Coregistration and Spatial Normalisation Ana Saraiva Britt Hoffland

Overview f. MRI time-series Motion correction kernel Design matrix Smoothing General Linear Model (Co-registration and) Spatial normalisation Standard template Statistical Parametric Map Parameter Estimates

• Co-registration • Between modality co-registration PET T 1 MRI

Why is between-modality coregistration useful? • Significant advantages in research and clinical settings

Principles of co-registration Registration Transformation 6 Parameters for motion correction

Different for between-modality coregistration • Shape • Signal intensities T 2 T 1 Transm EPI PD PET

Between modality registration • Manually (homologous landmarks) • I via templates • II mutual information

Via Templates • 12 parameter affine transformations • Templates conform to the same anatomical space • Simultaneous registration

1. Affine Registration • 12 parameter affine transform – – 3 translations 3 rotations 3 zooms 3 shears • Fits overall shape and size z Algorithm simultaneously minimises y Mean-squared difference between template and source image y Squared distance between parameters and their expected values (regularisation)

However… • Image MRI Template MRI Scaling/shearing parameters Rigid body transformation parameters • Image PET Template PET

2. Segmentation • Partition in GM, WM, CSF Priors: Image: GM WM CSF Brain/skull

Registration of partitions Grey and white matter partitions are registered using a rigid body transformation, Simultaneously minimise sum of squared difference…

Between Modality Coregistration: II. Mutual Information PET T 1 MRI

Co-registration in SPM

Co-registration in SPM Make selection Explains each option

Template: image that remains stationary Image that is ‘jiggled about’ to match template Defaults used by SPM for estimating the match, including Normalised Mutual Information Run Reslice options: choose from the menu for each of the three options (usually just defaults)

Spatial Normalisation

f. MRI pre-processing sequence • Realignment – Motion correction: Adjust for movement between slices ü Coregistration ü Overlay structural and functional images: Link functional scans to anatomical scan • Normalisation – Warp images to fit to a standard template brain • Smoothing – To increase signal-to-noise ratio • Extras (optional) – Slice timing correction; unwarping

What is spatial normalisation? • Establishes a one-to-one correspondence between the brains of different individuals by matching each subject to a standard template • Allows: – Signal averaging across subjects – Determination of what happens generically over individuals – Identify commonalities and differences between groups (e. g. patients vs. healthy individuals) • Advantages: – Activation sites can be reported according to their Euclidian coordinates within a standard space (e. g. MNI or Tailarach & Tournoux, 1988) – Increases statistical power

Methods of registering images 1. Label-based – – Identifies homologous features (points, lines and surfaces) in the image and template and finds the transformations that best superimpose them Limitations: few identifiable features; features can be identified manually (time consuming & subjective) 2. Non-label based (aka intensity based) – Identifies a spatial transformation that optimizes some voxelsimilarity between a source and image measure by: • • – Minimising the sum of squared differences between the object and template image Maximising correlation coefficient between the images. Limitation: susceptible to poor starting estimates

Spatial Normalisation in SPM • 2 steps involved in registering any pair of images: 1. Linear registration - 12 -parameter affine transformation – accounts for major differences in head shape and position 2. Nonlinear registration – warping – accounts for smaller-scale anatomical differences

Priors/Constraints • Both linear and non-linear registrations use prior knowledge of the variability of the head and size to determine constraints • Priors/constraints are calculated using estimators such as the maximum a posteriori (MAP) or the minimum variance estimate (MVE)

Step 1 – Affine transformation (Linear) • Aim: to fit the source image f to a template image g, using a 12 -parameter affine transformation • Performed automatically by minimizing squared distance between parameters and expected values • 12 parameters = 3 translations and 3 rotations (rigid-body) + 3 shears and 3 zooms • Accounts for overall shape, size, position and orientation rotation sheer translation zoom

Step 2 – Warping (non-linear) • Corrects gross differences in head shapes that cannot be accounted for by the affine transformation • Warps are modelled by linear combinations of smooth discrete cosine transform basis functions • Uses relatively small number of parameters (approx. 1000)

Non-linear basis functions Deformations are modelled with a linear combination of non -linear basis functions

Over-fitting • Regularisation – necessary so that nonlinear registration does not introduce unnecessary deformations • Ensures voxels stay close to their neighbours Template Non-linear registration with regularisation Affine registration (linear) Non-linear registration without regularisation

Limitations • Difficult to attempt exact structural matches between subjects, due to individual anatomical differences • Even if anatomical areas were exactly matched, it does not mean functionally homologous areas are matched too • This is particularly problematic in patient studies with lesioned brains • Solution: To correct gross differences followed by spatial smoothing of normalised images…

Normalisation in SPM Calculates warps needed to get from your selected images – saves in sn. mat file

1. Select the image that will be matched to the template 2. Select image(s) to be warped using the sn. mat calculated from the Source Image 3. Select SPM template 4. Select voxel sizes for warped output images

References • Ashburner & Friston – Spatial Normalisation Using Basis Functions, Chapter 3, Human Brain Function, 2 nd Ed • Ashburner & Friston – Nonlinear Spatial Normalisation Using Basis Functions, Human Brain Mapping, 1999 • Ashburner & Friston - Multimodal image coregistration and partitioning--a unified framework, Neuroimage, 1997 • MFD slides from previous years • http: //www. fil. ion. ucl. ac. uk/spm/course/slides 08 -zurich/