Conclusion and outlooks - Signal Processing in MRS with Biomedical Applications - page 393

through this major picture and mechanism of resonant collision physics in
the BreitWignerPade setting that many elementary particles in nature were
detected and accurately quantified for their masses and lifetimes. This is a
continuing story of physics - it was like this decades ago and it is likely to
persevere for a long time to come.
•(ii) Absorption spectra for general systems in magnetic fields can also be
studied to uncover the hidden internal structure of such systems. For example,
a quantitative proton MRS in clinical diagnostics can, in principle, determine
the intrinsic structure of the scanned tissue yielding the precise biochemical
content and concentrations or abundance of the involved molecules or metabo
lites. This is done by in vivo proton MRS through detection of time signals
emanating from the selected tissue of examined patients. The sought absorp
tion spectrum in the frequency domain is not actually measured, but rather
it is computed by applying certain mathematical transformations (Fourier,
Pade, etc.) to the encoded time signals. However, such spectra cannot, on
their own, give the sought unequivocal internal biochemical structure of the
scanned tissue. This can unambiguously be obtained only by an adequate
spectral analyses (quantification) of the measured time signals to reconstruct
the concentrations of the main diagnostically interpretable metabolites. Such
concentrations are related to the abundance of these resonating protons from
the tissue. On the other hand, it is the number of resonating protons which
gives the intensity of the tissue response to the external excitations. Thus,
the intensity I k or amplitude |d k | of each of the constituents of the ensu
ing time signal becomes crucial for extraction of every concrete metabolite
concentrations. This presumes that the number of resonances has also been
retrieved. Finally, resonances are assigned to metabolites. Each metabolite
can be associated with more than one resonance. Resonating protons bound
in these molecules respond differently to the same applied frequency due to
unequal shielding from the surrounding electronic clouds. These small differ
ences (chemical shifts) in the resonant frequencies of various protons in dif
ferent chemical environments are the very basis of MRS. Such tiny differences
in chemical shifts permit differentiation among various molecules into which
protons are bound, and this gives the possibility for metabolite assignments.
Hence, reconstruction of chemical shifts, as the real part of the corresponding
complexvalued fundamental frequencies{ω k }, followed by retrieval of the as

sociated moduli of amplitudes{|d k |}is critical to the diagnostic task of MRS.
This amounts to extraction of biochemical information from the examined
tissue via metabolite assignments and concentrations. The imaginary parts of
{ω k }and phase of{d k }are also useful in providing the lifetimes of metastable
transients in the time signal and its phase, respectively.
Whether exemplified by topic (i) or (ii) or by a myriad of other related phe
nomena from interactive dynamics, we see that the fundamental frequencies
{ω k }of the given system can be identified as the poles of the corresponding
response function. Rational polynomials via the unique Pade approximant as
the response function of the studied system, are optimally suitable for this