Evaluation of voxel-based group-level analysis of diffusion tensor images using simulated brain lesions

Neuroscience Research 71 (2011) 377–386

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Evaluation of voxel-based group-level analysis of diffusion tensor images using simulated brain lesions Jaana Hiltunen a,b,∗ , Mika Seppä a,b , Riitta Hari a,b a b

Brain Research Unit, Low Temperature Laboratory, Aalto University School of Science, P.O. Box 15100, 00076-AALTO, Finland Advanced Magnetic Imaging Centre, Aalto University School of Science, P.O. Box 13000, 00076-AALTO, Finland

a r t i c l e

i n f o

Article history: Received 20 April 2011 Received in revised form 22 August 2011 Accepted 9 September 2011 Available online 29 September 2011 Keywords: Diffusion tensor imaging (DTI) Group analysis Fractional anisotropy Mean diffusivity SPM Voxel-based analysis (VBA)

a b s t r a c t We simulated brain lesions in mean diffusivity (MD) and fractional anisotropy (FA) images of healthy subjects to evaluate the performance of voxel-based analysis (VBA) with SPM2. We increased MD and decreased FA, simulating the most typical abnormalities in brain pathologies, in the superior longitudinal fasciculus (SLF), corticospinal tract (CST), and corpus callosum (CC). Lesion sizes varied from 10 to 400 voxels (10.5 mm3 each) and intensity changes from 10 to 100%. The VBA contained eddy current correction, spatial normalization, smoothing, and statistical analysis. The preprocessing steps changed the intensities of MD and FA lesions from the original values, and many lesions remained undetected. The detection thresholds varied between the three brain areas, and between MD and FA images. Although spatial smoothing often improved the sensitivity, it also markedly enlarged the estimated lesion sizes. Since conventional VBA preprocessing significantly affected the outcome and sensitivity of the method itself, the impact of analysis steps should be verified and considered before interpreting the findings. Our results provide insight into the sizes and intensity changes of lesions that can be detected with VBA applied to diffusion tensor imaging (DTI) data. © 2011 Elsevier Ireland Ltd and the Japan Neuroscience Society. All rights reserved.

1. Introduction Diffusion tensor imaging (DTI) employs random movements of water molecules to reveal tissue microstructure (Basser et al., 1994; Le Bihan, 1995). The measured diffusion-weighted images can be further analyzed to obtain parameter images that describe different characteristics of diffusion. For example, the mean diffusivity (MD) describes the overall strength of diffusion, and the fractional anisotropy (FA) describes the inhomogeneity of diffusion, i.e. whether diffusion has a preferable direction due to tissue structures (Basser and Pierpaoli, 1996). Increased MD and/or decreased FA are the most typical abnormalities in various brain pathologies, such as ischemia, tumors, traumatic brain injury, Alzheimer’s disease, Parkinson’s disease, multiple sclerosis, epilepsy, schizophrenia, and mild cognitive impairment; for reviews, see Kubicki et al. (2002), Assaf and Pasternak (2008), Kyriakopoulos et al. (2008) and Bodini and Ciccarelli (2009). Increased MD may result from infection or edema, whereas decreased FA may reflect damaged tissue microstructure,

∗ Corresponding author at: Advanced Magnetic Imaging Centre, Aalto University School of Science, Otakaari 5I, P.O. Box 13000, 00076-AALTO, Finland. Tel.: +358 444406319; fax: +358 9 4702 6172. E-mail address: [email protected].fi (J. Hiltunen).

axonal loss, or increase in isotropic water volume (Beaulieu, 2009; Bodini and Ciccarelli, 2009). Earlier, DTI images have mainly been analyzed on an individualsubject basis using visual inspection of images and regions of interest (ROIs), positioned on selected brain (or other) structures. However, this method is subjective and observer-dependent, and may thus bias the results. It has also been assumed that small disease-related changes, still invisible for human eye/expert radiologist, could be detected by pooling together a group of patients and by comparing the images voxel-wise with healthy subjects. Therefore, nowadays, the growing trend in DTI analysis is voxel-based analysis (VBA) to address group-level differences in parameter images describing anisotropy and diffusivity. Such an analysis has been applied to study e.g. amyotrophic lateral sclerosis (ALS) (Sage et al., 2007), Alzheimer’s disease (Rose et al., 2008), brain damage in boxers (Chappell et al., 2006), schizophrenia (White et al., 2007), and Parkinson’s disease (Zhang et al., 2011). The VBA analysis of DTI data contains correction for motion and eddy currents, spatial normalization, smoothing, and statistical voxel-by-voxel analysis; for methodological details of VBA, developed and applied first for the anatomical MR images (without eddy current correction), see Ashburner and Friston (2000, 2001). All processing steps in VBA attempt to enhance the images to allow higher statistical power in the voxel-wise analysis. Eddy currents in gradient coils cause distortions to images; the strength and

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appearance of distortions in DTI vary depending on the direction of diffusion sensitizing gradients. To correct for these distortions and subject motion, images are typically registered to a non-diffusionweighted reference image with affine transformation. Moreover, non-linear spatial normalization is applied to deform the individual brain to better match between-subjects anatomy. Finally, spatialsmoothing filter is applied to further compensate for anatomical variations across subjects and to decrease the effects of noise. Smoothing also helps to fulfill mathematical assumptions of continuity required for statistical testing. The size of the smoothing filter affects the results as has been demonstrated in several methodological studies applied to statistical parametric maps of brain-imaging data; see for example Friston et al. (1994), Poline et al. (1995), and Worsley et al. (1996). More recently, Park et al. (2004) showed in-practice differences in statistical values and extents of brain areas in assessing hemisphere asymmetries of healthy subjects with 3-, 6-, and 9 mm smoothing applied on FA images. Later, Jones et al. (2005), comparing schizophrenia patients with control subjects, derived four different conclusions from the same imaging data depending which smoothing kernels they used. With FWHM (full width at half maximum) filter widths ≤6 mm, patients and control subjects did not differ. With larger FWHM values, two brain areas (right superior temporal gyrus, STG, and left cerebellum) showed reduced FA in the patient group: STG alone with widths of 7 and 8 mm, both areas with widths of 9–14 mm, and cerebellum alone with widths ≥14 mm. In the above studies, the performance of DTI-VBA was evaluated using real images of patients. However, images with controlled artificial (i.e. simulated) lesions would be superior to real patient images in estimating the precision of VBA. Simulated brain lesions have been placed on anatomical MR images (Mehta et al., 2003; Stamatakis and Tyler, 2005), and more recently, on DTI images (Van Hecke et al., 2010) where anisotropic smoothing was found to increase VBA’s sensitivity in the analysis of FA images. Until now, no systematic studies exist about the sensitivity of the conventional DTI-VBA performed with statistical parametric mapping (SPM). We thus simulated lesions to MD and FA images of a group of healthy subjects to scrutinize the performance of the widely-applied group-level VBA, concentrating on the analysis chain from FA and MD images to statistical maps. We aimed to (i) specify detection thresholds, i.e. the extent and the intensity change of lesions that can be found with VBA with certain statistical criteria, and to (ii) find out how the analysis chain affects the sizes and intensity values of the detected lesions. We used SPM2 software, since most of the published clinical DTI-VBA applications have employed this software version (Buchel et al., 2004; Chappell et al., 2006; Sage et al., 2007, 2009; Shon et al., 2010; Snook et al., 2007; White et al., 2007). As our study thus was performed similarly as the mainstream DTI-VBA studies so far, it provides valuable information about the efficiency of the VBA method in the analysis of group-level differences in brain’s diffusivity and anisotropy images. 2. Materials and methods 2.1. Subjects Twenty healthy subjects (12 males, 8 females; mean ± SD age 29 ± 5 years) participated in the study. Informed consent was obtained from the subjects, and the study had the prior approval by the local ethics committee. 2.2. Diffusion tensor imaging MR images were acquired using a Signa VH/i 3.0 T MRI scanner (GE Healthcare, Chalfont St Giles, UK) and an 8-channel

high-resolution brain-array head coil. DTI data were acquired from 52 axial slices of 3 mm thickness, without spacing between the slices. The other imaging parameters were as follows: repetition time TR = 12,000 ms, echo time TE = 78 ms, field of view FOV = 24 cm, matrix 128 × 128. The voxel size was thus 1.88 mm × 1.88 mm × 3 mm. Twelve diffusion gradient orientations and a b0-image were acquired (Neeman et al., 1991). Diffusion sensitizing gradients lasted for 26 ms, with 34 ms interval in-between, and the b-value was 1000 s/mm2 . The diffusionsensitizing-gradient scheme was measured 8 times to improve the signal-to-noise ratio (SNR). The DICOM-format DW images were converted to ANALYZE format (Mayo Foundation, MN) using MRIcro software (University of Nottingham, UK). T1-weighted images covering the whole brain were also recorded with 1-mm3 isotropic voxels. The imaging parameters for the 3D spoiled gradient echo (SPGR) sequence were TR = 9 ms, TE = 1.9 ms, preparation time = 300 ms, flip angle FA = 15◦ , number of excitations NEX = 2.

2.3. Simulated lesions FA and MD maps were computed with the FDT analysis package of the FSL software (version 4.0, www.fmrib.ox.ac.uk/fsl). The measured DW images of each individual were first corrected for subject motion and eddy currents (Jenkinson and Smith, 2001). Then nonbrain structures were removed using Brain Extraction Tool (BET) (Smith et al., 2002). Finally MD and FA images for each subject were calculated using DTIFit program. We simulated the lesions on each individual FA and MD maps as well as on spatially normalized FA and MD maps to enable several testing procedures measuring the performance of VBA. The lesions were simulated within Matlab software (version 7.1, MathWorks, Inc., MA). We selected three white matter tracts (superior longitudinal fasciculus, SLF; corticospinal pathway, CST; body of corpus callosum, CC) as anatomical ROIs for simulated lesions, each representing one main direction (right–left, superior–inferior, and anterior–posterior). Fig. 1 shows the tracts that were identified from direction-encoded colour (DEC) images using the DTI atlas book (Mori et al., 2005). An axial slice covering maximally the body of corpus callosum was used for positioning the CC lesion (Fig. 1, right column), and this slice also served as the anatomical landmark for the other lesions. The CST lesion (Fig. 1, middle column) was positioned at the same slice level, left from CC, to a site where the fibers align maximally in superior–inferior direction. The SLF lesion (Fig. 1, left column) was positioned at the level of CC ± 1 slice, depending on where the fibers were maximally visible in the axial slices. From centers of these seeds (anatomical structure within slices), the cuboid-shape lesions extended within slice and to adjacent slices so that the size of lesion varied from 10 to 400 voxels (10, 25, 50, 100, 200, 300, 400 voxels; each 10.5 mm3 in size), corresponding to volumes of 106–4219 mm3 (106, 264, 527, 1055, 2109, 3164, 4219 mm3 ). Although real lesions vary in shape and size between individuals, we used a fixed set of lesion sizes and shapes in all simulations to minimize individual variance in the data. Otherwise it would have been difficult to assess which end results reflect methodological limitations and which are due to simulated individual variance. The lesion extensions within and between adjacent slices were as follows (voxels in right–left × anterior–posterior direction): 10voxel lesion (2 × 5) on a single slice, 25-voxel lesion (5 × 5) on a single slice, 50-voxel lesion on three slices (two 4 × 5 and one 2 × 5 lesions), 100-voxel lesion on three slices (two 6 × 5 and one 8 × 5 lesions), 200-voxel lesion on two slices (two 10 × 10 lesions), 300voxel lesion on two (one 10 × 20 and one 10 × 10 lesion in CC and SLF) or three slices (three 10 × 10 lesions in CST), 400-voxel lesion

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Fig. 1. Examples of sizes and intensities of simulated lesions in different brain regions: SLF (superior longitudinal fasciculus), CST (corticospinal tract), and CC (corpus callosum), positioned on DEC maps (white boxes, top panel), FA maps (middle panel) and MD maps (bottom panel). Left column: spatial extent of 200 voxels, and intensity change of −75% in FA and +75% in MD; middle column: spatial extent of 10 voxels, and intensity change of −100% in FA and +100% in MD; right column: spatial extent of 100 voxels, and intensity change of −30% in FA and +50% in MD.

on three (one 10 × 20 and two 10 × 10 lesions in CC and SLF) or four slices (four 10 × 10 lesions in CST). Two sets of intensity changes were introduced. First, decreased FA, a typical FA finding, was simulated by decreasing the voxel values within the lesion by 10%, 30%, 50%, 75%, and 100%. Increased MD was simulated by increasing the MD values by 10%, 30%, 50%, 75%, and 100%. Even though our most extreme intensity changes of 75–100% do not correspond to the typical changes in VBA applications, we included them since our pilot tests did not succeed in finding lesions of small intensity changes. We inserted altogether 35 simulated lesions (7 lesion sizes, 5 intensity-level changes) per anatomical area in each subject. 2.4. Voxel-based analysis of MD and FA images SPM version 2 (SPM2, Wellcome Department of Cognitive Neurology, London, UK) and Matlab were used in analyses. The MD and FA maps were spatially normalized into the standard anatomical space of Montreal Neurological Institute (MNI): The b0 image of each subject was first normalized into the EPI template of SPM2 using a 12-parameter affine transformation, followed by nonlinear warping with 7 × 9 × 7 basis functions. The voxel size was resampled to 2 mm × 2 mm × 2 mm. We used both the affine and

nonlinear transformations since the affine transform mainly fits the overall brain shape whereas the non-linear part also attempts to fit the inner structures. The normalization parameters were then applied to MD and FA maps that were filtered using a Gaussian smoothing kernel of 0 mm (i.e. no smoothing), 4 mm, 6 mm, 8 mm, or 10 mm of FWHM. The MD and FA maps were compared between the lesion and non-lesion groups using two-sample t-tests, based on general linear model in SPM2. Differences between groups were considered statistically significant if the voxels passed the height threshold of p < 0.001 (uncorrected), or p < 0.05 (FWE, family-wise error-rate correction). Extent threshold of 10 voxels was applied in realistic comparison between the two subject groups (see testing procedure 3 below). The estimated lesion, obtained as a result of a statistical analysis, was positioned on the normalized DEC map of one subject. The location of the lesion was then verified, using an anatomical atlas (Mori et al., 2005), to be within the original region of interest. 2.5. Testing procedure Three statistical analyses were performed. The first analysis (“best-case scenario”) provided reference values for sizes and

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Table 1 True and estimated lesion sizes (in voxels) for FA images (upper part) and MD images (bottom part) with intensity changes (from 100% to 10%) in the three brain regions (SLF/CST/CC). Threshold at p < 0.001. True size (voxels)

Intensity change (%) 100

75

50

30

10

400 300 200 100 50 25 10

Estimated size for FA images in SLF/CST/CC 400/400/400 400/400/400 300/300/300 300/300/300 200/200/200 200/200/200 100/100/100 100/100/100 50/50/50 50/50/50 25/25/25 25/25/25 10/10/10 10/10/10

400/400/384 300/300/285 197/200/195 100/100/100 50/50/50 25/25/25 10/10/10

339/359/225 260/262/187 171/178/121 93/87/77 49/50/44 25/25/25 10/10/10

3/75/0 3/53/0 2/20/0 2/18/0 2/18/0 2/9/0 0/5/0

400 300 200 100 50 25 10

Estimated size for MD images in SLF/CST/CC 400/400/400 400/399/398 300/300/300 300/299/300 200/200/200 200/200/200 100/100/100 100/100/100 50/50/50 50/50/50 25/25/25 25/25/25 10/10/10 10/10/10

400/369/299 300/269/227 200/179/131 100/94/59 50/46/32 25/24/18 10/10/9

398/295/162 298/218/158 199/143/75 100/72/29 40/42/18 25/22/9 10/10/5

272/267/4 217/199/5 167/126/0 87/66/0 47/36/0 24/19/0 10/10/0

FA, fractional anisotropy; MD, mean diffusivity; SLF, superior longitudinal fasciculus; CST, corticospinal tract; CC, corpus callosum.

intensity changes of lesions that can be found in optimal conditions. The second analysis explored the effect of preprocessing (spatial normalization and smoothing), and the third one was a realistic comparison between two subject groups, one with lesions and the other intact. (1) Reference values. To exclude the effect of the spatial normalization step, lesions were positioned onto normalized FA and MD images in MNI space. The anatomical areas of interest and the coordinates of the lesions were identified in the spatially normalized DEC map of Subject 3 (arbitrarily chosen). Subsequently, the same lesion MNI coordinates were applied to normalized FA and MD images of other subjects. These non-smoothed lesion images (N = 20 subjects) were statistically compared with the same images without lesion to estimate the smallest lesion sizes and intensity changes to be detected in optimal conditions. Next, the images were smoothed with 4 mm, 6 mm, 8 mm, and 10 mm FWHM Gaussian filters to study the effect of smoothing on perfectly registered images. (2) The effect of spatial normalization and smoothing. Lesion images (FA, MD) of each subject (N = 20), created in the individual imaging spaces, were spatially normalized into the MNI space, and then smoothed with the same kernels (0–10 mm FWHM). We thus compared all lesion images with the original intact images subjected to the same transformation into standard space. (3) Realistic lesion study, comparison between two groups. We divided the subjects into two age- and gender-matched groups (N = 10 vs. N = 10 subjects), one with simulated lesions and the other serving as a control group. The spatially normalized and smoothed images were compared between the age- and gender-matched lesion and control groups, ten subjects in each. 3. Results 3.1. Reference values Table 1 lists the true and estimated lesion sizes for FA and MD images (top and bottom parts of the table, respectively) at statistical threshold of p < 0.001. As expected, the detection sensitivity decreases when the size or the intensity change of the lesion decreases. All lesions with intensity changes of at least 30% were detected; the estimated sizes were 62–100% of the true values in FA images and 41–100% in MD images. The lesions with the smallest intensity

change (10%) were the hardest to find, and 8 (FA) and 5 (MD) of 21 lesions, mainly located in the CC, were not detected with the chosen statistical criteria. Differences between brain areas were evident at intensity changes of 10–50%. At 30% intensity changes, FA-lesions were found approximately similarly in SLF and CST, whereas at 10% intensity changes, the CST lesions were found more robustly. Instead, lesions in MD images were found slightly better in SLF than CST. The CC lesions were always detected the worst, probably because of the largest inter-subject variation of FA and MD values in CC. For example, the variation of original FA values, measured from the 50-voxel lesion area, was between 0.30 and 0.69 (mean ± SD 0.54 ± 0.11) in CC, 0.35 and 0.46 (0.40 ± 0.03) in CST, and 0.39 and 0.52 (0.46 ± 0.04) in SLF. The corresponding MD values (×10−3 mm2 /s) were 0.70–1.20 (0.89 ± 0.14) in CC, 0.65–0.73 (0.68 ± 0.02) in CST, and 0.62–0.75 (0.69 ± 0.03) in SLF.

3.2. Effect of smoothing on perfectly registered (“Reference”) values and on normalized images Fig. 2 shows—to save the space, for two lesion sizes only, that is, 50-voxel lesions in top panels and 200-voxel lesions in bottom panels—the effects of smoothing on the estimated lesion size (vertical axis) and the estimated intensity changes (numbers along the lines). The data are given for FA and MD lesions in CST, separately for 30% and 75% changes in Subject 5; the results of other subjects were similar. In general, filtering decreased the estimated intensity changes. The few negative (< 0%) changes in FA images refer to increased values instead of the applied intensity reductions (and vice versa in MD images). For 50-voxel lesions (top panel), the 30% intensity changes in FA images were almost unchanged in a few voxels but in the majority of the voxels the intensity changes decreased by 0–15%. With the corresponding 75% intensity changes, filtering decreased the values in the majority of voxels by 15–30%, and in a few voxels by 30–45%. For the 200-voxel lesions, the effects of filtering were about the same for 30% intensity changes and were closest (45–60%) to the simulated values only with the intensity change of 75%. Similarly as in FA images, small voxel intensity changes dominated the estimates in MD images (two right panels), and higher intensity changes (> 45%) were also present with the 200-voxellesion. The smoothed images were closest to the non-filtered values

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Fractional anisotropy

50

30

381

Mean diffusivity

Original intensity change 75% 30%

30%

75%

45

45

45 30

40

30

30

15

15 15

Number of voxels

20 10 0 200

15

0

0

0

0 60

45

60

30

30

45

45

160

30 15

120 15 30

80 0

40 0

15 0

4

6

8

Intensity change after smoothing

30

10

4

6

8

15

0

10

4

6

8

10

4

6

8

0

10

Filter FWHM (mm) Fig. 2. The effect of smoothing on original voxel values in FA (two left columns) and MD (two right columns) images. The contour lines show the number of voxels and their intensity changes (marked as numbers within the lines) after filtering with 4 mm, 6 mm, 8 mm, and 10 mm (FWHM) Gaussian filters. As an example, simulated intensity changes of 30% and 75% are shown for lesion sizes of 50 (top row) and 200 (bottom row) voxels in CST: results from Subject 5.

for the 200-voxel lesions, where the largest part of voxels almost reached the desired decrease level with 4 mm filter. Fig. 3 shows that the estimated lesion size increased with larger filter widths (“Reference values” in top panels). The lesion size was strongly overestimated with large FWHMs, even up to 10 times the original size (for 50-voxel lesions with 100% intensity changes at the largest 10 mm FWHM). The overestimation was most prominent for high-intensity changes and wide smoothing filters, and it was somewhat larger for MD than FA images. Underestimation was rare and mainly occurred for the smallest intensity changes.

3.3. The effect of spatial normalization and smoothing Lesion size. Middle panels of Fig. 3 show that the estimated lesion sizes increased as a function of filter FWHM, similarly as for the reference values in perfectly registered images, as discussed above. Lesion detection. Fig. 3 also shows that the detection thresholds for finding lesions were similar for reference values (top panels) vs. normalized and smoothed data (middle panels). Only the smallest lesion sizes and filter settings differed: normalized and smoothed lesions were not found with lesions ≤ 25 voxels and 4- or 6 mm filters, although they were visible in the reference experiment. Detection of lesions varied between the brain areas similarly as with reference values; lesions were found approximately similarly in SLF and CST, but clearly worse in CC. Fig. 4 shows a detected CC lesion in spatially normalized and smoothed FA and MD images (intensity change 50%, original lesion 200 voxels): the estimated lesion size in FA images was 101% (of the true size) with 4 mm smoothing, and 45% with 10 mm smoothing; the corresponding values in MD images were 3% and 19%, respectively. The lesions were found better in FA than MD images. FWE correction. False positive findings were absent even with our lenient statistical threshold of p < 0.001. With FWE correction,

only lesions ≥ 200 voxels and intensity changes ≥ 30% were reliably detected. From lesions of 50 to 100 voxels, only those with 75% and/or 100% intensity changes were found.

3.4. Realistic comparison between two subject groups Lesion detection and size. When images of a group of 10 subjects with inserted lesions were compared with another group of 10 “healthy” subjects, VBA detected the lesions worse than predicted from the two experiments above. The differences were most prominent for small (≤ 25 voxels, intensity change ≤ 30%) lesions that were sometimes found in the above experiments, but now always remained undetected. For example in CST, the smallest intensity changes of 10% were mostly missing in the graphs, and with FA in 50-voxel lesion, only the largest intensities ≥ 75% were systematically detected. The estimated size increased as a function of filter FWHM similarly as with earlier experiments. Lesions with large intensity changes of 75–100% were typically over-estimated in size, whereas small lesions with ≤ 30% intensity changes were underestimated. With FWE correction, the lesion sizes were typically 1–46% of the original size. Fig. 5 shows the detection thresholds for lesion intensity changes at p < 0.001. The lesions were found better (i.e. at lower detection thresholds) in MD than FA images. The 25-voxel lesions, mostly invisible in FA images, were found in MD images in SLF and CST; in CST, even the 10-voxel lesions were found with filter values of 8 and 10 mm (these values can be compared with Fig. 3, bottom panels). Again, lesions in CC were the hardest to detect. Wider filters lowered the detection thresholds for FA images, but in MD images, the opposite sometimes occurred (Fig. 5; right panels). In FA images, the lesions of ≥ 200 voxels were found most robustly, already at intensity changes of 10–30%, whereas for 50–100-voxel lesions the intensity change had to be larger, from

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Fig. 4. The effect of normalization and smoothing on the detection of the CC lesions in FA (left panels) and MD (right panels) images. Images of Subject 11 (statistical threshold p < 0.001, intensity change 50%, true lesion size of 264 voxels instead of 200 voxels since images were resampled during normalization into 2 mm × 2 mm × 2 mm voxel size) are shown in coronal (top panels) and axial view (bottom panels). Red colour indicates the detected lesion with 4 mm smoothing, yellow with 10 mm smoothing, and orange the overlap of these.

Fig. 3. The effect of smoothing on lesions sizes: the estimated lesion sizes (percentage of the original lesion size) as a function of intensity change in FA (left column) and MD (right column) images at different filter values (no filtering, 4 mm, 6 mm, 8 mm, and 10 mm). The results for reference values with optimally registered images (top panels), the effect of spatial normalization and smoothing (middle panels), and realistic group comparison (bottom panels). The true lesion sizes of 50 and 200 voxels in CST are indicated at the top-right corners of the panels.

Fig. 5. Examples of the detection thresholds for lesions: the smallest actual intensity changes for FA (left panels) and MD (right panels) with which lesions were found as a function of lesion size in realistic group study. Different filter widths (no filtering, 4 mm, 6 mm, 8 mm, and 10 mm) are shown in each brain area (SLF, CST, CC).

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Fig. 7. Example of statistical results for SLF and CST lesions in FA and MD images (true lesion size originally 200 voxels, intensity change 30%, smoothing 8 mm). The colours depict two statistical thresholds. Yellow: p < 0.001 with extent threshold of 10 voxels. Orange: p < 0.05 with FWE correction.

Fig. 6. Example of results obtained in SLF with statistical threshold p < 0.001 and extent threshold 10 voxels (true lesion size originally 200 voxels, intensity change 30%, smoothing 8 mm). Five largest clusters: (A) and (B) are false findings in anterior corona radiata, (C) is the correct finding in superior longitudinal fasciculus, and (D) is a false finding in inferior longitudinal fasciculus. (E) The number of false positives as a function of filter FWHM in FA and MD images. Two extent thresholds, k = 0 (no threshold) and k = 10 were applied.

50 to even 75%. In CC, wider smoothing (8–10 mm) was required for detecting 30%-intensity changes. In MD images (SLF and CST), already 100-voxel lesion was found reliably with intensity change of 30%, and 50-voxel lesions with intensity changes of 30–50%. In CC, however, only 200-voxel lesions were detected with intensity changes of 30–50% (smoothing 4–8 mm). False positive findings, smoothing, and correction for multiple comparisons. Some false positive findings were easily identified, such as those partially outside of the brain. However, false positives were also present in plausible locations, and some of them were larger in size than the correct findings. Fig. 6 shows an example of statistical results in SLF (extent threshold 10 voxels, original lesion 200 voxels, intensity change 30%, smoothing 8 mm). The five largest clusters are illustrated: one

is real (C) and four (A, B and D) are false positives. With these settings, altogether 13 false positives appeared (among the 1 real finding), with extents of 13–238 voxels. Filtering affected also the size of the false positives that ranged from 6 (no filtering) to 349 (10 mm filtering) voxels. The brain areas of the false positives were realistic, located in anterior corona radiata (A and B), and inferior longitudinal fasciculus (D). The true finding (C) was the 4th largest in statistical significance (p < 0.0001) and extent. Smoothing effectively decreased high-frequency noise in the statistical parameter maps: the number of false positive findings decreased from 107 to 22 in FA, and from 104 to 10 in MD images for 0 mm to 10 mm smoothing without extent threshold (k = 0); see Fig. 6E. When the extent threshold k was applied as well, for example k = 10, as we used, the number of false positives decreased to 5–11 in FA and 3–4 in MD. The increase of filter width improved the detection sensitivity only marginally since false positives of similar statistical significance and extent then appeared. FWE correction effectively decreased false positives but thereafter only lesions with large sizes and intensity changes remained: in FA images, ≥ 200-voxel lesions with intensity changes of 75%, and ≥ 300 with intensity changes of 50%. Lesions in MD images survived better the FWE correction: ≥ 200-voxel lesions with intensity changes of 30% were found in CST and SLF. No CC lesions survived FWE correction. Fig. 7 shows an example of statistical maps in CST and SLF for p < 0.001, extent threshold 10 voxels (yellow colour) and for p < 0.05 (FWE corrected; orange colour). The lesions (when found) were within the true lesion area. Smoothing sometimes changed the peak coordinates by a few millimetres (maximum 4.7 mm within the same lesions with different filter settings). With wide smoothing and large lesions, the lesion sizes were sometimes overestimated and lesions extended to the surrounding structures.

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4. Discussion We simulated lesions on FA and MD images to find out what kind of lesions can, in principle, be found with the widely used voxelbased analysis. The parameters of interest were the lesion extent (10–400 voxels) and the change in voxel intensity (10–100%). Although the lesion sizes differ from subject to subject in any real group analysis, we by purpose positioned lesions of the same size to each subject’s images to decrease inter-subject variance and thereby to assess the sensitivity of the method itself. Positioning the lesions directly on FA and MD maps allowed us to scrutinize the analysis chain from DTI parameter maps (FA, MD) to statistical maps. The computation of the parameter maps from DW images was intentionally left outside of this study. We proceeded from the best-case scenario for detecting lesions of different extents and intensity changes in the presence of perfect spatial registration to a realistic simulated group comparison. 4.1. Lesion detection thresholds Altogether, in the best-case scenario, performed in the absence of preprocessing effects, non-filtered lesions with intensity changes ≥ 30% and extents of 10 voxels were found reliably in all studied brain areas. For spatially normalized and smoothed lesion images, the thresholds for detecting lesions were similar, but the smallest lesions of 10 and 25 voxels typically remained undetected. Moreover, in the realistic simulated group comparison, containing both preprocessing effects and inter-subject variation, the detection thresholds were again higher and it was difficult to detect small lesions. Generally, it was not possible to detect lesions with intensity changes of 10–50% if the lesion was smaller than 50 voxels. More precisely, for FA images, ≥ 200-voxel lesions were required for detection with intensity changes of 10–30%; wider smoothing kernels (8 or 10 mm) were required in CC to detect the 30% changes. In MD images, the corresponding detection thresholds were ≥ 100 voxels for SLF and CST at intensity changes of 30%, and ≥ 200 voxels for CC at intensity changes of 30–50% (smoothing with 4- or 6 mm kernel). With such high detection thresholds, DTI-VBA does not outperform the visual inspection of lesion images. We expected the sufficient intensity reduction/increase for lesion detection to be 5–20%. However, on the basis of our pilot analysis, we had to extend this range up to 100% since we failed to detect some lesions with the smaller intensity reductions; in some brain areas (mainly corpus callosum) and parameter settings, the detection thresholds were far higher than our preliminary assumption. Although the most drastic intensity changes are realistic only with e.g. ischemic changes or tumors, and although VBA would be an inadequate analysis method in such studies, we applied these values to find out how high the detection thresholds can raise. VBA-DTI application articles typically do not report the percentage changes, nor actual FA or MD values, but only the statistical significance levels for group-level differences. 4.2. Reliability of results Generally, the locations of all detected lesions were accurate. However, small lesions were especially challenging as they sometimes disappeared (in statistical sense) after normalization and smoothing steps, in part, because the lesions of different subjects did not perfectly overlap. Smoothing increased the inter-subject overlap but did not improve the results for small lesions. Moreover, the probability for false positives was higher for small than large lesions. Although FWE correction improved the specificity of the analysis, it was far too conservative for our small sample size: detection threshold increased to 200 voxels and to intensity change of 75% (FA) and 30% (MD). Thus as an alternative to FWE, the

reliability of the results could be improved by applying an extent threshold of 50–100 voxels. Due to the low sensitivity (and small sample size), we used uncorrected statistical significance level (p < 0.01). In practical SPM analysis of brain imaging data, statistical height threshold typically works best for detecting sharp foci whereas methods considering spatial extent are better for extended regions (Friston et al., 1994; Worsley et al., 1996). However, with VBA, the statistics based on cluster sizes is invalid due to non-stationarity of residuals and thus only height threshold should be used (Ashburner and Friston, 2000). Thus, in practice, the general linear model is not optimal for some brain regions. Instead, the data may contain e.g. trends or non-linearities arising from the true neuroanatomical variability or from artifacts; the trends and non-linearities should be taken into account in the model as well. The estimated lesion sizes were often very inaccurate. Sizes of small lesions were typically underestimated and FWE even accentuated the results, whereas large lesions were strongly overestimated, especially with wide smoothing, even up to ten times the original size (for 50-voxel lesions with 100% intensity change at the largest 10 mm FWHM; figure not shown). In such cases, the lesions sometimes extended to adjacent brain structures. Accurate size estimate may be important in real lesion studies that aim to determine crucial brain areas necessary for certain normal functions by correlating damages in anatomical structures with abnormal functions (Mehta et al., 2003). In addition to non-stationarity of residuals, bias in cluster size can also be due to variance of smoothness (Poline et al., 1995). Smoothness, usually due to filtering, describes the spatial correlation of voxels and is typically estimated from the data and further used in computing the statistical significance levels. Poline et al. (1995) reported a variability of 20% in p-values (for p-values around 0.05) due to variability of smoothness, which would affect directly the estimated sizes, specifically when statistical inference is based on height thresholds.

4.3. The effect of smoothing During smoothing, new voxel values are calculated as a weighted average of the current and the neighbouring voxel values. The filter FWHM defines how strongly distant voxels contribute to the values, and the properties of the surrounding tissues can thereby greatly affect the smoothed values. The gray matter has low, and the white matter moderate-to-high FA values, whereas mean diffusivities are approximately the same in both tissue types. On the other hand, low FA and high MD in cerebrospinal fluid can confuse the analysis in brain areas nearby. Smoothing and gray matter contamination of lesion values is a likely reason for our observation of different optimal filter widths for FA (8 and 10 mm) and MD (4 and 6 mm). With wider filters, low FA values of the surrounding gray matter degrade the voxel values in lesions with FA decrease, thus improving the detection sensitivity, whereas for lesions with MD increases, the equal MD values of the surrounding gray matter do not affect the result. After smoothing, the intensity changes (Fig. 2) were smaller than in the original, non-filtered lesions, and FA sometimes even increased instead of decreased (and vice versa in MD images). The original values were retained best for large lesions where many voxels within the lesion remained unaffected by out-of-lesion values during smoothing. A generally optimal filter width (FWHM) remained unsolved in this study, and we emphasize the importance of analysing the non-filtered images as well. Although smoothing improves detection sensitivity for lesions of the size of the smoothing kernels, our results suggest that the contribution of surrounding tissues has to be considered as well. Anisotropic smoothing may overcome this

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problem, as it can preserve better the original FA values (Van Hecke et al., 2010). 4.4. Differences between the brain areas The CST lesions were found the best, SLF lesions slightly worse, and CC lesions were always the hardest to find. This difference between brain areas can have several reasons. First, the CC lesions had the largest inter-subject variability of FA and MD values, probably due to the nearby CSF; DTI of CC and other brain structures adjacent to CSF is known to be challenging with ordinary DTI sequences without utilizing fluid-attenuation inversion recovery (FLAIR) since the partial volume effect can reduce the volume of the structure, lower the anisotropy, and increase the mean diffusivity (Chou et al., 2005; Concha et al., 2005; Papadakis et al., 2002). Moreover, in spatial normalization and smoothing, the surrounding CSF may have affected more strongly the values in the small-sized CC than in the other two brain areas. Second, the small registration errors during spatial normalization have likely had more prominent role in CC than in the two other areas because of the sharp transition boundaries in FA and MD values. Finally, the requirement of Gaussianity of residuals may not be fulfilled in CC (Jones et al., 2005), thus decreasing the power of the parametric t-test. Earlier, also in VBA of anatomical MR images, detection sensitivity was found spatially heterogeneous (Mehta et al., 2003). 4.5. Comparison with earlier studies Compared with an earlier simulation study (Van Hecke et al., 2010), larger lesions (in size and intensity change) were required in our study for reliable detection. Our thresholds for robust detection of FA lesions were about 30% for intensity changes and 200 voxels for size whereas Van Hecke et al. (2010) found lesions with intensity changes of 7–22%. The main reason for the difference seems to be the applied analysis chain: we used a conventional VBA with SPM2, trying to follow the mainstream of earlier DTI-VBA applications, whereas Van Hecke et al. (2010) exploited recently proposed methods, for example, anisotropic smoothing. Further differences existed in the applied statistical tests, in sample size, and simulations. Our simulations were positioned directly on FA and MD maps instead of DW images, and we employed FSL and SPM2 softwares instead of ExploreDTI. Moreover, our experiment, resembling a typical DTI study, employed 10 + 10 subjects whereas Van Hecke et al. (2010) had 20 + 20 subjects. However, the effect of sample size on current differences is hard to estimate: in principle, increasing the √ sample size from 10 to 20 increases the SNR by approximately 2, but of course any procedures increasing SNR improve the sensitivity of the analysis. Thus, the observed differences likely result from several factors affecting the detection sensitivity. Our results are well in line with earlier VBA evaluations using simulated lesions on anatomical MR images. Mehta et al. (2003) compared a single simulated lesion image and real patients with focal lesions (single-subject-wise) with a group (N = 18) of healthy subjects. With VBA, they detected all the simulated lesions and the size estimates were larger and more close to the correct lesion size than what happened with the real focal lesions in the patient group. However, for the real patient data, VBA finally had low sensitivity. Detection sensitivity was spatially heterogeneous and depended on preprocessing steps and parameters. Moreover, the spatial extents of the detected lesions were underestimated. Later on, Stamatakis and Tyler (2005) validated and improved the VBA of anatomical MR images using comparisons of a single simulated lesion image with a group (N = 32) control images. Lesion detection was optimal with 10 mm smoothing and statistical threshold of p < 0.001 (uncorrected). Small lesions (< 0.5 cm3 ) were problematic as they blended with background signals, specifically with larger

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smoothing kernels. Both these studies reported underestimation of detected lesion size, whereas we found mostly overestimation in DTI parameter images; this difference is most likely due to differences in methodologies and images (anatomical MRI vs. DTI). 4.6. Methodological improvements Besides anisotropic smoothing (Van Hecke et al., 2010), other methodological improvements have also been recently suggested for DTI-VBA. For example, realignment of diffusion gradient orientation (b-matrix) according to motion-correction parameters helps to avoid errors in diffusion measures and fiber orientation (Leemans and Jones, 2009), and improved coregistration methods lead to more reliable statistical results (Sage et al., 2009). Moreover, tractbased spatial statistics (TBSS) (Smith et al., 2006, 2007), as a novel DTI-VBA technique, has improved the registration of the tracts in individual FA images without a need for smoothing. We intentionally left TBSS outside of our study with the aim to focus on filter effects and detection threshold of conventional VBA, to be able to compare our results with already published studies. Further studies are needed to search for the most suitable methods for group-level analysis of DTI images. As far as we know, the full analysis chain from diffusion-weighted images to parameter maps (e.g. FA and MD) has not been studied yet although different numerical methods can be applied in tensor calculations, for example to assure the positive semi-definite nature of the tensor. In addition, spatial normalization methods in DTI should be studied and optimised. In conclusion, we found that VBA preprocessing steps affect considerably the outcome of the analysis, even to such an extent that we failed to detect some lesions. The detection thresholds varied between the brain areas, and they were different for MD and FA images. Spatial smoothing had a very strong effect on both detection thresholds and estimated lesions sizes. In addition to preprocessing, inter-subject variation in lesion area affected the detection sensitivity. Consequently, the impact of preprocessing steps should be considered when interpreting the VBA results. Smoothing and extent threshold can be used for reducing the number of false positives, as FWE correction may be too conservative, especially for small group sizes. The present study provides insight into intensity changes and lesion sizes that can be found with conventional DTI-VBA. The decreased contrast between lesions and normal-appearing tissue in various brain pathologies may render the detection of real lesions even more challenging. Acknowledgements This study was financially supported by the Instrumentarium Foundation (JH), Academy of Finland (National Centers of Excellence Program 2006–2011), Louis-Jeantet Foundation (Switzerland), Jenny and Antti Wihuri Foundation (Finland), and aivoAALTO research project of the Aalto University. We gratefully acknowledge the DTI sequence and code from Drs Roland Bammer, Michael Moseley and Gary Glover, supported by the NIH NCRR grant “Stanford Center for Advanced Magnetic Resonance Technology”, P41 RR09784 (PI: G. Glover). References Ashburner, J., Friston, K.J., 2000. Voxel-based morphometry—the methods. Neuroimage 11, 805–821. Ashburner, J., Friston, K.J., 2001. Why voxel-based morphometry should be used. Neuroimage 14, 1238–1243. Assaf, Y., Pasternak, O., 2008. Diffusion tensor imaging (DTI)-based white matter mapping in brain research: a review. J. Mol. Neurosci. 34, 51–61. Basser, P.J., Mattiello, J., LeBihan, D., 1994. MR diffusion tensor spectroscopy and imaging. Biophys. J. 66, 259–267.

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