Download Brain morphometrics from MRI scans data

Brain Morphometrics from
MRI Scans
John Ashburner
The Wellcome Trust Centre for Neuroimaging
12 Queen Square, London, UK.
Contents
• Introduction
• Voxel-based Morphometry
• Diffeomorphic Shape Modelling
Introduction
Neuroscientists currently model a fraction
of the available information in MRI data.
– Models are geared for questions with
relatively simple answers.
• Findings are easier to explain and visualize
on the printed page.
– Two main approaches commonly used:
1.
2.
Examine whole brain and assume
independence among regions.
Focus attention on a few specific brain
regions
–
.
Findings from whole brain multivariate
analyses are too complicated to add to
human understanding of the brain.
•
See what data mining can achieve from it.
Scavenging for data is
likely to become easier.
•Some journals require
primary data to be made
available.
•Funding bodies now
promote data sharing.
Example data management and
sharing policies
• UK Wellcome Trust
– “The Trust considers that the benefits gained from research data will be
maximised when they are made widely available to the research
community as soon as feasible, so that they can be verified, built upon
and used to advance knowledge.”
–
http://www.wellcome.ac.uk/About-us/Policy/Policy-and-position-statements/WTX035043.htm
• UK Medical Research Council
– “The MRC Data Sharing and Preservation Initiative aims to maximise
opportunities for enabling wider and better use of this data for further
high quality, ethical research.”
–
http://www.mrc.ac.uk/Ourresearch/Ethicsresearchguidance/Datasharinginitiative/index.htm
• USA NIH
– “Data should be made as widely and freely available as possible
while safeguarding the privacy of participants, and protecting
confidential and proprietary data.”
–
http://grants.nih.gov/grants/policy/data_sharing/data_sharing_guidance.htm
Some currently available datasets
•
IXI: Brain MR images from 550 normal subjects between 20 and 80 years.
– http://www.ixi.org.uk/
•
OASIS: Cross-sectional MRI Data in young, middle aged, nondemented
and demented older adults. 416 subjects, aged 18 to 96.
– http://www.oasis-brains.org/
•
ADNI: 200 elderly controls, 400 subjects with mild cognitive impairment and
200 subjects with Alzheimer’s.
– http://www.adni-info.org/
•
MIRAID & ELUDE: Late life depression data.
– http://nirlarc.duhs.duke.edu/
The Extensible Neuroimaging Archive Toolkit (XNAT) is an open
source software platform designed to facilitate management and exploration
of neuroimaging and related data.
– http://www.xnat.org/index.html
Typical anatomical
MRI data
Many other types of MRI can be
collected. Eg. Functional MRI (fMRI).
Diffusion Weighted Images (DWI).
Anatomical scans are volumetric,
typically of about 1mm isotropic
resolution. Image dimensions are about
256x256x150 voxels.
T1weighted
MRA
Proton
Density
weighted
T2weighted
Grey
matter
White
matter
Grey and white matter segmented from
original scans.
Contents
• Introduction
• Voxel-based Morphometry
• Diffeomorphic Shape Modeling
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.
Volumetry
T1-Weighted MRI
Grey Matter
Probably the easiest approach to understand and describe.
Images are blurred
Each voxel after blurring effectively
becomes the result of applying a weighted
region of interest (ROI).
Before convolution
Convolved with a circle
Convolved with a Gaussian
Statistical Parametric
Mapping…
–
group 1

parameter estimate
standard error
=
statistic image
or
SPM
group 2
voxel by voxel
modelling
Statistics are corrected for multiple
dependent comparisons using Gaussian
random field theory.
Possible Explanations for
Findings
Mis-classify
Mis-register
Folding
Thickening
Thinning
Mis-register
Mis-classify
Contents
• Introduction
• Voxel-based Morphometry
• Diffeomorphic Shape Modelling
D’Arcy Thompson (1917). GROWTH AND FORM.
The morphologist, when comparing one organism with
another, describes the differences between them point by
point, and “character” by “character”. If he is from time to
time constrained to admit the existence of “correlation”
between characters (as a hundred years ago Cuvier first
showed the way), yet all the while he recognises this fact of
correlation somewhat vaguely, as a phenomenon due to
causes which, except in rare instances, he cannot hope to
trace; and he falls readily into the habit of thinking and
talking of evolution as though it had proceeded on the lines
of his own descriptions, point by point and character by
character. But if, on the other hand, diverse and dissimilar
[fish/brains] can be referred as a whole to identical functions
of very different coordinate systems, this fact will of itself
constitute a proof that a comprehensive “law of growth” has
pervaded the whole structure in its integrity, and that some
more or less simple and recognizable system of forces has
been at work.
A shape-based generative model
t – individual’s data (diverse and dissimilar brains)
μ – template (identical function)
Φ – deformation (very different coordinate systems)
Template data
ϕ1
t1
ϕ2
μ
Grey matter
average of
471 subjects
t2
t5
ϕ3
ϕ5
t4
ϕ4
t3
White matter
average of
471 subjects
Individual
Warped Individual
Template
Deformations and Jacobian
Deformation Field
Jacobians determinants
(should be positive)
Displacements don’t add linearly
Forward
Inverse
Composed
Subtracted
Diffeomorphisms: a more sophisticated
shape modelling framework.
• Diffeomorphisms are a key component of Pattern Theory.
• Smooth, continuous one-to-one mappings.
• Provide parsimonious representations of relative shapes.
– Metrics describing similarities between shapes.
– Shapes can be encoded by initial velocity/momentum.
Image registration usually by a variational approach
based on the principle of stationary action (LDDMM):
Geodesic Shooting:
Generating warps from initial velocities
Forward Deformation
Jacobians
Velocity
Magnitude of
momentum
Inverse Deformation
Jacobians
+
-
Diffeomorphic Eigenwarps
1st
550 scans from the IXI dataset, registered to
a common average using a diffeomorphic
registration model.
Eigen-decomposition of initial
velocities/momenta.
3rd
Exaggerated warps generated by a
geodesic shooting method.
- Preserves one-to-one mapping.
10th
Predictions
Brain shapes can be used to
make predictions about
individuals.
This figure shows predictions
of subjects ages made from
IXI dataset using Tipping’s
Relevance Vector Regression
(a kernel method).
More useful predictions may
be possible from other data.
Cross-validation results for age predictions.
Some References on Diffeomorphisms
•
•
•
•
M. F. Beg, M. I. Miller, A.Trouve & L. Younes. "Computing Large
Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms".
International Journal Of Computer Vision (2003).
M. I. Miller, A. Trouve, & L. Younes. "Geodesic Shooting for Computational
Anatomy". Journal of Mathematical Imaging and Vision (2004)
L. Wang, M. F. Beg, J. T. Ratnanather, C. Ceritoglu, L. Younes, J. C.
Morris, J. G. Csernansky & M. I. Miller. "Large Deformation Diffeomorphism
and Momentum Based Hippocampal Shape Discrimination in Dementia of
the Alzheimer Type". IEEE Trans. Med Imaging (2006)
L. Younes, F. Arrate & M. I. Miller. "Evolution Equations in Computational
Anatomy". Neuroimage (2008)
And my own approximation to this is:
• J. Ashburner. “A fast diffeomorphic image registration algorithm”.
NeuroImage (2007).
Contents
•
•
•
•
Introduction
Voxel-based Morphometry
Segmentation
Diffeomorphic Shape Modelling
Image Intensity Distributions
(T1-weighted MRI)
Tissue Probability
Maps
Tissue probability maps
(TPMs) are used to
represent the prior
probabilities of different
tissues at each location.
Note the similarity with some non-negative
matrix factorization models.
Factors are:
Tissue intensity distributions
Tissue probability maps
•
•
Deforming the Tissue Probability Maps
Tissue probability
maps are deformed
so that they can be
overlaid on top of the
image to segment.
Modelling intensity nonuniformity artifact
A bias field can by modelled by a linear
combination of spatial basis functions.
Corrupted image
Bias Field
Corrected image
Principle of Stationary Action
Lagrangian = Kinetic Energy – Potential Energy
Position
Velocity
Principle of stationary action:
LDDMM is a variational method based on this principle.
Hamiltonian Mechanics
Introduce momentum:
The Hamiltonian formalism gives:
The dynamical system equations are then
and
Hamiltonian for diffeomorphisms
In the landmark-based framework
So update equations are
t=1
See e.g. the work of Steve Marsland et al
t=0