B rain I mage A nalysis U nit Biostatistics & Computing I nstitute of Psychiatry London, U . K.

1. Vincent P. Giampietro V.Giampietro@iop.kcl.ac.uk Introduction to fMRI Analysis Brain Image Analysis UnitBiostatistics & ComputingInstitute of PsychiatryLondon, U.K.

2. London

3. London

4. London • The Institute of Psychiatry is in Camberwell…

5. London • The Institute of Psychiatry is in Camberwell…

6. My goals • To fight against the black box way of analysing fMRI datasets • To give you a good idea of what fMRI analysis really does • Without showing you any of these:

7. The fMRI challenge • In fMRI, the signal change due to activation (BOLD effect) is very subtle: it amounts to about less than 4% of the baseline signal at 1.5T (double that at 3T) • The challenge is to detect a small signal embedded in background noise • fMRI analysis is a digital signal processing problem • Some of the analysis methods are directly adapted from other signal processing domains, such as voice recognition (wavelet transforms)

8. How large is a 1.5T magnetic field? • Roughly the same as • More or less 50000 times

9. 5mn 39s 30s 3.75mm 10 volumes 64 voxels 7.7mm 64 voxels 3.75mm 1 image voxel Voxel=pixel in 3D 3s (TR) 16 7.7mm thick slicesmatrix size = 64x64 3D brain volume A simple fMRI experiment AUDIO Multiplex audio-visual (e.g. internal control check for global changes in drug trials) VISUAL

10. t=1xTR=3s 1 TR = 3s 64 voxels 64 voxels 3.75mm 3.75mm t=100xTR=300s The data One slice100 images One image4096 voxels Voxels

11. I have scanned a subjectWhat should I do next?How do I get the red blobs? fMRI analysis • Getting the images from the MR scanner • Pre-processing the raw data • Analysing a single subject experiment • Analysing a group of subjects • Comparing different groups • Using more advanced analysis methods

12. MR scanner The files are anonymised Public server your Sun/PC Getting the data from MR The grand image format debate Now - Native MR scanner format Soon - DICOM format Digital Imaging and COmmunication in Medicine http://medical.nema.org/http://www.psychology.nottingham.ac.uk/staff/cr1/dicom.html Now - Analyze format Soon - NIfTI format Neuroimaging Informatics Technology Initiative http://nifti.nimh.nih.gov/

13. Without With Pre-processing the raw data Do we need it ? Really bad dataset with huge head motion Simon Surguladze

14. raw data movement correction 1 detrending 2 smoothing preprocessed data 3 Pre-processing the raw data

15. Pre-processing the raw data Movement correction The two main movement artefacts in fMRI are: between scans stimulus correlated Rozmin Halari

16. 3D average registration template Rigid body realignment (3 translations + 3 rotations) Registered images written by tricubic spline/linear interpolation Pre-processing the raw data Movement correction (co-registration)

17. Pre-processing the raw data Stimulus correlated motion Analysis only • Stimulus correlated motion is fitted as “activated” by the model • Without motion and spin correction, the results are useless Motion correction + analysis Motion correction + spin excitation history correction + analysis

18. Pre-processing the raw data Stimulus uncorrelated motion Analysis only • Stimulus uncorrelated motion doesn’t “mess up” the results • Motion and spin correction increase the power the fMRI analysis Motion correction + analysis Motion correction + spin excitation history correction + analysis

19. With Without Pre-processing the raw data Detrending – Spin excitation history correction • Movement-related autocorrelation • In the magnet, the positions of the nuclei at time t are spatially and temporally related to the positions of the same nuclei at time t-1 (and actually up to t-3) • Can be corrected by using autoregressive pre-whitening

20. Magneticfield Pre-processing the raw data Detrending – Spin excitation history correction Problem in space Problem in time

21. time Before After Pre-processing the raw data Detrending – Scanner drift • Linear trend • Non-uniformity in the magnetic field • Electronic interferences due to temperature fluctuations in the imaging hardware

22. Ray Norbury Pre-processing the raw data Detrending – Other trends • Non-linear but periodic trends • Easily “filtered out” using high/low/band-pass filters

23. f( ) Filter kernel Pre-processing the raw data Smoothing – Spatial filtering • Digital filtering Y X f(X) f(Y) Original Image Filtered Image = convolution (~the image is multiplied by the filter kernel)

24. 1138 1 1 1 1 1 1 1 1 1 (convolution) 850 1014 1125 3x3 mean filter 1138 1243 1310 1282 1338 1315 Σ New value = 1/9 x Pixeli,j x Filteri,j Pre-processing the raw data Smoothing – Spatial filtering • Mean filter 126 1180

25. 2D Gaussian distribution (mean (0,0) and σ=1) Discrete approximation to Gaussian function with σ =1.0 standard deviation Full Width at Half MaximumFWHM = 2.355 x σFWHM = 2.355 voxelsVoxel size = 3.75x3.75mmFWHM = 8.83 mm Pre-processing the raw data Smoothing – Spatial filtering • Gaussian filter

26. Pre-processing the raw data Smoothing – Spatial filtering • The problem… • To maximise the effect, the size of the filter should match the size of the activated regions in the image • But brain structures come in many different sizes and shapes so smoothing the images may do more harm than good… • To smooth or not to smooth? • Adaptive (steerable) filtering (CCA - Canonical Correlation Analysis) • No smoothing at all… • But it is worth remembering that some analysis packages require smoothing for their statistical analysis to work…

27. Time Pre-processing the raw data Smoothing – Temporal filtering • Moving average filter 8-point low pass

28. 5mn AUDIO 30s VISUAL 39s 1 TR (3s) t=0.501s t=14.560s Analysing a single subject experiment The model file – Experiment description 1111111111111 1111111111111 0000000000000 0000000000000 1111111111 1111111111 0000000000 0000000000 …000000000 00000000 000101 0101111… …0.501 14.56052.517 25.50998.517 39.509110.517 62.517120.517 72.517133.509 84.517172.501 146.501247.525 158.501259.525 186.501269.525 197.509280.517 211.509… Model file for event related design Model file for block design

29. Experiment Real BOLD response 4s 8s Gamma Variate Kernels Analysing a single subject experiment The model file – Experiment description - 1 Gamma function & its 1st derivative - Physiological models (Balloon model) or - Adaptive models (GLM extensions) - Model free analysis (ICA)

30. (convolution) 4 Analysing a single subject experiment The model file – Experiment description

31. Model for the visual stimulation Real time series from the visual cortex Real time series from the auditory cortex Analysing a single subject experiment Model fitting The model is usually fitted using least square fitting

32. Real time series Fitted model Analysing a single subject experiment Model fitting – Good fit (1 gamma function)

33. Analysing a single subject experiment Model fitting – Bad fit (1 gamma function)

34. Analysing a single subject experiment Model fitting • Calculate a goodness of fit statistic • For each pixel • For each condition • This generates statistical maps of the brain (one per condition and per interaction) • Null hypothesis • There is no experimental effect • There is no relationship between the voxel time series and the experimental model • How do you decide if your statistics are significant or not ? • Parametric statistics (lots of assumptions…among other things the data need to have a Normal distribution) • Non parametric statistics (distribution-free)

35. Analysing a single subject experiment Model fitting • Non parametric statistics (the way we do it) • Statistic used: Sum of Square Quotient (SSQ) • SSQ = ratio of model to residual sum of squares • Use randomisation testing to determinate the p value of the statistic ( this is the non-parametric bit) • If p< α then the null hypothesis is rejected, there is a statistically significant relationship between the experimental model and the studied voxel time series • The voxel is activated and gets coloured

36. Analysing a single subject experiment Randomisation tests ??? • Statistical tests in which the data are repeatedly mixed • A test statistic is computed for each data shuffle • The proportion of data divisions with as large a test statistic value as the value for the original results determinates the significance of the results • Computer intensive and memory hungry… (E.S. Edgington 1995)

37. Analysing a single subject experiment Randomisation tests ??? • A simple example • 2 treatments A and B • Hypothesis:A measurements > B measurements • 4 patients a, b, c and d

38. Analysing a single subject experiment Randomisation tests ??? • A Simple example • 6 permutations possible of the patients to form 2 groups • We calculate the t statistic for every permutation real (observed)situation • None of the permutations have a statistical value higher or equal to 4.24 (the statistical value for the real situation). • The one-tailed significance (p value) associated with the obtained results is therefore 1/6=0.167

39. Analysing a single subject experiment Cluster analysis • Clustering • Connects activated voxels from the same brain structure • Can reinforce sub-threshold activations by “pushing them to the surface” and eliminates single activated voxels • Levels of clustering • Per slice (2D) • Per volume (3D) • In time (4D) You get the idea !

40. AUDIO VISUAL Analysing a single subject experiment The results

41. Interlude…

42. Interlude…

43. Spatial Normalisation • What is it? • Process of transforming an image for an individual subject to match a standard brain or brain template • What do we want to do with it ? • Check the activations on the standard atlas (functional localisation) • Compare groups of subjects • How do we do it ? • Mostly by using automatic warping methods

44. Spatial Normalisation Brain templates • Talairach atlas (Talairach and Tournoux) • “Co-Planar Stereotaxic Atlas of the Human Brain” (1988) • Detailed atlas of brain sections with a coordinate system and Brodmann regions • “Proportional grid” of brain imaging • But…made from the post-mortem brain of a 60-year old alcoholic french woman • MNI/ICBM templates • Montreal Neurological Institute / International Consortium of Brain Mapping • Average of hundreds of brains • 241 brains were manually scaled to the Talairach brain to produce an temporary template • MNI305 is made of 305 brains mapped to this template • ICBM152 is made of 152 brains registered to MNI305 (current template) • No Brodmann regions…

45. High-resolutionstructural image fMRI Structural space Talairach template Talairach space Spatial Normalisation Talairach mapping 1st registration 2nd registration

46. Spatial Normalisation Talairach mapping • More smoothing if needed… • More statistical analysis… • More cluster analysis… • More pretty pictures… but…

47. Spatial Normalisation The results • Strongest activated cluster • 64 voxels. • Talairach coordinates: x=-55, y=-14, z=9 (activation focus). • Left side, slice 10. • Brodmann Area 42, Auditory Association Cortex

48. Spatial Normalisation The results

49. 2D Spatial Normalisation The results 3 D

50. Spatial Normalisation The results in virtual reality