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Last Time• Motion Correction

– Mutual Information– Optimization– Decoupling Translation & Rotation– Interpolation

• SPM Example (Least Squares & MI)• A Simple Derivation

This Time• Reslice example…• Spatial Normalization• SPM Example

Spatial Normalization: Remind ourselves what a typical functional image volume looks like:

1) Non-uniform Local Field Causes Local Dephasing

Sagittal Bo field map at 3T5 water protons in different parts of the voxel…

z

slowest

fastestx

y

z90°

T = 0 T = TE

Local susceptibility gradients: thru-plane dephasing

Bad for thick slice above frontal sinus…

Thru-plane dephasing: worse at long TE

3T, TE = 21, 30, 40, 50, 60ms

2

Susceptibility in EPI can give either a compression or expansion

Altering the direction kspace is transversed causes either local compression or expansion.

choose your poison…

3T whole body gradients

Susceptibility Causes Image Distortion

Field near sinus

z

Echoplanar Image, Δθ α encode time α 1/BW

Encode time = 34, 26, 22, 17ms 3T head gradients

Use shortest possible encoding

RealignmentRealignment

fMRI timefMRI time--seriesseries

Slice Slice orderorder

‘‘UnwarpUnwarp’’

Slice timingSlice timing

ReorientReorient

fMRI Data analysis fMRI Data analysis

fMRI Data analysis

RealignmentRealignment

fMRI timefMRI time--seriesseries

NormalisationNormalisation

TemplateTemplate

Slice Slice orderorder

‘‘UnwarpUnwarp’’

Slice timingSlice timing

ReorientReorient

TalairachTalairach Coordinate SystemCoordinate System

to provide mechanism for comparing data

across different labs/studies

Talairach coordinate system (space)• Atlas provided by Talairach

and Tournoux– Based on a French woman’s

brain– Center (0,0,0 is on the anterior

commisure)– Line passes through the

Anterior commisure – Posterior commisure line (a.k.a., AC-PC line)

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Talairach Coordinate System

Source: Brain Voyager course slidesNote: That’s TalAIRach, not TAILarach!

Individual brains are different shapes and sizes…How can we compare or average brains?

Talairach & Tournoux, 1988• squish or stretch brain into “shoe box”• extract 3D coordinate (x, y, z) for each activation focus

Rotate brain into ACPC plane

Find posterior commisure (PC)

Find anterior commisure (AC)

ACPC line= horizontal axis

Corpus Callosum

Fornix

Pineal Body“bent asparagus”

Note: official Tal sez use top of AC and bottom of PC

Source: Duvernoy, 1999

Squish or stretch brain to fit in “shoebox”of Tal system

Deform brain into Talairach space

yAC=0 y>0y<0

ACPC=0

y>0

y<0

z

x

Extract 3 coordinates

Mark 8 points in the brain:• anterior commisure• posterior commisure• front• back• top• bottom (of temporal lobe)• left• right

Talairach Atlas

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Talairach Pros and ConsAdvantages• widespread system• allows averaging of fMRI data between subjects• allows researchers to compare activation foci• easy to use

Disadvantages• based on the squished brain of an elderly alcoholic woman (how representative is that?!)• not appropriate for all brains (e.g., Japanese brains don’t fit well)• activation foci can vary considerably – other landmarks like sulci may be more reliable•Ignores left/right differences

Left is what?!!!Neurologic (i.e. sensible) convention

• left is left, right is right

L R

Radiologic (i.e. stupid) convention• left is right, right is left

R L

Note: Make sure you know what your magnet and software are doing before publishing left/right info!

x = 0-+

x = 0+-

Note: If you’re really unsure which side is which, tape a vitamin E capsule to the one side of the subject’s head. It will show up on the anatomical image.

Talairach vs MNI

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

Talairach space• Revised in spm96 using MNI brain

– Montreal Neurological Institute• Based on 304 normal subjects • More representative of population• 10-15% larger than Talairach space

• Much confusion in the literature• Must convert to ‘Talairach’ to ‘MNI’ space• Meta-analyses• Planning studies, regions of interest• Different groups/software use different methods• Manuscripts must specify the ‘actual space’ used

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Spatial Transformations: Warping Strategies

• Label-based (identifiable features)– Identification of homologous structures

(features, landmarks) between 2 images– Find transformation that best superposes

labeled points• Non-label-based (no corresponding feature)

– Spatial transformation minimizing index of difference between images

Spatial Normalization

RealignmentRealignment

fMRI timefMRI time--seriesseries

NormalisationNormalisation

TemplateTemplate

Slice Slice orderorder

‘‘UnwarpUnwarp’’

Slice timingSlice timing

‘‘MeanMean’’ functional EPI imagefunctional EPI image StructuralStructural imageimage (T1)(T1)

EPI templateEPI template T1 templateT1 template

Spatial Normalization‘‘MeanMean’’ functional imagefunctional image StructuralStructural imageimage (T1)(T1)

EPI templateEPI template T1 templateT1 template

CoCoregister subjectregister subject’’s s ‘‘mean EPImean EPI’’to to ‘‘structural T1 imagestructural T1 image’’

Problems:Problems:-- coregcoreg is linear operation is linear operation ––

-- EPI warping andEPI warping and-- EPI distortion not accountedEPI distortion not accounted

--Unless you have:Unless you have:‘‘field map correctionfield map correction’’--issues issues –– slow acquisitionslow acquisition

Normalize T1 Normalize T1 to T1 Templateto T1 Template

Spatial Normalization‘‘MeanMean’’ functional imagefunctional image StructuralStructural imageimage (T1)(T1)

EPI templateEPI template T1 templateT1 template

Good:Good:-- normalization has linear and normalization has linear and

nonlinear componentsnonlinear components-- EPI warping andEPI warping and-- EPI distortion accounted forEPI distortion accounted for

--Even better if you have:Even better if you have:‘‘field map correctionfield map correction’’--issues issues –– slow acquisitionslow acquisition

Bad Bad –– If If ‘‘mean EPImean EPI’’ is different is different from from ‘‘EPI templateEPI template’’normalization can go wrong normalization can go wrong

-- tune normalization tune normalization -- customize basis functionscustomize basis functions-- create create ‘‘sitesite’’ templatetemplate

Normalize Normalize ‘‘mean EPImean EPI’’ to to EPI TemplateEPI Template

Spatial Normalization Spatial Normalization• Data must be ‘resliced’ into new MNI

(Talairach space)• Data must be ‘interpolated’ – sinc most

likely best • Must choose voxel sizes to reslice into:

– Inputs were 3.44 x 3.44 x 5.00mm • Default is 2.00 x 2.00 x 2.00 • We use 3.00 x 3.00 x 3.00

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Spatial Normalisation - Non-linearDeformations consist of a linear combination of smooth basis functions

These are the lowest frequencies of a 3D discrete cosine transform (DCT)

Algorithm simultaneously minimises* Mean squared difference between

template and source image * Squared distance between parameters

and their known expectation

TemplateTemplateWarpedOriginal

Deformation Field

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⎤

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⎡=

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⎣

⎡

)z,y,x(t)z,y,x(t)z,y,x(t

'z'y'x

3

2

1

Deformation field

Jacobians

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

z'z

y'z

x'z

z'y

y'y

x'y

z'x

y'x

x'x

jjjjjjjjj

J

333231

232221

131211

Jacobian Matrix (or just “Jacobian”)

)jjjj(j)jjjj(j)jjjj(jJ 221323123132133312213223332211 −+−−−=

Jacobian Determinant (or just “Jacobian”) - relative volumes

Spatial Normalisation - Procedure

Non-linear registration

Begin with affine registrationNon-linear registration (about 1000 parameters)

Affine registration

Affine vs Non-Rigid – A Look at the transformation

Non-Rigid ~ 2000 parametersAffine – 12 parameters

Affine vs Non-Rigid

Average Anatomical Images from 10 Subjects displayed at 1.5x1.5x1.5 mm

Affine Non-Rigid

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SPM Example

• Spatial Normalization

Next Time

• Filtering of Physiologic Signals, Drift, Etc