COMPUTATIONAL (NEURO)ANATOMY Duygu Tosun-Turgut, Ph.D. Center for Imaging of Neurodegenerative Diseases Department of Radiology and Biomedical Imaging duygu.tosun@ucsf.edu

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

HUMAN NEUROANATOMY

CLINICAL PRACTICE

Correlations Associations …

•  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

T1-weighted MRI

Gray matter volume

White matter volume

CSF volume

GLOBAL MEASURES!

Lobar ROIs

Frontal Lobe intelligence, behavior motor control

Parietal Lobe sensory perception

language

Occipital Lobe vision

Temporal Lobe hearing, smell language

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

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

~29-30 slices

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

Identify structures on

template brain

Warp template to new subject using gray

scale images, sometimes landmark

assisted

Apply resultant transformation to

template ROIs

Semi-automated vs automated hippocampal segmentation

Method Amygdala Hippo GM Fimbria / Alveus

Intralimbic Gyrus

Parahippo Gyrus

SNT No Yes No No No

Freesurfer Partial Yes Yes Yes Partial

Surgical Navigation Technologies (SNT) FreeSurfer

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

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Volu

me

in m

m3

corr

ecte

d fo

r IC

V

ERC Sub CA1 CA1-2 transition CA3&DG

*

Con

trol

PT

SD

- 11.8%

[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

Individual FA

‘DARTEL’ Register to Template

Jacobian Determinant

‘DARTEL’ Create Template

Averaged Template

‘DARTEL’ Inverse Warping

‘DARTEL’ Warp Images

Susumu’s ICBM FA Template with Fibers

(22 TOIs)

‘DARTEL’

Individual FA+TOI FA+TOI in common

space

5% 20%

Anterior thalamic radiation

Neurodegeneration on cingulum bundle in AD contiuum

MCI CN

CN (n=32)

MCI (n=30)

aMCI (n=15)

AD (n=30)

MCI<CN p

aMCI<CN p

AD<CN p

L. t.CG FA 0.36 (0.02)

0.36 (0.02)

0.35 (0.02)

0.33 (0.03)

n.s. n.s. <0.001

R. t.CG FA 0.37 (0.03)

0.37 (0.02)

0.37 (0.02)

0.34 (0.03)

n.s. n.s. <0.001

L. t.CG Vol [‰]

0.98 (0.15)

0.91 (0.13)

0.88 (0.12)

0.77 (0.15)

0.04 0.03 <0.001

R. t.CG Vol [‰]

1.10 (0.21)

1.04 (0.14)

1.02 (0.12)

0.84 (0.17)

n.s. n.s. <0.001

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 image

Spatially normalised

Segmented grey matter

Smoothed

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 •  R middle temporal gyrus •  intraparietal sulci

•  mesial temporal •  temporal pole •  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 •  Gray matter •  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)]

.

Intensity histogram fit by multi-Gaussians

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 • 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)

Empirically generated priors

With & Without the Bayesian formulation Affine Registration

(χ2 = 472.1) Template

image

Non-linear registration

without regularisation (χ2 = 287.3)

Non-linear registration

with regularisation (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)

Gaussian smoothing kernel

FWHM

Before convolution Convolved with a circle

Convolved with a 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

Thickening Thinning

Folding

Mis-classify

Mis-classify

Mis-register

Mis-register

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

Disease Effect

White Matter Loss

Apparent loss of grey matter in this individual as less tissue falls inside model region

Grey matter displaced outside expected region appears as loss

It’s more than a spatial normalization!

Spatial Normalisation

Original image

Template image

Spatially normalized

Deformation field

Morphometry on deformation fields Deformation-based morphometry looks at absolute displacements

Tensor-based morphometry looks at local shapes

Vector field Tensor field

Comparing VBM to deformation morphometry

Compare regional stats: e.g. Gray Matter density

Coarse non-rigid transformation

Transformation describes all differences

Fine+Accurate Nonlinear

transformation

Voxel-based morphometry

Deformation or tensor-

based morphometry

Deformation field

Template Warped Original

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J =j11 j12 j13j21 j22 j23j31 j32 j33

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“the pointwise volume change at each point”

J = j11( j22 j33 − j23 j32 )− j21( j12 j33 − j13 j32 )+ j31( j12 j23 − j13 j22 )

Jacobian Matrix of partial derivatives

y=T(x)

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

x=T-1(y)

X Y

J(x1, y1, z1) = V2

V1

>1, voxel expansion

J(x1, y1, z1) = V2

V1

<1, voxel shrinkage

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

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 •  Smoothing is averaging of nearby voxels 7mm FWHM

14mm FWHM

Volume-based Smoothing

•  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

14mm FWHM

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.

Input: T1-weighted (MPRAGE,SPGR)

(.dcm/.nii)

Output: Segmented & parcellated

conformed volume (.mgz)

Volumes Surfaces Surface Overlays ROI Summaries

Structural MRI Acquisition Methods for Brain: PD, T1, T2 and T2* weighting

Which is best for brain morphometry/FreeSurfer?

PD-weighting (proton/spin density)

+ T1-weighting (gray/white contrast)

+ T2-weighting (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

65

001.mgz

002.mgz

+ rawavg.mgz

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

Conform

rawavg.mgz

•  Changes to 2563 image volume with 1mm3

voxel dimensions. •  All volumes will be conformed.

orig.mgz

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

Skull stripping •  Removes all non-brain image voxels

•  Skull, eyes, neck, dura

•  An atlas-based approach

70

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

Automatic volume labeling •  Fill in subcortical structures

to create subcortical mass

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

• Useful in ROI-based morphometry

71

Segmented image volume [mri/aseg.mgz]

Caudate

Pallidum

Putamen

Amygdala

Hippocampus

Lateral Ventricle

Thalamus

White Matter Cortex

White matter segmentation •  Separates white matter

from everything else

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

•  Removes cerebellum, but keeps brain stem intact

72

WM image volume [mri/wm.mgz]

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 triangles “tessellation”

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

vertex

Topological defects

77

Fornix

Pallidum and

Putamen

hippocampus

Ventricles and Caudate

Cortical Defects

•  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]

Surface “mapping”

81

•  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]

Surface inflation

84

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

Sulcal depth

[surv/?h.sulc]

A surface-based coordinate system

Parcellation vs. segmentation (subcortical) segmentation (cortical) parcellation

[mri/aparc+aseg.mgz]

ICBM Atlas

12 DOF (Affine)

Why not just register to an ROI Atlas?

Subject 1

Problems with affine (12 DOF) registration

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

Kuperberg et al., 2003

Gold et al., 2005

Rauch et al., 2004 Salat et al., 2004

Fischl et al., 2000

Sailer et al., 2003

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.  ….