Fast computation of full density matrix of multispin systems for spatially localizedin vivomagnetic resonance spectroscopy

Abstract

Numerical simulations of three-dimensionally localized MRS spectra have been very time consuming for multispin systems because the current state-of-the-art method requires computation of a large ensemble of spins pixel-by-pixel in three dimensional space. This paper describes a highly accelerated technique for computing spatially localized MRS spectra using the full solution to the Liouville-von Neumann equation. The time evolution of spatially localized multispin density matrix as the full solution to the Liouville-von Neumann equationwas analyzed. A new technique based on one dimensional spatial projection of the full density matrix was proposed. This method was implemented using a computer program written in Java language. The MRS spectra calculated using the new method were found to be identical to conventional three-dimensional simulation for the same digitization of the voxel while the new method reduced computation time by orders of magnitude and led to not only improved speed but also accuracy. Applications of the new method to phantom studies of multispin systems and quantification of invivo MRS spectra of brain were demonstrated. The dramatically enhanced computational efficiency makes accurate simulation of localized MRS spectra highly accessible for calculating basis sets for spectral quantification and for optimizing pulse sequences.