A spin-product-operator analysis of the dephasing requirement in STEAM-localized NMR spectroscopy

Abstract

The STEAM sequence (I) is frequently used in volume-localized NMR spectroscopy. Its application requires that the spin coherence created by the first 90” pulse be completely dephased before the application of the second pulse (2, 3). Although the fulfillment of this dephasing requirement is essential for the correct interpretation of the STEAM-localized spectra, its importance has not always been fully recognized in the analysis of the sequence. A recent calculation (4)) which ignored the dephasing requirement, yielded undesired modulations of the stimulated-echo (STE) signal by the chemical shift. The purpose of this paper is to analyze the time evolution of a spin system subjected to the STEAM sequence and to demonstrate the importance of the dephasing requirement when using the STEAM sequence for volume-localized NMR spectroscopy. The time evolution of a single spin (I = 4) system is calculated using the spin product operator formalism (5), with the effects of spin relaxation and diffusion ignored. The STEAM sequence used for the analysis is depicted in Fig. 1 with indication of the points on the time axis where the spin density operator is calculated. For simplicity, the gradients in the three time intervals are the averaged gradients. The calculation is performed under the following conditions: (a) the TE gradients are balanced, i.e., GTr( 1) = GTE( 2); (b) the TM gradient is applied to destroy the transverse magnetization after the second RF pulse. Calculation of the density operator at the successive time points yields