Evaluating Frequency and Phase Drift Correction Methods for Brain MRS

Simulated brain proton MRS data were generated with known frequency and phase drift errors to evaluate the performance of the proposed method and compare it with previously described methods. First, simulated point resolved spectroscopy pulse sequence (PRESS) model spectra (echo time [TE] = 80 ms; 2048 points; spectral width = 2000 Hz; B₀ = 3T) were generated for 22 metabolites, six macromolecule resonances, and a water resonance using an in-house MATLAB-based implementation of the density matrix formalism as described previously (10 (link)). The model spectra were then exponentially line-broadened to a linewidth of 6 Hz and combined in approximately physiological concentrations to produce a simulated, noise-free MR spectrum. The amplitude of the simulated residual water resonance was chosen to be approximately twice the height of the N-acetyl aspartate (NAA) resonance. The spectrum was then replicated 128 times to simulate 128 acquired averages, and frequency and phase drifts were applied to each average. The frequency error, f, of each average, N, was chosen as a linear slope superposed with noise, ε_f, according to:f (N) = (5/128)N + ε_f Hz, and the phase error, φ, of each average was chosen as a flat slope superposed with noise, ε_φ, according to: φ(N) − (0)N + εφ degrees. The added noise terms, ε_f and ε_φ, involved the addition of a random value at each point N with mean values of zero and standard deviations of 0.2 Hz and 2 degrees, respectively. These terms were used to roughly approximate the effects of physiological and bulk noise. Finally, a normally distributed random noise seed was added to the each of the simulated averages to achieve the desired SNR. To approximate a range of SNR conditions, spectra were generated using per-average SNR values (measured as the peak NAA amplitude divided by the standard deviation of the added noise) of 20, 10, 5, and 2.5. For each SNR value, 10 simulated datasets (each with 128 averages) were generated as described above, and a frequency and phase drift correction was performed on each dataset using the spectral registration method, as well as two existing correction methods; the creatine fitting method (7 (link)), and the residual water method (2 (link)), as described below. To evaluate the various correction methods, the frequency estimation error and phase estimation error were quantified for each of the correction methods. Specifically, the estimation error was obtained by taking the difference between the measured drift and the actual drift and calculating the standard deviation of this residual difference across all 128 averages.