High dynamic‐range magnetic resonance spectroscopy (MRS) time‐domain signal analysis

Abstract

In the absence of water signal suppression, the proton magnetic resonance spectroscopy ( 1 H MRS) in vivo water resonance signal-to-noise ratio (SNR) is orders of magnitude larger than the SNR of all the other resonances. In this case, because the high-SNR water resonance dominates the data, it is difficult to obtain reliable parameter estimates for the low SNR resonances. Herein, a new model is described that offers a solution to this problem. In this model, the time-domain signal for the low SNR resonances is represented as the conventional sum of exponentially decaying complex sinusoids. However, the timedomain signal for the high SNR water resonance is assumed to be a complex sinusoid whose amplitude is slowly varying from pure exponential decay and whose phase is slowly varying from a constant frequency. Thus, the water resonance has only an instantaneous amplitude and frequency. The water signal is neither filtered nor subtracted from the data. Instead, Bayesian probability theory is used to simultaneously estimate the frequencies, decay-rate constants, and amplitudes for all the low SNR resonances, along with the water resonance's time- Key words: magnetic resonance spectroscopy; NMR; MRS; in vivo; signal modeling; water suppression; water filter; parameter estimates; Bayesian; probability theoryThe signal-to-noise ratio (SNR) of the water signal in proton magnetic resonance spectroscopy ( 1 H MRS) data from intact biological systems can be orders of magnitude greater than the SNR of the metabolite resonances of interest. The water resonance lineshape in these systems can be broad and asymmetric due to tissue magnetic susceptibility gradients and insufficient magnet shim capabilities. Instrumental instabilities present during data acquisition can cause the water signal's phase and amplitude to vary with time. The result is a water signal with a complicated, nonexponential, non-single-frequency time-domain evolution. The water resonance's high SNR and nonideal behavior, combined with the modest resonance frequency dispersion found at static field strengths common to 1 H MRS in vivo, make it challenging to obtain accurate parameter estimates for the frequencies, amplitudes, and decay-rate constants of the low SNR metabolite resonances.Of particular note, in the frequency domain, the wings of the high SNR water lineshape extend across and beyond (thus, alias within) the spectral bandwidth, and underlie the low SNR resonances. Increasing the bandwidth minimizes aliasing effects but increases the noise. Analysis in the time domain avoids this problem because these effects are implicit in the model, but it requires a model for the water signal capable of modeling the water down to the noise level. However, it is impossible to model a high-SNR water signal down to the noise level by exploiting analytical expressions for the water lineshape such as a pure exponential, Gaussian, or a combination thereof, because these models ignore phase variations, and are inherently symmetrical in the frequency domain.The develo...

Proton MRS and MRSI of the brain without water suppression

“…These methods are very fast and perform adequately for the water-suppressed spectrum in terms of high degree of water removal and minimal distortion of the remaining metabolite signal. When processing MRS signals acquired without WS, however, they have several distinct shortcomings: (1) they cannot remove the water signal satisfactorily because the water signal is so strong and broad that it extends far into the region of the metabolite signals [111,112], (2) they may cause distortions and frequency-dependent phase shifts in the remaining spectrum [106,109], and (3) they are unable to handle problems caused by experimental imperfections. The problems of baseline roll and phase errors shown in Fig.…”

Magnetic resonance data modeling: The Bayesian analysis toolbox

“…Under these conditions, artifacts and deviations in the large peak from the pure exponentially decaying sinusoidal model can be much larger than the small peaks. Here, the large peak is modeled using a more complex model (an exponentially decaying sinusoid with slowly varying amplitude and phase) and is marginalized from the calculation, allowing accurate estimation of the amplitudes, phases, and frequencies of the small peaks …”

“…Here, the large peak is modeled using a more complex model (an exponentially decaying sinusoid with slowly varying amplitude and phase) and is marginalized from the calculation, allowing accurate estimation of the amplitudes, phases, and frequencies of the small peaks. 43…”

Variational Bayesian analysis of nonuniformly sampled NMR data

“…[35][36][37] We are now in a position to write down the full joint distribution for the fixed-basis signal model, pðD; a; n; sÞ ¼ pðDja; sÞpðajnÞpðnÞpðsÞ (30) where once again, our goal of obtaining the posterior distribution, pða; n; sjDÞ ¼ pðD; a; n; sÞ pðDÞ In general, we can safely choose small values for a = b % 10 À6 , resulting in a relatively uninformative prior over ξ.…”

“…Because Student's-t distributions share the sparsity promoting properties of the Laplace distribution, we see that the hierarchical prior will also favor sparse posterior estimates of a. [35][36][37] We are now in a position to write down the full joint distribution for the fixed-basis signal model, pðD; a; n; sÞ ¼ pðDja; sÞpðajnÞpðnÞpðsÞ (30) where once again, our goal of obtaining the posterior distribution, pða; n; sjDÞ ¼ pðD; a; n; sÞ pðDÞ…”