1. Spatial processing of FMRI data And why you may care

2. With slides from: John Ashburner Chloe Hutton Chris Rorden

3. Spatial processing and statistics Spatial processing is an important part of the statistical analysis Important practical and theoretical issues –Many false positive and false negative errors are caused by problems with spatial processing –Problems in the time series –Problems in location of signal –Problems averaging across subjects The goal of some spatial processing is not yet agreed

4. Slice timing correction Almost all FMRI scanning collects every slice separately Each slice is collected at a different time Slice timing correction (sinc interpolation) shifts each voxel's time series so all voxels in a given volume appear to have been captured at exactly the same time; makes later time series analysis more accurate

5. Slice timing Voxel in slice 1 Voxel in slice 5 10 slice volume Interpolated time course Estimated value at time of first slice

6. Within subject Registration / transformation of the time series Coregistration Single subject statistics +/- adjustment Motion correction Coregistration

7. Between subjects Subject 3 Subject 2 Subject 1 Template Average activation

8. Motion correction - why? Subjects will move... Small movements can cause large changes in signal A major, but not the only cause of this change in signal, is spatial mismatch Changes in signal due to movement can be much larger than BOLD activation signal –artefacts –increased variance in statistics due to noise

9. Motion correction and realignment registration - i.e. determining the 6 parameters that describe the rigid body transformation between each image and a reference image. transformation - i.e. resampling each image according to the determined transformation parameters. adjustment - signal in the spatially transformed images that could still have arisen due to movement is removed.

10. Registration - process Smooth the images –reduces high frequency noise Iterative automated scheme to calculate optimum parameters for rigid body transformations = translations in x y and z, rotations around x, y and z

11. Registration Automated realignments minimise a mathematical measure of image mismatch The measure is called the “cost function” In SPM the cost function is the (squared) difference of voxel intensities between the images

12. Cost function - on smoothed images Image 1 Image 2 DifferenceVariance

13. Registration: in summary Start somewhere Calculate the changes in the cost function, for all voxels, with small changes in the 6 parameters Put into matrices, and invert, to give a least squares linear guess at next best position, considering all voxels and all 6 parameters Iterate until there is a good match (small difference

14. Transformation (resampling) Creation of new images with transformation applied The positions of the voxels no longer exactly match the position of the original voxels We have to estimate the value of the voxel in the new position using the values of the surrounding voxels

15. Transformation - continued Bilinear Sinc

16. Transformation - summary On functional images, use linear interpolation –it is faster –after smoothing (for the statistics) there is little difference between sinc and linear interpolation –there may be problems using sinc interpolation on EPI images

17. Motion correction - problems... Even after realignment there is considerable movement related variance left. Possible reasons differ for PET and fMRI For PET - maybe mismatch between attenuation scan and emission scans over the scanning session For FMRI - more complex

18. Remaining movement effects Before realignmentAfter realignment Variance maps

19. Motion correction - FMRI Susceptibility artefacts –rigid body transform may be an inadequate model. Resampling can introduce errors –especially bi-linear interpolation Ghosts (and other artefacts) in the images –do not move according to the same rigid body rules Slices are not acquired simultaneously Spin excitation history effects.

20. Distortion A short return to MRI physics During image acquisition, a gradient is applied briefly in the phase-encode direction, to change the phase of the spins across the image +- Phase encode magnetic field gradient

21. Distortion, more The phase determines where the signal will go to in the image (in the phase-encode direction) If the magnetic field is different from that predicted by the gradient –the pixel will go to the wrong place –higher field - signal goes higher –lower field - signal goes lower The head changes the magnetic field -> distortions +-

22. Distortion T1T1 Raw EPI Why does this matter to the realignment? –Distortions depend on head position –As head position changes, so does the image shape –> rigid body realignment will not succeed

23. Distortion = non-rigid body OriginalDistorted Rotated, distorted and realigned ABCDE B - D

24. Distortion varying with movement Measurement of magnetic field at each pixel, for each EPI image - predicted distortions over time Distortions correlated with estimated motion Figure shows voxels with time-varying distortions that correlate with the motion parameters for rotation about x-axis (given below). Overlay on image slices shows voxels in which the variation in geometric distortion significantly correlates with subject rotation about x-axis (ear-to-ear).

25. Adjustment for motion Means using the derived movement parameters, or a function thereof, as confounds in the analysis. Was originally predicated on spin excitation history effects, but will in practice account for artefacts, ghosts etc. May remove parts of the signal of interest. Very small movements (<1mm, 1 degree) that correlate with the paradigm may be due to artefacts in the calculated registration caused by the activation signal

26. Coregistration Registration / transformation of the time series Coregistration Single subject statistics +/- adjustment Motion correction Coregistration

27. Matching the functional image to the structural image –Overlaying activation on individual anatomy –Better spatial image for normalization Two significant differences between coregistration and motion correction –The images do not have the same signal in the same areas - they cannot be subtracted –They may not be the same shape – EPI distortion

28. Problem 1: images are different When the images are perfectly matched, there will be large differences in signal (d(i)) between the images - we cannot do a simple least squares match Solution –Use a different cost function (AIR, FLIRT, SPM mutual information registration) EPIStructural

29. Images not the same - different cost function Mutual information –Measure of overlap of information between two images –Independent of actual intensities of corresponding areas in different images –Constructed from joint histogram of two images

30. Mutual Information Matching images without as many assumptions.

31. Mutual Information Matching images without as many assumptions.

32. Mutual information T2T1 T2 histogramT1 histogram Joint histogram After 10mm translation T2

33. Benefits of mutual information Less susceptible to holes in the image Does not require prior normalization and consequent potential for error Relatively quick Implemented in SPM and various other freely available packages

34. Working with more than one subject... May require spatial matching of brains = normalization Choices –Don’t normalize (highly recommended) –Use sulcal / fluid mechanical method need structural –Normalize using shape matching (SPM, AIR…) functional (EPI) or structural

35. for cross subject analyses –generalise findings to populations –compare populations to standard space –for reporting & comparison –e.g. “Talairach” space –defined by template image (s) Possibilities: –affine – translations, rotations, zooms, shears –non-linear – via spatial basis warps… –fluid Spatial normalization

36. Goal –To maximize the overlap of homologous areas between the two images –Reporting in standard space Problem –Huge variation in individual anatomy –No exact match between structure and function (as far as we know) Methods –Shape matching –Sulcal matching

37. Sulcal matching methods Fischl et al 1999 Shrink wrap method Shape matching method

38. Sulcal /FM matching methods Fischl et al Thompson et al Problems –Constraints may be necessary –Depend on sulcal functional correspondence –Good matching of cortex, not deep structures Schormann, Zilles et al (fluid mechanical) –Constraints / sulcal functional correspondence

39. Normalization - shape matching SPM, AIR, MNI, etc Start with affine match –Translations, rotations, zooms, maybe shears Nonlinear match –Optimize best series of nonlinear transformations to match image shape –In SPM - nonlinear transformations are cosine basis functions

40. Affine transformations Translation Rotation Zoom Shear

41. Deformation a linear combination of smooth basis warps 3D discrete cosine transform basis set Non-linear spatial normalisation…

42. Non-linear basis functions Light = shift voxels up (to brain left) Dark = shift voxels down (to right)

43. Deformations consist of a linear combination of smooth basis images. These are the lowest frequency basis images of a 3-D discrete cosine transform (DCT). Can be generated rapidly from a separable form. Algorithm simultaneously minimises –Sum of squared difference between template and object image. –Squared distance between the parameters and their known expectation (p T C 0 -1 p). p T C 0 -1 p describes the membrane energy of the deformations. Algorithm simultaneously minimises –Sum of squared difference between template and object image. –Squared distance between the parameters and their known expectation (p T C 0 -1 p). p T C 0 -1 p describes the membrane energy of the deformations. Non-linear normalization

44. Templat e image Affine Registration. (  2 = 472.1) Non-linear registration without regularisatio n. (  2 = 287.3) Non-linear registration using regularisatio n. (  2 = 302.7) Without the Bayesian formulation, the non-linear spatial normalisation can introduce unnecessary warping into the spatially normalised images.

45. Segmentation / normalization Create a probability function describing the likelihood of the current segmentation Combine with bias field and normalization Iterate to find the combination of gray / white distributions and bias / normalization parameters that are most probable in the image

46. The procedure Affine registration to template gray / white / csf using mutual information Estimate gray / white distributions Repeat until convergence –Optimize bias field –Optimize warping parameters –Optimize gray / white distributions Admire result

47. Initial Affine Registration The procedure begins with a Mutual Information affine registration of the image with the tissue probability maps. MI is computed from a 4x256 joint probability histogram. See D'Agostino, Maes, Vandermeulen & P. Suetens. “Non-rigid Atlas-to-Image Registration by Minimization of Class- Conditional Image Entropy”. Proc. MICCAI 2004. LNCS 3216, 2004. Pages 745-753. Background voxels excluded Joint Probability Histogram

48. Maximizing probability Create a probability model of the observed gray / white / CSF classification Use measure of probability over all voxels as measure of goodness of fit Maximize probability

49. A probability distribution Imagine the distribution of intensities of gray matter is Gaussian, mean5 and variance 2 Scale distribution to have area 1 Y axis is now probability of observing intensity

50. Assigning probability to the image In reality we don’t know the parameters of our model. They are what we want to estimate. You have your data Calculate your likelihoods p=0.069*0.162*0.003*... =1.86*10 -30 Not brilliant! ”Guess” values for the parameters, here µ=7 and σ 2 =1

51. Trying other parameters So, let us try some other values for the parameters. p=1.38*10 -15 Not bad! µ=5, σ 2 =4 p=9.41*10 -13 Wow! µ=5, σ 2 =1.5 µ=4.95, σ 2 =0.79 p=5.28*10 -12 And we have a winner (an ML estimate)! And, that is actually how simple it is (promise)!

52. More than one tissue class Multiple Gaussians per tissue class allow non- Gaussian intensity distributions to be modelled. –E.g. accounting for partial volume effects

53. Tissue Probability Maps Tissue probability maps (TPMs) are used instead of the proportion of voxels in each Gaussian as the prior. ICBM Tissue Probabilistic Atlases. These tissue probability maps are kindly provided by the International Consortium for Brain Mapping, John C. Mazziotta and Arthur W. Toga.

54. “Mixing Proportions” * Tissue probability maps for each class are included. * These maps give the probability of obtaining class k at voxel i

55. Modelling a Bias Field Non-homogeneity of the FMRI scanner ()() y y ()y ()

56. Deforming the Tissue Probability Maps * Tissue probability images are deformed according to parameters . * The probability of obtaining class k at voxel i, given weights  and parameters  is then:

57. The procedure - again Affine registration to template gray / white / csf using mutual information Estimate gray / white distributions Repeat until convergence –Optimize bias field –Optimize warping parameters –Optimize gray / white distributions (Gaussian means, variances, mixing proportions Admire result

58. Why this is a good thing Normalizing to tissue types makes customized templates less necessary It works very well!

59. Spatial normalization - problems Images may be far apart before matching - local minima Low resolution / image problems -> bizarre warps that may be difficult to diagnose Matching susceptible to deviations from the template image –intensity –image abnormalities

60. Spatial normalization - solutions Carefully inspect images for distortions Adjust image position before normalization to reduce risk of local minimum Intensity differences - consider local template Image abnormalities - cost function masking

61. Cost function masking

62. The End