Quantitative T₂ analysis: The effects of noise, regularization, and multivoxel approaches

Abstract

Typical quantitative T 2 (qT 2 ) analysis involves creating T 2 distributions using a regularized algorithm from region-of-interest averaged decay data. This study uses qT 2 analysis of simulated and experimental decay signals to determine how (a) noise-type, (b) regularization, and (c) region-of-interest versus multivoxel analyses affect T 2 distributions. Our simulations indicate that regularization causes myelin water fraction and intra/extracellular water geometric mean T 2 underestimation that worsens as the signal-to-noise ratio decreases. The underestimation was greater for intra/extracellular water geometric mean T 2 measures using Rician noise. Simulations showed significant differences between myelin water fractions determined using region-of-interest and multivoxel approaches compared to the true value. The nonregularized voxel-based approach gave the most accurate measure of myelin water fraction and intra/extracellular water geometric mean T 2 for a given signal-to-noise ratio and noise type. Additionally, multivoxel analysis provides important information about the variability of the analysis. Results obtained from in vivo rat data were similar to our simulation results. In each case, a nonregularized, multivoxel analysis provided myelin water fractions significantly different from the regularized approaches and obtained the largest myelin water fraction. We conclude that quantitative T 2 analysis is best performed using a nonregularized, multivoxel approach.Magn Reson Med 63:212-217, 2010. © 2009 Wiley-Liss, Inc. Key words: T 2 relaxation; T 2 distribution; voxel-based analysis; white matter; rat T 2 decay measured by MRI is influenced by a number of factors, including diffusion, cross-relaxation, and compartmentalization of water within voxels. The resulting macroscopic signal is best described using a weighted combination of exponential decays (1), where the weights represent relative contributions of distinct water compartments to the measured T 2 decay. Using a multiecho acquisition to measure T 2 decays and fitting a weighted combination of exponential decays to the data is called quantitative T 2 (qT 2 ), which is sensitive to myelin content (2,3) and has uncovered previously undetected water environments in human brain pathology in vivo (4).

Temporal phase correction of multiple echo T2 magnetic resonance images

“…Bjarnason et al also noted changes in the IEW gmT 2 with noise type: Rician noise caused a reduction in IEW gmT 2 when compared to Gaussian noise [19]. The data presented here show that the IEW gmT 2 is longer when comparing Rician distributed noise data with Gaussian distributed noise data.…”

“…Representative T 2 distributions are shown in Fig 9. Previous research suggested that changing the noise type from Rician to Gaussian would have dramatic effects on the measured MWF [19]; most notably an increase in MWF would occur as SNR decreases. No significant change was observed for the data presented here in Table 1.…”

“…Equation 4 shows that Rician distributed noise exactly becomes Rayleigh distributed noise for zero SNR. For very low SNR, the Rician distribution approaches the Rayleigh distribution, as shown in Fig 1D. The presence of noise in the multiple echo T 2 data will influence NNLS fitting [19], but the effect of noise type on T 2 distributions has not been examined. Rician noise can be divided into three segments [2], all of which exist for a magnitude-valued exponential decay that starts with a high SNR and ends with pure noise: 1) high SNR data where the noise is Gaussian distributed; 2) zero SNR data, such as regions of air, where the noise is Rayleigh distributed and can be called the Rayleigh noise floor; and 3) between these two extremes is a transitional region where the noise cannot be described as either Gaussian or Rayleigh distributed.…”

QuantitativeT2: interactive quantitative T2 MRI witnessed in mouse glioblastoma

“…18,19 The typical qT2 analysis proceeds as follows: (1) a multiecho T2 MR image is acquired; (2) a region of interest (ROI) is specified on the image; (3) decay data within the ROI are averaged; and (4) a T2 distribution is created by fitting a sum of weighted exponential decays to the averaged decay data. 20 To make the fit more resilient to noise, a regularization routine is often applied.…”

“…Third, the regularization causes underestimation of the myelin water fraction (MWF), and this error increases as the signal-tonoise ratio decreases. 20 Fourth, the analysis often requires multiple software programs with different interfaces and input requirements. The main objective of this study was to overcome these limitations and establish an advanced analytical platform for complex pathologies, in vivo.…”