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**Introduction to fMRI Analysis Vincent P. Giampietro**

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

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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 The Institute of Psychiatry is in Camberwell…

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**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:

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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**

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

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**The data 64 voxels 64 voxels One slice 100 images**

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

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**fMRI analysis Getting the images from the MR scanner**

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

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**Getting the data from MR**

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

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**Pre-processing the raw data**

Do we need it ? Really bad dataset with huge head motion Without With Simon Surguladze

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**Pre-processing the raw data**

movement correction 1 detrending 2 smoothing 3 preprocessed data

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**Pre-processing the raw data**

Movement correction The two main movement artefacts in fMRI are: between scans stimulus correlated Rozmin Halari

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**Pre-processing the raw data**

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

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**Pre-processing the raw data**

Stimulus correlated motion Analysis only Motion correction + analysis Motion correction + spin excitation history correction + analysis Stimulus correlated motion is fitted as “activated” by the model Without motion and spin correction, the results are useless

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**Pre-processing the raw data**

Stimulus uncorrelated motion Analysis only Motion correction + analysis Motion correction + spin excitation history correction + analysis Stimulus uncorrelated motion doesn’t “mess up” the results Motion and spin correction increase the power the fMRI analysis

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**Pre-processing the raw data**

Detrending – Spin excitation history correction Without With 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

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**Pre-processing the raw data**

Detrending – Spin excitation history correction Magnetic field Problem in space Problem in time

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**Pre-processing the raw data**

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

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**Pre-processing the raw data**

Detrending – Other trends Ray Norbury Non-linear but periodic trends Easily “filtered out” using high/low/band-pass filters

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**Pre-processing the raw data**

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

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**Pre-processing the raw data**

Smoothing – Spatial filtering Mean filter 1125 1014 850 1310 1243 1138 1315 1338 1282 126 1 3x3 mean filter (convolution) 1180 Σ New value = 1/9 x Pixeli,j x Filteri,j

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**Pre-processing the raw data**

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

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**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…

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**Pre-processing the raw data**

Smoothing – Temporal filtering Moving average filter Time 8-point low pass

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**Analysing a single subject experiment**

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

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**Analysing a single subject experiment**

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

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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 series Fitted model

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**Analysing a single subject experiment**

Model fitting – Bad fit (1 gamma function)

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**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)

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**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

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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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**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

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**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

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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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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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**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…

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**Spatial Normalisation**

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

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**Spatial Normalisation**

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

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**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

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**Spatial Normalisation**

The results

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**Spatial Normalisation**

The results 2D 3 D

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**Spatial Normalisation**

The results in virtual reality

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**Analysing groups of subjects**

Group mapping differences Individual analysis ANCOVA Individual analysis similarities 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 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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**Introduction to fMRI Analysis Vincent P. Giampietro**

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

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Opportunity to Participate EEG studies of vision/hearing/decision making – takes about 2 hours Sign up at www.tatalab.cawww.tatalab.ca – Keep checking.

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