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BIAU Brain Image Analysis Unit Biostatistics & Computing Institute of Psychiatry London, U.K. Vincent P. Giampietro Introduction to fMRI Analysis

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London

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London

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London The Institute of Psychiatry is in Camberwell…

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London

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

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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)

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

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

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The data One slice 100 images One image 4096 voxels Voxels 64 voxels 3.75mm 1 TR = 3s t=1xTR=3s t=100xTR=300s

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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 I have scanned a subject What should I do next? How do I get the red blobs?

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Getting the data from MR The grand image format debate Public server your Sun/PC Soon - DICOM format DICOM Digital Imaging and COmmunication in Medicine Now - Native MR scanner format Soon - NIfTI format NIfTI Neuroimaging Informatics Technology Initiative MR scanner Now - Analyze format The files are anonymised

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Pre-processing the raw data Do we need it ? WithoutWith Really bad dataset with huge head motion Simon Surguladze

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Pre-processing the raw data raw data movement correctiondetrendingsmoothing preprocessed data 123

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

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

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

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Pre-processing the raw data Stimulus uncorrelated motion Stimulus uncorrelated motion doesnt mess up the results Motion and spin correction increase the power the fMRI analysis Motion correction + spin excitation history correction + analysis Analysis only Motion correction + analysis

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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 Pre-processing the raw data Detrending – Spin excitation history correction Without With

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Problem in space Magnetic field Problem in time Pre-processing the raw data Detrending – Spin excitation history correction

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

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

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

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Pre-processing the raw data Smoothing – Spatial filtering Mean filter Σ New value = 1/9 x Pixel i,j x Filter i,j x3 mean filter (convolution)

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

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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? CC A –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… Pre-processing the raw data Smoothing – Spatial filtering

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

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Analysing a single subject experiment The model file – Experiment description 39s 30s AUDIO VISUAL 5mn … … … … Model file for block design Model file for event related design t=0.501s t=14.560s 1 TR (3s)

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Analysing a single subject experiment 4s8s Gamma Variate Kernels The model file – Experiment description Experiment Real BOLD response or - Physiological models (Balloon model) - Adaptive models (GLM extensions) - Model free analysis (ICA) - 1 Gamma function & its 1 st derivative

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

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

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Analysing a single subject experiment Model fitting – Good fit (1 gamma function) Real time seriesFitted model

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

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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) Analysing a single subject experiment Model fitting

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Non parametric statistics (the way we do it) –Statistic used: Sum of Square Quotient (SSQ) –SSQ = ratio of model to residual sum of squares Analysing a single subject experiment Model fitting –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

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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)

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

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A Simple example –6 permutations possible of the patients to form 2 groups –We calculate the t statistic for every permutation Analysing a single subject experiment Randomisation tests ??? –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 real (observed) situation

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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 !

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Analysing a single subject experiment The results AUDIO VISUAL

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Interlude…

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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

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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 –MNIICB M –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… Spatial Normalisation Brain templates

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Spatial Normalisation Talairach mapping fMRI 1st registration Structural space 2nd registration Talairach space High-resolution structural image Talairach template

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

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The results Spatial Normalisation 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

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Spatial Normalisation The results

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Spatial Normalisation 2D The results

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The results in virtual reality Spatial Normalisation

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Analysing groups of subjects Individual analysis Group mapping ANCOVA differences similarities Individual analysis Group mapping

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Using more advanced analysis methods Improved registration/warping (e.g. non-linear) Constrained BOLD fit / Wavelet denoising New randomisation methods (e.g. cyclic wavelet permutation of the residuals) Trend analysis Path analysis Connectivity analysis Time series extraction Correlation/Partial Correlation analysis Real time fMRI analysis Combined EEG/fMRI …

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Conclusion Most of the analysis packages give you robust semi-automated methods of fMRI analysis from MR to ANCOVA and much more… The analysis process can look like a black box but we make our best to try to explain what we are doing validating In all the labs, there is constant work on improving and validating the existing methods and on writing the next ones… Please, be patient and understanding !!! (especially if you are a beta tester…)

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BIAU Brain Image Analysis Unit Biostatistics & Computing Institute of Psychiatry London, U.K. Vincent P. Giampietro Introduction to fMRI Analysis

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