1. Structural Images
杜政昊Cheng-Hao Tu, PhD

2. Outlines Computational Anatomy Voxel-based Morphometry (VBM)
Diffusion Tensor Imaging (DTI)

3. 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

4. Computational Neuroanatomy
Baseline Image
Standard clinical MRI
1.5T T1 SPGR
1x1x1.5mm voxels
Repeat image
12 month follow-up rigidly registered
Subtraction image

5. 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

6. 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

7. 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

8. 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.

9. Preprocessing – Optimized VBM

10. Segmentation- basic approach
Intensities are modelled by a Gaussian Mixture Model
Parameterised by means, variances and mixing proportions

11. Segmentation – modified approach
Multiple components per tissue class allow non-Gaussian distributions to be modelled
accounting for partial volume effects

12. Tissue Probability Maps
Tissue probability maps (TPMs) can be used to provide a spatially varying prior distribution, which is tuned by the mixing proportions
GM WM CSF Other

13. 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

14. 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
Most probable solution (global optimum)
Objective function
Local optimum
Local optimum
Value of parameter

15. Spatial normalization
Estimate 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.
Original
Warped
Template

16. Modulation
1 1
Native
Multiplication of the warped (normalised) tissue intensities so that their regional or global volume is preserved
Can detect differences in completely registered areas
Unmodulated
Modulated
2/3 1/3 1/3 2/3
Clarify, modulation not a step (as spm2) but an option in the segment and the normalise GUIs
Original
Warped
Modulated

17. 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

18. 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

19. Simultaneous registration of GM to GM and WM to WM
Subject 1
Grey matter
White matter
Subject 3
Grey matter
White matter
Grey matter
White matter
Grey matter
White matter
Template
Grey matter
White matter
Subject 2
Subject 4

20. Interpreting findings
Folding
Mis-classify
Mis-register
Thickening
Thinning
Mis-classify
Mis-register

21. “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
Note globals don’t help distinguish the thickened or folded cortex...
(ii) is globally thicker, but locally thinner than (i) – either of these effects may be of interest to us.

22. 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

23. 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

24. 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…

25. 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

26. 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

27. Diffusion Tensor Imaging (DTI)
Non invasive way of understanding brain structural connectivity
Macroscopic axonal organization
Contrast based on the directional rate of diffusion of water molecules

28. Diffusion

29. 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

30. Effect of Varying Gradient Direction
DWI z DWI x DWI y

31. 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 33 tensor matrix*
*P. Basser and D. Jone, NMR in Biomedicine, 2002.

33. `Diffusion MRI`
Johansen-Berg and Behrens

34. Indices of Diffusion Simplest method is the MEAN DIFFUSIVITY (MD):
l1+l2+l3
MD = <l> = 3
This is equivalent to the orientationally averaged mean diffusivity

35. 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)

36. 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.

37. 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

38. 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)

39. Tractography – Techniques
Degree of anisotropy Streamline tractography Probabilistic tractography
Nucifora et al. Radiology 245:2 (2007)

40. 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)

41. 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

42. Crossing/Kissing fibres
Crossing fibres
Kissing fibres
Low FA within the voxels of intersection

43. Crossing/Kissing fibres
Assaf et al. J Mol Neurosci 34(1) (2008)

44. DTI - Tracts Corticospinal Tracts - Streamline
Corticospinal Tracts -Probabilistic
Nucifora et al. Radiology 245:2 (2007)

45. Questions?