Breast cancer and non-malignant breast data: Quantification by FPT - Signal Processing in MRS with Biomedical Applications - page 322

For the fibroadenoma data the convergence of metabolite concentrations
at N P = 1000, 1500 and 2000 is displayed in Fig. 10.4 . At N P = 1000
neither the concentrations of phosphocholine nor phosphoethanolamine are
accurately assessed in the reconstruction (top panel (i)), and there is a slight
discrepancy in the concentrations of Cho (k = 3) and GPC (k = 6). At
N P = 1500 (middle panel (ii)) and N P = 2000 (bottom panel (iii)), all of the
metabolite concentrations are correct, as seen both numerically and by the
graphic representations. The metabolite concentrations were verified to be
correct at even higher partial signal lengths and at the full signal length.

10.4.3 Pade-reconstruction of MRS data from breast cancer
Table 10.4 shows the reconstructed data by the FPT (−) for breast cancer at
the three partial signal lengths: N P = 1000, 1500 and 2000. As was the case
for the data corresponding to normal breast tissue and to fibroadenoma, only
eight of the nine resonances were identified at N P = 1000 (upper panel (i)
of Table 10.4). In the interval where there should have been two resonances,
phosphocholine at 3.220012 ppm and phosphoethanolamine at 3.220215 ppm,
there was only one peak identified at 3.220166 ppm. The reconstructed am
plitudes and concentrations for that single peak were approximately the sum
of (PCho + PE). Once again, since that single peak was closer to phospho
ethanolamine, it was assigned as PE. At N P = 1000 all the reconstructed
spectral parameters were exact for Lac (k = 1), Ala (k = 2) and mIns
(k = 9). For peak k = 3 (Cho) the reconstructed Re(ν − k ) and Im(ν − k ) were
exact to 5 of six decimal places (3.210122 ppm and 0.000830 ppm instead of
the correct values 3.210124 ppm and 0.000834 ppm, respectively). The re

constructed|d − k |for choline was 0.00444 au while the correct value is 0.00446

au. The concentration for choline was computed to be 0.1111 M/g ww at
N P = 1000, although it should be 0.1115 M/g ww. For peak k = 6 (GPC) at
N P = 1000 the reconstructed Re(ν − k ) was correct to 5 of 6 decimal places, the
Im(ν − k ) to 4 of 6 decimal places, the |d − k

|was 0.00933 au rather than 0.00936
au, and the concentration was 0.2332 M/g ww while the correct value is
0.2340 M/g ww. For peak k = 7 (β−Glc) and peak k = 8 (Tau), the
reconstructed Re(ν − k ), Im(ν − k ) and|d − k |were correct to all decimal places, but

the computed concentrations were exact to 3 of the 4 decimal places.
Full convergence was attained at partial signal length N P = 1500 for all
the reconstructed parameters of all nine resonances corresponding to the data
from breast cancer tissue (middle panel (ii) of Table 10.4). The stability of
convergence at N P = 2000 is also shown. On the bottom panel (iii) of Table
10.4, all the retrieved parameters are shown to be exact. This remains true
even for higher partial signal lengths, as well as for the full signal length N.
The absorption component shape spectra and the total shape spectra recon
structed via the FPT are shown in Fig. 10.5 at N P = 1000, 1500 and 2000 for
the breast cancer data. At N P = 1000 (right upper panel (iv)), the absorption
total shape spectrum is converged. This was not the case for the component