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

Abstract

Purpose Numerical simulations of three-dimensionally localized MRS spectra have been very time-consuming for multi-spin systems because the current state-of-the-art 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. Methods The time evolution of spatially localized multispin density matrix as the full solution to the Liouville–von Neumann equation was 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. Results 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 improved not only speed but also accuracy. Applications of the new method to phantom studies of multispin systems and quantification of in vivo MRS spectra of brain were demonstrated. Conclusion 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.

Advanced Hadamard-encoded editing of seven low-concentration brain metabolites: Principles of HERCULES

“…Chemical shifts and coupling constants were taken from literature (Govind et al, 2015;Govindaraju et al, 2000;Near et al, 2013). To account for the spatially varying editing efficiency within the voxel due to chemical shift displacement effects Kaiser et al, 2008;Near et al,2013), a fast computation algorithm for spatially localized MRS was employed (Zhang et al, 2017). All simulations were performed on a three-dimensional grid of 21 × 21 × 21 spatial points within a 3 × 3 × 3 cm 3 voxel, using ideal excitation and shaped refocusing pulses.…”

Simultaneous edited MRS of GABA, glutathione, and ethanol

“…The localized density‐matrix simulations of the GABA, GSH, and EtOH spin systems following the HERMES experiment at 3T were performed in FID‐A, accelerated by the recently published spatial averaging method . Ideal excitation and experimental refocusing and editing pulses were used.…”

“…The localized density-matrix simulations of the GABA, GSH, and EtOH spin systems following the HERMES experiment at 3T were performed in FID-A, 18 accelerated by the recently published spatial averaging method. 19 Ideal excitation and experimental refocusing and editing pulses were used. Simulations were performed on a 101 × 101 two-dimensional spatial array in the dimensions defined by the refocusing pulses spanning 4.5 × 4.5 cm 2 (ie the voxel length plus 50% in each dimension), with the following parameters: T E 80 ms; 20 ms editing pulse duration; 8192 data points; 5 kHz spectral width; 2 Hz simulated linewidth; additional line broadening using a 2 Hz exponential filter.…”

Quantification of in vivo transverse relaxation of glutamate in the frontal cortex of human brain by radio frequency pulse-driven longitudinal steady state

“…Metabolite concentrations were determined using an LCModel fitting routine developed in-house [14–16]. To generate the basis set for LCModel fitting, the exact PRESS readout sequence used in the in vivo studies was simulated using the highly accelerated one-dimensional projection technique [21]. Effects of scalar evolution of the Glu signal during iPFG train were quantified and results are included in the supporting information.…”