Statistical Parametric Mapping (SPM) 1. Talk I: Spatial Preprocessing 2. Talk II: General Linear Model 3. Talk III:Statistical Inference 3. Talk IV: Experimental Design. Spatial Preprocessing & Computational Neuroanatomy With thanks to:
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Statistical Parametric
Mapping (SPM)
1. Talk I: Spatial Preprocessing
2. Talk II: General Linear Model
3. Talk III:Statistical Inference
3. Talk IV: Experimental Design
Spatial Preprocessing &
Computational Neuroanatomy
With thanks to:
John Ashburner, Jesper Andersson
Statistical Parametric Map
Design matrix
fMRI timeseries
kernel
Motion
correction
Smoothing
General Linear Model
Spatial
normalisation
Parameter Estimates
Standard
template
Overview
Overview
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Betweenmodality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
Overview
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Betweenmodality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
Squared Error
Rigid body transformations parameterised by:
Translations
Pitch
Roll
Yaw
x1 = m1,1x0 + m1,2y0 + m1,3z0 + m1,4
y1 = m2,1x0 + m2,2y0 + m2,3z0 + m2,4
z1 = m3,1x0 + m3,2y0 + m3,3z0 + m3,4
Nearest Neighbour
Linear
Full sinc (no alias)
Windowed sinc
2. Transformation (reslicing)
Residual Errors after Realignment
New in
SPM2
Fieldmap
Distorted image
Corrected image
Unwarp
New in
SPM2
Estimated derivative fields
Pitch
+
B0
Roll
Unwarp
New in
SPM2
(0thorder term can be determined from fieldmap)
+ error
+
=
+
B0{i}
fi
f1
B0

+2
1
i
i
+ ... +5
+ ...
i
Unwarp
New in
SPM2
No correction
Correction by covariation
Correction by Unwarp
tmax=13.38
tmax=5.06
tmax=9.57
Unwarp
Example: Movement correlated with design
Overview
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Betweenmodality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
Spatially normalised
Original image
Spatial Normalisation
Template
image
Deformation field
Rigid body
Rotation
Shear
Translation
Zoom
Insufficieny of Affineonly normalisation
Six affine + nonlinear registered
Template
image
Affine Registration
(2 = 472.1)
Nonlinear
registration
with
regularisation
(2 = 302.7)
Nonlinear
registration
without
regularisation
(2 = 287.3)
Without the Bayesian formulation, the nonlinear spatial normalisation can introduce unnecessary warping into the spatially normalised images
Empirically generated priors
1) affine transformations
2) nonlinear deformations
Overview
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Betweenmodality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
FWHM
Gaussian smoothing kernel
Overview
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Betweenmodality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
T1
Transm
T2
PD
PET
EPI
I. Via Templates:
1) Simultaneous affine registrations between each image and samemodality template
2) Segmentation into grey and white matter
3) Final simultaneous registration of segments
II. Mutual Information
Between Modality Coregistration: I. Via Templates
1. Affine Registrations
2. Segmentation
New in
SPM2
Another way is to maximise the Mutual Information in the 2D histogram (plot of one image against other)
For histograms normalised to integrate to unity, the Mutual Information is:
SiSj hij log hij
Sk hikSl hlj
PET
T1 MRI
Overview
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Betweenmodality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
Priors:
Intensity histogram
fit by multiGaussians
.
Image:
GM
WM
CSF
Brain/skull
Overview
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Betweenmodality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
Original
Template
Spatial Normalisation
Normalised
Deformation field
TBM
VBM
DBM
Spatially
normalised
Segmented
grey matter
Original
image
Smoothed
SPM
VoxelBased Morphometry (VBM)
A voxel by voxel statistical analysis is used to detect regional differences in the amount of grey matter between populations
“Optimised” VBM involves segmenting images before normalising, so as to normalise gray matter / white matter / CSF separately...
T1 image
template
Optimised VBM
Affine registration
Affine transform
priors
Segmentation & Extraction
STATS
volume
smooth
Spatial normalisation
Modulation
Apply deformation
Segmentation & extraction
Normalised T1
STATS
concentration
smooth
Grey matter volume
loss with age
superior parietal
pre and post central
insula
cingulate/parafalcine
VBM Examples: Aging
Females > Males
Males > Females
L superior temporal sulcus
R middle temporal gyrus
intraparietal sulci
mesial temporal
temporal pole
anterior cerebellar
VBM Examples: Sex Differences
Right frontal and left occipital petalia
VBM Examples: Brain Asymmetries
Vector field
Tensor field
Morphometry on deformation fields: DBM/TBM
Deformationbased Morphometry
looks at absolute displacements
Tensorbased Morphometry
looks at local shapes
Deformation
fields
...
Remove positional and size information  leave shape
Parameter reduction using principal component analysis (SVD)
Multivariate analysis of covariance used to identify differences between groups
Canonical correlation analysis used to characterise differences between groups
Deformationbased Morphometry (DBM)
Nonlinear warps of sex differences characterised by canonical variates analysis
Mean differences (mapping from an average female to male brain)
DBM Example: Sex Differences
Original
Warped
Template
Relative volumes
Strain tensor
Tensorbased morphometry
If the original Jacobian matrix is donated by A, then this can be decomposed into: A = RU, where R is an orthonormal rotation matrix, and U is a symmetric matrix containing only zooms and shears.
Strain tensors are defined that model the amount of distortion. If there is no strain, then tensors are all zero. Generically, the family of Lagrangean strain tensors are given by: (UmI)/m when m~=0, and log(U) if m==0.
References
Friston et al (1995): Spatial registration and normalisation of images.Human Brain Mapping 3(3):165189
Ashburner & Friston (1997): Multimodal image coregistration and partitioning  a unified framework.NeuroImage 6(3):209217
Collignon et al (1995): Automated multimodality image registration based on information theory.IPMI’95 pp 263274
Ashburner et al (1997): Incorporating prior knowledge into image registration.NeuroImage 6(4):344352
Ashburner et al (1999): Nonlinear spatial normalisation using basis functions.Human Brain Mapping 7(4):254266
Ashburner & Friston (2000): Voxelbased morphometry  the methods.NeuroImage 11:805821