Structural Images 杜政昊 Cheng-Hao Tu, PhD. Outlines Computational Anatomy Voxel-based Morphometry (VBM) Diffusion Tensor Imaging (DTI)

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?