MRS BEYOND INHOMOGENEITY AND NOISE LIMITS

Ales Gottvald


Institute of Scientific Instruments, Academy of Sciences of the CR,
Kralovopolska 147, CZ-612 64 Brno, Czech Republic. E-MAIL: gott@isibrno.cz

Abstract: A new methodology is proposed for quantifying signal parameters in Magnetic Resonance Spectroscopy (MRS). This methodology is based on Meta-Evolutionary optimization and Bayesian Statistics, applied to a class of generalized FID-signals. Inhomogeneity, noise, phase, truncation, apodization and some other spectral artifacts are involved in this approach. An important prior information, namely inhomogeneity functions, are carefully identified using experimental data. Additional prior information, both deterministic and probabilistic, may be imposed as well. In contrast to conventional DFT-based approach, this new quantification methodology is (much) more immune to various artifacts, while providing detailed accuracy analysis. These features may be very useful for both In Vivo and In Vitro MRS. Conventional DFT-based quantifications may be used as the first guess, which may be substantially improved in many non-ideal regimes.

Introduction Quantification of spectral (or signal) parameters is of paramount importance in Magnetic Resonance Spectroscopy (MRS) [1-4]. Biomedical information obtainable via MRS often critically depends on the accuracy and reliability of the quantifications. Major artifacts, obscuring the biomedical information in MRS, may be attributed to inhomogeneity and noise distortions. Other artifacts may be associated with phase, amplitude, base-line, truncation, apodization or sampling distortions [3-7]. In Vivo MRS is a typical area where these artifacts are very common even under extremely demanding and expensive physical conditions [2]. Considering MRS beyond conventional physical limits, all these artifacts are inevitably enforced. Inhomogeneity and noise play very central roles among these artifacts [5-8].

Conventional quantifications, based on Discrete Fourier Transform (DFT), are very valuable for the signals and spectra without significant distortions [3, 4]. However, this requires experimental conditions that are not only very expensive, but also physically strongly restrictive. In contrast to this conventional DFT-based approach, some optimization-based quantification methodologies may be generalized also for highly non-ideal signals or spectra. Moreover, some prior knowledge, which is often available for In Vivo MRS, may be applied in a theoretically optimal way. In this context, conventional DFT-based quantifications may be treated as the first guess (initial iteration) which may be substantially enhanced in many cases.

How redundant are contemporary experimental requirements of MRS? What are the most likely estimates of spectral parameters for a given prior information? How some prior information may improve the accuracy of parameter estimates? What uncertainty of quantification arises for a given prior information? ... These are examples of important questions that naturally arise in connection with quantification methodologies in MRS.

New methodologies of quantitative MRS, which may answer the above questions, are a vital challenge for many researches. Useful reviews of several deterministic time-domain methods are presented in [1, 2]. Detailed analyses show that some quantification methodologies are comparable to their DFT-based counterparts under ideal conditions, while showing principal advantages for many non-ideal situations [3, 4].

References
[1] de Beer R. - van Ormondt D.: "Analysis of NMR Data Using Time Domain Fitting Procedures". NMR - Basic Concepts and Progress, Springer-Verlag, Berlin, 1992, pp. 202 - 248
[2] Haselgrove J. C. et al.: "Analysis of In Vivo NMR Spectra". Reviews of Magn. Reson. in Medicine 2, 2, 1987, pp. 167 - 222
[3] Kotyk et al.: "Comparison of Fourier and Bayesian Analysis of NMR Signals". Part I. - J. Magn. Reson. 98, 1992, pp. 483 - 500; Part II. - J. Magn Reson. A 116, 1995, pp. 1 - 9
[4] Johnson G. et al.: "Multiple-Window Spectrum Estimation Applied to in Vivo NMR Spectroscopy". J. Magn. Reson. B 110, 1996, pp. 138 - 149
[5] 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
[6] Gottvald A.: "Meta-Evolutionary Optimization & Bayesian Statistics: MRS Beyond Inhomogeneity and Noise Limits". To be published, ISI-AS CR, 1996
[7] Malczyk R. - Gottvald A.: "Modelling Inhomogeneity Phenomena in MRS". Biosignal '96 - an accompanying paper.
[8] Kucharova H. - Gottvald A.: "Identifying Inhomogeneity Functions in MRS". Biosignal '96 - an accompanying paper.

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