Pad´e quantification of malignant and benign ovarian MRS data - Signal Processing in MRS with Biomedical Applications - page 289

the FFT is found to converge at N = 32K = 32768. Nevertheless, it should be
reemphasized that this Fourier convergence is concerned only with the line
shapes, and not with quantification, which in this methodology necessitates
postprocessing via fittings or peak integrations that are nonunique and often
ambiguous, especially when spectral crowding occurs.
9.3.2 Pade versus Fourier for MRS data derived from ma-
lignant ovarian cyst fluid
The spectral parameters reconstructed by the FPT for the data derived from
malignant ovarian cysts are shown i n Table 9.3 , at three signal lengths, N/32 =
32,N/16 = 64 and N/8 = 128. Once again, at N/32 = 32 signal points as
presented on the upper panel in Table 9.3, only nine of the twelve peaks were
identified. Isoleucine and threonine were undetected at N/32, and only one
peak was identified in the region between 3.07 ppm and 5.22 ppm. It was
only for glucose at 5.220345 ppm that the spectral parameters and computed
concentration for the malignant case were fully correct. Thus, 32 FID points
were also insu cient to converge to all the physical resonances for the data
derived from malignant ovarian cysts.
Shown on the middle panel in Table 9.3, the FPT reconstructed exactly
to all six decimal places all the spectral parameters of each of the twelve
peaks with N/16 = 64 signal points for data derived from malignant ovarian
cysts. It can be seen from the comparison of Tables 9.1 and 9.3 that the
spectral parameters and concentrations retrieved by the FPT for N/16 = 64
are exactly equal to the input data.
The bottom panel in Table 9.3 shows that the convergence is also stable at
N/8 = 128, for which all of the spectral parameters remain identical to those
at N/16 = 64. At even longer fractions N/M (M < 8) of the full FID including
N = 1024 (M = 1), we verified that all the peak parameters reconstructed by
the FPT remained constant for the malignant ovarian data.
With respect to the absorption total shape spectra, a similar pattern is also
seen for the malignant case, as illustrated in Fig. 9.3 . Namely, the three
panels on the left present the absorption spectra of the FFT at N/32 = 32
(top, (i)), N/16 = 64 (middle, (ii)) and N/8 = 128 (bottom, (iii)) which are all
rough and uninterpretable. The panels on the right show the Padegenerated
spectra at these same three signal lengths. Also concordant with Table 9.3,
at N/32 = 32, nine of the twelve metabolites are detected and identified
via the FPT. Isoleucine, threonine and choline need 64 signal points to be
identified. At this latter signal length, all the peak heights are correct, and, in
agreement with Table 9.3, at N/16 = 64 the total absorption shape spectrum
is fully converged in the FPT. At the longer signal length of N/8 = 128, the
convergence of the FPT is fully maintained, i.e., it is stable for the malignant
case, as well.
The convergence patterns of the FFT and FPT for the malignant ovarian
cyst data are further compared in Fig. 9.4 . The top two panels once again