OverviewOverviewOverviewOverview

Motioncorrection

Smoothing

kernel

Spatialnormalisation

Standardtemplate

fMRI time-series Statistical Parametric Map

General Linear Model

Design matrix

Parameter Estimates

PHJPHJa) Direct Normalization a) Direct Normalization

i) Realign -> Slice Time* -> Normalization -> i) Realign -> Slice Time* -> Normalization -> Smoothing Smoothing

b) Indirect Normalization b) Indirect Normalization

i)i) Realign -> Slice Time* -> Coregistration -> Realign -> Slice Time* -> Coregistration -> Segmentation -> Normalization ->Smoothing Segmentation -> Normalization ->Smoothing

* optional* optional

fMRI time-series

Motion corrected Mean functional

REALIGN

Lars KasperLars Kasper

33Signal, Noise and PreprocessingSignal, Noise and Preprocessing

RealignmentRealignment

Aligns all volumes of all runs spatially

Rigid-body transformation: three translations, three rotations

Objective function: mean squared error of corresponding voxel intensities

Voxel correspondence via Interpolation

Realignment Output: Realignment Output: ParametersParameters

Lars KasperLars Kasper

Signal, Noise and PreprocessingSignal, Noise and Preprocessing 44

The preprocessing sequence revistedThe preprocessing sequence revisted

RealignmentRealignment– Motion correction: Adjust for movement between Motion correction: Adjust for movement between

slicesslices

CoregistrationCoregistration– Overlay structural and functional images: Link Overlay structural and functional images: Link

functional scans to anatomical scanfunctional scans to anatomical scan

NormalisationNormalisation– Warp images to fit to a standard template brainWarp images to fit to a standard template brain

SmoothingSmoothing– To increase signal-to-noise ratioTo increase signal-to-noise ratio

Extras (optional)Extras (optional)– Slice timing correction; unwarpingSlice timing correction; unwarping

Co-registrationCo-registration

Term co-registration applies to any Term co-registration applies to any method for aligning imagesmethod for aligning images– By this token, motion correction is also co-By this token, motion correction is also co-

registrationregistration

However, term is usually used to refer to However, term is usually used to refer to alignment of images from different alignment of images from different modalities. E.g.:modalities. E.g.:– Low resolution T2* fMRI scan (EPI image) to Low resolution T2* fMRI scan (EPI image) to

high resolution, T1, structural image from the high resolution, T1, structural image from the same individualsame individual

Co-registration: Principles behind Co-registration: Principles behind this step of processingthis step of processing

When several images of the same When several images of the same participants have been acquired, it is participants have been acquired, it is useful to have them all in registeruseful to have them all in register

Image registration involves estimating a Image registration involves estimating a set of parameters describing a spatial set of parameters describing a spatial transformation that ‘best ‘ matches the transformation that ‘best ‘ matches the images togetherimages together

fMRI to structuralfMRI to structural

Matching the functional image Matching the functional image to the structural imageto the structural image– Overlaying activation on Overlaying activation on

individual anatomyindividual anatomy– Better spatial image for Better spatial image for

normalisationnormalisation

Two significant differences Two significant differences between co-registering to between co-registering to structural scans and motion structural scans and motion correctioncorrection– When co-registering to When co-registering to

structural, the images do not structural, the images do not have the same signal intensity have the same signal intensity in the same areas; they in the same areas; they cannot be subtractedcannot be subtracted

– They may not be the same They may not be the same shapeshape

Problem: Images are differentProblem: Images are different

Differences in signal intensity between the Differences in signal intensity between the imagesimages

Normalise to appropriate template (EPI to EPI; T1 to T1), then segmentNormalise to appropriate template (EPI to EPI; T1 to T1), then segment

SegmentationSegmentation

Use the gray/white estimates from the Use the gray/white estimates from the normalisation step as starting estimates of the normalisation step as starting estimates of the probability of each voxel being grey or white probability of each voxel being grey or white mattermatterEstimate the mean and variance of the Estimate the mean and variance of the gray/white matter signal intensitiesgray/white matter signal intensitiesReassign probabilities for voxels on basis ofReassign probabilities for voxels on basis of– Probability map from templateProbability map from template– Signal intensity and distributions of intensity for Signal intensity and distributions of intensity for

gray/white mattergray/white matter

Iterate until there is a good fitIterate until there is a good fit

Register segmented imagesRegister segmented images

Grey/white/CSF probability images for EPI Grey/white/CSF probability images for EPI (T2*) and T1(T2*) and T1

Combined least squares match Combined least squares match (simultaneously) of gray/white/CSF (simultaneously) of gray/white/CSF images of EPI (T2*) + T1 segmented images of EPI (T2*) + T1 segmented imagesimages

The preprocessing sequence revistedThe preprocessing sequence revisted

RealignmentRealignment– Motion correction: Adjust for movement between Motion correction: Adjust for movement between

slicesslices

CoregistrationCoregistration– Overlay structural and functional images: Link Overlay structural and functional images: Link

functional scans to anatomical scanfunctional scans to anatomical scan

NormalisationNormalisation– Warp images to fit to a standard template brainWarp images to fit to a standard template brain

SmoothingSmoothing– To increase signal-to-noise ratioTo increase signal-to-noise ratio

Extras (optional)Extras (optional)– Slice timing correction; unwarpingSlice timing correction; unwarping

NormalisationNormalisation

This enables:This enables:– Signal averaging across Signal averaging across

participants:participants:Derive group statistics -> generalise Derive group statistics -> generalise findings to populationfindings to populationIdentify commonalities and differences Identify commonalities and differences between groups (e.g., patient vs. between groups (e.g., patient vs. healthy)healthy)

– Report results in standard co-Report results in standard co-ordinate system (e.g. Talairach and ordinate system (e.g. Talairach and Tournoux stereotactic space)Tournoux stereotactic space)

Goal:Goal: Register images from different participants Register images from different participants into roughly the same co-ordinate system (where the into roughly the same co-ordinate system (where the co-ordinate system is defined by a template image)co-ordinate system is defined by a template image)

Matthew Brett

Standard spacesStandard spaces

The MNI template follows the convention of T&T, but doesn’t match the particular brain

Recommended reading: http://imaging.mrc-cbu.cam.ac.uk/imaging/MniTalairach

The Talairach Atlas The MNI/ICBM AVG152 Template

SPM: Spatial NormalisationSPM: Spatial Normalisation

SPM adopts a two-stage procedure to determine SPM adopts a two-stage procedure to determine a transformation that minimises the sum of a transformation that minimises the sum of squared differences between images:squared differences between images:

Step 1:Step 1: Linear transformation (12-parameter affine) Linear transformation (12-parameter affine)Step 2:Step 2: Non-linear transformation (warping) Non-linear transformation (warping)

High-dimensionality problemHigh-dimensionality problemThe affine and warping transformations are The affine and warping transformations are constrained within an empirical Bayesian constrained within an empirical Bayesian framework (i.e., using prior knowledge of the framework (i.e., using prior knowledge of the variability of head shape and size): “variability of head shape and size): “maximum a maximum a posteriori” posteriori” (MAP)(MAP) estimates of the registration estimates of the registration parametersparameters

Step 1: Affine TransformationStep 1: Affine Transformation

Determines the Determines the optimum 12-parameter optimum 12-parameter affine transformation to affine transformation to match the match the sizesize and and positionposition of the images of the images12 parameters = 3 12 parameters = 3 translations and 3 translations and 3 rotations (rigid-body) + rotations (rigid-body) + 3 shears and 3 zooms3 shears and 3 zooms

Rotation Shear

Translation Zoom

Step 2: Non-linear RegistrationStep 2: Non-linear Registration

Assumes prior approximate Assumes prior approximate registration with 12-parameter registration with 12-parameter affine stepaffine step

Modelled by linear Modelled by linear combinations of smooth combinations of smooth discrete cosine basis functions discrete cosine basis functions (3D)(3D)

Choice of basis functions Choice of basis functions depend on distribution of warps depend on distribution of warps likely to be requiredlikely to be required

For speed and simplicity, uses For speed and simplicity, uses a “small” number of a “small” number of parameters (~1000)parameters (~1000)

Matthew Brett

2-D visualisation 2-D visualisation (horizontal and vertical (horizontal and vertical deformations):deformations):

BrainBrain visualisation:visualisation:

Ashburner; HBF Chap 3

Source

Deformation field

Warped image

Template

SMOOTH

GLMMNI Space

SmoothingSmoothing

Signal, Noise and Signal, Noise and PreprocessingPreprocessing 2222

Why blurring the data?Why blurring the data? Improves spatial overlap by blurring over Improves spatial overlap by blurring over

anatomical differencesanatomical differences Suppresses thermal noise (Suppresses thermal noise (averagingaveraging)) Increases sensitivity to effects of similar Increases sensitivity to effects of similar

scale to kernel (scale to kernel (matched filter theoremmatched filter theorem)) Makes data more normally distributed Makes data more normally distributed

((central limit theoremcentral limit theorem)) Reduces the effective number of multiple Reduces the effective number of multiple

comparisonscomparisons

Lars KasperLars Kasper

How is it implemented? Convolution with a 3D Gaussian

kernel, of specified full-width at half-maximum (FWHM) in mm

SmoothingSmoothingLars Kasper: A ToolboxLars Kasper: A Toolbox

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