fMRI: Biological Basis and Experiment Design Lecture 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 correlation Uncorrelated noiseSmoothed 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

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 < 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