Basic tasks of signal processing in spectroscopy - Signal Processing in MRS with Biomedical Applications - page 2

in modern diagnostics.
One of the main goals of the present book is to show how MRS can poten
tially establish its theoretically anticipated, but thus far unrealized highrank
status. This can be accomplished through performing data processing by an
exclusive reliance upon ab initio spectral analyses of proven validity from the
realm of quantum mechanics as the most successful physics theory. The pro
posed strategy is expected to shed new light upon MRSI by providing the
most adequate, unequivocal quantitative tabular and graphical data of con
centrations of many MRdetectable and clinically informative metabolites.
Such analytical chemistry type spectroscopic data contain not only concen
trations, but also chemical shifts and relaxation times of all the reconstructed
physical metabolites. These detailed data would be impoverished if they were
reduced only to chemical shift colorcoding of MRI scans. Rather, they require
a novel look at MRSI whose proper interpretation necessitates spectroscopic
skills from mainstream mathematical physics and chemistry. Indeed, such a
comprehensive strategy is dictated by the interdisciplinarity of MR phenom
ena. It is through this fresh avenue that imaging and spectroscopy could be
synergistically integrated within magnetic resonance into MRSI and, as such,
would have a greater chance of attaining its full potential of becoming an
unprecedented diagnostic modality.
The experimentally measured or encoded data from MRS and MRSI are
time signals, or alternatively, free induction decay (FID) curves. These data
then undergo spectral analysis. This is achieved by solving an inverse problem
called quantification, entailing the reconstruction of quantitative physical and
biochemical information from the examined tissue. The sought data include
the number of metabolites, their chemical shifts, relaxation times as well as
their abundance, i.e., concentrations. Within the realm of medical diagnostics,
the obtained results are typically compared to normative data.
From the mathematical standpoint, the quantification problem involves the
use of encoded time signals to reconstruct the true number of harmonic tran
sients and the pairs of spectral parameters that are complexvalued physical
quantities - the frequencies and the corresponding amplitudes. These quan
tities are the sole elements of the fundamental harmonics that comprise the
FID under study. Each harmonic transient possesses a resonant frequency,
relaxation time, as well as intensity and phase. These four parameters com
pletely characterize the underlying normalmode damped oscillations in the
FID. From the reconstructed complex frequencies and amplitudes these four
realvalued parameters can be identified directly, and thereby the peak ar
eas of the associated resonance profiles in the corresponding spectrum can be
obtained. The relative concentrations of various metabolites can then also
be obtained, since these are proportional to the computed peak areas. Here,
constants of proportionality are the concentrations of certain chosen reference
metabolites, e.g., water or some other molecules.
The total number of harmonic transients is also a quantifiable parameter,
and can be reconstructed during spectral analysis of the FID. Quantification