Non - regularized multivoxel NNLS is

Introduction: Quantitative T2 (qT2) enables scientists to discern tissue microcompartments by measuring multiple T2 decays using a multiecho acquisition [1]. This technique is sensitive to myelin content [2] and has uncovered previously undetected microcompartments in MS and PKU pathological tissue [3]. We show that traditional qT2 analysis using a smoothing constraint underestimates the myelin water fraction (MWF) as the signal to noise ration (SNR) decreases. Furthermore, the variance of the measurement cannot be determined for a single ROI analysis using traditional qT2, so multiple subjects are needed. In order to use qT2 clinically, however, the variance of a single ROI measurement is required to determine if, and to what degree, the MWF deviates from normal. We present a robust approach to qT2 that more accurately estimates the MWF with decreasing SNR, provides error bounds on a single ROI, and has confidence intervals on the T2 distribution. Methods: Synthetic Decay Data – This portion of the study characterizes how the measured MWF is affected using regularized and non-regularized fitting routines at various SNRs. Simulations are performed using a rat white matter multiexponential model, where MWF = 7 %, using 1000 realizations of Gaussian noise at SNRs 1000, 400, 200, 100, and 50. Gaussian noise is used to ensure no bias is introduced from a Rician noise-floor that can be misinterpreted as a DC offset in the decay data, potentially causing a source of MWF underestimation. These data are analyzed by creating the T2 distribution with and without a smoothing constraint. The T2 distributions are generated using a multiexponential basis set with intensities that are determined using NNLS [4]. The smoothing constraint, used for rNNLS, consists of allowing the curvature of the fit to vary such that 1.01χmin< χ< 1.015χmin [4]. Rat Data – The second portion of this study compares analysis workflows. The traditional analysis workflow, called regularized ROI NNLS (rrNNLS), consists of drawing an ROI, averaging the decay values together within the ROI, creating a T2 distribution with smoothing, and determining MWF. The proposed workflow consists of determining the T2 distribution for each voxel, drawing an ROI, averaging T2 distributions together, and calculating MWFs with variance estimates. The multi-voxel approach can be conducted two ways, with regularization (rmNNLS) [5] or without (nmNNLS). Single slice, 3ms spaced 128 multiecho rat in vivo data at 9.4-T data were collected and rrNNLS, rmNNLS, and nmNNLS are performed on data resulting from an ROI drawn in the corpus callosum using AnalyzeNNLS [6]. The resulting MWFs were compared using a 1-factor ANOVA with Student-Newman-Keuls posthoc testing where p < 0.05 is considered significant. Results: Synthetic Decay Data – NNLS analysis overestimates the true MWF as SNR decreases, while rNNLS underestimates the MWF, as shown in Table 1. However, the magnitude difference from the true MWF is less for NNLS compared to rNNLS at any given SNR. Rat Data – The nmNNLS workflow provides the largest MWF and is statistically different from rrNNLS and rmNNLS workflows, which are not statistically different from each other, as shown in Table 2. Fig 1 shows the T2 distributions using rrNNLS and nmNNLS analysis techniques. The 95 % confidence interval is shown with the dashed lines, and the gray region represents the T2 times used to determine the MWF. Discussion: The synthetic and rat data both have the highest MWFs when using non-regularized NNLS. A benefit of using the rmNNLS and nmNNLS analysis workflows is that 95% confidence intervals are placed on the T2 distributions, allowing estimates of variance for MWF using a single ROI, allowing individual time-course studies and comparison with healthy peers. Since rmNNLS is based on rNNLS, which suffers from greater difference from the true value in the synthetic data than NNLS, we suggest that nmNNLS is more robust and should be used for qT2 analysis. References: [1] MacKay et al. MRI 24: 515-24 (2006). [2] Laule et al. MS 12: 747-53 (2006). [3] Laule et al. JMRI 26: 1117-21 (2007). [4] Whittall & MacKay JMR 84: 134-52 (1989). [5] Meyers et al. ISMRM 16: 3044 (2008). [6] www.imaginginformatics.ca/open-source/analyzennls. We acknowledge financial support from the AHFMR and iCORE. Fig 1: T2 distributions from rrNNLS and nmNNLS from the same scan. Dashed lines represent the 95 % confidence intervals for the T2 distribution amplitudes. The gray region represents the T2 times used to calculate the MWF.