Statistical Parametric Mapping (SPM) 1. Talk I: Spatial Pre-processing

Statistical ParametricMapping (SPM)

1. Talk I: Spatial Pre-processing

2. Talk II: General Linear Model

3. Talk III: Statistical Inference

3. Talk IV: Experimental Design

Statistical ParametricMapping (SPM)

1. Talk I: Spatial Pre-processing

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

Spatial Preprocessing & Computational Neuroanatomy

With thanks to: John Ashburner, Jesper Andersson

OverviewOverviewOverviewOverview

Motioncorrection

Smoothing

kernel

Spatialnormalisation

Standardtemplate

fMRI time-series Statistical Parametric Map

General Linear Model

Design matrix

Parameter Estimates

1. Realignment (motion correction)

2. Normalisation (to stereotactic space)

3. Smoothing

4. Between-modality Coregistration

5. Segmentation (to gray/white/CSF)

6. Morphometry (VBM/DBM/TBM)



3. Smoothing







3. Smoothing






3. Smoothing





Reasons for Motion CorrectionReasons for Motion CorrectionReasons for Motion CorrectionReasons for Motion Correction

• Subjects will always move in the scannerSubjects will always move in the scanner

• The sensitivity of the analysis depends on the residual noise in the image series, so The sensitivity of the analysis depends on the residual noise in the image series, so movement that is unrelated to the subject’s task will add to this noise and hence movement that is unrelated to the subject’s task will add to this noise and hence realignment will increase the sensitivity realignment will increase the sensitivity

• However, subject movement may also correlate with the task…However, subject movement may also correlate with the task…

• ……in which case realignment may reduce sensitivity (and it may not be possible to in which case realignment may reduce sensitivity (and it may not be possible to discount artefacts that owe to motion)discount artefacts that owe to motion)

• Subjects will always move in the scannerSubjects will always move in the scanner

• The sensitivity of the analysis depends on the residual noise in the image series, so The sensitivity of the analysis depends on the residual noise in the image series, so movement that is unrelated to the subject’s task will add to this noise and hence movement that is unrelated to the subject’s task will add to this noise and hence realignment will increase the sensitivity realignment will increase the sensitivity

• However, subject movement may also correlate with the task…However, subject movement may also correlate with the task…

• ……in which case realignment may reduce sensitivity (and it may not be possible to in which case realignment may reduce sensitivity (and it may not be possible to discount artefacts that owe to motion)discount artefacts that owe to motion)

• RealignmentRealignment (of (of same-modality same-modality images from images from same subjectsame subject) involves two stages:) involves two stages:

– 1. Registration1. Registration - determining the 6 parameters that describe the rigid body - determining the 6 parameters that describe the rigid body transformation between each image and a reference imagetransformation between each image and a reference image

– 2. Transformation (reslicing) 2. Transformation (reslicing) - re-sampling each image according to the - re-sampling each image according to the determined transformation parametersdetermined transformation parameters

• RealignmentRealignment (of (of same-modality same-modality images from images from same subjectsame subject) involves two stages:) involves two stages:

– 1. Registration1. Registration - determining the 6 parameters that describe the rigid body - determining the 6 parameters that describe the rigid body transformation between each image and a reference imagetransformation between each image and a reference image

– 2. Transformation (reslicing) 2. Transformation (reslicing) - re-sampling each image according to the - re-sampling each image according to the determined transformation parametersdetermined transformation parameters

1. Registration1. Registration1. Registration1. Registration

• Determine the Determine the rigid body transformationrigid body transformation that minimises the sum of squared that minimises the sum of squared difference between imagesdifference between images

• Rigid body transformation is defined by:Rigid body transformation is defined by:– 3 3 translationstranslations - in X, Y & Z directions - in X, Y & Z directions

– 3 3 rotationsrotations - about X, Y & Z axes - about X, Y & Z axes

• Operations can be represented as Operations can be represented as affineaffine transformation matrices: transformation matrices:

xx11 = m = m1,11,1xx00 + m + m1,21,2yy00 + m + m1,31,3zz00 + m + m1,41,4

yy11 = m = m2,12,1xx00 + m + m2,22,2yy00 + m + m2,32,3zz00 + m + m2,42,4

zz11 = m = m3,13,1xx00 + m + m3,23,2yy00 + m + m3,33,3zz00 + m + m3,43,4

• Determine the Determine the rigid body transformationrigid body transformation that minimises the sum of squared that minimises the sum of squared difference between imagesdifference between images

• Rigid body transformation is defined by:Rigid body transformation is defined by:– 3 3 translationstranslations - in X, Y & Z directions - in X, Y & Z directions

– 3 3 rotationsrotations - about X, Y & Z axes - about X, Y & Z axes

• Operations can be represented as Operations can be represented as affineaffine transformation matrices: transformation matrices:

xx11 = m = m1,11,1xx00 + m + m1,21,2yy00 + m + m1,31,3zz00 + m + m1,41,4

yy11 = m = m2,12,1xx00 + m + m2,22,2yy00 + m + m2,32,3zz00 + m + m2,42,4

zz11 = m = m3,13,1xx00 + m + m3,23,2yy00 + m + m3,33,3zz00 + m + m3,43,4

1 0 0 Xtrans

0 1 0 Ytrans

0 0 1 Ztrans

0 0 0 1

1 0 0 0

0 cos() sin() 0

0 sin() cos() 0

0 0 0 1

cos() 0 sin() 0

0 1 0 0

sin() 0 cos() 0

0 0 0 1

cos() sin() 0 0

sin() cos() 0 0

0 0 1 0

0 0 0 1

Translations Pitch Roll Yaw

Rigid body transformations parameterised by:

Squared Error

1. Registration1. Registration1. Registration1. Registration

• Iterative procedure (Gauss-Iterative procedure (Gauss-Newton ascent)Newton ascent)

• Additional scaling parameterAdditional scaling parameter

• Nx6 matrix of realignment Nx6 matrix of realignment parameters written to file (N is parameters written to file (N is number of scans)number of scans)

• Orientation matrices in *.mat Orientation matrices in *.mat file updated for each volume file updated for each volume (do not have to be resliced) (do not have to be resliced)

• Slice-timing correction can be Slice-timing correction can be performed before or after performed before or after realignment (depending on realignment (depending on acquisition)acquisition)

• Iterative procedure (Gauss-Iterative procedure (Gauss-Newton ascent)Newton ascent)

• Additional scaling parameterAdditional scaling parameter

• Nx6 matrix of realignment Nx6 matrix of realignment parameters written to file (N is parameters written to file (N is number of scans)number of scans)

• Orientation matrices in *.mat Orientation matrices in *.mat file updated for each volume file updated for each volume (do not have to be resliced) (do not have to be resliced)

• Slice-timing correction can be Slice-timing correction can be performed before or after performed before or after realignment (depending on realignment (depending on acquisition)acquisition)

• Application of registration parameters involves Application of registration parameters involves re-samplingre-sampling the image to create new voxels by the image to create new voxels by interpolation from existing voxelsinterpolation from existing voxels

• InterpolationInterpolation can be nearest neighbour ( can be nearest neighbour (00-order), -order), tri-linear (tri-linear (11st-order), (windowed) fourier/sinc, or st-order), (windowed) fourier/sinc, or in SPM2, in SPM2, nnth-order “th-order “b-splines”b-splines”

• Application of registration parameters involves Application of registration parameters involves re-samplingre-sampling the image to create new voxels by the image to create new voxels by interpolation from existing voxelsinterpolation from existing voxels

• InterpolationInterpolation can be nearest neighbour ( can be nearest neighbour (00-order), -order), tri-linear (tri-linear (11st-order), (windowed) fourier/sinc, or st-order), (windowed) fourier/sinc, or in SPM2, in SPM2, nnth-order “th-order “b-splines”b-splines”

2. Transformation (reslicing)2. Transformation (reslicing)2. Transformation (reslicing)2. Transformation (reslicing)

d1 d2

d3

d4

v1

v4

v2

v3

Nearest Neighbour

Linear

Full sinc (no alias)

Windowed sinc

• Interpolation errors, especially with tri-linear interpolation and small-window sincInterpolation errors, especially with tri-linear interpolation and small-window sinc

• PET: PET:

– Incorrect attenuation correction because scans are no longer aligned with transmission Incorrect attenuation correction because scans are no longer aligned with transmission scan (a transmission scan is often acquired to give a map of local positron attenuation)scan (a transmission scan is often acquired to give a map of local positron attenuation)

• fMRI (EPI): fMRI (EPI):

– Ghosts (and other artefacts) in the image (which do not move as a rigid body)Ghosts (and other artefacts) in the image (which do not move as a rigid body)

– Rapid movements Rapid movements withinwithin a scan (which cause non-rigid image deformation) a scan (which cause non-rigid image deformation)

– Spin excitation history effects (residual magnetisation effects of previous scans)Spin excitation history effects (residual magnetisation effects of previous scans)

– Interaction between movement and local field inhomogeniety, giving non-rigid distortionInteraction between movement and local field inhomogeniety, giving non-rigid distortion

• Interpolation errors, especially with tri-linear interpolation and small-window sincInterpolation errors, especially with tri-linear interpolation and small-window sinc

• PET: PET:

– Incorrect attenuation correction because scans are no longer aligned with transmission Incorrect attenuation correction because scans are no longer aligned with transmission scan (a transmission scan is often acquired to give a map of local positron attenuation)scan (a transmission scan is often acquired to give a map of local positron attenuation)

• fMRI (EPI): fMRI (EPI):

– Ghosts (and other artefacts) in the image (which do not move as a rigid body)Ghosts (and other artefacts) in the image (which do not move as a rigid body)

– Rapid movements Rapid movements withinwithin a scan (which cause non-rigid image deformation) a scan (which cause non-rigid image deformation)

– Spin excitation history effects (residual magnetisation effects of previous scans)Spin excitation history effects (residual magnetisation effects of previous scans)

– Interaction between movement and local field inhomogeniety, giving non-rigid distortionInteraction between movement and local field inhomogeniety, giving non-rigid distortion

Residual Errors after RealignmentResidual Errors after RealignmentResidual Errors after RealignmentResidual Errors after Realignment

• Echo-planar images (EPI) contain Echo-planar images (EPI) contain distortionsdistortions owing to owing to field inhomogenieties (susceptibility artifacts, field inhomogenieties (susceptibility artifacts, particularly in phase-encoding direction)particularly in phase-encoding direction)

• They can be “undistorted” by use of a They can be “undistorted” by use of a field-map field-map (available in the “FieldMap” SPM toolbox)(available in the “FieldMap” SPM toolbox)

• (Note that susceptibility artifacts that cause (Note that susceptibility artifacts that cause drop-out drop-out are more difficult to correct)are more difficult to correct)

• However, movement interacts with the field However, movement interacts with the field inhomogeniety (presence of object affects Binhomogeniety (presence of object affects B00), ie ), ie

distortions change with position of object in fielddistortions change with position of object in field

• This movement-by-distortion can be accommodated This movement-by-distortion can be accommodated during realignment using “unwarp”during realignment using “unwarp”

• Echo-planar images (EPI) contain Echo-planar images (EPI) contain distortionsdistortions owing to owing to field inhomogenieties (susceptibility artifacts, field inhomogenieties (susceptibility artifacts, particularly in phase-encoding direction)particularly in phase-encoding direction)

• They can be “undistorted” by use of a They can be “undistorted” by use of a field-map field-map (available in the “FieldMap” SPM toolbox)(available in the “FieldMap” SPM toolbox)

• (Note that susceptibility artifacts that cause (Note that susceptibility artifacts that cause drop-out drop-out are more difficult to correct)are more difficult to correct)

• However, movement interacts with the field However, movement interacts with the field inhomogeniety (presence of object affects Binhomogeniety (presence of object affects B00), ie ), ie

distortions change with position of object in fielddistortions change with position of object in field

• This movement-by-distortion can be accommodated This movement-by-distortion can be accommodated during realignment using “unwarp”during realignment using “unwarp”

UnwarpUnwarpUnwarpUnwarpNew inSPM2

Distorted image

Corrected image

Field-map

• One could include the movement parameters as confounds One could include the movement parameters as confounds in the statistical model of activationsin the statistical model of activations

• However, this may remove activations of interest if they However, this may remove activations of interest if they are correlated with the movementare correlated with the movement

• Better is to incorporate physics knowledge, eg to model Better is to incorporate physics knowledge, eg to model how field changes as function of how field changes as function of pitchpitch and and rollroll (assuming (assuming phase-encoding is in y-direction)…phase-encoding is in y-direction)…

• … … using Taylor expansion (about mean realigned image):using Taylor expansion (about mean realigned image):

• Iterate: 1) estimate movement parameters (Iterate: 1) estimate movement parameters (, ), 2) ), 2) estimate deformation fields, 1) re-estimate movement …estimate deformation fields, 1) re-estimate movement …

• Fields expressed by spatial basis functions (3D discrete Fields expressed by spatial basis functions (3D discrete cosine set)…cosine set)…

• One could include the movement parameters as confounds One could include the movement parameters as confounds in the statistical model of activationsin the statistical model of activations

• However, this may remove activations of interest if they However, this may remove activations of interest if they are correlated with the movementare correlated with the movement

• Better is to incorporate physics knowledge, eg to model Better is to incorporate physics knowledge, eg to model how field changes as function of how field changes as function of pitchpitch and and rollroll (assuming (assuming phase-encoding is in y-direction)…phase-encoding is in y-direction)…

• … … using Taylor expansion (about mean realigned image):using Taylor expansion (about mean realigned image):

• Iterate: 1) estimate movement parameters (Iterate: 1) estimate movement parameters (, ), 2) ), 2) estimate deformation fields, 1) re-estimate movement …estimate deformation fields, 1) re-estimate movement …

• Fields expressed by spatial basis functions (3D discrete Fields expressed by spatial basis functions (3D discrete cosine set)…cosine set)…


Roll

Pitch

Estimated derivative fields

0B 0B + B0

UnwarpUnwarpUnwarpUnwarp

B0{i} B0 0B 0B

= + + + error(0th-order term

can be determined from fieldmap)

-f1 fi

1 +2 + ... +5 + ...1 y f 0 1

B

i 0 2

B 1 y f

i 0 5

B 1 y f

i

5

i

f

3

i

f

1

i

f

New inSPM2


Example: Movement correlated with design

tmax=13.38

No correction

tmax=5.06

Correction by covariation

tmax=9.57

Correction by Unwarp



3. Smoothing






3. Smoothing





Reasons for NormalisationReasons for NormalisationReasons for NormalisationReasons for Normalisation

• Inter-subject averagingInter-subject averaging

– extrapolate findings to the population as a wholeextrapolate findings to the population as a whole

– increase statistical power above that obtained from single subjectincrease statistical power above that obtained from single subject

• Reporting of activations as co-ordinates within a standard stereotactic spaceReporting of activations as co-ordinates within a standard stereotactic space

– e.g. the space described by e.g. the space described by Talairach & TournouxTalairach & Tournoux

• Inter-subject averagingInter-subject averaging

– extrapolate findings to the population as a wholeextrapolate findings to the population as a whole

– increase statistical power above that obtained from single subjectincrease statistical power above that obtained from single subject

• Reporting of activations as co-ordinates within a standard stereotactic spaceReporting of activations as co-ordinates within a standard stereotactic space

– e.g. the space described by e.g. the space described by Talairach & TournouxTalairach & Tournoux

• Label-basedLabel-based approaches: Warp the images such that defined landmarks approaches: Warp the images such that defined landmarks (points/lines/surfaces) are aligned(points/lines/surfaces) are aligned

– but few readily identifiable landmarks (and manually defined?)but few readily identifiable landmarks (and manually defined?)

• Intensity-basedIntensity-based approaches: Warp to images to maximise some voxel-wise approaches: Warp to images to maximise some voxel-wise similarity measuresimilarity measure

– eg, squared error, assuming intensity correspondence (within-modality)eg, squared error, assuming intensity correspondence (within-modality)

• Normalisation constrained to correct for only gross differences; residual Normalisation constrained to correct for only gross differences; residual variabilility accommodated by subsequent spatial smoothingvariabilility accommodated by subsequent spatial smoothing

• Label-basedLabel-based approaches: Warp the images such that defined landmarks approaches: Warp the images such that defined landmarks (points/lines/surfaces) are aligned(points/lines/surfaces) are aligned

– but few readily identifiable landmarks (and manually defined?)but few readily identifiable landmarks (and manually defined?)

• Intensity-basedIntensity-based approaches: Warp to images to maximise some voxel-wise approaches: Warp to images to maximise some voxel-wise similarity measuresimilarity measure

– eg, squared error, assuming intensity correspondence (within-modality)eg, squared error, assuming intensity correspondence (within-modality)

• Normalisation constrained to correct for only gross differences; residual Normalisation constrained to correct for only gross differences; residual variabilility accommodated by subsequent spatial smoothingvariabilility accommodated by subsequent spatial smoothing

SummarySummarySummarySummary

Spatial Normalisation

Original image

Templateimage

Spatially normalised

Deformation field

• Determine transformation that minimises the sum of squared difference between an image and a (combination of) template image(s)

• Two stages:

1. affine registration to match size and position of the images

2. non-linear warping to match the overall brain shape

• Uses a Bayesian framework to constrain affine and warps

• Determine transformation that minimises the sum of squared difference between an image and a (combination of) template image(s)

• Two stages:

1. affine registration to match size and position of the images

2. non-linear warping to match the overall brain shape

• Uses a Bayesian framework to constrain affine and warps

Stage 1. Full Affine TransformationStage 1. Full Affine Transformation

• The first part of normalisation is a The first part of normalisation is a 12 parameter affine transformation12 parameter affine transformation

– 3 translations3 translations

– 3 rotations3 rotations

– 3 zooms3 zooms

– 3 shears3 shears

• Better if template image in same Better if template image in same modality (eg because of image modality (eg because of image distortions in EPI but not T1)distortions in EPI but not T1)

1000

0100

00)cos()sin(

00)sin()cos(

1000

0)cos(0)sin(

0010

0)sin(0)cos(

1000

0)cos()sin(0

0)sin()cos(0

0001

1000

Z100

Y010

X001

trans

trans

trans

1000

0100

0YZ10

0XZXY1

1000

0Z00

00Y0

000X

shear

shearshear

zoom

zoom

zoom

Rotation

Translation Zoom

Shear

Rigid body

Six affine registered imagesSix affine registered imagesSix affine registered imagesSix affine registered images Six affine + nonlinear registeredSix affine + nonlinear registeredSix affine + nonlinear registeredSix affine + nonlinear registered

Insufficieny of Affine-only normalisationInsufficieny of Affine-only normalisationInsufficieny of Affine-only normalisationInsufficieny of Affine-only normalisation

Stage 2. Nonlinear WarpsStage 2. Nonlinear Warps Stage 2. Nonlinear WarpsStage 2. Nonlinear Warps

• Deformations consist of a linear Deformations consist of a linear combination of smooth combination of smooth basis imagesbasis images

• These are the lowest frequency basis These are the lowest frequency basis images of a 3-D discrete cosine transformimages of a 3-D discrete cosine transform

• Brain masks can be applied (eg for lesions)Brain masks can be applied (eg for lesions)

Affine Registration(2 = 472.1)

Affine Registration(2 = 472.1)

Templateimage

Templateimage

Non-linearregistration

withoutregularisation(2 = 287.3)


withoutregularisation(2 = 287.3)


withregularisation(2 = 302.7)


withregularisation(2 = 302.7)

Without the Bayesian formulation, the non-linear spatial normalisation can introduce unnecessary warping into the spatially normalised images

Bayesian ConstraintsBayesian ConstraintsBayesian ConstraintsBayesian Constraints

• Using Bayes rule, we can constrain (“regularise”) the nonlinear fit by incorporating prior knowledge of the likely extent of deformations:

p(p|e) p(e|p) p(p) (Bayes Rule)

p(p|e) is the a posteriori probability of parameters p given errors ep(e|p) is the likelihood of observing errors e given parameters pp(p) is the a priori probability of parameters p

• For Maximum a posteriori (MAP) estimate, we minimise (taking logs):

H(p|e) H(e|p) + H(p) (Gibbs potential)

H(e|p) (-log p(e|p)) is the squared difference between the images (error)H(p) -log p(p)) constrains parameters (penalises unlikely deformations) is “regularisation” hyperparameter, weighting effect of “priors”


• Algorithm simultaneously minimises:Algorithm simultaneously minimises:

– Sum of squared difference Sum of squared difference between template and objectbetween template and object

– Squared distance between the Squared distance between the parameters and their expectation parameters and their expectation

• Bayesian constraints applied to both:Bayesian constraints applied to both:

1) affine transformations1) affine transformations

– based on empirical prior rangesbased on empirical prior ranges

2) nonlinear deformations2) nonlinear deformations

– based on smoothness constraint based on smoothness constraint (minimising (minimising membrane energymembrane energy))

Empirically generated priors




3. Smoothing






3. Smoothing





Reasons for SmoothingReasons for SmoothingReasons for SmoothingReasons for Smoothing

• Potentially increase signal to noise (matched filter theorem)Potentially increase signal to noise (matched filter theorem)

• Inter-subject averagingInter-subject averaging (allowing for residual differences after normalisation)(allowing for residual differences after normalisation)

• Increase validity of statistics (more likely that errors distributed normally)Increase validity of statistics (more likely that errors distributed normally)

• Potentially increase signal to noise (matched filter theorem)Potentially increase signal to noise (matched filter theorem)

• Inter-subject averagingInter-subject averaging (allowing for residual differences after normalisation)(allowing for residual differences after normalisation)

• Increase validity of statistics (more likely that errors distributed normally)Increase validity of statistics (more likely that errors distributed normally)

Gaussian smoothing kernel

• Kernel defined in terms of FWHM (full width at half maximum) of filter - Kernel defined in terms of FWHM (full width at half maximum) of filter - usually ~16-20mm (PET) or ~6-8mm (fMRI) of a Gaussianusually ~16-20mm (PET) or ~6-8mm (fMRI) of a Gaussian

• Ultimate smoothness is function of Ultimate smoothness is function of appliedapplied smoothing and smoothing and intrinsicintrinsic image image smoothness (sometimes expressed as smoothness (sometimes expressed as “resels”“resels” - RESolvable Elements) - RESolvable Elements)

• Kernel defined in terms of FWHM (full width at half maximum) of filter - Kernel defined in terms of FWHM (full width at half maximum) of filter - usually ~16-20mm (PET) or ~6-8mm (fMRI) of a Gaussianusually ~16-20mm (PET) or ~6-8mm (fMRI) of a Gaussian

• Ultimate smoothness is function of Ultimate smoothness is function of appliedapplied smoothing and smoothing and intrinsicintrinsic image image smoothness (sometimes expressed as smoothness (sometimes expressed as “resels”“resels” - RESolvable Elements) - RESolvable Elements)

FWHM



3. Smoothing






3. Smoothing





Between Modality Co-registrationBetween Modality Co-registrationBetween Modality Co-registrationBetween Modality Co-registration

• Because different modality images have Because different modality images have different properties (e.g., relative intensity different properties (e.g., relative intensity of gray/white matter), cannot simply of gray/white matter), cannot simply minimise difference between imagesminimise difference between images

• Two main approaches:Two main approaches:

I. Via Templates:I. Via Templates:

1) Simultaneous affine registrations 1) Simultaneous affine registrations between between each image and same-modality each image and same-modality templatetemplate

2) Segmentation into grey and white matter2) Segmentation into grey and white matter

3) Final simultaneous registration of segments3) Final simultaneous registration of segments

II. Mutual InformationII. Mutual Information

• Because different modality images have Because different modality images have different properties (e.g., relative intensity different properties (e.g., relative intensity of gray/white matter), cannot simply of gray/white matter), cannot simply minimise difference between imagesminimise difference between images

• Two main approaches:Two main approaches:

I. Via Templates:I. Via Templates:

1) Simultaneous affine registrations 1) Simultaneous affine registrations between between each image and same-modality each image and same-modality templatetemplate

2) Segmentation into grey and white matter2) Segmentation into grey and white matter

3) Final simultaneous registration of segments3) Final simultaneous registration of segments

II. Mutual InformationII. Mutual Information

EPI

T2 T1 Transm

PD PET

• Useful, for example, to display Useful, for example, to display functional results (EPI) onto high functional results (EPI) onto high resolution anatomical image (T1)resolution anatomical image (T1)

• Useful, for example, to display Useful, for example, to display functional results (EPI) onto high functional results (EPI) onto high resolution anatomical image (T1)resolution anatomical image (T1)

3. Registration of Partitions3. Registration of Partitions3. Registration of Partitions3. Registration of Partitions

1. Affine Registrations1. Affine Registrations1. Affine Registrations1. Affine Registrations

• Both images are registered - using 12 parameter affine Both images are registered - using 12 parameter affine transformations - to their corresponding templates...transformations - to their corresponding templates...

• … … but only the rigid-body transformation parameters allowed to but only the rigid-body transformation parameters allowed to differ between the two registrationsdiffer between the two registrations

• This gives:This gives:

– rigid body mapping between the imagesrigid body mapping between the images

– affine mappings between the images and the templatesaffine mappings between the images and the templates

• Both images are registered - using 12 parameter affine Both images are registered - using 12 parameter affine transformations - to their corresponding templates...transformations - to their corresponding templates...

• … … but only the rigid-body transformation parameters allowed to but only the rigid-body transformation parameters allowed to differ between the two registrationsdiffer between the two registrations

• This gives:This gives:

– rigid body mapping between the imagesrigid body mapping between the images

– affine mappings between the images and the templatesaffine mappings between the images and the templates

2. Segmentation2. Segmentation2. Segmentation2. Segmentation

• ‘‘Mixture Model’ cluster Mixture Model’ cluster analysis to classify MR analysis to classify MR image as GM, WM & CSFimage as GM, WM & CSF

• Additional information is Additional information is obtained from obtained from a priori a priori probability images - probability images - see latersee later

• ‘‘Mixture Model’ cluster Mixture Model’ cluster analysis to classify MR analysis to classify MR image as GM, WM & CSFimage as GM, WM & CSF

• Additional information is Additional information is obtained from obtained from a priori a priori probability images - probability images - see latersee later

Between Modality Co-registration: I. Via TemplatesBetween Modality Co-registration: I. Via TemplatesBetween Modality Co-registration: I. Via TemplatesBetween Modality Co-registration: I. Via Templates

• Grey and white matter Grey and white matter partitions are registered using a partitions are registered using a rigid body transformation rigid body transformation

• Simultaneously minimise sum Simultaneously minimise sum of squared differenceof squared difference

• Grey and white matter Grey and white matter partitions are registered using a partitions are registered using a rigid body transformation rigid body transformation

• Simultaneously minimise sum Simultaneously minimise sum of squared differenceof squared difference

Between Modality Coregistration: II. Mutual InformationBetween Modality Coregistration: II. Mutual Information Between Modality Coregistration: II. Mutual InformationBetween Modality Coregistration: II. Mutual Information

PET T1 MRI

Another way is to maximise Another way is to maximise the the Mutual InformationMutual Information in in the 2D histogram (plot of the 2D histogram (plot of one image against other)one image against other)

For histograms normalised For histograms normalised to integrate to unity, the to integrate to unity, the Mutual Information is:Mutual Information is:

iijj h hijij log h log hijij

kk h hikik ll h hljlj

Another way is to maximise Another way is to maximise the the Mutual InformationMutual Information in in the 2D histogram (plot of the 2D histogram (plot of one image against other)one image against other)

For histograms normalised For histograms normalised to integrate to unity, the to integrate to unity, the Mutual Information is:Mutual Information is:

iijj h hijij log h log hijij

kk h hikik ll h hljlj

New inSPM2



3. Smoothing






3. Smoothing





Image SegmentationImage SegmentationImage SegmentationImage Segmentation

• Partition into gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF)Partition into gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF)

• ‘‘Mixture ModelMixture Model’ cluster analysis used, which assumes each voxel is one of a number ’ cluster analysis used, which assumes each voxel is one of a number of distinct tissue types (clusters), each with a (multivariate) normal distributionof distinct tissue types (clusters), each with a (multivariate) normal distribution

• Further Bayesian constraints fromFurther Bayesian constraints from prior probability imagesprior probability images, which are overlaid, which are overlaid

• Additional correction for intensity inhomogeniety possibleAdditional correction for intensity inhomogeniety possible

• Partition into gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF)Partition into gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF)

• ‘‘Mixture ModelMixture Model’ cluster analysis used, which assumes each voxel is one of a number ’ cluster analysis used, which assumes each voxel is one of a number of distinct tissue types (clusters), each with a (multivariate) normal distributionof distinct tissue types (clusters), each with a (multivariate) normal distribution

• Further Bayesian constraints fromFurther Bayesian constraints from prior probability imagesprior probability images, which are overlaid, which are overlaid

• Additional correction for intensity inhomogeniety possibleAdditional correction for intensity inhomogeniety possible

.

Intensity histogramfit by multi-Gaussians

Priors:

Image:

Brain/skullCSFWMGM



3. Smoothing






3. Smoothing





Morphometry Morphometry (Computational Neuroanatomy)(Computational Neuroanatomy)

Morphometry Morphometry (Computational Neuroanatomy)(Computational Neuroanatomy)

• Voxel-by-voxelVoxel-by-voxel: : where are the where are the differences between populations?differences between populations?

– Univariate: e.g, Voxel-Based Univariate: e.g, Voxel-Based Morphometry (VBM)Morphometry (VBM)

– Multivariate: e.g, Tensor-Based Multivariate: e.g, Tensor-Based Morphometry (TBM)Morphometry (TBM)

• Volume-basedVolume-based: : is there a difference is there a difference between populations?between populations?

– Multivariate: e.g, Deformation-Multivariate: e.g, Deformation-Based Morphometry (DBM)Based Morphometry (DBM)

• Continuum:Continuum:

– perfect normalisation => all perfect normalisation => all information in Deformation field information in Deformation field (no VBM differences)(no VBM differences)

– no normalisation => all in VBMno normalisation => all in VBM

• Voxel-by-voxelVoxel-by-voxel: : where are the where are the differences between populations?differences between populations?

– Univariate: e.g, Voxel-Based Univariate: e.g, Voxel-Based Morphometry (VBM)Morphometry (VBM)

– Multivariate: e.g, Tensor-Based Multivariate: e.g, Tensor-Based Morphometry (TBM)Morphometry (TBM)

• Volume-basedVolume-based: : is there a difference is there a difference between populations?between populations?

– Multivariate: e.g, Deformation-Multivariate: e.g, Deformation-Based Morphometry (DBM)Based Morphometry (DBM)

• Continuum:Continuum:

– perfect normalisation => all perfect normalisation => all information in Deformation field information in Deformation field (no VBM differences)(no VBM differences)

– no normalisation => all in VBMno normalisation => all in VBM

Spatial Normalisation

Original Template

Normalised Deformation field

VBM TBM DBM

Originalimage

Spatiallynormalised

Segmentedgrey matter

Smoothed

“Optimised” VBM involves segmenting images before normalising, so as to normalise gray matter / white matter / CSF separately...

A voxel by voxel statistical analysis is used to detect regional differences in the amount of grey matter between populations

Voxel-Based Morphometry (VBM)Voxel-Based Morphometry (VBM)Voxel-Based Morphometry (VBM)Voxel-Based Morphometry (VBM)

SPM

Affine registration

Apply deformation

Segmentation & Extraction

Affine transform

Segmentation & extraction

Spatial normalisation

priors

Modulation

smooth

smoothSTATSvolume

STATSconcentration

template

Normalised T1

T1 image

Optimised VBMOptimised VBMOptimised VBMOptimised VBM

Grey matter volume loss with age

superior parietalpre and post central

insulacingulate/parafalcine

VBM Examples: AgingVBM Examples: AgingVBM Examples: AgingVBM Examples: Aging

Males > FemalesFemales > Males

L superior temporal sulcusR middle temporal gyrus

intraparietal sulci

mesial temporaltemporal pole

anterior cerebellar

VBM Examples: Sex DifferencesVBM Examples: Sex DifferencesVBM Examples: Sex DifferencesVBM Examples: Sex Differences

Right frontal and left occipital petalia

VBM Examples: Brain AsymmetriesVBM Examples: Brain AsymmetriesVBM Examples: Brain AsymmetriesVBM Examples: Brain Asymmetries

Deformation-based Morphometrylooks at absolute displacements

Tensor-based Morphometry looks at local shapes

Morphometry on deformation fields: DBM/TBMMorphometry on deformation fields: DBM/TBMMorphometry on deformation fields: DBM/TBMMorphometry on deformation fields: DBM/TBM

Vector field Tensor field

Deformationfields ...

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

Remove positional and size information - leave shape

Deformation-based Morphometry (DBM)Deformation-based Morphometry (DBM)Deformation-based Morphometry (DBM)Deformation-based Morphometry (DBM)

Non-linear warps of sex differences characterised by

canonical variates analysis

Mean differences (mapping from an average female to

male brain)

DBM Example: Sex DifferencesDBM Example: Sex DifferencesDBM Example: Sex DifferencesDBM Example: Sex Differences

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.

TemplateTemplateWarpedOriginal

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: (Um-I)/m when m~=0, and log(U) if m==0.

Relative volumes

Strain tensor

Tensor-based morphometry

References

Friston et al (1995): Spatial registration and normalisation of images.Human Brain Mapping 3(3):165-189

Ashburner & Friston (1997): Multimodal image coregistration and partitioning - a unified framework.NeuroImage 6(3):209-217

Collignon et al (1995): Automated multi-modality image registration based on information theory.IPMI’95 pp 263-274

Ashburner et al (1997): Incorporating prior knowledge into image registration.NeuroImage 6(4):344-352

Ashburner et al (1999): Nonlinear spatial normalisation using basis functions.Human Brain Mapping 7(4):254-266

Ashburner & Friston (2000): Voxel-based morphometry - the methods.NeuroImage 11:805-821

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Statistical Parametric Mapping (SPM) 1. Talk I: Spatial Pre-processing

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