Discrete analysis of stochastic NMR. I

Abstract

Stochastic NMR is an efficient technique for high-field in vivo imaging and spectroscopic studies where the peak RF power required may be prohibitively high for conventional pulsed NMR techniques. This paper presents a theoretical analysis of a stochastic NMR spectroscopy experiment that consists of exciting the spin system with RE pulses where the flip angles or the phases of the pulses are samples of a discrete stochastic process. The experiment is formulated as a stochastic difference equation which is then converted to ordinary deterministic difference equations describing the input-output cross-correlation, average signal power, and signal-power spectrum. The solutions of these equations are used to study spectral distortions as the spin system is saturated with a highpower excitation, to obtain an optimum excitation power level that gives the maximum signal-to-noise ratio and to evaluate the contribution of systematic noise to the overall signal-to-noise ratio of the experiment. The specific case of random-flip-angle excitation is analyzed. Results show that high-power excitation may cause line broadening, a notch artifact, and nonuniform response across the spectrum. Experimental results are also presented to show that the discrete analysis provides an accurate description of practical experiments.