Statistical Parametric MappingStatistical Parametric Mapping

Lecture 16 - Chapter 15Registration, brain atlases and cortical

flattening

Textbook: Functional MRI an introduction to methods, Peter Jezzard, Paul Matthews, and Stephen Smith

Many thanks to those that share their MRI slides online

Structural Analysis

• Physical meaning of functional findings• Registration

– image-to-image– image-to-atlas– combine functional and anatomical images

• 3-D Affine, warping• Flattening of cortex

Figure 15.2 An example of the unwarping transformation to remove geometric distortion.

Acquire field map image (Jezzard and Balaban 1995). Calculate local geometric distortion due to field changes and warp to correct. Use Jacobian (local ratio of volume elements) to correct for signal intensity when stretching or compressing.

Figure 15.3 An illustration of automatic removal of non-brain structures using BET (Smith 2000).

non-brain structures vary by individual and include additional tissue types (bone, muscle, fat)

Start with small sphere within brain and inflate until certain boundary conditions are met.

Figure 15.4 An example of bias field removal; original image, estimated bias field and restored image (Zhang et al. 2001).

At higher field strengths RF penetration issues lead to RF inhomogeneity (depend on shape of transmit and receive coils). The bias field image is calculated and multiplied by the uncorrected image for correction.

• iterate segmentation and bias field correction until acceptable bias field obtained (Zhang et al. 2001).

• search for bias field that maximizes some measure of ‘sharpness’ or entropy in the image (Sled et al. 1998). Uses joint histogram (see Fig 15.13).

Figure 15.5 An illustrative example showing a translation of 20 units to the right.

Registration includes translation, rotation, scaling for 9-parameter affine transform and adds skewing for 12-parameter transform.

Figure 15.6 Various examples of linear transformations of an original image on the left. The order of rotations, translations, scaling and skew are important. However, two different orderings that lead to the same 4x4 transform matrix produce the same effect.

• Rigid-body (6 degrees of freedom) - translation, rotation only• Similarity (7 DOF) - translation, rotation, single global scaling• Affine (9 or 12 DOF) - translation, rotation, scale, (skew)

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rotation matrix Rx for rotation about x-axis (1 parameter)

rotation matrix Ry for rotation about y-axis (1 parameter)

rotation matrix Rz for rotation about z-axis (1 parameter)

M= [S][Rx][Ry][Rz][T]

Above ordering does translations first to match origins, then rotations about new origin, and finally scaling of the aligned image. Most software used 9 or 12 parameters (sometimes called degrees of freedom) for registration.

9-Parameter Affine Transform

12-Parameter affine transform matrix used with 3-D images

m14, m24, and m34 are x, y, and z translations

3 each rotations, scales, shears

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Figure 15.7 Examples of topology preserving (left) and non-preserving (right) warps applied to the original image shown if figure 15.6. Note hole near ventricle (upper right) and splitting of the lateral ventricles (lower right).

High DOF warping of brain image volumes

Topology preserving means that joined structures remain joined after warp. Violation leads to folding over, holes, and disjoint tissues.

Deformation vector matrix matched to image used. Local smoothness of Jacobian can be used to preserve topology.

Figure 15.8 A 1-D example of linear interpolation. Solid lines show alignment of initial data points. Lines between closed circles are linear trend between adjacent data points. Dotted lines show the the alignment of desired data points.

Initial data points

linear interpolation

resampled data points

Higher order interpolation may be a 2nd or 3rd order polynomial fit through the initial data points.

Sinc function interpolation is considered the most accurate, but problem with extent that must be truncated.

What to do at the ends?

Figure 15.9 Example showing block-like artificial boundaries when NN interpolation is used with low resolution image. Zooming of original 8x8x8 mm spacing matrix to a 1x1x1 mm display emphasizes this. Trilinear interpolation leads to a smoother and perhaps more realistic image for this low resolution image.

Nearest Neighbor (NN) Trilinear

Nearest Neighbor Trilinear

Figure 15.10 Example of ‘artifacts’ (diagonal discontinuities) when NN interpolation is used with rotation. Trilinear interpolation produces a smoother result.

• For many images trilinear interpolation is often adequate.• NN used to conserve histogram only.• sinc interpolation used when highest quality is critical.

Manual or Semi-Automated Registration

• Identifying landmarks

• point-like (AC and PC)

• centroid of highly penetrant features

• mid-sagittal plane

• fiducials (good for MRI, CT, PET, SPECT registration)

• Mango image processing application

• landmark based (load landmark coordinates from file)

• point matching (pick corresponding landmarks in two images)

• atlas based (Talairach atlas method called SN which uses key landmarks of the atlas brain)

Automated Registration

• Remove interoperator variability

• Automated landmark matching (fiducials)

• Iteratively adjust some coordinate transform using some measure of similarity between source and target image

• similarity function/cost function as terminology

• Measuring Similarity

• intra-modality

• inter-modality

Intra-modal Registration

image pairs should map to the same or similar intensity and have similar contrast mechanism

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Similarity Function(maximize)

IAi is voxel value ‘i’ in image A and IBi is the voxel value in image B, and we are matching image A to image B.

Cost Functions(minimize)

Figure 15.11 Example showing difference image formed for large rotation (top), small rotation (middle), and different signal contrast and levels.

Image 1 Image 2 – Image 1Image 2

white --> +grey --> 0black --> -

Inter-modal Registration

Image pairs do not map to the same or similar intensity and/or have different contrast mechanism. Assumes similar image regions have similar intensities.

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MutualInformation = H(IA ) + H(IB ) − H(IA ,IB )

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where k2 is the variance, k the mean and nk is the number of voxels in region k

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Cost Function(minimize)

and 2 is the total variance across the image. H(IA) and H(IB) are individual image histograms, H(IA,IB) the joint entropy and nij is the number of voxels in each histogram bin (i,j). Recall that entropy (H) is a positive measure of disorder.

Figure 15.12 Illustration of region formed to support fitting using the Woods cost function. Here k would be four.

Region 2Region 1

Region 4Region 3

Regions (white) are used to evaluate Woods cost function in image to be transformed.

The assumption is that if the regions which represent similar tissues in the target brain have lower variance in the source brain then match is improving.

T1 weighted Joint HistogramT2 weighted

Figure 15.13 Illustration of typical joint histograms for T1 and T2 weighted images with differing spatial mismatch due to rotation. Entropy calculated from joint histogram.

~ perfectalignment

Intermediatealignment

pooralignment

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Figure 15.14 Illustration, using similarity measures calculated from a real image pair, showing both local maxima and global maximum.

Optimization of fitting

1 mm

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Figure 15.15 Example showing image with 1x1x1 mm voxels and three subsamplings to 2 mm, 4 mm, and 8 mm sample spacings.

Optimization of fitting

Multi-scale approach analysis starting at 8 mm and progressing stepwise to 1 mm helps to avoid local maxima or minima.

-faster processing at lower resolution-each successive step seeded by better estimate from lower resolution step

Tested Software for Registration

Automated Image Registration (AIR) - Woods et al. 1993 (Woods function)

FMRIB Linear Image Registration Tool (FLIRT) - Jenkinson and Smith 2001 (various options but default is correlation ratio)

MRITOTAL - Collins et al. 1994 (Mutual Information)

SPM - Friston, Ashburner, et al. 1995 (MSD and modality specific templates)

UMDS - Studholme et al. 1996 (Mutual Information)

Many other software solutions are available for registration so look for the one that best suits your needs.

Fox, et alWash. U.

• Lateral Skull X-Ray

• Horizontal Grid Lines

• A-P Dimension

• S-I Dimension

• Transform PET

• Talairach Atlas 1967

– AC-PC line

– Origin

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1. Set Transformed = Source.2. Extract features (F's).3. Compare features (F).4. Transform source to match features.5. Repeat 2-4 until done.

Spatial Normalization Algorithm

The schematic plan for manual spatial normalization of brain images.

Axial views of the brain before (left) and after (right) alignment to the mid-sagittal plane (red line). The image was rotated clockwise and translated to the right in this example. Note the marker used to identify the right side of the patient.

Anterior-Right Anterior-Right

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Coronal views of brain images before (left) and after (right) alignment to the mid-sagittal plane (red line). The brain was rotated counter clockwise and translated to the right.

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Mid-sagittal section views of the brain before (left) and after (right) AC-PC alignment using a four-point fitting method. The four landmarks are the anterior-inferior margin of the corpus callosum (blue), inferior margin of the thalamus nucleus (yellow), the superior colliculus (green), and the apex of the cerebellum.

Axial and sagittal views of the bounding box after manual adjustment to match the bounding limits of the cerebrum. The anterior, posterior, left, right, superior,and inferior bounds are illustrated. Bounds do not generally fall within any one view of the brain.

Axial View Sagittal View+y

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In the axial view the anterior commissure (AC) and posterior commissure (PC) appear as thin white lines connecting white matter between hemispheres. In the sagittal view the AC is a conspicuous white, slightly elliptical structure, and the PC is at the elbow between the pineal body (pb) and superior colliculus (sc).

Axial View Sagittal View

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15O-water 18F-FDG MRI

Before

After

Talairach Convex Hull Template

Convex Hull Surface-Based Registration

Lancaster et al. 1999

Average Brain Templates Used for Registration

Octree Spatial Normalization (OSN)

A. Conv. Hull global SN)

B. OSN regional SN brain surface only

A B

C D

C. OSN regional SN following GM, WM, and CSF

D. Target image

High DOF Warp

Figure 15.16 Example of axial, sagittal, and coronal section MR images with points used to specify Talairach space.

• x-y-z origin at the anterior commissure (AC)• mid-sagittal plane is the y-z plane.• y-axis defined by AC-PC line• bounding box of aligned cerebrum to match that

of the 1988 Talairach atlas.

Atlases

Talariach's Coordinate System

• AC-PC line• AC as origin• Bounding Box

– 136 x 172 x 118 mm

• Right-handed system

Z = +1 mm

Origin(AC)

Using FLIRT to fit a T1W MR image to the MNI305 3-D average brain template (template brain feature outline indicated by red lines).

Note the large rotation about the y-axis indicated in the left image.

Montreal Neurological Institute (MNI) Coordinates

Level 5 - Cell Type

Level 4 - Tissue Type

Level 3 - Gyral

Level 1- Hemisphere

Level 2 - Lobar

Z = +1

Automated Atlas Labels Using Talairach Coordiantes

Probabilistic Atlas (Toga et al. 2006).

LONI Probabilistic Brain AtlasMaximum probability labels for various brain areas following fitting to the ICBM452 brain template using AIR with non-linear warping.

Data based on brain images from 40 healthy subjects. Segmentation of each region done by experts with review by neuroanatomists.

Figure 15.17 Example images showing the different stages of flattening in one particular approach (Dale et al. 1999; Fischl et al. 1999), courtesy of R. Tootell and N. Hadjikhani. Inflation removes the main folds of the sulci and gyri, and flattening produces a planar surface on which different functional areas are shown.

Cuts are necessary to make flat maps of the cortical surface.

Figure 15.18 Example of ‘flattened activation’ courtesy of R. Tootell and N. Hadjikhani. The different parts of the visual cortex are identified using phase-encoded simulation.