Data Analysis

Data analysis was undertaken using the XBAM software package written and maintained by the Institute of Psychiatry at King’s College London, UK

(http://brainmap.it). It was conceived by Ed Bullmore and Michael Brammer in 1995 with the aim of writing “an fMRI analysis package with the minimum possible

number of assumptions” because testing for activation at thousands of different points in the brain required rigorous methods. The standard methods at the time involved either correlational analysis between the experimental design and the time series at each voxel (volumetric pixels), or t-statistics using means and variance. Both these approaches assume normal theory approximations, which have not being established in large samples of fMRI data. These types of analyses are typical of the more commonly used fMRI analysis software packages such as SPM

(http://www.fil.ion.ucl.ac.uk/spm/), which are more sensitive than non-parametric approaches such as XBAM but also more prone to false positives. SPM is probably the most widely used functional neuroimaging analysis package and the default analysis settings are usually appropriate for analysing functional data from healthy control groups. XBAM analysis differs significantly from SPM analysis by not assuming normality of activation data and consequently implements permutation testing to construct the null distribution to make inference about the probability of activation under the null hypothesis. A recent large fMRI study (81 subjects) investigated the assumption of normality in fMRI analysis and found substantial departure in 22% of voxels; this was improved to 9% using the standardized statistics adopted by XBAM (Thirion et al., 2007). Based on their findings the authors

recommended the use of cluster level statistics, robust and permutation-based testing rather than normal theory based inference, strategies already adopted by XBAM.

Median statistics are used in XBAM rather than means in order to control for outlier effects. XBAM analysis adopts a two-level approach to data analysis in which the response sizes computed from the model fit for each individual are standardised with respect to their variances before embarking on the second, multi-subject, phase of analysis. This permits mixed-effects analyses of group level fMRI data by taking into

account both intra and inter subject variances. Mixed-effects analysis allows

generalisation of findings from the participant population to the sampled population (Brammer et al., 1997). Wavelet-based time series permutation is used to control for the noise in fMRI data (Bullmore et al., 2001; Bullmore et al., 1999). XBAM uses 3-dimentional cluster-level statistics based on cluster mass (the sum of all statistical values from all the voxels in the cluster) for activation thresholding and the typical statistical threshold is therefore usually described as the probability value where less than one false cluster will be evident per volume. We next look in more detail at the implementation of the analysis at individual and group levels.

3.8.4.1 Individual analysis

To minimise motion related artefact, the data were first realigned by calculating a 3-dimensional volume template consisting of the average intensity at each voxel over the whole experiment and then realigning 3-dimensional image volume at each time point to this template by computing the combination of rotations (around the x, y, and z axes) and translations (in x, y and z) that maximised the correlation between the image intensities of the volume in question and the template (Bullmore et al., 1999).

The data were then smoothed using a Gaussian filter (full width at half maximum of 5 mm) to improve signal to noise characteristics of the images. This resulting value for each voxel is the weighted average of all the neighbouring voxels with the average more weighted towards the central voxel. Responses to the experimental paradigms were then detected by time-series analysis using Gamma variate functions (peak responses at 4 and 8 sec) to model the BOLD response. The analysis was

implemented as follows. First, each experimental condition was convolved separately with the 4 and 8 second Poisson functions to yield two models of the expected

haemodynamic response to that condition. The weighted sum of these two

convolutions that gave the best fit to the time series at each voxel was then computed.

This weighted sum effectively allows voxel-wise variability in time to peak haemodynamic response. In order to constrain the possible range of fits

physiologically plausible BOLD responses, a constrained fitting procedure was used (Friman et al., 2003). Following this fitting operation, a goodness of fit statistic was computed at each voxel. This was the ratio of the sum of squares of deviations from the mean intensity value due to the model (fitted time series) divided by the sum of squares due to the residuals (original time series minus model time series). This statistic is called the SSQratio. The percentage BOLD signal change at each voxel was also calculated. This was: ((fitmax – fitmin)/mean signal intensity) * 100, where fitmax and fitmin were the maximum and minimum values of the fitted response for the time series in question.

In order to sample the distribution of SSQratio under the null hypothesis that observed values of SSQratio were not determined by experimental design (with minimal assumptions), the time series at each voxel was permuted using a wavelet-based resampling method (Breakspear et al., 2003; Bullmore et al., 2001). This process was repeated 20 times at each voxel and the data combined over all voxels, resulting in 20 permuted parametric maps of SSQratio at each plane for each subject.

The same permutation strategy was applied at each voxel to preserve spatial

correlational structure in the data during randomisation. Combining the randomised data over all voxels yields the distribution of SSQratio under the null hypothesis. A test that any given voxel is activated at any required type I error can then be carried out by obtaining the appropriate critical value of SSQratio from the null distribution.

For example, SSQratio values in the observed data lying above the 99^th percentile of

the null distribution have a probability under the null hypothesis of <=0.01. This permutation method gives very good type I error control with minimal distributional assumptions (Breakspear et al., 2003; Bullmore et al., 2001).

3.8.4.2 Group mapping

In order to extend inference to the group level, the observed and randomised SSQratio maps were transformed into the standard space. This involved a two stage process requiring first a rigid body transformation of the fMRI data into a high-resolution gradient echo image of the same subject followed by an affine transformation on to a structural template (Brammer et al., 1997). By applying the two spatial

transformations computed above for each subject to the statistic maps obtained by analysing the observed and wavelet-randomised data, a generic brain activation map could be produced for each experimental condition. The median observed SSQratio over all subjects at each voxel (median values were used to minimise outlier effects) can then be tested at each intracerebral voxel in standard space against a critical value of the permutation distribution for median SSQratio ascertained from the spatially transformed wavelet-permuted data (Brammer et al., 1997). The standard space used for analyses in this study was that of Talairach (Talairach, 1988). In order to increase sensitivity and reduce the multiple comparison problem encountered in fMRI,

hypothesis testing was carried out at the cluster level using a method shown to give excellent cluster-wise type I error control in functional fMRI analysis (Bullmore et al., 1999). When applied to fMRI data, this method estimates the probability of

occurrence of clusters under the null hypothesis using the distribution of median SSQratio computed from spatially transformed data obtained from wavelet

permutation of the time series at each voxel. Image-wise expectation of the number

of false positive clusters under the null hypothesis is set for each analysis at <1.

Consequently, correction for multiple comparisons was not required, as thresholds were set on an image-wide basis, not a voxel-wise basis.

3.8.4.3 Group differences

For group comparisons, analysis of variance was carried out on the SSQratio maps in standard space by first computing the difference in median SSQratio between groups at each voxel. Subsequent inference of the probability of this difference under the null hypothesis was made by reference to the null distribution obtained by repeated

random permutation of group membership and recomputation of the difference in median SSQratios between the two groups obtained from the resampling process. As with the generic brain activation maps, cluster-level maps were then obtained with the cluster-wise probability equivalent to less than one false positive cluster per image.

3.8.4.4 Correlation analysis

Correlational analysis can be performed between the BOLD effect data for each individual and behavioural data. To implement this, the Pearson product-moment correlation coefficient (r) between the observed behavioural and BOLD effect data is first calculated, followed by calculation of the null distribution of correlation

coefficients by permuting the BOLD data at each voxel many times (a minimum of 50) and combining the data over all voxels. Thresholded voxel and cluster level maps where r is significant can then be computed at any desired level of expected voxel or cluster-level type I error.

Correlations between activation data and behavioural data can also be

examined by extracting the peak SSQ value for each participant from the coordinates of the most activated voxel in a cluster of difference. Spearman’s correlation

coefficients are then calculated due to the relatively small sample sizes and non-normally distributed data. Values deviating more then 2 standard deviations from the mean are excluded.

3.8.4.5 Interaction analysis

Interaction effects are tested for in factorial design studies where two (or more) groups (i.e. controls and patients) perform a single task at two time points (baseline and follow-up). The analysis is implemented by constructing a design matrix coding for the non-repeated group factor, the repeated condition factor and the interaction, which is the product of the first two factors. The interaction column tests for regions where the effect of one factor is modulated by the status of the other. If there is no interaction between group and condition, supporting the null-hypothesis, then plotting mean data for the groups and conditions will reveal parallel lines between the two time points. Conversely, if an interaction is present then the lines will deviate.

Interpreting interactions therefore requires plots of activation data to be examined along with interaction maps.

3.4.8.6 Local permutation

For group comparisons of functional data we used an advanced method compared to our earliest reports. This method became available during the course of this study. It was designed to be more sensitive in brain areas where there is relatively smaller

signal change. It entailed a different method of random permutation, which is the process of generating a null distribution by repeated random sampling of the observed data at all, time points. This local permutation involved calculating a voxel-specific critical threshold as opposed to a critical threshold calculated from all voxels in the volume studied (global permutation). With global permutation, statistics from each voxel from the observed data is compared against a single threshold of significance used across the brain, which is taken from the null distribution of F-statistics calculated from all voxels over all randomisations. Therefore, voxel statistics from areas with large signal change enter into the global distribution and increase the significance threshold across the brain, decreasing detection in areas with smaller signal change. The magnitude of differences at thousands of spatially removed voxels therefore determines the significance at any one voxel. At a voxel threshold of e.g.

0.05 the value of the test statistic at that percentile (95^th) of the null distribution is calculated and any voxel with a test statistic larger than the critical value is identified as significant. Global permutation therefore assumes uniform voxel statistic

magnitudes across the brain, an assumption that has not been established and is unlikely to hold in disease states such as AD. With local permutation a voxel-specific threshold is calculated and significance at each voxel is assessed against its own null distribution. This voxel-specific threshold is therefore not contaminated by statistics from other brain areas. Cluster level significance testing was still done against a null distribution of cluster mass generated from supra threshold voxel statistics across the brain as a local test of cluster mass is not available yet. However, the cluster level null distribution now included statistics from voxels that would otherwise not have

contributed due to their comparatively smaller task related signal change.

3.4.8.7 UNIX analysis

Anonymised data were transferred to the UNIX computer system at the Institute of Psychiatry at King’s College London. Each experiment was assigned a unique identifier. Corrupted data files were removed and raw experimental data were archived. A specific data file containing information about the experimental conditions was created for each experiment; these are known as infiles for block-designed experiments and as newstarts for event related designs. Table 4 shows the infile data for the encoding task, and how it corresponds to the experimental condition and stimuli for the task. Experiments were processed in batches using server clusters.

Most of the analyses were carried out remotely via the Internet, using Secure Shell Host and Hummingbird Exceed software. Each analysis step produces a log file and each of these were examined to ensure that the analysis ran as planned.

Infile data Condition Stimulus 1 Experimental flag 1 Experimental cross 1 Experimental pole 1 Experimental symbol 1 Experimental stars 1 Experimental stripes 1 Experimental march 1 Experimental England 0 Control wait 0 Control wait 0 Control wait 0 Control wait 1 Experimental cabin 1 Experimental scout 1 Experimental summer 1 Experimental pack 1 Experimental lake 1 Experimental trail 1 Experimental canvas 1 Experimental holiday

Table 4. Infile data for experimental analysis.

The data in the Infile data column informs the analysis procedure by indicating if the volume acquired represents the experimental or control condition. In this example from the encoding paradigm, it can be seen that the experimental condition is coded with the digit 1, and this corresponds to the presentation of different English nouns.

The repeated presentation of the word “wait” comprises the control condition that is coded with the digit 0.

3.4.8.8 Identifying areas of activation

Brain areas where task related activation or group differences occurred were identified by their coordinates and cluster size using the Talairach atlas (Talairach, 1988). Clusters containing less than 10 voxels were ignored. Brain areas containing a cluster and surrounding areas up to 10 mm away were included in identified areas.

Clusters were followed in all three spatial dimensions in order to identify all relevant brain areas. Figure 8 shows the Talairach z-coordinates for axial images from the Talairach template used in XBAM; it has 25 slices with a 5.5mm gap between slices.

Figure 8. Talairach template.

The map shows axial brain slices with corresponding Talairach atlas z-coordinates.

Slices with a negative z-value are located below the line that extends from the anterior commisure to the posterior commisure (AC_PC) that serves as an anatomical

landmark. Axial slices proceed from left to right, from the most caudal in the top left corner to the most rostral in the right bottom corner of the map. The left hemisphere appears on the right and vice-versa.