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Detecting Subtle Changes in Structure

Chris Rorden– Voxel Based Morphometry

Segmentation – identifying gray and white matter Modulation- adjusting for normalization’s spatial distortions.

– Diffusion Tensor Imaging Measuring white matter integrity Tractography and analysis.

Many images are from Christian Gaser. You can see his presentations and get his VBM scripts from these sites:

fmri.uib.no/workshops/2006/mai/fmri/index.shtml dbm.neuro.uni-jena.de/home/

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Voxel Based Morphometry

Most lectures in course focus on functional MRI. However, anatomical scans can also help us infer

brain function.– Do people with chronic epilepsy show brain atrophy?– Which brain regions atrophy with age?– Do people with good spatial memory (taxi drivers) have

different anatomy than other people? Voxel based morphometry is a tool to relate gray and

white matter concentration with medical history and behavior

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Morphometry

Morphometry examines the shape, volume and integrity of structures.

Classically, morphometry was conducted by manually segmenting a few regions of interest.

Voxel based morphometry conducts an independent statistical comparison for each voxel in the brain.

Images from Christian Gaser

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Voxel Based Morphometry

VBM has some advantages over manual tracing:– Automated: fast and not subject to individual bias.– Able to examine regions that are not anatomically

well defined.– Able to see the whole brain– Normalization compensates for overall differences

in brain volume, which can add variance to manual tracing of un-normalized images.

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VBM disadvantages

VBM has clear disadvantages– Crucially depends on accurate normalization.– Low power: gray matter random fields are very

heterogenous (individual patterns of sulcal folding registration is always poor.

– Crucially depends on a priori probability maps.– Assumes normal gray-white contrast. Focal Cortical

Dysplasia – Looks for differences in volume, can be disrupted if shape

of brain is different: problem for developmental disorders

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Segmentation

Start with high quality MRI scan

Classify tissue types (gray matter in this example)

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Partitioning Tissue Types

VBM segments image into three tissue types: gray matter, white matter and CSF.– Typically done on T1 scans (best spatial resolution, good gray-white contrast).– Only three tissue types: will not cope with large lesions.– Probability map: each voxel has a 0..100% chance of being one of the 3 tissue types.

TT11 whitewhitegraygray CSFCSFImages from Christian Gaser

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Segmentation I: Image Intensity

CSFCSF

WMWM

GMGMback-back-

groundground

Image intensityImage intensity

freq

uen

cyfr

equ

ency

estimate for GMestimate for GM

p=0.95p=0.95

p=0.05p=0.05

Images from Christian Gaser

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Segmentation II: Voxel location

Maximization of a posteriori probability: Bayesian approach (expectation maximization)

Analogy:– We know that last year there were 248 of 365 days with rain in Norway (p=0.68)– the conditional (or posterior) probability for rain in Bergen will be p>0.5

TT11 WMWMGMGM CSFCSF

Probability maps (n=152)Probability maps (n=152)

Images and text from Christian Gaser

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Segmentation overviewSegmentation overview

Intensity based Intensity based estimate for GMestimate for GM

p=0.95p=0.95

p=0.95p=0.95 p=0.90p=0.90

p=0.05p=0.05Final resultFinal result

a prioria priori GM map GM mapp=0.95p=0.95

p=0.05p=0.05

Source ImageSource Image

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Voxel Based Morphometry Steps

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Homogeneity correction crucial

Field inhomogeneity will disrupt intensity based segmentation. Bias correction required.

no correction

T1 WMGMEstimate

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Normalization is crucial

Poor normalization has two problems– Image will not be registered with a priori map = poor

segmentation.– Images from different people will not be registered: we will

compare different brain areas. Custom template and prior is useful

– Accounts for characteristics of your scanner.– Accounts for characteristics of your population (e.g. age).– Must be independent of your analysis:

Either formed from combination of both groups (control+experimental) or from independent control group.

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Two step segmentation

segmentation II

customized template

averaging

MNI template

segmentation I

norma-lization

segmentation II

Step I:Creation of customized template

segmentation I

norma-lization

Step II:Optimized segmentation

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Image cleanup

segmented

mask

maskedT1

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Overview of ‘Optimized VBM’

T1 normalized segmented II smoothedsegmented I masked

customized template

mask

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VBM designs

Longitudinal VBM:– Sensitive way to detect atrophy through time.

Using the same individual reduces variability.Cross sectional studies

– Can compare two distinct populations– Can also examine atrophy through time, though

will require more people than longitudinal VBM.Most VBM studies use t-test (two group or

timepoints), but correlational analysis also powerful.

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SPM5 segmentation

Unified segmentation• Iterated steps of segmentation estimation,

bias correction and warping

Impact• Warping of prior images during

segmentation makes segmentation more independent from size, position, and shape of prior images

• much slower than SPM2

40 iterationssegmentation

40 iterationsbias correction

20 iterationswarping

no significant change of estimate

significant change of estimate

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Voxel Based Morphometry

We can statistically analyze gray matter atrophy

Epilepsy

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Segmentation Problem

If someone has atrophy, normalization will stretch gray matter to make brain match healthy template.

This will reduce ability to detect differences

Normalization will squish this region

Normalization will stretch this region

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Image Modulation

– Analogy: as we blow up a balloon, the surface becomes thinner. Likewise, as we expand a brain area it’s volume is reduced.

Source TemplateModulated

Without modulation

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Image Modulation

Optimized Segmentation can adjust for distortions caused during normalization.

Areas that had to be stretched are assumed to have less volume than areas that were compressed.– Corrects for changes in volume induced by nonlinear

normalization– Multiplies voxel intensities by a modulation matrix derived

from the normalization step – Allows us to make inferences about volume, instead of

concentration.

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VBM and developmental syndromes

Williams Syndrome– Developmental syndrome:

Chromosome 7– Manual Morphology shows

8-18% decrease in posterior GM/WM

• Most consistent finding is reduced intra-parietal sulcus depth and superior parietal lobe volume (see figure)

• Relatively preserved frontal GM/WM

• Creates unique shape– Unique spatial distribution of

gross volume loss influences VBM results depending on whether modulation is used

Eckert et al. 2006b,c

Control WS

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Modulation and shape

Eckert et al., 2006a

Shape differences influence modulated data.

Deformation Based Morphometry can identify shape/gross volumetric differences.

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Modulation is optional and controversial

Modulation will smooth images, specificity will decrease

Alternatively, you can covary overall brain volume by including GM or GM+WM as nuisance regressor.

Example showing danger of modulation. This image comes from an elderly participant, with relatively large ventricles. Normalization adjusts ventricle size, but the deformations are spatially smooth, so tissue near the ventricles (e.g. caudate) are also being spatially compressed.

[Deformations exaggerated for exposition]

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DBM (from Henson)

Deformation-based Morphometry examines absolute displacements.

E.G. Mean differences (mapping from an average female to male brain).

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Cortical Thickness

New methods can complement VBM.Freesurfer’s cortical thickness is powerful tool.Requires very good T1 scans.

Modulated VBM Freesurfer

Age-related declines in gray matter volume and cortical thickness

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VBM comments

VBM findings are first step in understanding strucutural changes.

Methods are a work in progress.– www.tina-vision.net/docs/memos/2003-011.pdf– Bookstein, 2001– Davatzikos, 2004– http://fmri.uib.no/workshops/2006/mai/fmri/index.shtml– Christian Gaser Markov Random Fields dbm.neuro.uni-

jena.de/home/

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Diffusion Weighted Imaging

T1/T2 scans do not show acute injury. Diffusion weighted scans do.

DW scans identify areas of permanent injury Measures random motion of water molecules.

– In ventricles, CSF is unconstrained, so high velocity diffusion

– In brain tissue, CSF more constrained, so less diffusion.

T2

DW

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Diffusion Tensor Imaging (DTI)

DTI is an extension of DWI that allows us to measure direction of motion.

DTI allows us to measure both the velocity and preferred direction of diffusion– In gray matter, diffusion is isotropic (similar in all directions)– In white matter, diffusion is anisotropic (prefers motion along

fibers).

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DTI

The amount of diffusion occurring in one pixel of a MR image is termed the Apparent Diffusion Coefficient (ADC) or Mean Diffusivity (MD).

The non-uniformity of diffusion with direction is usually described by the term Fractional Anisotropy (FA).

MD differs FA differs

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What is a tensor?

A tensor is composed of three vectors.– Think of a vector like an arrow

in 3D space – it points in a direction and has a length.

The first vector is the longest – it points along the principle axis.

The second and third vectors are orthogonal to the first.

Sphere: V1=V2=V3Football: V1>V2 V1>V3 V3 = V2???: V1>V2>V3

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Diffusion Tensor Imaging

To create a tensor, we need to collect multiple directions.

Typically 12-16 directions.

More directions offer a better estimate of optimal tensor.

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DTI

MD FA Principle Tensor Vector

DTI Tutorial

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Tractography

DTI can be used for tractography.

This can identify whether pathways are abnormal.

Inferior frontal occipital tract

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Kissing or crossing?

Modelling each voxel as a tensor has limitations.

Cannot model fiber crossings.