Exact quantum-mechanical, Pad´e-based recovery of spectral parameters - Signal Processing in MRS with Biomedical Applications - page 139

create enormous problems for attempts at quantification by processing via
fitting techniques. Furthermore, the powerful extrapolation characteristics of
the FPT imply that long total acquisition times T of encoded FIDs, as re
quired by the FFT, may not be needed. Such extrapolation advantages of the
FPT also improve SNR relative to the FFT. Poor SNR has been cited in the
literature as one of the major obstacles to the overall diagnostic performance
of in vivo MRS [7, 116].
Originally, MRS was imported to medicine from basic laboratory research
in physics and chemistry where it is known as NMR, which is one of the best
spectroscopic methods available. However, the accompanying welldeveloped
theoretical methods in the corresponding signal processing from physics and
chemistry have not yet been widely imported to MRS. This situation should
be improved on a more satisfying and deeper level in this extremely beneficial
interdisciplinary crossfertilization.
Recall that the information which is sought from the tissue via MRS is
acquired in two separate stages. In the first instance, the experimental mea
surement is used to encode a number of FIDs in a scanner 3 . Next, in the
second step, analytical methods are used through mathematical processing to
quantify the averaged FID. The results of parametric signal processing are
the spectral parameters. These parameters are used to generate a frequency
spectrum which has a number of peaks representing resonances at different
chemical shifts. These peaks can be isolated, overlapped, tightly overlapped,
nearly degenerate or degenerate (confluent). Each metabolite is linked to one
or more resonances. The extracted spectral parameters determine the areas
underneath these peaks in the frequency spectrum. The peak areas are pro
portional to the sought concentrations of metabolites. The retrieved spectral
parameters for every individual resonance are the pairs of fundamental com
plex frequencies and the associated complex amplitudes. The peak position
or chemical shift is the real part of the complex frequency. The peak width is
proportional to the imaginary part of the complex frequency. The relaxation
times of metabolites are equal to the inverse of the imaginary frequencies,
as per (2.186). The peak height is proportional to the quotient of the ab
solute value of the amplitude and the associated imaginary frequency. The
phase of the individual harmonic component of the FID is the phase of the
complexvalued amplitude.
Thus, the reconstructed spectral parameters provide all the quantitative
physical and biochemical information about metabolites of the scanned tissue,
such as their concentrations, relaxation times, etc. The process of reconstruc
tion of the pairs of complexvalued spectral parameters and the true number of
resonances for the given FID represents an inverse nonlinear problem. In many
research areas, this type of problem is encountered under a number of different
3 Usually the number of encoded FIDs is of the order of 200. Such measured FIDs are after-
wards averaged to improve SNR. The averaged FID is then subjected to signal processing.