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