Study design Analysis topics

1
Study design / Analysis topics

• Preprocessing - steps to condition the raw data
  such that each voxels MRI signal best reflects
  BOLD response.
• Model driven and data driven analysis methods.
• Multi-subject study approaches.
• Relationship between BOLD response, neuronal
  activity, cognitive processes, and brain
  organization.

Study design
Analysis
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image data
parameter estimates
designmatrix
kernel

• General Linear Model
• model fitting
• statistic image

random field theory
realignment motioncorrection
smoothing
normalisation
StatisticalParametric Map
anatomicalreference
corrected p-values
3
Preprocessing
Goal is to reduce artifactual signal variance in
voxel time series

• Image reconstruction
• Data handling, file formats, conversion, imaging
  parameters
• Motion correction
• Mean intensity adjustment
• Coregistration of structural and functional
  images
• Spatial smoothing
• Temporal smoothing
• Slice timing correction

4
Motion correction (realignment)

• Estimate rigid-body transform that minimizes
  differences between each functional volume and a
  reference scan.
• Resample each rotated/translated volume
• - accurate to a fraction of a millimeter

5
Movement related effects
BUT

• Effect of subject motion is not removed by
  realignment
• Subject motion between slices
• Interpolation artifacts (from resampling
  functional volumes)
• Non-linear spatial distortions
• Spin-excitation history effects
• -- it is possible to include motion effects in
  statistical model

6
Model driven statistical analysis

• Model expected response time course
• Stimuli time course hemodynamic response
  function
• Other potential confounds
• Apply statistical model at every voxel
• Linear correlation
• General Linear Model (GLM)

7
Spatial smoothing

• Reduces effects of noise, emphasizes effects at
  the size of the smoothing kernal
• Results in more normal noise distribution
• For inter-subject averaging, increases functional
  homologies

8
Localization wrt. Structural image

• Cross modal coregistration of functional and
  anatomical images
• Find 6-DOF transformation to match T2 image
  features with T1 image features
• Higher DOF?

9
Voxel by voxel statistics
model specification
parameter estimation
hypothesis
statistic
statistic image or SPM
f MRI time series
voxel time series
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Voxel statistics

• parametric
• one sample t-test
• two sample t-test
• paired t-test
• Anova
• AnCova
• correlation
• linear regression
• multiple regression
• F-tests
• etc

all cases of theGeneral Linear Model
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e.g. two-sample t-test?
t-statistic imageSPMt
Image intensity
compares size of effect to its error standard
deviation

• standard t-test assumes independence? ignores
  temporal autocorrelation!

voxel time series
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data vector (voxel time series)
parameters
error vector
design matrix
a


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?
?

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Y
X
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General Linear Model

• fMRI time series Y1 ,,Ys ,,YN
• acquired at times t1,,ts,,tN
• Model Linear combination of basis functions
• Ys ?1 f 1(ts ) ?l f l(ts )
  ?L f L(ts ) ?s
• f l (.) basis functions
• reference waveforms
• dummy variables
• ?l parameters (fixed effects)
• amplitudes of basis functions (regression slopes)
• ?s residual errors ?s N(0,?2)
• identically distributed
• independent, or serially correlated (Generalised
  Linear Model ? GLM)

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What questions do statistical maps answer?

• Identify regions of interest?
• Are sites of focal activations (modules?)
  necessary or sufficient?
• False negatives?
• Magnitude of BOLD response?
• Relative contribution of regions?
• Probability that a random individual uses a
  particular region for this task?
• Modulation of neural activity?

15
Analysis software

• SPM - Matlab environment, statistical parametric
  mapping using the General Linear Model (GLM),
  widely used, free.
• AFNI - Unix environment, widely used, fast, many
  plug-ins for specific use.
• BrainVoyager MS Windows environment, several
  types of analysis options, commercial, some
  integration with SPM, cortex based analysis tools
  (inflation/flattening).
• ICA toolbox Matlab environment, a type of data
  driven analysis.
• Others

Each has many auxiliary tools which may or may
not be easy to use, transparent, or well
documented motion correction, coregistration,
normalization, ROI/VOI delineation, segmentation,
file format conversion, rendering, scripting etc.
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Analysis software and analysis discussion groups

• SPM99. Wellcome Department of Cognitive
  Neurology. http//www.fil.ion.ucl.ac.uk
• AFNI Information Central. http//afni.nimh.gov/afn
  i

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Study design / Analysis topics

• Preprocessing - steps to condition the raw data
  such that each voxels MRI signal best reflects
  BOLD response.
• Model driven and data driven analysis methods.
• Multi-subject study approaches.
• Relationship between BOLD response, neuronal
  activity, cognitive processes, and brain
  organization.

Study design
Analysis
18
BOLD modeling assuming linear response

• Model response to experiment Assume a canonical
  HRF, convolve with experimental events to form a
  model response OR Estimate an HRF from separate
  stimulation and assume it holds across the brain
• Assume that BOLD response to multiple events adds
  linearly
• Model other expected signal components
• Heart and breathing
• Residual motion artifacts
• Low temporal frequency artifacts due to aliased
  physiological effects or scanner instability

19
Multiple regression

• Estimate best fit parameters. (Find the ßs that
  minimize differences between measured and modeled
  response, using least sum of squares)
• Calculate a statistic T (ß1-ß2)/s2
• where ß1-ß2 is a contrast of two conditions and
  s2 is an estimate of mean square error

20
Lies, Damned Lies, and Statistical maps

• What do statistical maps tell us?
• Where is there BOLD variability due to task
  variability, and what is our confidence in these
  activations
• How is variability modulated by the task (but be
  careful because we cant know that activation
  did not occur, and statistics dont tell us
  everything about how much activation occurred)

21
Hypothesis testing

• Form a null hypothesis (no effect) about
  whether the experimental conditions influence the
  measurement
• A statistic summarizes evidence about the
  hypothesis
• p-value summarizes the evidence against the null
  hypothesis ( probability that a measured
  statistic gt threshold statistic given the null
  hypothesis is true, or PT gt t H0 )
• If we reject the null hypothesis when p lt .001,
  then the false positive rate is lt .001

22
Accounting for spatial information in statistical
maps

• Multiple comparison problem voxel-wise p-values
  dont account for the number of voxels tested
• Control FamilyWise error rate (chance of getting
  a false positive for any voxel). Bonferroni
  correction too conservative because
• Voxel-wise statistics dont account for
  covariance of voxels across space noise in data
  is not spatially independent.
• Random Field Theory is often used to estimate a
  corrected p-value. This requires some degree of
  spatial smoothing to be valid.
• We fit a time course to each voxel, and get a
  statistical measure of significance. But wed
  like to know about the relevance of spatial
  patterns
• Assess clusters of voxels above a statistical
  threshold. Calculate p-value for the cluster as a
  whole. This p-value refers to activation within
  the region, not to any particular voxel of the
  region.

23
Multiple sessions, multiple subjects

• Different variance, perhaps truly different
  response. How to find a statistical measure of
  confidence?
• Fixed Effect model
• Random Effects model
• Conjunction of activation

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Fixed effects

• Fixed Effects model tests the intersection of
  null hypothesis across sessions/subjects. If an
  effect is highly significant for one
  session/subject, then it can dominate a set of
  subjects/sessions.
• Doesnt account for inter-session/subject
  variability

25
Random Effects

• Mean of the set of sessions/subjects responses
  is tested.
• A special case when each session/subject design
  Assume each has same variance, compute a
  statistical test on the contrast images.

26
Conjunction

• Which voxels are active for all
  sessions/subjects?
• Use the minimum statistic of all sessions/subjects

27
Also see

• http//www.sph.umich.edu/nichols/fMRIcourse/2001/