Face fMRI data ¶

As another, more sophisticated example, consider the data from a repetition priming experiment performed using event-related fMRI. Briefly, this is a 2\(\times\)2 factorial study with factors “fame” and “repetition” where famous and non-famous faces were presented twice against a checkerboard baseline (for more details, see (Henson et al. 2002)). The subject was asked to make fame judgements by making key presses. There are thus four event-types of interest; first and second presentations of famous and non-famous faces, which we denote N1, N2, F1 and F2. The experimental stimuli and timings of events are shown in Figures 1.1 and 1.2.

**Face repetition paradigm**: There were 2 presentations of 26 Famous and 26 Nonfamous Greyscale photographs, for 0.5s each, randomly intermixed. The minimal Stimulus Onset Asynchrony (SOA)=4.5s, with probability 2/3 (ie 1/3 null events). The subject made one of two right finger key presses denoting whether or not the subject thought the face was famous.

Images were acquired using continuous Echo-Planar Imaging (EPI) with TE=40ms, TR=2s and 24 descending slices (64\(\times\)64 3\(\times\)3 mm\(^2\)), 3mm thick with a 1.5mm gap. The data archive is available from the SPM website¹. This contains 351 Analyze format functional images sM03953_0005_*.{hdr,img} of dimension 64\(\times\)64\(\times\)24 with 3\(\times\)3\(\times\)4.5 mm\(^3\) voxels. A structural image is also provided in Analyze format (sM03953_0007.{hdr,img}).

To analyse the data, first create a new directory DIR eg. C:\(\backslash\)data\(\backslash\)face_rep, in which to place the results of your analysis. Then create 4 subdirectories (i) jobs, (ii) categorical, (iii) parametric and (iv) bayesian. As the analysis proceeds these directories will be filled with job-specification files, design matrices and models estimated using classical or Bayesian methods.

As well as the classical/Bayesian distinction we will show how this data can be analysed from a parametric as well as a categorical perspective. We will look at the main effects of fame and repetition and in the parameteric analysis we will look at responses as a function of “lag”, that is, the number of faces intervening between repetition of a specific face.

Start up MATLAB, enter your jobs directory and type spm fmri at the MATLAB prompt. SPM will then open in fMRI mode with three windows (1) the top-left or “Menu” window, (2) the bottom-left or “Interactive” window and (3) the right-hand or “Graphics” window. Analysis then takes place in three major stages (i) spatial pre-processing, (ii) model specification, review and estimation and (iii) inference. These stages organise the buttons in SPM’s base window.

Spatial pre-processing¶

Display¶

Display eg. the first functional image using the “Display” button. Note orbitofrontal and inferior temporal drop-out and ghosting. This can be seen more clearly by selecting “Brighten” from the “Effects” menu in the “Colours” menu from the “SPM Figure” tab at the top of the Graphics window.

Realignment¶

Under the spatial pre-processing section of the SPM base window select Realign (Est & Res) from the Realign pulldown menu. This will call up a realignment job specification in the batch editor window. Then

Highlight data, select “New Session”, then highlight the newly created “Session” option.
Select “Specify Files” and use the SPM file selector to choose all of your functional images eg. sM03953_0005_*.img. You should select 351 files.
Save the job file as eg. DIR/jobs/realign.mat.
Press the Run button in the batch editor window (green triangle).

This will run the realign job which will write realigned images into the directory where the functional images are. These new images will be prefixed with the letter “r”. SPM will then plot the estimated time series of translations and rotations shown in Figure 1.5. These data, the realignment parameters, are also saved to a file eg. rp_sM03953_0005_0006.txt, so that these variables can be used as regressors when fitting GLMs. This allows movements effects to be discounted when looking for brain activations.

SPM will also create a mean image eg. meansM03953_0005_0006.{hdr,img} which will be used in the next step of spatial processing - coregistration.

**Realignment of face data**: Movement less than the size of a voxel, which for this data set is 3mm, is not considered problematic.

Slice timing correction¶

Press the Slice timing button. This will call up the specification of a slice timing job in the batch editor window. Note that these data consist of N=24 axial slices acquired continuously with a TR=2s (ie TA = TR - TR/N, where TA is the time between the onset of the first and last slice of one volume, and the TR is the time between the onset of the first slice of one volume and the first slice of next volume) and in a descending order (ie, most superior slice was sampled first). The data however are ordered within the file such that the first slice (slice number 1) is the most inferior slice, making the slice acquisition order [24 23 22 ... 1].

Highlight “Data” and select “New Sessions”
Highlight the newly create “Sessions” option, “Specify Files” and select the 351 realigned functional images using the filter ^r.*.
Select “Number of Slices” and enter 24.
Select TR and enter 2.
Select TA and enter 1.92 (or 2 - 2/24).
Select “Slice order” and enter 241.
Select “Reference Slice”, and enter 12.
Save the job as slice_timing.mat and press the “Run” button.

SPM will write slice-time corrected files with the prefix “a” in the functional data directory.

Coregistration¶

Select Coregister (Estimate) from the Coregister pulldown menu. This will call up the specification of a coregistration job in the batch editor window.

Highlight “Reference Image” and then select the mean functional image meansM03953_0005_0006.img.
Highlight “Source Image” and then select the structural image eg. sM03953_0007.img.
Press the “Save” button and save the job as coreg.job
Then press the “Run” button.

SPM will then implement a coregistration between the structural and functional data that maximises the mutual information. The image in figure 1.6 should then appear in the Graphics window. SPM will have changed the header of the source file which in this case is the structural image sM03953_0007.hdr.

*Mutual Information Coregistration of Face data.*

Segmentation¶

Press the Segment button. This will call up the specification of a segmentation job in the batch editor window. Highlight the “Volumes” field in “Data \(>\) Channels” and then select the subjects coregistered anatomical image eg. sM03953_0007.img. Change “Save Bias Corrected” so that it contains “Save Bias Corrected” instead of “Save Nothing”. At the bottom of the list, select “Forward” in “Deformation Fields”. Save the job file as segment.mat and then press the Run button. SPM will segment the structural image using the default tissue probability maps as priors. SPM will create, by default, gray and white matter images and bias-field corrected structral image. These can be viewed using the CheckReg facility as described in the previous section. Figure 1.7 shows the gray matter image, c1sM03953_0007.nii, along with the original structural².

SPM will also write a spatial normalisation deformation field file eg. y_sM03953_0007.nii file in the original structural directory. This will be used in the next section to normalise the functional data.

Normalise¶

Select Normalise (Write) from the Normalise pulldown menu. This will call up the specification of a normalise job in the batch editor window.

Highlight “Data”, select “New Subject”.
Open “Subject”, highlight “Deformation field” and select the y_sM03953_0007.nii file that you created in the previous section.
Highlight “Images to write” and select all of the slice-time corrected, realigned functional images arsM*.img. Note: This can be done efficiently by changing the filter in the SPM file selector to ^ar.*. You can then right click over the listed files, choose “Select all”. You might also want to select the mean functional image created during realignment (which would not be affected by slice-time correction), i.e, the meansM03953_0005_006.img. Then press “Done”.
Open “Writing Options”, and change “Voxel sizes” from [2 2 2] to [3 3 3]³.
Press “Save”, save the job as normalise.mat and then press the Run button.

SPM will then write spatially normalised files to the functional data directory. These files have the prefix “w”.

If you wish to superimpose a subject’s functional activations on their own anatomy⁴ you will also need to apply the spatial normalisation parameters to their (bias-corrected) anatomical image. To do this

Select Normalise (Write), highlight ‘Data’, select “New Subject”.
Highlight “Deformation field”, select the y_sM03953_0007.nii file that you created in the previous section, press “Done”.
Highlight “Images to Write”, select the bias-corrected structural eg. msM03953_0007.nii, press “Done”.
Open “Writing Options”, select voxel sizes and change the default [2 2 2] to [1 1 1] which better matches the original resolution of the images [1 1 1.5].
Save the job as norm_struct.mat and press Run button.

Smoothing¶

Press the Smooth button⁵. This will call up the specification of a smooth job in the batch editor window.

Select “Images to Smooth” and then select the spatially normalised files created in the last section eg. war*.img.
Save the job as smooth.mat and press Run button.

This will smooth the data by (the default) 8mm in each direction, the default smoothing kernel width.

*Functional image (top) and 8mm-smoothed functional image (bottom). These images were plotted using SPM’s "CheckReg" facility.*

Modelling categorical responses¶

Before setting up the design matrix we must first load the Stimulus Onsets Times (SOTs) into MATLAB . SOTs are stored in the sots.mat file in a cell array such that eg. sot{1} contains stimulus onset times in TRs for event type 1, which is N1. Event-types 2, 3 and 4 are N2, F1 and F2.⁶

At the MATLAB command prompt type load sots

Now press the Specify 1st-level button. This will call up the specification of a fMRI specification job in the batch editor window. Then

For “Directory”, select the “categorical” folder you created earlier,
In the “Timing parameters” option,
Highlight “Units for design” and select “Scans”,
Highlight “Interscan interval” and enter 2,
Highlight “Microtime resolution” and enter 24,
Highlight “Microtime onset” and enter 12. These last two options make the creating of regressors commensurate with the slice-time correction we have applied to the data, given that there are 24 slices and that the reference slice to which the data were slice-time corrected was the 12th (middle slice in time).
Highlight “Data and Design” and select “New Subject/Session”.
Highlight “Scans” and use SPM’s file selector to choose the 351 smoothed, normalised, slice-time corrected, realigned functional images ie swarsM.img. These can be selected easily using the ^swar.* filter, and select all. Then press “Done”.
Highlight “Conditions” and select “New condition”⁷.
Open the newly created “Condition” option. Highlight “Name” and enter “N1”. Highlight “Onsets” and enter sot{1}. Highlight “Durations” and enter 0.
Highlight “Conditions” and select “Replicate condition”.
Open the newly created “Condition” option (the lowest one). Highlight “Name” and change to “N2”. Highlight “Onsets” and enter sot{2}.
Highlight “Conditions” and select “Replicate condition”.
Open the newly created “Condition” option (the lowest one). Highlight “Name” and change to “F1”. Highlight “Onsets” and enter sot{3}.
Highlight “Conditions” and select “Replicate condition”.
Open the newly created “Condition” option (the lowest one). Highlight “Name” and change to “F2”. Highlight “Onsets” and enter sot{4}.
Highlight “Multiple Regressors” and select the realignment parameter file rp_sM03953_0005_0006.txt file that was saved during the realignment preprocessing step in the folder containing the fMRI data⁸.
Highlight “Factorial Design”, select “New Factor”, open the newly created “Factor” option, highlight “Name” and enter “Fam”, highlight “Levels” and enter 2.
Highlight “Factorial Design”, select “New Factor”, open the newly created “Factor” option, highlight “Name” and enter “Rep”, highlight “Levels” and enter 2⁹.
Open “Canonical HRF” under “Basis Functions”. Select “Model derivatives” and select “Time and Dispersion derivatives”.
Highlight “Directory” and select the DIR/categorical directory you created earlier.
Save the job as categorical_spec.mat and press the Run button.

SPM will then write an SPM.mat file to the DIR/categorical directory. It will also plot the design matrix, as shown in Figure 1.9.

At this stage it is advisable to check your model specification using SPM’s review facility which is accessed via the “Review” button. This brings up a “Design” tab on the interactive window clicking on which produces a pulldown menu. If you select the first item “Design Matrix” SPM will produce the image shown in Figure 1.9. If you select “Explore” then “Session 1” then “N1”, SPM will produce the plots shown in Figure 1.10.

**Exploring the design matrix in Figure 1.9**. This shows the time series of the "N1" regressor (top left), the three basis functions used to convert assumed neuronal activity into hemodynamic activity (bottom left), and a frequency domain plot of the three regressors for the basis functions in this condition (top right). The frequency domain plot shows that the frequency content of the "N1" condition is generally above the set frequencies that are removed by the High Pass Filter (HPF) (these are shown in gray - in this model we accepted the default HPF cut-off of 128s or 0.008Hz).

Estimate¶

Press the Estimate button. This will call up the specification of an fMRI estimation job in the batch editor window. Then

Highlight the “Select SPM.mat” option and then choose the SPM.mat file saved in the DIR/categorical directory.
Save the job as categorical_est.job and press Run button.

SPM will write a number of files into the selected directory including an SPM.mat file.

Inference for categorical design¶

Press “Results” and select the SPM.mat file from DIR/categorical. This will again invoke the contrast manager. Because we specified that our model was using a “Factorial design” a number of contrasts have been specified automatically, as shown in Figure 1.11.

*Contrast Manager containing default contrasts for categorical design.*

Select contrast number 5. This is a t-contrast Positive effect of condition_1 This will show regions where the average effect of presenting faces is significantly positive, as modelled by the first regressor (hence the _1), the canonical HRF. Press ‘Done’‘.
Apply masking ? [None/Contrast/Image]
Specify None.
p value adjustment to control: [FWE/none]
Select FWE
Corrected p value(family-wise error)
Accept the default value, 0.05
Extent threshold {voxels} [0]
Accept the default value, 0.

SPM will then produce the MIP shown in Figure 1.12.

Statistical tables¶

To get a summary of local maxima, press the “whole brain” button in the p-values section of the interactive window. This will list all clusters above the chosen level of significance as well as separate (\(>\)8mm apart) maxima within a cluster, with details of significance thresholds and search volume underneath, as shown in Figure 1.12

**MIP and Volume table for Canonical HRF**: Faces > Baseline.

The columns in volume table show, from right to left:

x, y, z (mm): coordinates in MNI space for each maximum.
peak-level: the chance (p) of finding (under the null hypothesis) a peak with this or a greater height (T- or Z-statistic), corrected (FWE or FDR)/ uncorrected for search volume.
cluster-level: the chance (p) of finding a cluster with this many(ke) or a greater number of voxels, corrected (FWE or FDR)/ uncorrected for search volume.
set-level: the chance (p) of finding this (c) or a greater number of clusters in the search volume.

Right-click on the MIP and select “goto global maximum”. The cursor will move to [39 -70 -14]. You can view this activation on the subject’s normalised, bias-corrected structural (wmsM03953_0007i̇mg), which gives best anatomical precision, or on the normalised mean functional (wmeansM03953_0005_0006.nii), which is closer to the true data and spatial resolution (including distortions in the functional EPI data).

If you select “plot” and choose “Contrast of estimates and 90% C.I” (confidence interval), and select the “Average effect of condition” contrast, you will see three bars corresponding to the parameter estimates for each basis function (summed across the 4 conditions). The BOLD impulse response in this voxel loads mainly on the canonical HRF, but also significantly (given that the error bars do not overlap zero) on the temporal and dispersion derivatives (see next Chapter).

F-contrasts¶

To assess the main effect of repeating faces, as characterised by both the hrf and its derivatives, an F-contrats is required. This is really asking whether repetition changes the shape of the impulse response (e.g, it might affect its latency but not peak amplitude), at least the range of shapes defined by the three basis functions. Because we have told SPM that we have a factorial design, this required contrast will have been created automatically - it is number 3.

Press “Results” and select the SPM.mat file in the DIR/categorical directory.
Select the “F-contrast” toggle and the contrast number 3, as shown in Figure 1.13. Press “Done”.
Apply masking ? [None/Contrast/Image].
Specify “Contrast”.
Select contrast 5 - Positive effect of condition_1 (the T-contrast of activation versus baseline, collapsed across conditions, that we evaluated above)
uncorrected mask p-value ?
Change to 0.001
nature of mask?
Select ‘inclusive’
p value adjustment to control: [FWE/none]
Select none
threshold (F or p value)
Accept the default value, 0.001
Extent threshold {voxels} [0]
Accept the default value, 0

A MIP should then appear, the top half of which should look like Figure 1.14.

*Contrast manager showing selection of the first contrast "Main effect of Rep" (repetition: F1 and N1 vs F2 and N2)*

*MIP for Main effect of Rep, masked inclusively with Canonical HRF: Faces > Baseline at p<.001 uncorrected. Shown below are the best-fitting responses and peri-stimulus histograms (PSTH) for F1 and F2.*

Note that this contrast will identify regions showing any effect of repetition (e.g, decreased or increased amplitudes) within those regions showing activations (on the canonical HRF) to faces versus baseline (at p\(<\).05 uncorrected). Select “goto global max”, which is in right ventral temporal cortex [42 -64 -8].

If you press plot and select “Event-related responses”, then “F1”, then “fitted response and PSTH”, you will see the best fitting linear combination of the canonical HRF and its two derivatives (thin red line), plus the “selectively-averaged” data (peri-stimulus histogram, PSTH), based on an FIR refit (see next Chapter). If you then select the “hold” button on the Interactive window, and then “plot” and repeat the above process for the “F2” rather than “F1” condition, you will see two estimated event-related responses, in which repetition decreases the peak response (ie F2\(<\)F1), as shown in Figure 1.14.

You can explore further F-contrasts, which are a powerful tool once you understand them. For example, the MIP produced by the “Average effect of condition” F-contrast looks similar to the earlier T-contrast, but importantly shows the areas for which the sums across conditions of the parameter estimates for the canonical hrf and/or its temporal derivative and/or its dispersion derivative are different from zero (baseline). The first row of this F-contrast ([1 0 0 1 0 0 1 0 0 1 0 0]) is also a two-tailed version of the above T-contrast, ie testing for both activations and deactivations versus baseline. This also means that the F-contrasts [1 0 0 1 0 0 1 0 0 1 0 0] and [-1 0 0 -1 0 0 -1 0 0 -1 0 0] are equivalent. Finally, note that an F- (or t-) contrast such as [1 1 1 1 1 1 1 1 1 1 1], which tests whether the mean of the canonical hrf AND its derivatives for all conditions are different from (larger than) zero is not sensible. This is because the canonical hrf and its temporal derivative may cancel each other out while being significant in their own right. The basis functions are really quite different things, and need to represent separate rows in an F-contrast.

F-contrasts for testing effects of movement¶

To assess movement-related activation

Press “Results”, select the SPM.mat file, select “F-contrast” in the Contrast Manager. Specify e.g. “Movement-related effects” (name) and in the “contrasts weights matrix” window, or “1:12 19” in the “columns for reduced design” window.
Submit and select the contrast, specify “Apply masking?” (none), “corrected height threshold” (FWE), and “corrected p-value” (accept default).
When the MIP appears, select “sections” from the “overlays” pulldown menu, and select the normalised structural image (wmsM03953_0007.nii).

You will see there is a lot of residual movement-related artifact in the data (despite spatial realignment), which tends to be concentrated near the boundaries of tissue types (eg the edge of the brain; see Figure 1.15). (Note how the MIP can be misleading in this respect, since though it appears that the whole brain is affected, this reflects the nature of the (X-ray like) projections onto each orthogonal view; displaying the same datae as sections in 3D shows that not every voxel is suprathreshold.) Even though we are not interested in such artifact, by including the realignment parameters in our design matrix, we “covary out” (linear components) of subject movement, reducing the residual error, and hence improve our statistics for the effects of interest.

Movement-related activations. These spurious ‘activations’ are due to residual movement of the head during scanning. These effects occur at tissue boundaries and boundaries between brain and non-brain, as this is where contrast differences are greatest. Including these regressors in the design matrix means these effects cannot be falsely attributed to neuronal activity.

Modelling parametric responses¶

Before setting up the design matrix, we must first load into MATLAB the Stimulus Onsets Times (SOTs), as before, and also the “Lags”, which are specific to this experiment, and which will be used as parametric modulators. The Lags code, for each second presentation of a face (N2 and F2), the number of other faces intervening between this (repeated) presentation and its previous (first) presentation. Both SOTs and Lags are represented by Matlab cell arrays, stored in the sots.mat file.

At the MATLAB command prompt type load sots. This loads the stimulus onset times and the lags (the latter in a cell array called itemlag.

Now press the Specify 1st-level button. This will call up the specification of a fMRI specification job in the batch editor window. Then

Press “Load” and select the categorical_spec.mat job file you created earlier.
Open “Conditions” and then open the second “Condition”.
Highlight “Parametric Modulations”, select “New Parameter”.
Highlight “Name” and enter “Lag”, highlight values and enter itemlag{2}, highlight polynomial expansion and “2nd order”.
Now open the fourth “Condition” under “Conditions”.
Highlight “Parametric Modulations”, select “New Parameter”.
Highlight “Name” and enter “Lag”, highlight values and enter itemlag{4}, highlight polynomial expansion and “2nd order”.
Open “Canonical HRF” under “Basis Functions”, highlight “Model derivatives” and select “No derivatives” (to make the design matrix a bit simpler for present purposes!).
Highlight “Directory” and select DIR/parametric (having “unselected” the current definition of directory from the Categorical analysis).
Save the job as parametric_spec and press the Run button.

This should produce the design matrix shown in Figure 1.16.

**Design matrix for testing repetition effects parametrically.** Regressor 2 indicates the second occurrence of a nonfamous face. Regressor 3 modulates this linearly as a function of lag (ie. how many faces have been shown since that face was first presented), and regressor 4 modulates this quadratically as a function of lag. Regressors 6,7 and 8 play the same roles, but for famous faces.

Estimate¶

Press the Estimate button. This will call up the specification of an fMRI estimation job in the batch editor window. Then

Highlight the “Select SPM.mat” option and then choose the SPM.mat file saved in the DIR/parametric directory.
Save the job as parametric_est.job and press the Run button.

SPM will write a number of files into the selected directory including an SPM.mat file.

Plotting parametric responses¶

We will look at the effect of lag (up to second order, ie using linear and quadratic terms) on the response to repeated Famous faces, within those regions generally activated by faces versus baseline. To do this

Press “Results” and select the SPM.mat file in the DIR/parametric directory.
Press “Define new contrast”, enter the name “Famous Lag”, press the “F-contrast” radio button, enter “1:6 9:15” in the “columns in reduced design” window, press “submit”, “OK” and “Done”.
Select the “Famous Lag” contrast.
Apply masking ? [None/Contrast/Image]
Specify “Contrast”.
Select the “Positive Effect of Condition 1” T contrast.
Change to an 0.05 uncorrected mask p-value.
Nature of Mask ? inclusive.
p value adjustment to control: [FWE/none]
Select None
Threshold {F or p value}
Accept the default value, 0.001
Extent threshold {voxels} [0]
Accept the default value, 0.

Figure 1.17 shows the MIP and an overlay of this parametric effect using overlays, sections and selecting the wmsM03953_0007.nii image.

*MIP and overlay of parametric lag effect in parietal cortex.*

The effect is plotted in the time domain in figure 1.18. This was obtained by

Right clicking on the MIP and selecting “global maxima”.
Pressing Plot, and selecting “parametric responses” from the pull-down menu.
Which effect ? select “F2”.

This shows a quadratic effect of lag, in which the response appears negative for short-lags, but positive and maximal for lags of about 40 intervening faces (note that this is a very approximate fit, since there are not many trials, and is also confounded by time during the session, since longer lags necessarily occur later (for further discussion of this issue, see the SPM2 example analysis of these data on the webpage).

Bayesian analysis¶

Specification¶

Press the Specify 1st-level button. This will call up an fMRI specification job in the batch editor window. Then

Load the categorical_spec.mat job file created for the classical analysis.
Open “Subject/Session”, highlight “Scans”.
Deselect the smoothed functional images using the ‘unselect all’ option available from a right mouse click in the SPM file selector (bottom window).
Select the unsmoothed functional images using the ^wa.* filter and “select all” option available from a right mouse click in the SPM file selector (top right window). The Bayesian analysis uses a spatial prior where the spatial regularity in the signal is estimated from the data. It is therefore not necessary to create smoothed images if you are only going to do a Bayesian analysis.
Press “Done”.
Highlight “Directory” and select the DIR/bayesian directory you created earlier (you will first need to deselect the DIR/categorical directory).
Save the job as specify_bayesian.mat and press the Run button.

Estimation¶

Press the Estimate button. This will call up the specification of an fMRI estimation job in the batch editor window. Then

Highlight the “Select SPM.mat” option and then choose the SPM.mat file saved in the DIR/bayesian subdirectory
Highlight “Method” and select the “Choose Bayesian 1st-level” option.
Save the job as estimate_bayesian.job and press the Run button.

*Bayesian analysis: Estimated AR(1) coefficient image indicating heterogeneity near the circle of Willis*

SPM will write a number of files into the output directory including

An SPM.mat file.
Images Cbeta_k.nii where \(k\) indexes the \(k\)th estimated regression coefficient. These filenames are prefixed with a “C”‘ indicating that these are the mean values of the “Conditional” or “Posterior” density.
Images of error bars/standard deviations on the regression coefficients SDbeta_k.nii.
An image of the standard deviation of the error Sess1_SDerror.nii.
An image mask.nii indicating which voxels were included in the analysis.
Images Sess1_AR_p.nii where \(p\) indexes the \(p\)th AR coefficient. See eg. Figure 1.19.
Images con_i.nii and con_sd_i.nii which are the mean and standard deviation of the \(i\)th pre-defined contrast.

Inference¶

After estimation, we can make a posterior inference using a PPM. Basically, we identify regions in which we have a high probability (level of confidence) that the response exceeds a particular size (eg, % signal change). This is quite different from the classical inferences above, where we look for low probabilities of the null hypothesis that the size of the response is zero.

To determine a particular response size (“size threshold”) in units of PEAK % signal change, we first need to do a bit of calculation concerning the scaling of the parameter estimates. The parameter estimates themselves have arbitrary scaling, since they depend on the scaling of the regressors. The scaling of the regressors in the present examples depends on the scaling of the basis functions. To determine this scaling, load the “SPM.mat” file and type in MATLAB sf = max(SPM.xBF.bf(:,1))/SPM.xBF.dt (alternatively, press “Design:Explore:Session 1” and select any of the conditions, then read off the peak height of the canonical HRF basis function (bottom left)).

Then, if you want a size threshold of 1% peak signal change, the value you need to enter for the PPM threshold (ie the number in the units of the parameter estimates) is 1/sf (which should be 4.75 in the present case).¹⁰

Finally, if we want to ask where is there a signal greater than 1% (with a certain confidence) to faces versus baseline, we need to create a new contrast that takes the AVERAGE of the parameter estimates for the canonical HRF across the four conditions (N1 to F2), rather than the default Positive effect of condition_1 contrast, which actually calculates the SUM of the parameter estimates for the canonical HRF across conditions (the average vs sum makes no difference for the classical statistics).

Press “Results”.
Select the SPM.mat file created in the last section.
Press “Define new contrast”, enter the name “AVERAGE Canonical HRF: Faces \(>\) Baseline”, press the “T-contrast” radio button, enter the contrast [1 0 0 1 0 0 1 0 0 1 0 0]/4, press “submit”, “OK” and “Done”.
Apply masking ? [None/Contrast/Image]
Specify None
Effect size threshold for PPM
Enter the value
Log Odds Threshold for PPM
Enter the value 10
Extent threshold [0]
Accept the default value

SPM will then plot a map of effect sizes at voxels where it is 95% sure that the effect size is greater than 1% of the global mean. Then use overlays, sections, select the normalised structural image created earlier and move the cursor to the activation in the left hemisphere. This should create the plot shown in Figure 1.20.

Bayesian analysis: MIP and overlay of effect sizes at voxels where PPM is 95% sure that the effect size is greater than 1% of the global mean. The cursor is at the location x = 30, y = − 82, z = − 17mm

Henson, R. N. A., T. Shallice, M. L. Gorno-Tempini, and R. Dolan. 2002. "Face Repetition Effects in Implicit and Explicit Memory Tests as Measured by fMRI." *Cerebral Cortex* 12: 178--86.

Face Repetition dataset: http://www.fil.ion.ucl.ac.uk/spm/data/face_rep/ ↩
Segmentation can sometimes fail if the source (structural) image is not close in orientation to the MNI templates. It is generally advisable to manually orient the structural to match the template (ie MNI space) as close as possible by using the “Display” button, adjusting x/y/z/pitch/roll/yaw, and then pressing the “Reorient” button. ↩
This step is not strictly necessary. It will write images out at a resolution closer to that at which they were acquired. This will speed up subsequent analysis and is necessary, for example, to make Bayesian fMRI analysis computationally efficient. ↩
Beginners may wish to skip this step, and instead just superimpose functional activations on an “canonical structural image”. ↩
The smoothing step is unnecessary if you are only interested in Bayesian analysis of your functional data. ↩
Unlike previous analyses of these data in SPM99 and SPM2, we will not bother with extra event-types for the (rare) error trials. ↩
It is also possible to enter information about all of the conditions in one go. This requires much less button pressing and can be implemented by highlighting the “Multiple conditions” option and then selecting the all-conditions.mat file, which is also provided on the webpage. ↩
It is also possible to enter regressors one by one by highlighting “Regressors” and selecting “New Regressor” for each one. Here, we benefit from the fact that the realignment stage produced a text file with the correct number of rows (351) and columns (6) for SPM to add 6 regressors to model (linear) rigid-body movement effects. ↩
The order of naming these factors is important - the factor to be specified first is the one that “changes slowest” ie. as we go through the list of conditions N1, N2, F1, F2 the factor “repetition” changes every condition and the factor “fame” changes every other condition. So “Fam” changes slowest and is entered first. ↩
Strictly speaking, this is the peak height of the canonical component of the best fitting BOLD impulse response: the peak of the complete fit would need to take into account all three basis functions and their parameter estimates. ↩