Pad´e quantification of malignant and benign ovarian MRS data - Signal Processing in MRS with Biomedical Applications - page 296

which convergence is achieved via the FPT and the shape spectrum attained
via the FFT at the same signal length, for both the benign and malignant
ovarian data. Fully converged absorption total shape spectra were obtained
using only N/16 = 64 signal points via the FPT, for the benign case (top
right panel (iii)) and malignant case (bottom right panel (iv)). In sharp
contradistinction, the spectra generated using the FFT at the latter signal
length are completely uninterpretable (top left panel (i), benign case; bottom
left panel (ii), malignant case).
The convergence pattern of the metabolite concentrations computed using
the FPT for benign versus malignant ovarian cyst fluid is presented in Fig.
9.8 . The chemical shifts are displayed along the abscissae of the six panels (i)
(vi), with concentrations as the ordinates. The input data are represented
by the symbol x, whereas the Padereconstructed data are shown as open
circles. The data corresponding to the benign and malignant cases are pre
sented in the left ((i) (iii)) and right panels ((iv) (vi)), respectively. Prior
to convergence, at N/32 = 32 (top panels (i) and (iv)), the only metabolite
for which the fully correct concentrations were obtained in both the benign
and malignant cases is glucose at 5.22 ppm (1387 M/L (benign) and 260
M/L (malignant), respectively). At N/16 = 64 (middle panels (ii) and
(v)) and N/8 = 128 (bottom panels (iii) and (vi)), all of the reconstructed
metabolite concentrations are completely correct, as seen both numerically
and by the graphic representations. Thus, for N/16 and N/8, the x's are pre
cisely centered within the open circles. This indicates that there was complete
agreement between the input and reconstructed data.
Figure 9.9 is a recapitulation of the absorption spectra and the retrieved
concentrations when full convergence is achieved by the FPT using N/16 = 64
signal points. This figure provides graphic illustration of the capabilities of the
FPT, in providing both a shape estimation and quantification, without any
postprocessing and without reliance upon any other estimator. We consider
Fig. 9.9 to be the most useful for clinicians, by giving both a graphic as
well as a quantitative summary of the results obtained via the FPT, besides
providing insight into how the FPT actually works. In other words, this figure
illustrates the essential concepts of signal processing, by showing both line
shape estimation and quantification. Most importantly in the clinical setting,
all the reconstructed concentrations for the benign and malignant cases, i.e.,
the diagnostically most relevant information can be readily deciphered.
Applying the fast Pade transform to MR data from benign and malignant
ovarian cyst fluid clearly shows the powerful extrapolation features of the
FPT. With only 64 data points, the Pade absorption spectra are fully con
verged, including a delineation of closely lying resonances such as alanine,
lactate and threonine in the region between 1.3 ppm and 1.51 ppm, and even
the nearly overlapping isoleucine and valine which are separated by only 0.02
ppm. In marked contrast, the FFT yielded entirely uninterpretable spectra
at these short signal lengths. As discussed earlier in this topic, the envelopes
of MR time signals decay exponentially such that the signal intensity is the