fMRI: Biological Basis and Experiment Design Lecture 26: Significance

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fMRI Biological Basis and Experiment
DesignLecture 26 Significance

• Review of GLM results
• Baseline trends
• Block designs Fourier analysis (correlation)
• Significance and confidence intervals

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Noise in brains

• Spatially correlated
• Big vessels
• Blurring in image
• Neural activity is correlated
• Temporally correlated
• Noise processes have memory

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Noise in brains spatial correlation

• Spatial correlation use one voxel as "seed"
  (template) calculate correlation with neighbors
  (whole brain, if you have time ...)
• Basis of functional connectivity

Seed voxel
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Picking a voxel not significantly modulated by
the stimulus, we still see correlations locally
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Correlation is not seen in white matter
organized in gray matter
Picking a voxel in white matter, we still few
correlated voxels either locally or globally.
Picking a voxel significantly modulated by the
stimulus, we still see correlations all over
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Noise in brains temporal correlation
Uncorrelated noise
Smoothed noise
Time domain
Frequency domain
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Noise in brains temporal correlation

• Drift and long trends have biggest effects

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Noise in brains temporal correlations

• (Missing slides, where I took 8 sample gray
  matter pixels and 8 sample white matter pixels
  and looked at the autorcorrelation function for
  each pixel)

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Noise in brains temporal correlation

• How to detect?
• Auto correlation with varying lags
• FT low temporal frequency components indicate
  temporal structure
• How to compensate?
• "pre-whiten" data (same effect as low-pass
  filtering?)
• Reduce degrees of freedom in analysis.

10
Fourier analysis

• Correlation with basis set sines and cosines
• Stimulus-related component amplitude at
  stimulus-related frequency (can be z-scored by
  full spectrum)
• Phase of stimulus-related component has timing
  information

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Fourier analysis of block design experiment
Time from stim onset
0s 12s
24s
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Fourier analysis of block design experiment
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Fourier analysis of block design experiment
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Significance

• Which voxels are activated?

15
Significance ROI-based analysis

• ICE15.m shows a comparison of 2 methods for
  assigning confidence intervals to estimated
  regression coefficients
• Bootstrapping repeat simulation many times
  (1000 times), and look at the distribution of
  fits. A 95 confidence interval can be
  calculated directly from the standard deviation
  of this distribution (/- 1.96sigma)
• Matlabs regress.m function, which relies the
  assumption of normally distributed independent
  noise
• The residuals after the fit are used to estimate
  the distribution of noise
• The standard error of the regression weights is
  calculated, based on the standard deviaion of the
  noise (residuals), and used to assign 95
  confidence intervals.
• When the noise is normal and independent, these
  two methods should agree

16
Multiple comparisons

• How do we correct for the fact that, just by
  chance, we could see as many as 500 false
  positives in our data?
• Bonferonni correction divide desired
  significance level (e.g. p lt .05) by number of
  comparisons (e.g. 10,000 voxels) - display only
  voxels significant at p lt .000005.
• Too stringent!
• False Discovery Rate currently implemented in
  most software packages
• FDR controls the expected proportion of false
  positives among suprathreshold voxels. A FDR
  threshold is determined from the observed p-value
  distribution, and hence is adaptive to the amount
  of signal in your data. (Tom Nichols website)
• See http//www.sph.umich.edu/nichols/FDR/