Event Models

Bradley R. Buchsbaum

2019-09-29

Source: vignettes/event_models.Rmd

fMRI event models

An “event model” is a description of an fMRI experiment, which consists of a collection of experimental “events” (stimuli/conditions/responses) which are embedded in an experimental design. By convolving each event type with a hemodynamic response function we from a set of regressors that are used to model and make inferences about the BOLD response.

A simple fMRI design

Consider a basic design, consisting of four stimulus types, each repeated 4 times over the course of a single scanning run. The stimuli are pictures of faces, scenes, tools and object presented for 2s a piece in a pseudorandom order. There is a uniformly distributed (4-7s) inter-stimulus interval (ISI) separating each stimulus presentation.

cond <- c("face", "scene", "tool", "object")
NSTIM <- length(cond)*4

Now we contruct a “design table” by randomly sampling from the four conditions:

simple_design <- data.frame(stim=factor(sample(rep(cond, 4))), 
                     ISI=sample(4:7, NSTIM, replace=TRUE), 
                     run=rep(1, NSTIM),
                     trial=factor(1:NSTIM))

Event onsets are calculated as the cumulative sum of the ISI variables. Then we construct a sampling_frame which define the temporal sampling and block structure of the experiment. Here we have only 1 block and a repetition frequency (TR) of 2.

Now the fun part. We create an event_model that describes the experimental model in terms of the stimulus onsets, conditions, and hemodynamic response function (‘hrf’).

print(emodel)
## event_model 
##   onset ~ hrf(stim) 
##   Num Terms 1 
##   Num Events:  16 
##   Num Columns:  4 
##   Num Blocks:  1 
## 
## Term: 1  fmri_term:  convolved_term 
##    Term Name:  stim 
##    Formula:   ~ (stim - 1) 
##    Num Events:  16 
##    Num Rows:  70 
##    Num Columns:  4 
##    Conditions:  stim[face] stim[object] stim[scene] stim[tool] 
##    Term Types:  event_factor

And we can plot the model:

plot(emodel)

A simple fMRI design with multiple blocks

## event_model 
##   onset ~ hrf(stim) 
##   Num Terms 1 
##   Num Events:  32 
##   Num Columns:  4 
##   Num Blocks:  2 
## 
## Term: 1  fmri_term:  convolved_term 
##    Term Name:  stim 
##    Formula:   ~ (stim - 1) 
##    Num Events:  32 
##    Num Rows:  140 
##    Num Columns:  4 
##    Conditions:  stim[face] stim[object] stim[scene] stim[tool] 
##    Term Types:  event_factor
plot(emodel)

A two-factor fMRI design with multiple blocks

cond1 <- c("face", "scene", "tool", "object")
cond2 <- c("attend", "ignore")
comb <- expand.grid(stim=cond1, task=cond2)
NSTIM <- nrow(comb) * 4

design <- do.call(rbind, lapply(1:2, function(i) {
  ind <- sample(rep(1:nrow(comb), length.out=NSTIM))
  d <- data.frame(stim=factor(comb$stim[ind]),
             task=factor(comb$task[ind]),
             ISI=sample(2:6, NSTIM, replace=TRUE), 
             run=rep(i, NSTIM))
  d$onset <- cumsum(d$ISI+2) -2
  d
}))

head(design)
##    stim   task ISI run onset
## 1  tool ignore   6   1     6
## 2  tool attend   4   1    12
## 3 scene ignore   2   1    16
## 4  tool attend   5   1    23
## 5  tool attend   6   1    31
## 6  tool attend   4   1    37
## event_model 
##   onset ~ hrf(stim, task) 
##   Num Terms 1 
##   Num Events:  64 
##   Num Columns:  8 
##   Num Blocks:  2 
## 
## Term: 1  fmri_term:  convolved_term 
##    Term Name:  stim:task 
##    Formula:   ~ (stim:task - 1) 
##    Num Events:  64 
##    Num Rows:  200 
##    Num Columns:  8 
##    Conditions:  stim[face]:task[attend] stim[scene]:task[attend] stim[tool]:task[attend] stim[object]:task[attend] stim[face]:task[ignore] stim[scene]:task[ignore] stim[tool]:task[ignore] stim[object]:task[ignore] 
##    Term Types:  event_factor event_factor
plot(emodel)

Trialwise event model to construct “beta-series” estimates

## event_model 
##   onset ~ trialwise() 
##   Num Terms 1 
##   Num Events:  16 
##   Num Columns:  16 
##   Num Blocks:  1 
## 
## Term: 1  fmri_term:  trialwise_convolved_term 
##    Term Name:  trialwise 
##    Formula:   ~ (trialwise - 1) 
##    Num Events:  16 
##    Num Rows:  70 
##    Num Columns:  16 
##    Conditions:  trialwise[1] trialwise[2] trialwise[3] trialwise[4] trialwise[5] trialwise[6] trialwise[7] trialwise[8] trialwise[9] trialwise[10] trialwise[11] trialwise[12] trialwise[13] trialwise[14] trialwise[15] trialwise[16] 
##    Term Types:  event_factor
plot(emodel, "trialwise")