lated statistics (e. g., confidence intervals (CIs) and coefficients of variation (CVs)) of DT derived variables. Studies to date (Basser and Jones, 2002; Jones, 2003) have aimed to approximate analytically intractable probability distributions of DT derived variables for single voxels or regions of interest.
In this work, we extended the non-parametric bootstrap approach to generate an overall DTI data quality descriptor suitable for application studies. Toward that end, we eval- uated the performance of derived quality measures by focusing on two aspects thought to directly or indirectly affect DTI data quality in a clinical setting: 1) We addressed the issue of noise systematically by artificially increasing background noise or applying voxelwise and spatial smoothing (Hahn et al., 2001). 2) We also studied the influence of both experimentally enhanced (voluntary) subject motion and reduced motion due to the use of a vacuum device. To further evaluate the relevance of data quality differences as potential confounds in group comparison studies, we tested for systematic gender and age effects.
2.2 Methods and materials
Data acquisition and processing
All DTI data sets were acquired at 1.5 T (Signa Echospeed; GE Medical Systems) using a spin-echo echo-planar sequence with TR/TE= 4200 ms/120 ms and diffusion gradients in a six noncollinear directions. A total of 20 images (three and two repetitions for b = 880 and b = 0 s/mm2, respectively) consisting of 24 slices with 1.875×1.875 mm2
in-plane resolution and 3 mm thickness (1 mm gap) were obtained. The effective DT and fractional anisotropy (FA) were calculated as previously described (G¨ossl et al., 2002), according to (Papadakis et al., 1999; Basser and Pierpaoli, 1996):
FA = q 3 2 P3 i=1 ¡ ξi−ξ¯ ¢2 qP3 i=1ξ2i , (2.1)
24 2. Noise analysis of DTI data using bootstrap
where ξi is ith eigenvalue of the tensor, i = 1,2,3. In addition, Clinear (an anisotropy
measure focusing on the tensor shape) was computed as defined in Westin et al. (2002):
Clinear =
ξ1−ξ2
qP3
i=1ξi2 ,
whereξ1 ≥ξ2 ≥ξ3 are eigenvalues of the tensor.
To systematically assess the suitability of an overall data quality measure, we separately analyzed brain white (WM) and gray matter (GM), thus creating a compartment with relatively high and low anisotropy. Semiautomated segmentation was performed. In a first step, we removed extracerebral tissue semiautomatically, applying a region growing algorithm and manual corrections where needed. We then separated brain WM and GM using empirically derived diffusivity and FA thresholds, as previously proposed (Cercignani et al., 2001; Chabriat et al., 1999). A cut-off of mean diffusivity ¯ξ ≤ 1.8×10−3mm2/s
effectively suppressed cerebrospinal fluid (CSF) (typical ¯ξ = 3.0×10−3mm2/s). Voxels
with FA>0.2 and ≤0.2 were classified as WM and GM, respectively.
Bootstrap method
The bootstrap method (Efron, 1979; Efron and Tibshirani, 1993) is a non-parametric technique that is used to analyze variables of partly or entirely unknown distributions, such as those of FA (Skare et al., 2000b; Pajevic and Basser, 2003; Pierpaoli and Basser, 1996). The application of the bootstrap procedure yields N subsamples or resamples of a given data set by drawing with replacement, and thus provides various parameters describing the statistical properties of a measure of interest. Figure2.2depicts the bootstrap scheme that matches our clinical acquisition design. The sij labels the jth measurement belonging to the ith gradient direction. In order to maintain the original structure of two unweighted (s0j, j = 1,2) and three times six weighted (sij, i = 1, . . . ,6, j = 1,2,3) images, the resampling is subjected to the seven subsets represented by the rows. The order within each row need not be considered, because a subsequent regression analysis is used for tensor calculation. Hence there are¡ni+ki−1
ki
¢
possible combinations per gradient direction i= 1, . . . ,6, where ni designates the number of repeats, andki is the number of drawings (here ni = ki = 3). Multiplication with the combinations from the unweighted case
2.2. Methods and materials 25
Figure 2.2: Graphic illustration of the bootstrap method adapted to the present data acquisition scheme. A (resampled) volume of 20 images is represented by one box, with rows accounting for the applied gradient direction, and columns indicating the corresponding repeated measurements. Resamples are gained by drawing with replacement of each row belonging to the original data set box. The quantity of interest (e. g., an FA map) is computed from each bootstrap resample. These replicates can be transferred into one single map of voxelwise CIs.
(n0 = k0 = 2) yields a total of 3·106 possible new data sets. Evidently, the reliability
of the bootstrap method depends on the number N of resamples and the number ni of equivalent observations.
For the purpose of inferring the overall uncertainty contained in a single data set,N = 100 resamples are generated, yielding a voxelwise distribution of the respective variable (such as FA, Clinear, or mean diffusivity) from which the width of the 95% CI is extracted as the
key feature. This first information of voxelwise reliability is then comprised in a histogram whose mean, peak position, and height provide variables of the individual data set quality. Normalization to the corresponding number of studied pixels allows a direct comparison of each histogram’s shape.
To achieve comparability of the observed data quality between different acquisition or pro- cessing schemes, and between various DTI derived metrics, CVs were voxelwise extracted from the bootstrap derived distributions.
26 2. Noise analysis of DTI data using bootstrap
Noising
The mean SNR of a certain b-value image is defined by (Bastin et al., 1998; Parker et al., 2000): SNRb,i = SROI σn−0.5 i ,
where the mean magnitude signalS within a region of interest (ROI), calculated over the ni, i= 0, . . . ,6, available repetitions for a given b-value, determines the nominator. The denominator describes the Gaussian noise of the signal, which is estimated in accor- dance with Gudbjartsson and Patz (1995):
σ = σbackground
0.66 . (2.2)
The background ROI covered four bars that were positioned far enough away from both the skull and the image margins to avoid contamination due to artifacts. Modification with the factor 0.66 accounts for the Rayleigh distribution, while multiplication withn−0.5
i adjusts to repeated measurements. The SNR of one volume is then determined as the averaged SNRb,i, i= 0, . . . ,6 referring to our data acquisition scheme.
For the purpose of investigating the effect of thermal noise, 15 control data sets from an unrelated study (seven males and eight females, mean age = 28.47 years, range = 22−35 years) recorded under normal conditions were additionally impaired. Artificial noise was simulated from N(0, ασ2
0), with σ0 being an estimate of the present underlying Gaussian
noise (cf., Eq. (2.2)). Following Parker et al. (2000), the generated noise is added to the magnitude signals, such that the resulting negative intensities are set to zero. This operation leads to small deviations from the intended percentage increase of α·100% for the involved SNR range in the brain. With the aim of simulating pseudo-realistic noise levels, the maximal increment was chosen to reflect the spread of usual noise derived from a control group (N = 24), i. e., mean regular noise plus twice the standard deviation (SD). Table2.1details the resulting noise degrees and averaged SNRs for different regions of interest. The original mean Sbrain averaged to 123.41±12.99 SD, and the original
2.2. Methods and materials 27 Effective percentual increase of noise 0% 10% 20% 30% 40% Brain 19.80±2.59 18.01±2.35 16.73±2.18 15.35±2.01 14.34±1.88 White matter 18.28±2.20 16.62±2.00 15.45±1.86 14.17±1.71 13.24±1.60 Gray Matter 22.57±2.94 20.52±2.67 19.07±2.47 17.49±2.28 16.35±2.12
Table 2.1: Mean SNR±SD of three compartments corresponding to different levels of percentual noise increment.
Smoothing
Before the tensor calculation was performed, noise reduction was achieved by means of a non-linear spatial filter operating on the magnitude signal field. The filter consists of a chain of non-linear 3d Gaussian filters (Winkler et al., 1999) with chain parameters adapted to the specificities of DTI data (Hahn et al., 2001). The smoothing procedure is particularly appropriate for accounting for both the inherent discontinuities of DTI, such as edges in anisotropy values or in their main directions, and the appreciably curved smooth regions between such edges. An optimal approximation for this data type was ob- tained by three iterations of the chain, where both the linear spatial and the non-linear signal dependent windows of the filter were parametrized as proposed previously (Hahn et al., 2001). This filter construction estimates the local mean of the magnitude images, and is statistically robust to the minor skewness and heteroscedasticity of the correspond- ing Rician noise distributions at locally low SNR (Gudbjartsson and Patz, 1995).
Motion experiments
For this small experimental study, six volunteers (three females and three males, mean age = 26.8 years, range = 22−31 years) were investigated under three different condi- tions during one session. To reduce motion as much as possible, we performed the DTI acquisition while the subjects were held fixed by a vacuum cushion. Then, each subject was instructed to lie as still as possible in the scanner with standard fixation but no vac- uum cushion (i. e., the standard clinical setting). During the last DTI acquisition, the subjects were asked to yawn, chew, shake, or nod their head in order to voluntarily induce
28 2. Noise analysis of DTI data using bootstrap
motion in thex-,y-, andz-directions. The subjects gave their consent in accordance with the Declaration of Helsinki, and the scanning protocol was approved by the institutional ethics committee.
Gender and age effects
Confounding effects from data quality differences may have important practical implica- tions when they are uncontrolled in group comparison studies, as is currently done in neurobiologic and clinical studies. To test whether the reported inconsistencies regarding gender differences in FA (Virta et al., 1999; Sullivan et al., 2001; Westerhausen et al., 2003) and the more consistently observed age effects (Abe et al., 2002; O’Sullivan et al., 2001) may be related to data quality, we applied a bootstrap analysis to a larger data sample from 45 controls (21 males and 24 females, age = 48.5±18.6 years, range = 22−84).
Statistical analysis
We examined the results of the experiments by multivariate repeated measurements anal- ysis, using the mean CI, peak position, and height as response variables (unless otherwise indicated). The results from multivariate analysis of variance (MANOVA) were inter- preted by means of Wilks’ Lambda, followed by univariate F-tests. The significance level was set to 0.05. Pearson’s coefficient of correlation r with uncorrected P-values for two- tailed tests served as the interrelation measure. In case of small sample sizes however, a Spearman rank analysis was performed. The reported values are given as the mean and SD.