COMPUTATIONAL (NEURO)ANATOMY

Duygu Tosun-Turgut, Ph.D. Center for Imaging of Neurodegenerative Diseases Department of Radiology and Biomedical Imaging [email protected] Computational anatomy

• Computational Anatomy's goal is to define methods for the quantization of shape within biological structures. • Origins of Computational Anatomy (CA) may be found in the central thesis of Sir D'Arcy Wentworth Thompson’s 1917 book entitled On Growth and Form.

D'Arcy believed that biologists of his day over emphasized the role of evolution, and under emphasized the roles of physical laws and mechanics, as determinants of the form and structure of living organisms. Scientific goal

Correlations Associations … HUMAN CLINICAL NEUROANATOMY PRACTICE

• Disease • Cognitive function • Treatment effect Quantitative neuroanatomy

• Traditional volumetrics • Tissue volumes • Measures from manually/automatically delineated region-of- interests (ROIs)

• Voxel-based morphometry (VBM)

• Tensor-based / deformation-based morphometry (TBM / DBM)

• Surface-based morphometry (e.g., FreeSurfer) Tissue-type volumetrics

Gray matter White matter CSF volume volume volume T1-weighted MRI GLOBAL MEASURES! Lobar ROIs

Frontal Lobe Parietal Lobe intelligence, behavior sensory perception motor control language

Temporal Lobe hearing, smell Occipital Lobe language vision Basal ganglia voluntary motor control, procedural learning relating to routine behaviors or "habits" Thalamus

relaying sensory and motor signals to the cerebral cortex, regulating consciousness, sleep, and alertness Hippocampus

consolidation of information from short-term memory to long-term memory and spatial navigation

[Frank Gaillard Designs] Manual anatomical delineation

~29-30 slices

• High intra- and inter-rater reliability requires rigorous training • Enormous investment of time • Prone to error Semi-automated hippocampal delination

4 marks are placed on 5 slices along its length representing the width of the hippocampus (medial, inferior, lateral, superior) Automatic anatomical delineation

Warp template to new subject using gray Identify scale images, structures on sometimes landmark template brain assisted

Apply resultant transformation to template ROIs Semi-automated vs automated hippocampal segmentation

Surgical Navigation Technologies (SNT) FreeSurfer

Fimbria / Intralimbic Parahippo Method Amygdala Hippo GM Alveus Gyrus Gyrus SNT No Yes No No No Freesurfer Partial Yes Yes Yes Partial Comparison of hippocampal volume

The error bars show the standard deviation. The numbers at the base of the bars indicate the adjusted hippocampal volume in mm3 PTSD effect on hippocampal subfields

0.45

0.40

0.35 - 11.8% 0.30 * 0.25

0.20

0.15

0.10 Volume in mm3 corrected for ICV for corrected mm3 in Volume

0.05 Control Control PTSD 0.00 ERC Sub CA1 CA1-2 transition CA3&DG

[Wang et al. Arch Gen Psychiatry 2010, 67: 296 – 303] Not limited to structural MRI…

Probabilistic maps for 11 tract-of-interests (TOIs) [Huan et al. 2008] Auto Tract-of-Interest Measurement

‘ ’ DARTEL ‘DARTEL’ Create Template

Individual FA Averaged Template Susumu’s ICBM FA Template with Fibers ‘DARTEL’ (22 TOIs) Register to Template

‘DARTEL’ ‘DARTEL’ Inverse Warping Warp Images

Individual FA+TOI Jacobian FA+TOI in Determinant common space Anterior thalamic radiation

5% 20% Neurodegeneration on cingulum bundle in AD contiuum

CN MCI aMCI AD MCI

L. t.CG FA 0.36 0.36 0.35 0.33 n.s. n.s. <0.001 (0.02) (0.02) (0.02) (0.03) R. t.CG FA 0.37 0.37 0.37 0.34 n.s. n.s. <0.001 (0.03) (0.02) (0.02) (0.03)

L. t.CG Vol 0.98 0.91 0.88 0.77 0.04 0.03 <0.001 [‰] (0.15) (0.13) (0.12) (0.15) R. t.CG Vol 1.10 1.04 1.02 0.84 n.s. n.s. <0.001 [‰] (0.21) (0.14) (0.12) (0.17)

CN MCI Limitations of traditional volumetrics

• A priori selection of ROIs is required.

• Disease pathology and cognitive involvement may not be confined in anatomical boundaries. • Effect may be localized; obscured by ROI

• Common ROIs are affected by variety of diseases (low specificity).

• Suggested solutions: • Look at smaller ROIs (limit is single voxel) • Identify spatial pattern of effects (statistical ROI) “Voxel-wise” morphometry

• Suited for discerning patterns of structural change

• Explore location and extent of variation

• Use nonlinear registration or “warping” of images • Automated • “within” subject to capture changes in brain over time • “between” subject to measure deviation from a reference • “between” subject to relate anatomy to clinical/functional scores

• Independently estimated statistics at each voxel • Multiple comparison • Low statistical power Voxel-based morphometry (VBM)

A voxel by voxel statistical analysis is used • to detect regional differences in the amount of grey matter between populations • to identify correlations with age, cognitive-scores etc.

Original Spatially Segmented Smoothed image normalised grey matter

The data are pre-processed to sensitize the tests to regional tissue volumes, usually grey or white matter. [SPM, FSL, HAMMER,…]

Preprocessing Standard Protocol

Optimized Protocol Involves segmenting images before normalizing, so as to normalize gray matter / white matter / CSF separately… VBM example: Aging

Significant grey matter volume loss with age • superior parietal • pre and post central • insula • cingulate VBM example: Sex differences

Females > Males Males > Females

• L superior temporal sulcus • mesial temporal • R middle temporal gyrus • temporal pole • intraparietal sulci • anterior cerebellar VBM example: brain asymmetry

Right frontal and left occipital petalia Function of preprocessing

• To shape the data in such a way that makes statistical analysis sensitive for local changes in tissue composition.

• 3 general steps for preprocessing a T1 image for standard/optimized VBM • segmentation • spatially normalization • smoothing

• The optimized procedure also involves modulating the data to yield volume information.

[Good et. al., A Voxel-Based Morphometric Study of Ageing in 465 Normal Adult Human Brains (2001)] Segmentation

• Segmentation is the process to label/ identify voxels in native T1 space as Intensity histogram • Gray matter fit by multi-Gaussians • White matter • CSF . • Other (skull, dura, fat, background, etc…)

• Segmentation is an automated process that separates tissue types with mixture model cluster analysis based on… 1. Voxel intensities 2. A priori knowledge of the location of gray matter, white matter, CSF, and other tissues in normal brains

[Good et. al., A Voxel-Based Morphometric Study of Ageing in 465 Normal Adult Human Brains (2001)] Spatial normalization: Why?

• Inter-subject averaging extrapolate findings to the population as a whole • increase statistical power above that obtained from single subject

• Reporting of significances/activations as coordinates within a standard stereotactic space • e.g. the space described by Talairach & Tournoux • e.g. a tissue-specific template created by the investigator from study-specific subject data

[Good et. al., A Voxel-Based Morphometric Study of Ageing in 465 Normal Adult Human Brains (2001)] [Mechelli et. al., Voxel-Based Morphometry of the Human Brain: Methods and Applications (2005)] [Ashburner and Friston, Why Voxel-Based Morphometry Should Be Used (2001)] Spatial normalization

• Determine transformation that minimizes the dissimilarity / maximizes the similarity 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 detailed brain shape • brain masks can be applied (e.g. for lesions) • Bayesian constraints

• A mask weights the normalization to brain instead of non- brain Bayesian constraints Empirically generated priors • Algorithm simultaneously minimizes: • Sum of squared difference between template and subject • Squared distance between the parameters and their expectation

• Bayesian constraints applied to both: • affine transformation • based on empirical prior ranges • nonlinear deformation • based on smoothness constraint (minimizing membrane energy) With & Without the Bayesian formulation

Template Affine Registration image (χ2 = 472.1)

Non-linear Non-linear registration registration without with regularisation regularisation (χ2 = 287.3) (χ2 = 302.7) Smoothing: Why?

• Potentially increase signal to noise (matched filter theorem)

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

• Increase validity of statistics (more likely that errors distributed normally) • Data must be normally distributed as a Gaussian field model is used for statistical analysis • Smoothing with an isotropic Gaussian kernel inherently makes the data more normally distributed by the central limit theorem • Central Limit Theorem: the summation of many variables which have a finite variance will produce a sum that is approximately normally distributed Smoothing • Convolution • Result of applying a weighted average • Kernel defined in terms of FWHM (full width at half maximum) of filter • ~16-20mm (PET) • ~6-8mm (fMRI) • Ultimate smoothness ~ applied smoothing + intrinsic image smoothness (“resels”: RESolvable Elements)

FWHM

Gaussian smoothing kernel

Convolved with a Convolved with a Before convolution circle Gaussian Preprocessed data for four subjects

Warped, modulated grey matter 12mm FWHM smoothed Optimized versus Standard VBM

• Nonlinear spatial normalization during preprocessing causes brain regions to differentially experience a change in volume

• Optimized VBM removes the mis-segmentation that is sometimes seen in standard VBM through the second segmentation step

• Optimized VBM also employs a modulation step • Modulation = (voxel values) x (Jacobian determinants) = (reestablishing volume information)

• Outputs: • No information on absolute volume size • Standard VBM: tissue concentration, or in other words, the proportion of the type of tissue to the proportion of all other tissue types in the given region • Optimized VBM: information about percentage of brain volume Final step…

… to create statistical parametric maps. Some explanations of the differences

Mis-classify Mis-register

Folding

Thinning Thickening Mis-register

Mis-classify Limitations of VBM

• Confuses tissue volume loss and displacement

• Relies on the automated segmentation of images

• Regions of abnormal WM may be incorrectly classified as GM • • Segmentation of subcortical structures can be problematic due to mixing of GM and WM Apparent loss of grey matter in this individual as less tissue falls inside model region

Grey matter displaced Disease Effect outside expected region appears as loss

White Matter Loss It’s more than a spatial normalization!

Original image Spatially normalized

Spatial Normalisation

Template image Deformation field Morphometry on deformation fields

Deformation-based morphometry Tensor-based morphometry looks at absolute displacements looks at local shapes

Vector field Tensor field Comparing VBM to deformation morphometry

Coarse non-rigid transformation Voxel-based morphometry Compare regional stats: e.g. Gray Matter density

Fine+Accurate Nonlinear Deformation transformation or tensor- based Transformation morphometry describes all differences Deformation field

Original Warped Template

&x'# &t1(x, y,z)# $y'! = $t (x, y,z)! $ ! $ 2 ! %$z'"! %$t3(x, y,z)"! Jacobian Matrix ‘Jacobian’

“the pointwise volume change at each point”

! ∂x' ∂x' ∂x' $ # & ! j j j $ ∂x ∂y ∂z # 11 12 13 & # & J j j j # ∂y' ∂y' ∂y' & = # 21 22 23 & = x y z # & # ∂ ∂ ∂ & j j j "# 31 32 33 %& # ∂z' ∂z' ∂z' & # & " ∂x ∂y ∂z %

J = j11( j22 j33 − j23 j32 )− j21( j12 j33 − j13 j32 )+ j31( j12 j23 − j13 j22 ) Jacobian Matrix of partial derivatives

When moving in a path across one anatomy, how quickly are we moving in each axis in the other anatomy?

y=T(x) X Y

x=(x1,x2) y=(y1,y2)

x=T-1(y)

V2 J(x1, y1, z1) = >1, voxel expansion V1

V2 J(x1, y1, z1) = <1, voxel shrinkage V1 Relative volumes

Deformation-based morphometry (DBM) Graphical flowchart of the analysis procedure used to compute the growth rate maps and identify regions with significant accelerations or decelerations.

Rajagopalan V et al. J. Neurosci. 2011;31:2878-2887 Local tissue growth rate patterns relative to cerebral growth rate, overlaid on the average brain.

Rajagopalan V et al. J. Neurosci. 2011;31:2878-2887 Deformation distance summary

• Deformations can be considered within a small or large deformation setting • Small deformation setting is a linear approximation • Large deformation setting accounts for the nonlinear nature of deformations • Uses Lie Group Theory Strain tensor

J: original Jacobian matrix J = RU

R: an orthonormal rotation matrix U: a symmetric matrix containing only zooms and shears.

Tensor-based morphometry (TBM) Detecting brain growth patterns in normal children using 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 • I. C. Wright et al. A Voxel-Based Method for the Statistical Analysis of Gray and White Matter Density Applied to Schizophrenia. NeuroImage 2:244-252 (1995). • I. C. Wright et al. Mapping of Grey Matter Changes in Schizophrenia. Schizophrenia Research 35:1-14 (1999). • J. Ashburner & K. J. Friston. Voxel-Based Morphometry - The Methods. NeuroImage 11:805-821 (2000). • J. Ashburner & K. J. Friston. Why Voxel-Based Morphometry Should Be Used. NeuroImage 14:1238-1243 (2001). • C. D. Good et al. Automatic Differentiation of Anatomical Patterns in the Human Brain: Validation with Studies of Degenerative Dementias. NeuroImage 17:29-46 (2002). • Bookstein FL. "Voxel-Based Morphometry" Should Not Be Used with Imperfectly Registered Images. NeuroImage 14:1454-1462 (2001). • W.R. Crum, L.D. Griffin, D.L.G. Hill & D.J. Hawkes. Zen and the art of medical image registration: correspondence, homology, and quality. NeuroImage 20:1425-1437 (2003). • N.A. Thacker. Tutorial: A Critical Analysis of Voxel-Based Morphometry. http://www.tina-vision.net/docs/memos/2003-011.pdf • Miller, Trouvé, Younes “On the Metrics and Euler-Lagrange Equations of Computational Anatomy”. Annual Review of Biomedical Engineering, 4:375-405 (2003) plus supplement • Beg, Miller, Trouvé, L. Younes. “Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms”. Int. J. Comp. Vision, 61:1573-1405 (2005) Nonlinear registration software

Only listing public software that can (probably) estimate detailed warps suitable for longitudinal analysis.

• HAMMER http://oasis.rad.upenn.edu/sbia/ • MNI_ANIMAL Software Package http://www.bic.mni.mcgill.ca/users/louis/MNI_ANIMAL_home/readme/ • SPM http://www.fil.ion.ucl.ac.uk/spm • VTK CISG Registration Toolkit http://www.image-registration.com/

…there is much more software that is less readily available... Need for surface-based morphometry

• Anatomical analysis is not like functional analysis – it is completely stereotyped. • Registration to a template (e.g. MNI/Talairach) doesn’t account for individual anatomy. • Even if you don’t care about the anatomy, anatomical models allow functional analysis not otherwise possible. • Function has surface-based organization.

• Inter-subject registration: anatomy, not intensity • Cortical parcellation: Automatically generated ROI tuned to each subject individually • Intrinsic smoothing (i.e., Like 3D, but 2D) • Intrinsic clustering • Visualization: Inflation/Flattening • Cortical morphometric measures Voxel versus surface voxel

surface Surface-based inter-subject registration

• Gray matter-to-gray matter (it’s all gray matter!)

• Gyrus-to-gyrus and sulcus-to-sulcus

• Some minor folding patterns won’t line up

• Fully automated or landmark-based

• Atlas registration is probabilistic, most variable regions get less weight Volume-based Smoothing

14mm FWHM • Smoothing is averaging of nearby 7mm FWHM voxels Volume-based Smoothing

14mm FWHM • 5 mm apart in 3D • 25 mm apart on surface! • Kernel much larger • Averaging with other tissue types (WM, CSF) • Averaging with other functional areas Why additional volume analysis?

• Surface-based coordinate system/registration appropriate for cortex but not for thalamus, ventricular system, basal ganglia, etc… Surface-based morphometry resources

• http://surfer.nmr.mgh.harvard.edu/ • http://brainvoyager.com/ • http://brainvisa.info/

• Some example references • B. Fischl & A.M. Dale. Measuring Thickness of the Human Cerebral Cortex from Magnetic Resonance Images. PNAS 97(20):11050-11055 (2000). • S.E. Jones, B.R. Buchbinder & I. Aharon. Three-dimensional mapping of cortical thickness using Laplace's equation. Human Brain Mapping 11 (1): 12-32 (2000). • J.P. Lerch et al. Focal Decline of Cortical Thickness in Alzheimer’s Disease Identified by Computational Neuroanatomy. Cereb Cortex (2004). • Narr et al. Mapping Cortical Thickness and Gray Matter Concentration in First Episode Schizophrenia. Cerebral Cortex (2005). • Thompson et al. Abnormal Cortical Complexity and Thickness Profiles Mapped in Williams Syndrome. Journal of Neuroscience 25(16):4146-4158 (2005). • J.-F. Mangin, D. Rivière, A. Cachia, E. Duchesnay, Y. Cointepas, D. Papadopoulos- Orfanos, D. L. Collins, A. C. Evans, and J. Régis. Object-Based Morphometry of the Cerebral Cortex. IEEE Trans. Medical Imaging 23(8):968-982 (2004). What FreeSurfer does…

FreeSurfer creates computerized models of the brain from MRI.

Volumes Surfaces Surface Overlays ROI Summaries

Input: Output: T1-weighted (MPRAGE,SPGR) Segmented & parcellated (.dcm/.nii) conformed volume (.mgz) Structural MRI Acquisition Methods for Brain: PD, T1, T2 and T2* weighting Which is best for brain morphometry/FreeSurfer?

PD-weighting + T1-weighting + T2-weighting (proton/spin density) (gray/white contrast) (bright CSF/tumor)

FLASH 5° FLASH 30° T2-SPACE MPRAGE (FLASH with inversion) has the best contrast for FreeSurfer because…

FLASH 30° MPRAGE • MPRAGE parameters chosen for “optimal” gray/white/CSF contrast • FreeSurfer statistics (priors) based on MPRAGE Motion correction and averaging

001.mgz

+ rawavg.mgz

002.mgz

• Usually only need one. • Does not change native resolution.

65 Conform

orig.mgz rawavg.mgz

• Changes to 2563 image volume with 1mm3 voxel dimensions. • All volumes will be conformed. Talairach transform

• Computes 12 DOF transform matrix

• Does NOT resample

• MNI305 template

• Mostly used to report coordinates Intensity bias

• Left side of the image much brighter than right side • Worse in multi-coil system • Makes gray/white segmentation difficult • “Nonparametric nonuniformity normalization (N3)” algorithm Intensity normalization

• Most WM = 110 intensity • Allows for atlas-based tissue segmentation 70

Skull stripping

• Removes all non-brain image voxels • Skull, eyes, neck, dura • An atlas-based approach

Input image volume Brain image volume [mri/brainmask.mgz] 71

Automatic volume labeling

• Fill in subcortical structures to create subcortical mass White Matter Cortex Lateral Ventricle

• Various atlases • e.g. RB_all_2008-03-26 Thalamus

• Useful in ROI-based Caudate Putamen morphometry Pallidum Amygdala

Hippocampus

Segmented image volume [mri/aseg.mgz] 72

White matter segmentation

• Separates white matter from everything else

• Uses segmented image volume to “fill in” subcortical structures

• Removes cerebellum, WM image volume [mri/wm.mgz] but keeps brain stem intact Surfaces: White and Pial “Subcortical mass”

• Includes all white matter

• Includes subcortical structures

• Includes ventricles

• Excludes brain stem and cerebellum

• Hemispheres separated

• Connected (no islands) Radiological or neurological convention?

Right Left “Tessellation”

Mosaic of vertex triangles “tessellation”

Errors: Donut holes, handles Due: Imaging noise, errors in previous processing steps 77

Topological defects

Fornix

hippocampus

Cortical Ventricles Pallidum Defects and Caudate and Putamen • Holes • Handles • Automatically Fixed Topological defects

• Nudge original surface • Follow T1 intensity gradients • Smoothness constraint • Vertex identity preserved Pial surface

• Nudge white surface • Follow T1 intensity gradients • Vertex identity preserved Non-cortical areas of surface

Amygdala, Putamen, Hippocampus, Caudate, Ventricles, CC

[surf/?h.cortex.label] 81

Surface “mapping”

• Mesh (“Finite Element”) • Vertex = point of triangles • Neighborhood • XYZ at each vertex • Triangles/Faces ~ 150,000 • Area, Distance • Curvature, Thickness • Moveable Cortical thickness

• Distance between white and pial surfaces

• One value per vertex

• In mm

• Surface-based more accurate than volume-based

[surf/?h.thickness] Curvature (Radial)

• Maximal circle tangent to surface at each vertex • Curvature measure ~ 1/radius of circle • One value per vertex • Signed (sulcus/gyrus) • Actually use Gaussian curvature

[surf/?h.curv] 84

Surface inflation

• Nudge vertices • No intensity constraint • See inside sulci • Used for sphere Sulcal depth

[surv/?h.sulc] A surface-based coordinate system Parcellation vs. segmentation

(cortical) parcellation (subcortical) segmentation

[mri/aparc+aseg.mgz] Why not just register to an ROI Atlas?

12 DOF (Affine)

ICBM Atlas Problems with affine (12 DOF) registration

Subject 1 Automatic surface segmentation

Precentral Gyrus Postcentral Gyrus

Superior Temporal Gyrus Based on individual’s folding pattern Borrowed from (Halgren et al., 1999) Rosas et al., 2002

Sailer et al., 2003 Kuperberg et al., 2003

Fischl et al., 2000

Gold et al., 2005

Salat et al., 2004 Rauch et al., 2004 Gyral white matter segmentation

+ +

Nearest cortical label to point in white matter Endless possibilities !?

• Longitudinal modeling • Multimodal integration! 1. fMRI 2. FDG-PET 3. DTI 4. ASL 5. Amyloid PET 6. ….