Model order selection for quantification of a multi-exponential magnetic resonance spectrum

Magnetic resonance spectroscopic signals analyzed by time-domain models in order to retrieve estimates of the model parameters usually require prior knowledge about the model order. For multi-exponential signals where a superpo- sition of peaks occurs at the same resonance frequency, but with different damping values, model order selection criteria from information theory can be used. In this study, several generalized versions of information criteria are compared using Monte-Carlo simulation signals. The best criterion is further applied for selecting the model order of experimental 13 C glycogen signals. I. INTRODUCTION Quantification of Magnetic Resonance Spectroscopic (MRS) signals can be done parametrically in the time domain by modeling the signal as a superposition of exponentially damped sinusoids. This supposes the model order to be known, which in practice is not the case. The determination of the model order is particularly difficult in the case that some of the exponentially damped sinusoids have the same frequency. This problem is encountered in the analysis of 13 C MRS signals where glycogen (GLY) is a superposition of an unknown number of exponentially damped sinusoids with the same frequency but with different damping factors: a multi-exponential signal (9). Model order selection criteria would allow an objective evaluation of the model order rather than the operator-biased evaluation of the residue. The glycogen signals were obtained during a 13 C-1 pulse- chase experiment, which followed the glycogen synthesis in a perfused rat liver and mainly consists of two pulse phases and a chase phase (1). Processing these signals demonstrated that a sum of exponentials was necessary to accurately quantify the changing glycogen signals during the experiment. Section II shortly describes some background about the considered NMR experiment, while section III mentions several concepts regarding the provided prior knowledge and model order selection. This analysis is then applied to simulation signals as well as experimental signals from the glycogen experiment. The simulation and experimental results are described and discussed in section IV. This includes the evaluation of the model order selection criteria, the optimal model order and the evolution of the signal parameters during the experiment.