SPM+fMRI

K space

K Space

Mechanism of BOLD Functional MRI Brain activity Oxygen consumptionCerebral blood flow Oxyhemoglobin Deoxyhemoglobin Magnetic susceptibility T2* MRI signal intesity

Magnetic Properties of Oxyhemoglobin and Deoxyhemoglobin Deoxyhemoglobin: paramagnetic (  > 0) paramagnetic with respect to the surrounding tissue Oxyhemoglobin: diamagnetic (  < 0) isomagnetic with respect to the surrounding tissue

T 2 * Effect in fMRI excitation reception MR signal (S) action rest TE t

Time Series and Activation Maps Off On Scan Number Signal Intensity

Temporal resolution  Impulse-response function 2s 5s 12s

PCA_IMAGE: PCA of time  space: 1: exclude first frames 2: drift 3: long-range correlation or anatomical effect: remove by converting to % of brain 4: signal?

OverviewOverview Motion correction Smoothing kernel Spatial normalisation Standard template fMRI time-series Statistical Parametric Map General Linear Model Design matrix Parameter Estimates

Reasons for Motion Correction Subjects will always move in the scanner Subjects will always move in the scanner 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 realignment will increase the sensitivity 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 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 discount artefacts that owe to motion) … in which case realignment may reduce sensitivity (and it may not be possible to discount artefacts that owe to motion) Subjects will always move in the scanner Subjects will always move in the scanner 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 realignment will increase the sensitivity 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 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 discount artefacts that owe to motion) … in which case realignment may reduce sensitivity (and it may not be possible to discount artefacts that owe to motion) Realignment (of same-modality images from same subject) involves two stages: Realignment (of same-modality images from same subject) involves two stages: 1. Registration - determining the 6 parameters that describe the rigid body transformation between each image and a reference image 1. Registration - determining the 6 parameters that describe the rigid body transformation between each image and a reference image 2. Transformation (reslicing) - re-sampling each image according to the determined transformation parameters 2. Transformation (reslicing) - re-sampling each image according to the determined transformation parameters Realignment (of same-modality images from same subject) involves two stages: Realignment (of same-modality images from same subject) involves two stages: 1. Registration - determining the 6 parameters that describe the rigid body transformation between each image and a reference image 1. Registration - determining the 6 parameters that describe the rigid body transformation between each image and a reference image 2. Transformation (reslicing) - re-sampling each image according to the determined transformation parameters 2. Transformation (reslicing) - re-sampling each image according to the determined transformation parameters

1. Registration Determine the rigid body transformation that minimises the sum of squared difference between images Determine the rigid body transformation that minimises the sum of squared difference between images Rigid body transformation is defined by: Rigid body transformation is defined by: 3 translations - in X, Y & Z directions 3 translations - in X, Y & Z directions 3 rotations - about X, Y & Z axes 3 rotations - about X, Y & Z axes Operations can be represented as affine transformation matrices: Operations can be represented as affine transformation matrices: x 1 = m 1,1 x 0 + m 1,2 y 0 + m 1,3 z 0 + m 1,4 y 1 = m 2,1 x 0 + m 2,2 y 0 + m 2,3 z 0 + m 2,4 z 1 = m 3,1 x 0 + m 3,2 y 0 + m 3,3 z 0 + m 3,4 Determine the rigid body transformation that minimises the sum of squared difference between images Determine the rigid body transformation that minimises the sum of squared difference between images Rigid body transformation is defined by: Rigid body transformation is defined by: 3 translations - in X, Y & Z directions 3 translations - in X, Y & Z directions 3 rotations - about X, Y & Z axes 3 rotations - about X, Y & Z axes Operations can be represented as affine transformation matrices: Operations can be represented as affine transformation matrices: x 1 = m 1,1 x 0 + m 1,2 y 0 + m 1,3 z 0 + m 1,4 y 1 = m 2,1 x 0 + m 2,2 y 0 + m 2,3 z 0 + m 2,4 z 1 = m 3,1 x 0 + m 3,2 y 0 + m 3,3 z 0 + m 3,4 TranslationsPitchRollYaw Rigid body transformations parameterised by: Squared Error

1. Registration Iterative procedure (Gauss- Newton ascent) Iterative procedure (Gauss- Newton ascent) Additional scaling parameter Additional scaling parameter Nx6 matrix of realignment parameters written to file (N is number of scans) Nx6 matrix of realignment parameters written to file (N is number of scans) Orientation matrices in *.mat file updated for each volume (do not have to be resliced) Orientation matrices in *.mat file updated for each volume (do not have to be resliced) Slice-timing correction can be performed before or after realignment (depending on acquisition) Slice-timing correction can be performed before or after realignment (depending on acquisition) Iterative procedure (Gauss- Newton ascent) Iterative procedure (Gauss- Newton ascent) Additional scaling parameter Additional scaling parameter Nx6 matrix of realignment parameters written to file (N is number of scans) Nx6 matrix of realignment parameters written to file (N is number of scans) Orientation matrices in *.mat file updated for each volume (do not have to be resliced) Orientation matrices in *.mat file updated for each volume (do not have to be resliced) Slice-timing correction can be performed before or after realignment (depending on acquisition) Slice-timing correction can be performed before or after realignment (depending on acquisition)

Application of registration parameters involves re- sampling the image to create new voxels by interpolation from existing voxels Application of registration parameters involves re- sampling the image to create new voxels by interpolation from existing voxels Interpolation can be nearest neighbour (0-order), tri-linear (1st-order), (windowed) fourier/sinc, or in SPM2, nth-order “ b-splines ” Interpolation can be nearest neighbour (0-order), tri-linear (1st-order), (windowed) fourier/sinc, or in SPM2, nth-order “ b-splines ” Application of registration parameters involves re- sampling the image to create new voxels by interpolation from existing voxels Application of registration parameters involves re- sampling the image to create new voxels by interpolation from existing voxels Interpolation can be nearest neighbour (0-order), tri-linear (1st-order), (windowed) fourier/sinc, or in SPM2, nth-order “ b-splines ” Interpolation can be nearest neighbour (0-order), tri-linear (1st-order), (windowed) fourier/sinc, or in SPM2, nth-order “ b-splines ” 2. Transformation (reslicing) Nearest Neighbour Linear Full sinc (no alias) Windowed sinc

Echo-planar images (EPI) contain distortions owing to field inhomogenieties (susceptibility artifacts, particularly in phase-encoding direction) Echo-planar images (EPI) contain distortions owing to field inhomogenieties (susceptibility artifacts, particularly in phase-encoding direction) They can be “ undistorted ” by use of a field- map (available in the “ FieldMap ” SPM toolbox) They can be “ undistorted ” by use of a field- map (available in the “ FieldMap ” SPM toolbox) However, movement interacts with the field inhomogeniety (presence of object affects B 0 ), ie distortions change with position of object in field However, movement interacts with the field inhomogeniety (presence of object affects B 0 ), ie distortions change with position of object in field This movement-by-distortion can be accommodated during realignment using “ unwarp ” This movement-by-distortion can be accommodated during realignment using “ unwarp ” Echo-planar images (EPI) contain distortions owing to field inhomogenieties (susceptibility artifacts, particularly in phase-encoding direction) Echo-planar images (EPI) contain distortions owing to field inhomogenieties (susceptibility artifacts, particularly in phase-encoding direction) They can be “ undistorted ” by use of a field- map (available in the “ FieldMap ” SPM toolbox) They can be “ undistorted ” by use of a field- map (available in the “ FieldMap ” SPM toolbox) However, movement interacts with the field inhomogeniety (presence of object affects B 0 ), ie distortions change with position of object in field However, movement interacts with the field inhomogeniety (presence of object affects B 0 ), ie distortions change with position of object in field This movement-by-distortion can be accommodated during realignment using “ unwarp ” This movement-by-distortion can be accommodated during realignment using “ unwarp ” UnwarpUnwarp Distorted image Corrected imageField-map

Field Warp

Reasons for Normalisation Inter-subject averaging Inter-subject averaging extrapolate findings to the population as a whole extrapolate findings to the population as a whole increase statistical power above that obtained from single subject increase statistical power above that obtained from single subject Reporting of activations as co-ordinates within a standard stereotactic space Reporting of activations as co-ordinates within a standard stereotactic space e.g. the space described by Talairach & Tournoux e.g. the space described by Talairach & Tournoux Inter-subject averaging Inter-subject averaging extrapolate findings to the population as a whole extrapolate findings to the population as a whole increase statistical power above that obtained from single subject increase statistical power above that obtained from single subject Reporting of activations as co-ordinates within a standard stereotactic space Reporting of activations as co-ordinates within a standard stereotactic space e.g. the space described by Talairach & Tournoux e.g. the space described by Talairach & Tournoux Label-based approaches: Warp the images such that defined landmarks (points/lines/surfaces) are aligned Label-based approaches: Warp the images such that defined landmarks (points/lines/surfaces) are aligned but few readily identifiable landmarks (and manually defined?) but few readily identifiable landmarks (and manually defined?) Intensity-based approaches: Warp to images to maximise some voxel- wise similarity measure Intensity-based approaches: Warp to images to maximise some voxel- wise similarity 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 variabilility accommodated by subsequent spatial smoothing Normalisation constrained to correct for only gross differences; residual variabilility accommodated by subsequent spatial smoothing Label-based approaches: Warp the images such that defined landmarks (points/lines/surfaces) are aligned Label-based approaches: Warp the images such that defined landmarks (points/lines/surfaces) are aligned but few readily identifiable landmarks (and manually defined?) but few readily identifiable landmarks (and manually defined?) Intensity-based approaches: Warp to images to maximise some voxel- wise similarity measure Intensity-based approaches: Warp to images to maximise some voxel- wise similarity 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 variabilility accommodated by subsequent spatial smoothing Normalisation constrained to correct for only gross differences; residual variabilility accommodated by subsequent spatial smoothing

SummarySummary Spatial Normalisation Original image Template image 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 Transformation The first part of normalisation is a 12 parameter affine transformation The first part of normalisation is a 12 parameter affine transformation 3 translations 3 translations 3 rotations 3 rotations 3 zooms 3 zooms 3 shears 3 shears Better if template image in same modality Better if template image in same modality Rotation TranslationZoom Shear Rigid body

Six affine registered images Six affine + nonlinear Insufficieny of Affine-only normalisation

Stage 2. Nonlinear Warps Stage 2. Nonlinear Warps Deformations consist of a linear combination of smooth basis images Deformations consist of a linear combination of smooth basis images These are the lowest frequency basis images of a 3-D discrete cosine transform These are the lowest frequency basis images 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) Template image Template image Non-linear registration without regularisation (  2 = 287.3) Non-linear registration without regularisation (  2 = 287.3) Non-linear registration with regularisation (  2 = 302.7) Non-linear registration with regularisation (  2 = 302.7) Without the Bayesian formulation, the non-linear spatial normalisation can introduce unnecessary warping into the spatially normalised images Bayesian 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)/p(e) (Bayes Rule) p(p|e) is the a posteriori probability of parameters p given errors e p(e|p) is the likelihood of observing errors e given parameters p p(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” Bayesian Constraints

Algorithm simultaneously minimises: Algorithm simultaneously minimises: Sum of squared difference between template and object Sum of squared difference between template and object Squared distance between the parameters and their expectation Squared distance between the parameters and their expectation Bayesian constraints applied to both: Bayesian constraints applied to both: 1) affine transformations 1) affine transformations based on empirical prior ranges based on empirical prior ranges 2) nonlinear deformations 2) nonlinear deformations based on smoothness constraint (minimising membrane energy) based on smoothness constraint (minimising membrane energy) Empirically generated priors Bayesian Constraints

SmoothingSmoothing Gaussian smoothing kernel FWHM

Between Modality Co-registration Because different modality images have different properties (e.g., relative intensity of gray/white matter), cannot simply minimise difference between images Because different modality images have different properties (e.g., relative intensity of gray/white matter), cannot simply minimise difference between images Two main approaches: Two main approaches: I. Via Templates: I. Via Templates: 1) Simultaneous affine registrations between each image and same-modality template 2) Segmentation into grey and white matter 3) Final simultaneous registration of segments II. Mutual Information II. Mutual Information Because different modality images have different properties (e.g., relative intensity of gray/white matter), cannot simply minimise difference between images Because different modality images have different properties (e.g., relative intensity of gray/white matter), cannot simply minimise difference between images Two main approaches: Two main approaches: I. Via Templates: I. Via Templates: 1) Simultaneous affine registrations between each image and same-modality template 2) Segmentation into grey and white matter 3) Final simultaneous registration of segments II. Mutual Information II. Mutual Information EPI T2 T1Transm PDPET Useful, for example, to display functional results (EPI) onto high resolution anatomical image (T1) Useful, for example, to display functional results (EPI) onto high resolution anatomical image (T1)

3. Registration of Partitions 1. Affine Registrations Both images are registered - using 12 parameter affine transformations - to their corresponding templates... Both images are registered - using 12 parameter affine transformations - to their corresponding templates... … but only the rigid-body transformation parameters allowed to differ between the two registrations … but only the rigid-body transformation parameters allowed to differ between the two registrations This gives: This gives: rigid body mapping between the images rigid body mapping between the images affine mappings between the images and the templates affine mappings between the images and the templates Both images are registered - using 12 parameter affine transformations - to their corresponding templates... Both images are registered - using 12 parameter affine transformations - to their corresponding templates... … but only the rigid-body transformation parameters allowed to differ between the two registrations … but only the rigid-body transformation parameters allowed to differ between the two registrations This gives: This gives: rigid body mapping between the images rigid body mapping between the images affine mappings between the images and the templates affine mappings between the images and the templates 2. Segmentation ‘ Mixture Model ’ cluster analysis to classify MR image as GM, WM & CSF ‘ Mixture Model ’ cluster analysis to classify MR image as GM, WM & CSF Additional information is obtained from a priori probability images - see later Additional information is obtained from a priori probability images - see later ‘ Mixture Model ’ cluster analysis to classify MR image as GM, WM & CSF ‘ Mixture Model ’ cluster analysis to classify MR image as GM, WM & CSF Additional information is obtained from a priori probability images - see later Additional information is obtained from a priori probability images - see later Between Modality Co-registration: I. Via Templates Grey and white matter partitions are registered using a rigid body transformation Grey and white matter partitions are registered using a rigid body transformation Simultaneously minimise sum of squared difference Simultaneously minimise sum of squared difference Grey and white matter partitions are registered using a rigid body transformation Grey and white matter partitions are registered using a rigid body transformation Simultaneously minimise sum of squared difference Simultaneously minimise sum of squared difference

Between Modality Coregistration: II. Mutual Information Between Modality Coregistration: II. Mutual Information PETT1 MRI