocholine peaks that are not seen on the total shape spectra.
The present analysis shows that the FPT unequivocally resolves multiplet
resonances, as well as providing exact quantification. This is true for regions
of otherwise very high spectral density.
Using the FFT and fitting via the LevenbergMarquardt algorithm, the
authors of Ref. [443] noted that spectral overlap compromised the accuracy
of quantification. Procedures that require integrating the areas under the
peaks in the Fourier absorption spectra are vulnerable to subjectivity due to
the uncertainty about lower and upper integration limits. Such techniques
for reconstructing metabolite concentrations are especially di cult with peak
overlap [346].
Padebased reconstruction yields not only the possibility to exactly extract
all the spectral frequencies and amplitudes of all the resonances, but also pro
vides certainty about their true number. This ensures unique and maximally
reliable quantification of all the physical metabolite concentrations, including
when there is an ample number of multiplet resonances, as seen in the present
analyses.
As we have discussed in the preceding chapters, the “spectral crowding”
problem does not obstruct the FPT, which via parametric analysis, without
any fitting or numerical integration of peak areas, reconstructed all the mul
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