Breast cancer and non-malignant breast data: Quantification by FPT - Signal Processing in MRS with Biomedical Applications - page 318

10.4.2 Pade-reconstruction of MRS data from fibroadenoma

For the fibroadenoma the data reconstructed by the FPT (−) are shown in
Table 10.3 for N P = 1000, 1500 and 2000. For partial signal length N P = 1000
(upper panel (i) of Table 10.3), only eight of the nine resonances were detected.
In the interval where there should be two peaks, phosphocholine (k = 4) at
3.220012 ppm and phosphoethanolamine (k = 5) at 3.220215 ppm, there was
only one resonance identified at 3.220169 ppm. Because this single peak was
closer to PE, we gave it that assignment. The reconstructed amplitude and
the concentration for that single resonance were approximately the sum of
(PCho + PE) at N P = 1000. At that partial signal length the reconstructed
spectral parameters were fully exact for Lac (k = 1), Ala (k = 2), β−Glc
(k = 7), Tau (k = 8) and mIns (k = 9). However, for Cho (k = 3) the
chemical shift frequency, Re(ν − k ) and the line width, Im(ν − k ) were correct for
five of the six digits (3.210122 ppm rather than 3.210124 ppm, 0.000830 ppm
rather than 0.000833 ppm, respectively). The reconstructed amplitude|d − k

|
for choline was fully correct, but the metabolite concentration was computed
to be 0.0219 M/g ww, rather than the correct value of 0.0220 M/g ww. For
glycerophosphocholine (k = 6), the chemical shift frequency, Re(ν − k ) and the
line width, Im(ν − k ) were correct for five of the six digits (3.230413 ppm rather
than 3.230412 ppm, 0.000831 ppm instead of 0.000833 ppm, respectively).
The reconstructed amplitude|d − k |was completely correct for GPC, although

the computed metabolite concentration was 0.0689 M/g ww, instead of the
correct value of 0.0690 M/g ww.
For the case of the data from the fibroadenoma, full convergence was
achieved at N P = 1500 for all the reconstructed parameters for all nine res
onances (middle panel (ii) of Table 10.3). The stability of convergence at
higher signal length N P = 2000 is shown on the bottom panel (iii) of Table
10.3, where it is seen that all the reconstructed parameters are also fully ex
act. This stable convergence was seen at longer signal lengths, as well as the
full signal length N.
The absorption component shape spectra and the total shape spectra re
constructed by the FPT (−) at N P = 1000, 1500 and 2000 for the fibroadenoma
are shown in Fig. 10.3 . At N P = 1000 (right upper panel (iv)), the absorption
total shape spectrum is converged. However, once again, this was not the case
for the component shape spectrum (left upper panel (i)), which shows only
one peak (PE, k = 5) at 3.22 ppm, which is overestimated, whereas PCho
(k = 4) is not resolved. At N P = 1500 in the left middle panel (ii) of Fig.
10.3 the component shape spectrum is converged whereby peaks k = 4 and 5
are resolved and have the correct heights, as is the case for the other peaks.
The small phosphocholine peak can be seen directly underneath PE. Stability
of convergence is confirmed here, as well, at N P = 2000 in the lower panels
for both the absorption component shape spectrum (iii) and the total shape
spectrum (vi) and this also holds true for longer signals lengths, including the
full signal length N.