IDENTIFYING INHOMOGENEITY FUNCTIONS IN MRS

Hana Kucharova, Ales Gottvald


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

Abstract: Inhomogeneity functions provide an indispensable prior information for accurate spectra quantifications in MRS under non-ideal conditions. A direct algebraic method is proposed and tested for identifying complex inhomogeneity functions from experimental data.

Introduction: identifying inhomogeneity functions from experimental data
Inhomogeneity functions w(t) and W(v):=F[w(t)] are major structures for incorporating inhomogeneity phenomena into qualitative and quantitative analysis of experimental data in Magnetic Resonance Spectroscopy (MRS). A definition and role of these functions is outlined in accompanying papers [1, 2]. A detailed theory of inhomogeneity functions may be found in [3, 4]. For an experimental context - see [5, 6]. In Vivo MRS is an important biomedical area where various applications of inhomogeneity functions may be very vital [2, 3]. Identification of inhomogeneity functions is a natural generalization of conventional "shimming" or "tuning" operations well known to every MR-spectroscopist. Conventionally, one takes a sample providing an "ideal" spectral line which is known   priori - when no inhomogeneity exists. Now, minimizing a magnetic field inhomogeneity with some correcting coils ("shimming"), one tries to arrive at the ideal spectral line without any inhomogeneity distortions. If this shimming operation is performed successfully (which may be difficult or even impossible in some cases), a special form of the inhomogeneity function, namely w(t)=1 or W(v)= d(v), is actually fixed. Conventionally, only this special form of the inhomogeneity function is used. Very often, a conventional DFT-based data processing forces the "homogeneous" form w(t)=1 even into "inhomogeneous" cases. However, neither qualitative nor quantitative analysis of the data is theoretically correct in this case.

Modern quantification methodologies in MRS are intrinsically capable of incorporating any inhomogeneity function [2, 3]. Hence, various inhomogeneity phenomena may be separated from the signals and the spectra. Being given a reference FID-signal z:=z(t,.) and an identification FID-signal u:=u(t,.), a general form of the inhomogeneity function may be identified. In the present article, we show examples of constructing the inhomogeneity functions directly from experimental data. The identification technique presented may be classified as a non-parametric algebraic method, working in a time domain.

References:
[1] Malczyk R. - Gottvald A.: "Modelling Inhomogeneity Phenomena in MRS". Biosignal '96 - an accompanying paper.
[2] Gottvald A.: "MRS Beyond Inhomogeneity and Noise Limits". Biosignal '96 - an accompanying paper
[3] Gottvald A.: "Meta-Evolutionary Optimization and Bayesian Statistics: MRS Beyond Homogeneity and Noise Limits". Manuscript to be published, ISI-ASCR, 1996
[4] Taquin J.: "Line-shape and resolution enhancement of high-resolution F.T.N.M.R. in an inhomogeneous magnetic field". Revue de Physique Apliquee 14, 1979, pp. 669 - 681.
[5] Chmurny G. N. - Hoult D.: "The Ancient and Honourable Art of Shimming". Concepts in Magnetic Resonance, 2, 1990, 131 - 149
[6] H. Barjat et al.: "Reference Deconvolution Using Multiplet Reference Signals". J. Magn. Reson. A, 116, 1995, 206 - 214

Back to: