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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)
3
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
4
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
5
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
6
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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⎣
⎡
)z,y,x(t)z,y,x(t)z,y,x(t
'z'y'x
3
2
1
Deformation field
Jacobians
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
∂∂
∂∂
∂∂
∂∂
∂∂
∂∂
∂∂
∂∂
∂∂
=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
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y'z
x'z
z'y
y'y
x'y
z'x
y'x
x'x
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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
7
SPM Example
• Spatial Normalization
Next Time
• Filtering of Physiologic Signals, Drift, Etc