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A comparison of methods for characterizing the event-related BOLD timeseries in rapid fMRI
John T. Serences
Separating events
• ‘Sluggish’ BOLD signal• Slow events: 20s ITI
– Few trials per run– Not psychologically ideal
• BOLD signal linear & time-invariant• Rapid events: > 2s ITI• Jittering overcomes overlap
Jitter
• Fixed interval designs provide too little information to resolve the BOLD response
• Jittering adds information• BOLD is an equation, with n
unknowns:
See also Burock et al. (1998)
Event-related averaging
GLM
Equation for n predictors
Collapses to vector equation
Least squares solution found by inverting design matrix
GLM
Boxcar function Convolve with assumed HDR:Design matrix
Fit to signal
Beta 1Beta 2Beta 3
Design matrix
• One column = assumed BOLD response for one stimulus type
• In this case, 3 columns
• Row = # timepoints
0.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.000 0.000 0.0000.008 0.000 0.0000.531 0.000 0.0000.892 0.000 0.0000.982 0.000 0.0000.998 0.000 0.0001.000 0.000 0.0001.000 0.000 0.0000.992 0.000 0.0000.469 0.000 0.0000.108 0.000 0.0000.018 0.008 0.0000.002 0.531 0.0000.000 0.892 0.0000.000 0.982 0.0000.000 0.998 0.0000.000 1.000 0.0000.000 1.000 0.0000.000 0.992 0.0000.000 0.469 0.0000.000 0.108 0.0000.000 0.018 0.0080.000 0.002 0.5310.000 0.000 0.8920.000 0.000 0.9820.000 0.000 0.9980.000 0.000 1.0000.000 0.000 1.0000.000 0.000 0.9920.000 0.000 0.4690.000 0.000 0.1080.008 0.000 0.0180.531 0.000 0.0020.892 0.000 0.000
Design matrix for deconvolution
• No assumed BOLD response• Assumed consistent over repetitions of same
type• Extra column for each time points in BOLD
response
Multicollinearity
• Each column in X must be linearly independent– Cannot make one column from linear
combinations of other columns
• Sequential events are perfectly correlated
• Partial trials omit second event to reduce multicollinearity
Experimental designs
1. Independent, randomly-timed events2. Sequentially dependant3. Sequentially dependant with 30%
partial trials
Jitter types
• Exponential distribution more efficient than uniform
Simulations
• 15 iterations of 12 runs of 256 sec• BOLD response is a gamma function
– Delta = 2, tau = 1.25
• Noise added– Non-zero Gaussian white noise– Temporally correlated noise at 1 Hz and 0.2 Hz
• Time series created at 10 Hz, then sampled at 1 Hz (TR = 1000 ms)
• Four events (A-D) of amplitude 1, 3, 1, and 1.
Calculations
• Event-related averaging– All time points 6 TRs before and 20 TRs after
each event averaged
• Deconvolution– GLM included 20 regressors for each stimulus
type
• Repeated measures t test for each time point within averaging window– Not usually done, but valid for comparison
only
Independent events
Compound trials
Partial trials
Comparison of t values
Conclusions
• Both event-related averaging and deconvolution can estimate the BOLD response for independent events
• Only deconvolution is robust for compound trials
• Using partial trials improves power at shorter ISIs