fMRI: Biological Basis and Experiment DesignLecture 26: Significance

• Review of GLM results• Baseline trends• Block designs; Fourier

analysis (correlation)• Significance and

confidence intervals

Noise in brains

• Spatially correlated– Big vessels– Blurring in image– Neural activity is correlated

• Temporally correlated– Noise processes have memory

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

Picking a voxel not significantly modulated by the stimulus, we still see correlations locally

Correlation is not seen in white matter; organized in gray matter

Picking a voxel significantly modulated by the stimulus, we still see correlations all over

Picking a voxel in white matter, we still few correlated voxels either locally or globally.

Noise in brains: temporal correlationUncorrelated noise Smoothed noise

Time domain

Frequency domain

Noise in brains: temporal correlation

• Drift and long trends have biggest effects

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)

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.

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

Fourier analysis of block design experiment

0s 12s 24s

Time from stim onset:

Fourier analysis of block design experiment

Fourier analysis of block design experiment

Significance

• Which voxels are activated?

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 (+/- 1.96*sigma)

– Matlab’s 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

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

< .05) by number of comparisons (e.g. 10,000 voxels) - display only voxels significant at p < .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/