structural images 杜政昊 cheng-hao tu, phd. outlines computational anatomy voxel-based...
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Structural Images
杜政昊 Cheng-Hao Tu, PhD
Outlines• Computational Anatomy
• Voxel-based Morphometry (VBM)
• Diffusion Tensor Imaging (DTI)
Aims of computational neuroanatomy
• Many interesting and clinically important questions might relate to the shape or local size of regions of the brain
• For example, whether (and where) local patterns of brain morphometry help to:? Distinguish schizophrenics from healthy controls? Understand plasticity, e.g. when learning new skills? Explain the changes seen in development and aging? Differentiate degenerative disease from healthy aging
Computational Neuroanatomy
Baseline ImageStandard clinical MRI1.5T T1 SPGR1x1x1.5mm voxels
Repeat image12 month follow-uprigidly registered
Subtraction image
Why we use VBM
The output of VBM can be either information concerning regional volume or tissue concentration (density)
VBM has been designed to be sensitive to differences in local compositions of various brain tissue types, such as gray matter
The output of VBM can be displayed as a statistical parametric map
Short history of VBM
• A Voxel-Based Method for the Statistical Analysis of Gray and White Matter Density… Wright, McGuire, Poline, Travere, Murrary, Frith, Frackowiak and Friston. NeuroImage 2(4), 1995 (!)– Rigid reorientation (by eye), semi-automatic scalp editing and
segmentation, 8mm smoothing, SPM statistics, global covars.
• Voxel-Based Morphometry – The Methods. Ashburner and Friston. NeuroImage 11(6 pt.1), 2000– Non-linear spatial normalisation, automatic segmentation– Thorough consideration of assumptions and confounds
Short history of VBM• A Voxel-Based Morphometric Study of Ageing… Good, Johnsrude,
Ashburner, Henson and Friston. NeuroImage 14(1), 2001– Optimised GM-normalisation (“a half-baked procedure”),
modulation of segments with Jacobian determinants
• Unified Segmentation. Ashburner and Friston. NeuroImage 26(3), 2005– Principled generative model for segmentation using
deformable priors
• A Fast Diffeomorphic Image Registration Algorithm. Ashburner. Neuroimage 38(1), 2007– Large deformation normalisation to average shape templates
Preprocessing – General steps
Segmentation: separate tissue types
Spatial normalization: corrects for global differences in position and transform to stereotactic space
(Modulation): keep volume information
Smooth: modifying the data to fit a certain distribution for statistical analysis.
Preprocessing – Optimized VBM
Segmentation- basic approach
• Intensities are modelled by a Gaussian Mixture Model
• Parameterised by means, variances and mixing proportions
Segmentation – modified approach
• Multiple components per tissue class allow non-Gaussian distributions to be modelledaccounting for partial volume effects
• Tissue probability maps (TPMs) can be used to provide a spatially varying prior distribution, which is tuned by the mixing proportions
Tissue Probability Maps
GM WM CSF Other
Image Registration
• Registration - i.e. Optimise the parameters that describe a spatial transformation between the source and reference (template) images
• Transformation - i.e. Re-sample according to the determined transformation parameters
Optimisation
• Optimisation involves finding some “best” parameters according to an “objective function”, which is either minimised or maximised
• The “objective function” is often related to a probability based on some model
Value of parameter
Objective function
Most probable solution (global
optimum)Local optimumLocal optimum
Spatial normalizationEstimate the best 12-parameter affine
transformation. Correction for non-linear, global differences. A mask weights the normalization to brain instead
of non-brain.Reslice the images.
WarpedOriginal Template
Modulation• Multiplication of the
warped (normalised) tissue intensities so that their regional or global volume is preservedCan detect differences in
completely registered areas
1 1
2/3 1/3 1/3 2/3
1 1 1 1
Modulated
Unmodulated
WarpedOriginal Modulated
Native
Smoothing
• The analysis will be most sensitive to effects that match the shape and size of the kernel
• The data will be more Gaussian and closer to a continuous random field for larger kernels
• Results will be rough and noise-like if too little smoothing is used
• Too much will lead to distributed, indistinct blobs
Smoothing• Between 7 and 14mm is probably reasonable
– (DARTEL’s greater precision allows less smoothing)– The results below show two fairly extreme choices, 5mm
on the left, and 16mm, right
Simultaneous registration of GM to GM and WM to WM
Grey matter
White matter
Grey matter
White matter
Grey matter
White matter
Grey matter
White matter
Grey matter
White matterTemplate
Subject 1
Subject 2
Subject 3
Subject 4
Interpreting findings
Thickening
Thinning
Folding
Mis-classify
Mis-classify
Mis-register
Mis-register
“Globals” for VBM• Shape is really a
multivariate concept– Dependencies among
volumes in different regions
• SPM is mass univariate– Combining voxel-wise
information with “global” integrated tissue volume provides a compromise
– Using either ANCOVA or proportional scaling
(ii) is globally thicker, but locally thinner than (i) – either of these effects may be of interest to us.
Total Intracranial Volume (TIV/ICV)• “Global” integrated tissue volume may be
correlated with interesting regional effects– Correcting for globals in this case may overly
reduce sensitivity to local differences– Total intracranial volume integrates GM, WM and
CSF, or attempts to measure the skull-volume directly
• Not sensitive to global reduction of GM+WM (cancelled out by CSF expansion – skull is fixed!)
– Correcting for TIV in VBM statistics may give more powerful and/or more interpretable results
VBM’s statistical validity
• Residuals are not normally distributed– Little impact on uncorrected statistics for
experiments comparing reasonably sized groups– Probably invalid for experiments that compare
single subjects or tiny patient groups with a larger control group
– Mitigate with large amounts of smoothing– Or use nonparametric tests that make fewer
assumptions, e.g. permutation testing with SnPM
VBM’s statistical validity
• Correction for multiple comparisons– RFT correction based on peak heights is fine
• Correction using cluster extents is problematic– SPM usually assumes that the smoothness of the
residuals is spatially stationary• VBM residuals have spatially varying smoothness• Bigger blobs expected in smoother regions
– Cluster-based correction accounting for nonstationary smoothness is under development
– Or use SnPM…
VBM’s statistical validity• False discovery rate
– Less conservative than FWE– Popular in morphometric work
• (almost universal for cortical thickness in FreeSurfer)
– Recently questioned…• Topological FDR (for clusters and peaks)
– See SPM8 release notes and Justin’s papers– http://dx.doi.org/10.1016/j.neuroimage.2008.05.0
21– http://dx.doi.org/10.1016/j.neuroimage.2009.10.0
90
Longitudinal VBM• The simplest method for longitudinal VBM is
to use cross-sectional preprocessing, but longitudinal statistical analyses– Standard preprocessing not optimal, but unbiased– Non-longitudinal statistics would be severely
biased• (Estimates of standard errors would be too small)
– Simplest longitudinal statistical analysis: two-stage summary statistic approach (common in fMRI)
• Within subject longitudinal differences or beta estimates from linear regressions against time
Diffusion Tensor Imaging (DTI)
Non invasive way of understanding brain structural connectivity
Macroscopic axonal organizationContrast based on the directional rate of
diffusion of water molecules
Diffusion
Imaging• MR signal is attenuated as a result of diffusion
– Brownian motion in the presence of gradients• Gradients are applied in different directions
and attenuation is measured– DTI reconstruction using linear system solution
Effect of Varying Gradient Direction
DWI z DWI x DWI y
What is b?
• b-value gives the degree of diffusion weighting and is related to the strength and duration of the pulse gradient as well as the interval between the gradients
• b changes by lengthening the separation of the 2 gradient pulses more time for water molecules to move around more signal loss (imperfect rephasing)
• G= gradient amplitude• δ = duration• = trailing to leading edge separation
32
Diffusion Tensor
• Mobility in a given direction is described by ADC• The tissue diffusivity is described by the tensor D• The diffusion equation
• Diffusion is represented by a 33 tensor matrix*
ADCbexpDxbexp)0(A)b(A
nAttenuatio3,2,1j,i
ijij
zzyzxz
yzyyxy
xzxyxx
DDD
DDD
DDD
D
3
2
1
00
00
00
diagD
*P. Basser and D. Jone, NMR in Biomedicine, 2002.
`Diffusion MRI` Johansen-Berg and Behrens
Indices of Diffusion
Simplest method is the MEAN DIFFUSIVITY (MD):l1+l2+l3MD = <l> = 3
- This is equivalent to the orientationally averaged mean diffusivity
Indices of Anisotropic Diffusion• Fractional anisotropy (FA):
The calculated FA value ranges from 0 – 1 :
FA= 0 → Diffusion is spherical (i.e. isotropic)
FA= 1 → Diffusion is tubular (i.e. anisotropic)
Color FA Map• Single Tensor estimation
• Estimation of direction is severely affected in the presence of noise*
*X. Ma, Y. Kadah, S. LaConte, and X. Hu, Magnetic Resonance in Medicine, 2004.
Source of noise in diffusion MRI• Statistical Noise
– Magnetic Filed inhomogeneity– Eddy currents– Thermal Noise– background signals caused by processing tissue
magnetization. • Systematic Noise
– from a number of patient motion, such as respiration, vascular, and CSF pulsations;
– receiver-coil or gradient-coil motion; aliasing; and data truncation (Gibbs) artifacts
DTI-Based Connectivity Mapping• Nerve fibers represent cylindrical-
shaped physical spaces with membrane acting like a barrier– DT shows diffusion preference along axon
• Measuring the diffusing anisotropy, we can estimate the dominant direction of the nerve bundle passing through each voxel
Johansen-Berg et al. Ann Rev. Neurosci 32:75-94 (2009)
Tractography – Techniques
Degree of anisotropy Streamline tractography Probabilistic tractography
Nucifora et al. Radiology 245:2 (2007)
Streamline (deterministic) tractography
• Connects neighbouring voxels from user defined voxels (SEED REGIONS) e.g. M1 for the CST
• User can define regions to restrict the output of a tract e.g. internal capsule for the CST
• Tracts are traced until termination criteria are met (e.g. anisotropy drops below a certain level or there is an abrupt angulation)
Probabilistic tractography• Value of each voxel in the map = the probability
the voxel is included in the diffusion path between the ROIs
• Run streamlines for each voxel in the seed ROI• Provides quantitative probability of connection at
each voxel • Allows tracking into regions where there is low
anisotropy e.g. crossing or kissing fibres
Crossing/Kissing fibres
Crossing fibres Kissing fibres
Low FA within the voxels of intersection
Crossing/Kissing fibres
Assaf et al. J Mol Neurosci 34(1) 51-61 (2008)
DTI - Tracts
Nucifora et al. Radiology 245:2 (2007)
Corticospinal Tracts -ProbabilisticCorticospinal Tracts - Streamline
Questions?