Introduction: towards MRS beyond conventional physical limits
Inhomogeneity and noise are major artifacts corrupting quantitative biomedical information obtainable by Magnetic Resonance Spectroscopy (MRS). Additional artifacts may correspond to some base-line, phase, amplitude, truncation, apodization or sampling distortions. Negative impacts of all these artifacts are especially profound in context of conventional spectra quantifications, based on Discrete Fourier Transform (DFT). In Vivo MRS is a typical area where these artifacts are common even under very demanding and expensive physical conditions. Considering MRS beyond conventional physical limits, all these artifacts are inevitably enforced. Various inhomogeneity phenomena play a very central role among these artifacts.
Recently, new quantification methodologies have been proposed in MRS [1-4]. Some of these methodologies are much less susceptible to artifacts than their DFT-based counterparts. A useful review of several deterministic time-domain methods is presented in . A powerful methodology of quantitative MRS may be based on Meta-Evolutionary optimization and Bayesian Statistics [2-4]. In comparison to a conventional DFT-based quantification, this new methodology is physically (much) less restrictive in many ways. In particular, even the signals acquired beyond conventional physical limits, in terms of inhomogeneity, noise, phase, truncation or apodization artifacts, may be quantified.
An important step towards this new quantitative methodology is understanding the inhomogeneity phenomena in MRS. Some qualitative rules are well known to experienced spectroscopists: complicated line-shapes arise, neighbouring lines overlap, signal-to-noise ratio decreases, etc. However, a rigorous quantitative treatment of the inhomogeneity phenomena, which is inevitable for minimizing experimental redundancy in MRS, is much less common. Hence, this article will be devoted to modelling the inhomogeneity phenomena in MRS.
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 Gottvald A.: "Inverse and Optimization Methodologies in MRS: Part 4: Applications to In Vivo Spectra Quantifications". In: Proc. of the 3rd Japanese-Czech-Slovak Joint Seminar on Applied Electromagnetics, Prague, July 5 - 7, 1995, pp. 17 - 20
 Gottvald A.: "Meta-Evolutionary Optimization and Bayesian Statistics: MRS Beyond Homogeneity and Noise Limits" (to be published)
 Gottvald A.: "MRS Beyond Inhomogeneity and Noise Limits". Biosignal '96 (an accompanying paper)