# SPM/VBM

< SPM

Voxel-Based Morphometry

## Criticisms of VBM

There are many criticisms that can be made of VBM. In particular, the accuracy of the spatial normalisation used by SPM is an issue that upsets many people. Spatial normalisation in SPM uses only about 1000 parameters, and only fits the overall brain shapes. It is unable to warp one brain so that it exactly matches another. In order to compensate for this inaccuracy, the data are smoothed, where the amount of smoothing should partially depend on the accuracy of the inter-subject registration. There are many ways of assessing the "accuracy" of spatial normalisation. One approach is to look at the amount of overlap among the different tissue classes. What this shows is that e.g. grey matter is matched with grey matter. It does not indicate that e.g. the various sulci of the different subjects are in alignment. For example, with a registration model that has too much freedom, a sulcus of one subject could be warped so that it appears to becomes a different sulcus of another subject. For the purpose of comparing brain images with mass-univariate statistics, the objective of spatial normalisation should not be about making the brains of different subjects appear identical, but should be about bringing homologous regions as closely into alignment as possible. There is indication that models with too much freedom can be worse than models with less freedom. For example, the evaluations of Hellier et al, whereby registration accuracy of different approaches are compared indicated that the spatial normalisation of SPM2 was as accurate as that of any of the other methods. The average distances between registered sulci were 9.9, 10.3, 11.5, 10.7 and 10.8mm for other methods. The average distance obtained by the simplistic approach in SPM2 was 8.7mm. Obviously, there is still plenty of scope for improvement, but for an almost fully automated approach, it does not do too badly. There are many inter-subject registration, and tissue segmentation programs out there. These can also be used for preprocessing if the functions within SPM are found wanting. In particular, surface based approaches may prove to be superior.

Another criticism is that shape is multivariate, so any kind of morphometry should be based on multivariate statistics, rather than mass-univariate tests. I (John Ashburner) largely agree with this. Unfortunately, the results of multivariate analyses can not be communicated quite so easily among the brain imaging community - especially if the results are limited to the 2D pictures required by papers. The community wants to localise a limited number of discrete volumetric differences (rather than have a full characterisation of the differences).

Another one is that different ways of doing an analysis give different results. The reason for this is that a different analysis is asking a different question, to which the answer is likely to be different. In particular, the choice of "global normalisation" method will dramatically change the resulting pattern of blobs. Note also that different preprocessing will also give different results. The most "accurate" preprocessing will give the most accurate interpretations of the results and the most sensitivity. Less accurate preprocessing will give less accurate interpretations. The fact that different registration or segmentation algorithms produce different results is exactly analagous to the fact that the use of different landmarks give different results for other kinds of morphometric analyses. Registration can never be perfect, so some spurious volumetric differences will be found. If one averages over larger regions (i.e. smoothes using a larger FWHM), then the effect of misregistration is reduced. It is therefore possible to be confident that any differences are really volumetric. If the arguments against VBM were taken seriously, then all manual volumetric analyses are wrong because structures can never be outlined with 100% accuracy.

The non-stationary residual variance from the t-tests is also a problem for interpreting results. This causes blobs to move towards brain regions with low residual variance, and away from regions with high residual variance; MASCOI may help with this problem. Many people see significant differences outside the brain because the residual variance approaches zero as one moves towards regions without any grey matter; this is one motivation for using some kind of mask (the other is to reduce the severity of the multiple-testing problem). Ask your local statistician for further explanations.

## Interpreting Results

The most general interpretation is that there is a significant difference in intensities in the preprocessed images in this region. The hard bit is to determine what may have caused these differences. The two possible explanations are:

1) The structure is smaller in one group than the other.

2) There is some other significant difference between the anatomies of the groups that shows up in the analysis in this region. There are loads of possibilities here.

Generally, we hope that the pre-processing has sensitised the tests to the first explanation, but other causes can never be discounted. e.g. one group has bigger ventricles, which will systematically influence spatial normalisation. Another possibility is that there is a contrast difference, and maybe the structure shows up better (and is therefore better segmented as grey matter) in one group rather than the other.

The t statistic is proportional to the difference between the groups, divided by the square root of the residual variability. If there is the same volumetric difference, but more variability in the grey matter, then the statstics in the grey matter will be less significant. There are also likely to be issues relating to estimated residual smoothness. If the residuals are more smooth, then the correction is less severe so the corrected stats are more significant.

The statistics are more sensitive further away from regions of greater variability. In VBM, this means a tendancy for the most significant difference to be shifted away from the centre of a structure.

The contrast images (con_*.img) that are estimated with VBM are the same as if you took the unsmoothed preprocessed data, made a difference image, and then smoothed this difference image. The initial difference is mostly at the edges, but is blurred (by the smoothing) so that it covers a larger region.

## "Modulation"

Spatial normalisation expands and contracts some brain regions. Modulation involves scaling by the amount of contraction, so that the total amount of grey matter in the modulated GM remains the same as it would be in the original images.

If you take the limiting case of extremely precise (not necessarily extremely accurate) registration and segmentation, the pre-processed concentration images are likely to be all identical. An analysis of these data would not show you anything. I therefore tend to interpret unmodulated data as a representation of registration error, rather than an attempt to preprocess the data in order to sensitise the t tests to more meaningful volumetric differences.

Shapes are multivariate. The volume of one structure is likely to be related to that of another. For example, smaller brains may have smaller putamen. If you include "globals" in the model by proportional scaling, then this could be accounted for. Similarly, the size of a putamen may, or may not, correlate with the size of surrounding structures. A modulated analysis attempts to correct the volumes for regional expansion/shrinkage during spatial normalisation. An unmodulated analysis would really be comparing volumes after scaling out the volume changes in neighbouring regions. The definition of a neighbouring region is vague, and is dependent on the precision of the spatial normalisation.

For example, consider that spatial normalisation is able to register only to the resolution of the temporal lobe, and everything in this brain region expands or contracts by roughly the same amount. If one group has hippocampi that are large w.r.t. the volume of the temporal lobe, then this procedure would be more sensitive to such differences. Unfortunately, it is not straightforward to say exactly what the scale of the spatial normalisation is, so the results of such an analysis are a little bit arbitrary.

## VBM in Practice

Basics

Start MATLAB, make sure SPM is in your path (e.g. run pathtool and add the SPM directory), and type spm pet to get the GUI up.

### Unified Segmentation in SPM5

Preliminaries

First ensure that your images are reasonably well aligned with the template: click Check Reg, go to the SPM5/templates/ directory and choose T1.nii then go to the directory with your dataset and select the images. If they are not approximately in registration, then you will need to use the Display button and then adjust the values (up, pitch, etc.) then click Reorient and reselect the image(s).

Segmentation

Clicking the Segment button will bring up a page of options; you must select your files (under Data), and you will probably want to change the Output Files options. Unless you have reason to do otherwise (these notes are meant for beginners!) select modulated normalised for the tissues that you are interested in, don't save bias corrected, and don't do cleanup. Leave all the Custom options as they are. You can now save the job (as a .mat file) if you want, and/or click Run to segment the images. As a very rough estimate, allow 30 minutes per image.

Smoothing

Click Smooth, select the images (Modulated normalised/Warped tissue Class images are prefixed with mwc), leave the data type option as same, and choose the smoothing width. This is a difficult decision... commonly used widths are 8 to 12 mm, you may have to experiment to decide what works best for your scans/subjects, though there is an argument that the kernel width should match the expected size of the difference for which you wish to search. Unless you have very good reasons to do otherwise enter the same number three times, since you normally wish to smooth equally in all directions (i.e. with an isotropic kernel).

Statistics

This is hard to give a short introduction to, since it very much depends on your experiment, but to give a very simple example of an unpaired two-group t-test: click Basic Models near the top-left of the GUI, then choose the two-sample t-test factorial design. Enter the scans, and enter any covariates that you want (e.g. age, Total Intracranial Volume, etc. See #Obtaining Covariates below). Now for masking... it's probably best, if this is your first attempt at VBM, to select absolute threshold masking and enter a value of 0.05. Rather like smoothing though, exactly what masking to use is a somewhat difficult decision. Set the output Directory where you want the results to be written. It's probably best to leave the other options alone on a first attempt, though maybe check the #Globals section below...

Click Run, check the design matrix that appears, and then click Estimate on the left, and choose the SPM.mat file in the directory you just chose for output. Then click Results, and choose this file again.

Now you need to worry about the general linear model contrasts, which can be quite a complicated area. For a simple unpaired two-group t-test with no covariates, a t-contrast of [-1 1] will give a right-tailed (group2 > group1) t-test; [1 -1] will give a left-tailed (group1 > group2) t-test, and an F-contrast of either [-1 1] or [1 -1] will give an F-test (group2 ${\displaystyle \neq }$ group1) equivalent to a two-tailed t-test.

After defining and choosing your contrast, you'll then be asked about masking it with others (say no, unless you know you want this kind of analysis). Next you'll be asked about how to correct/adjust for multiple comparisons. If you have no idea, I'd select FDR, and leave the default of 0.05; better still, read the Genovese and Nichols articles on FWE and FDR. You should then be presented with the standard Maximum Intensity Projection (MIP) plot of the significant regions. Clicking one of the p-values buttons on the left (probably want volume) will produce a table of results, while selecting overlays... sections and choosing e.g. the T1 template will allow you to move around in the brain viewing the significant areas.

### Optimised VBM in SPM2 and SPM99

This is not necessary for SPM5 because the Segment button should do everything in a single unified model. "Optimised VBM" was a half-baked procedure invented in about 10 minutes in order to provide a quick short term solution for improving the spatial normalisation in SPM. It does improve the spatial normalisation though, and should also give better inter-subject registration (and therefore better results) for fMRI data. If you want to do optimised VBM in SPM2 or SPM99, then the procedure is:

Segment the original images

This involves an implicit registration of a template to the image. The transformation that is estimated here is used to overlay the prior probability maps, which assist the segmentation. Before doing this step, you may need to reorient the images via Display. This is so that the affine registration has better starting estimates. A search for the keywords reorient Display at [[1]] will give you all the hints about this that you need.

Clean up the grey matter.

This is only for SPM99. In SPM2, this procedure is combined with the segmentation. The seg1 and seg2 images are entered into the program, and the result is a brain_*.img, which has values of 1 for brain, and 0 for non-brain. The resulting brain_*.img is used to remove a few misclassified voxels from the *_seg1.img file. This is done using ImCalc, selecting the seg1_, seg2_, seg3_, abd brain_ images, entering an output filename, and the following expression:

```       i1.*i4./(i1+i2+i3+eps)
```

Estimate warps from the GM.

The reason for the first segmentation and cleanup is so that a set of spatial normalisation parameters can be estimated by matching GM with GM. In SPM99, you would disable 'Mask brain when registering?', and set the resolution for the spatially normalised images to be higher than the current defaults. The template would be an image of grey mater, which could be the one in the apriori directory, or it could be a "custom" made template.

Apply these warps to the original T1 image. This gives you a spatially normalised T1 image, which should have a resolution of about 1mm isotropic. The original *_seg* and brain_* images could be deleted at this stage.

Segment the spatially normalised T1.

Tell the segmentation routine that the image is spatially normalised, so no affine registration is done.

Clean up the grey matter.

The same as above (only for SPM99).

Modulate

Spatial normalisation expands and contracts some brain regions. Modulation involves scaling by the amount of contraction, so that the total amount of grey matter in the modulated GM remains the same as it would be in the original images.

Smooth.

Best if you do this by about 12mm.

Stats.

The whole idea behind the pre-processing is that the t-tests are sensitised to volumetric differences in the GM. Remember that your results could reflect other differences among the images.

## Custom Templates

Spatial normalisation in versions of SPM prior to SPM5 required templates that had similar contrasts to the image to be matched with them. The reason for this is that the objective function is based on the mean squared difference between the images. This only makes sense if the intensities of the different tissue types correspond between the images (with an additional scaling factor that is estimated, which rescales the overall intensities). In SPM5, the segment button allows spatial normalisation to be achieved using a different objective function, which does not rely on a simple relationship between the intensities of a pair of images. For full details about the mechanism, I would suggest taking a look at Ashburner & Friston. Unified segmentation. NeuroImage 26(3):839-851 (2005).

The idea is that the segmentation of SPM5 warps a set of tissue probability maps so that they overlay on to the image to segment. After warping, these will represent (part of) the prior probability of each voxel belonging to a particular class.

Ideally, these tissue probability maps should represent the prior probabilities for the population under investigation, and are made by averaging a large number of spatially normalised tissue class images of different subjects (wc*.img). I suspect that if you don't have a large number of subjects, then the tissue probability maps released with SPM5 would be more representative than an average made up of only about 20 subjects.

## Globals

The mass univariate testing approach assumes that all voxels in an image are independent (apart from the GRF correction part). The use of "globals" is a compromise in order to model dependencies between each voxel and some global measure.

Most people who study shape use a multi-variate framework. Shape is based on the relationship between the positions of corresponding features, after accounting for size, position and orientation. Unfortunately, we do not have enough subjects to do a full multi-variate analysis, so we restrict our analyses to being mass-univariate, and possibly use a "global" as a confound, or use some kind of proportional scaling. We attempt to answer a more clinically interesting question by limiting our investigation to identifying regions of increased or decreased GM.

"Globals" are a compromise (fudge) that is needed to introduce some kind of multi-variateness into the analysis. People generally want to see a map of significant blobs, so a mass-univariate approach (SPM) is usually adopted. In reality, shape (and hence relative volumes) is really multivariate. The volume of one structure is related to the volume of another. Bigger brains may (on average) have bigger hippocampi. Brains with globally thicker grey matter are more likely to have grey matter that is thicker at a particular sulcus. Also, brains where the segmentation (for some reason) overestimates the amount of grey matter, are also likely to appear to have more grey at a particular region.

Unfortunately, this multi-variateness is not a simple linear relationship. For example, bigger brains are likely to have proportionally more white matter than grey. For brains that are globally different, it becomes very difficult to interpret exactly what the differences mean in a mass univariate way. Basically, it is not clear what to use as globals for any particular experiment. This will depend on what theory you have about your subjects.

Proportional scaling converts volumes into values that are a proportion of total brain/GM volume. For example, you may be able to say that a region around some point contains 3% of the total GM volume. If you are interested in differences in such measures, then a proportional scaling model may be preferable. Alternatively, if you want to localise regions where the trends in GM volume differ from the total GM volume, then an ANCOVA model may be preferable.

Using no "globals" and a "modulated" analysis is intended to show regions of absolute volumetric difference in grey matter. Using total grey matter as a confound will show regions of absolute difference that can not be explained by the total grey matter differences.

You can include additional columns in your design matrix that model various effects of no interest (e.g. an ANCOVA correction for some global measure). This allows you to localise differences that can not be explained by these uninteresting effects.

For example, in a group comparison, one group's brains may be bigger than those of the other group. In a situation like this, you may only be interested in patterns of volumetric differences that differ from those of the total brain size.

Using proportional scaling to total grey matter will show differences where a region contains a disproportionately large or small region of total grey matter. For example, a structure may normally represent 2% of the total brain grey matter, but in patients it may represent 1.5%.

The males versus females test is a tricky one. Human males are generally bigger than females, with bigger heads. If you were doing an analysis of nose sizes, then it is likely that males would have bigger noses. Maybe you would want to know if this extra size was still significant if total head size was taken into account, either by modelling head size as a covariate, or by proportionally scaling the noses such that they were rendered proportional to the total head size (giving us a measure of nose as a percentage of head volume).

Normally, a brain with e.g twice the volume of another brain will not have twice as much grey matter. The relationship between grey and white-matter volume approximately obeys a power law, with a 4/3 exponent (Zhang & Sejnowski, PNAS 97(10):5621-5626, 2000). If we use a proportional scaling model based on whole brain volume, our null hypothesis is that grey matter volume varies linearly with brain volume. This is simply not true, although it may serve as a useful first approximation.

The choice of model is up to the investigator, and it really does depend what you want to test. I would really rather not be give any firm recommendations. When a VBM experiment is written up, the model should be accurately described. Different models will give different results, which may appear to conflict with each other.

In the case of dementia, the total intra-cranial volume is often used to proportionally scale the data. Thus, each structure/region is treated as a proportion of intra-cranial volume. Head sizes vary, so this normalisation should reduce the residual variance from the model.

## Obtaining Covariates

Globals (total segmented tissue volumes)

spm_global is not a good way of computing "globals" for VBM, as it was intended to compute a kind of average brain intensity by excluding "non-brain" voxels (with the assumption that these are below a certain fraction of the pre-exclusion mean), and computing the mean of what is left.

The function spm_get_volumes can be used to integrate over tissue segmentations, returning volumes in litres. The differences between native space (c), DARTEL-Imported (rc), modulated normalised (mwc) and smoothed modulated normalised (smwc) segmentation volumes are usually very small. The main difference is the amount of the spinal cord included in the white matter segment, which depends on the field of view of the images. Manual segmentation protocols (e.g. as in Whitwell et al., 2001) often set an arbitrary cut-off, such as the most inferior slice (in MNI space) that includes cerebellum; this is perhaps closest to the results of mwc or smwc images.

Total Intracranial Volume

To get TIV, one option is to sum the volumes of GM, WM and CSF, for example using spm_get_volumes on each tissue class and then adding these results. Use of this approach with the mwc segments from the New Segmentation Toolbox in SPM8 performs very well compared to manual or other automatic measurements (Ridgway et al., 2011).