A 3D method called mdMRS for post-processing Magnetic Resonance Spectroscopy data

Abstract

The data obtained from a scanner for Magnetic Resonance Spectroscopy (MRS) is three-dimensional (3D) since the FID data from the scanner has spectrum values which are 2D complex numbers and 1D time values. This paper describes an MRS frequency-based post-processing method that has the advantage that it quickly determines the values needed for metabolite intensities and concentrations, even for most overlapping spectral terms.

The method of this paper does not depend on area under a curve or a user-chosen basis set. As few as three valid points corresponding to a peak on the spectral curve are all that is needed, other than similar information on a reference metabolite, for concentration determination of the associated metabolite. All four of the key values of peak location, amplitude, phase angle, and damping constant are determined simultaneously with high accuracy, dependent upon noise, and with computational simplicity from only three complex-valued constants. The theory behind mdMRS uses the knowledge that the projection of the 3D spectrum to the complex plane is a simple circle. Several concepts from complex variables theory are important, such as the Linear Fractional Transformation (LFT) that maps the frequency axis to that circle. The duality linking an LFT with a 2 $\times$ 2 Moebius matrix enables a fast iteration process that sharpens the four key value estimates on each iteration. The iteration removes all other terms when considering one of them. Applied to initial estimates, this leads to increasingly accurate output.

To be useful to clinicians and to researchers developing treatments based on metabolite concentrations, the goal for post-processing of the data include both fast and accurate computations, with speed sufficient to provide results “on console” and output provided as concentrations. Besides the number of protons associated with a metabolite, concentrations are determined using both amplitude and damping constant values. Since the methods of mdMRS provide both of those characteristics simultaneously, the time from data collection to metabolite concentration output is minimized. The name of this new post-processing method was chosen since the attributes of the method help bring that goal closer to reality for Medical Doctors.