Synopsis - VBM relies heavily on an accurate registration process before comparing different volumes at a voxel level. Typically, linear registration is used to conform all brains to the same shape, orientation and size. We have used non-linear registration of subjects to the average of their respective grouping to reduce normal, anatomical inter-subject variability and at the same time increase differences between groups. Results demonstrate (A) an increase in statistically significant voxels and (B) that a smaller smoothing kernel can be used to achieve the same statistical significance with improved spatial localization.
Abbreviations used - CSF (cerebro-spinal fluid), GLM (generalized linear model), GM (grey matter), HC (hippocampus), HA (HC atrophy), IGK (isotropic gaussian kernel), NC (normal controls), NL (non-linear), TLE (temporal lobe epilepsy), VBM (voxel-based morphometry), WM (white matter) 

Background – VBM consists in the statistical analysis of GLM results performed on a voxel-by-voxel basis on combined cohorts of co-registered subject data. Typically, linear registration is used to conform all brains to the same shape, orientation and size. Differences induced by mis-registration will result in added noise to the statistical results. One such source of noise is the presence of normal, anatomical variability in cortical and sub-cortical brain structures. While this forms the basis of some VBM anatomical analyses, it is undesirable in cases where the goal is to highlight pathologically-induced differences between populations. We hypothesise that intra-class inter-individual variability can be reduced by relying on NL registration prior to GLM. By reducing this important noise component a trade-off could be realized with smaller smoothing kernel size. Compared to a standard approach such as SPM99 [1], the VBM methodology proposed here includes some additional steps.

Methods – We studied 93 patients with medically intractable TLE (49 left HA and 44 right HA) and 51 NC. HC volumetric measurement was performed in all subjects. All patients had unilateral HA on the side of the seizure focus as determined by a comprehensive clinical and EEG evaluation including video-EEG telemetry. 
1)	Acquisition and Pre-processing: volumetric data consisted of T1-weighted MRI acquired on a 1.5 T scanner using a T1-fast field echo sequence (TR=18, TE=10, 1 acquisition average pulse sequence, flip angle=30o, matrix size=256x256, FOV=256, thickness=1mm). Intensity non-uniformity was corrected [2] and grey-level intensities were normalized to a common scale across subjects. 
2)	Linear registration: a 9 degrees of freedom rigid registration was used for global alignment [3]. The reference image was an average of 152 normal subjects in Talairach space taken from the ICBM study [4].
3)	NL registration. As we wished to investigate pathological differences between populations, we constructed an average for each sub-population under investigation (left HA, right HA, NC) from their linearly registered volumes. NL registration [5]  was then used to warp each subject to its population average. 
4)	Concentration map creation. An artificial neural net classifier [6] was used to separate the volume into GM, WM and CSF tissue components. Concentration maps were then smoothed using an IGK of specified kernel size (10, 5mm full width half maximum). 
5)	General Linear Model. Student's t-test statistical maps were derived from analysis of the concentration maps between populations using a locally developed GLM routine. Thresholds for statistical significance were calculated [7] and include correction for multiple comparisons.

L    : 10 mm

NL : 10 mm

NL :   5 mm

					
Fig. 1	Fig. 2	Fig. 3	Fig. 4	Fig. 5	

Fig. 1 - t-statistics map (thresholded for significance, P<0.05) of GM reduction in linearly registered patients with left TLE vs. NC, 10mm smoothing.  Fig. 2 – sagittal view of Fig. 1, centered on medial temporal lobe. Fig. 3 - t-statistics map (same significance threshold as Fig. 1,2) of GM reduction in NL patients with left TLE vs. NC, same view as Fig. 2.  Fig. 4 - t-statistics map (thresholded for significance, P<0.05) of GM reduction in NL patients with left TLE vs. NC, 5mm smoothing. Notice bilateral result as opposed Fig. 1. Fig. 5 - Joint histogram of significant voxels from linear (10mm), NL (10mm) and NL (5mm) registered data for the same subjects as before, showing increase in mean levels as well as absolute voxel counts. 

Results and Discussion - NL registration improves VBM results in two ways. (A) For equal input parameters and thus identical thresholds of statistical significance, more voxels emerge, with higher mean values. A t-statistic map using linear registration is shown in Fig. 1 and 2, and using the new methodology based on NL registration in Fig. 3. The histogram in Fig. 5 demonstrates the increase in absolute number of significant voxels and mean significance level. (B) VBM has been used in previous studies [8, 9], focusing on GM concentration maps with large IGK. The kernel size should be comparable to the spatial extent of the expected regional differences between the groups [1]. In the case of TLE, the largest atrophy is typically measured in the HC and thus has a radius of  ~5mm. With a smaller kernel value (5mm), NL noticeably improves VBM results. Bilateral reduction in GM is demonstrated in Fig. 4, as well as an increase in absolute number of significant voxel and mean significance levels (Fig. 5). Finally, it should be noted that NL techniques are usually accurate where topology is maintained, which is the case for sub-cortical structures. Interpretation of VBM results should be made knowing that present non-linear registration techniques cannot account for non-equivalent cortical topology.

Conclusion – When used in the manner described above, NL registration improves VBM by reducing the amount of normal intra-class anatomical variability and thus increases the difference between populations.
References 
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