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Computational Anatomy: VBM and Alternatives. Overview. Volumetric differences Serial Scans Jacobian Determinants Voxel-based Morphometry Multivariate Approaches Difference Measures Another approach. Deformation Field. Original. Warped. Template. Deformation field. Jacobians.

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overview
Overview
  • Volumetric differences
    • Serial Scans
    • Jacobian Determinants
  • Voxel-based Morphometry
  • Multivariate Approaches
  • Difference Measures
  • Another approach
slide3

Deformation Field

Original

Warped

Template

Deformation field

jacobians
Jacobians

Jacobian Matrix (or just “Jacobian”)

Jacobian Determinant (or just “Jacobian”) - relative volumes

serial scans
Serial Scans

Early

Late

Difference

Data from the Dementia Research Group, Queen Square.

regions of expansion and contraction
Regions of expansion and contraction
  • Relative volumes encoded in Jacobian determinants.
slide7

Late

Early

Late CSF

Early CSF

CSF “modulated” by relative volumes

Warped early

Difference

Relative volumes

slide8

Late CSF - modulated CSF

Late CSF - Early CSF

Smoothed

smoothing
Smoothing

Smoothing is done by convolution.

Each voxel after smoothing effectively becomes the result of applying a weighted region of interest (ROI).

Before convolution

Convolved with a circle

Convolved with a Gaussian

overview1
Overview
  • Volumetric differences
  • Voxel-based Morphometry
    • Method
    • Interpretation Issues
  • Multivariate Approaches
  • Difference Measures
  • Another approach
voxel based morphometry
Voxel-Based Morphometry
  • Produce a map of statistically significant differences among populations of subjects.
    • e.g. compare a patient group with a control group.
    • or identify correlations with age, test-score etc.
  • The data are pre-processed to sensitise the tests to regional tissue volumes.
    • Usually grey or white matter.
  • Can be done with SPM package, or e.g.
    • HAMMER and FSL

http://oasis.rad.upenn.edu/sbia/

http://www.fmrib.ox.ac.uk/fsl/

spm5 segmentation includes warping

c1

y1

m

g

c2

y2

s2

a

a0

c3

y3

b0

b

Ca

cI

yI

Cb

SPM5 Segmentation includes Warping

Tissue probability maps are deformed to match the image to segment

slide14

SPM5b Pre-processed data for four subjects

Warped, Modulated Grey Matter

12mm FWHM Smoothed Version

validity of the statistical tests in spm
Validity of the statistical tests in SPM
  • Residuals are not normally distributed.
    • Little impact on uncorrected statistics for experiments comparing groups.
    • Invalidates experiments that compare one subject with a group.
  • Corrections for multiple comparisons.
    • Mostly valid for corrections based on peak heights.
    • Not valid for corrections based on cluster extents.
      • SPM makes the inappropriate assumption that the smoothness of the residuals is stationary.
        • Bigger blobs expected in smoother regions.
interpretation problem
Interpretation Problem
  • What do the blobs really mean?
    • Unfortunate interaction between the algorithm's spatial normalization and voxelwise comparison steps.
  • 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
some explanations of the differences

Mis-register

Mis-classify

Folding

Thinning

Mis-register

Thickening

Mis-classify

Some Explanations of the Differences
overview2
Overview
  • Volumetric differences
  • Voxel-based Morphometry
  • Multivariate Approaches
    • Scan Classification
  • Difference Measures
  • Another approach
globals for vbm
“Globals” for VBM
  • Shape is multivariate
    • Dependencies among volumes in different regions
  • SPM is mass univariate
    • “globals” used as a compromise
    • Can be either ANCOVA or proportional scaling

Where should any difference between the two “brains” on the left and that on the right appear?

training and classifying

?

?

?

?

Training and Classifying

Control

Training Data

Patient

Training Data

classifying

?

?

?

?

Classifying

Controls

Patients

y=f(wTx+w0)

support vector classifier svc1
Support Vector Classifier (SVC)

w is a weighted linear combination of the support vectors

Support

Vector

Support

Vector

Support

Vector

overview3
Overview
  • Volumetric differences
  • Voxel-based Morphometry
  • Multivariate Approaches
  • Difference Measures
    • Derived from Deformations
    • Derived from Deformations + Residuals
  • Another approach
distance measures
Distance Measures
  • Classifiers such as SVC use measures of distance between data points (scans).
    • I.e. measure of how different each scan is from each other scan.
  • Distance measures can be derived from deformations.
deformation distance summary
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.
  • 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)
slide29

Computing the geodesic: problem statement

I0: Template

I1:Target

Slide from Tilak Ratnanather

one to one mappings
One-to-One Mappings
  • One-to-one mappings between individuals break down beyond a certain scale
  • The concept of a single “best” mapping may become meaningless at higher resolution

Pictures taken from http://www.messybeast.com/freak-face.htm

overview4
Overview
  • Volumetric differences
  • Voxel-based Morphometry
  • Multivariate Approaches
  • Difference Measures
  • Another approach
anatomist brainvisa framework
Anatomist/BrainVISA Framework
  • Free software available from: http://brainvisa.info/
  • Automated identification and labelling of sulci etc.
    • These could be used to help spatial normalisation etc.
    • Can do morphometry on sulcal areas, etc
  • 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)
slide33

Design of an artificial neuroanatomist

Elementary

folds

Fields of

view of

neural nets

3D

retina

Bottom-up

flow

Sulci

correlates of handedness
Correlates of handedness

14 subjects

128 subjects

Central sulcus

surface is larger

in dominant hemisphere

some of the potentially interesting posters
Some of the potentially interesting posters
  • (#728 T-PM ) A Matlab-based toolbox to facilitate multi-voxel pattern classification of fMRI data.
  • (#699 T-AM ) Pattern classification of hippocampal shape analysis in a study of Alzheimer's Disease
  • (#697 M-AM ) Metric distances between hippocampal shapes predict different rates of shape changes in dementia of Alzheimer type and nondemented subjects: a validation study
  • (#721 M-PM ) Unbiased Diffeomorphic Shape and Intensity Template Creation: Application to Canine Brain
  • (#171 T-AM ) A Population-Average, Landmark- and Surface-based (PALS) Atlas of Human Cerebral Cortex
  • (#70 M-PM ) Cortical Folding Hypotheses: What can be inferred from shape?
  • (#714 T-AM ) Shape Analysis of Neuroanatomical Structures Based on Spherical Wavelets