Event Models
Bradley R. Buchsbaum
2023-05-09
Source:vignettes/a_04_event_models.Rmd
a_04_event_models.RmdfMRI 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.
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.
simple_design$onset <- cumsum(simple_design$ISI+2) -2
TR <- 2
sframe <- sampling_frame(blocklens=70, TR)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’).
emodel <- event_model(onset ~ hrf(stim), data=simple_design, block = ~ run, sampling_frame=sframe)## [1] "onset" "hrf(stim)"
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_factorAnd we can plot the model:
plot(emodel)
A simple fMRI design with multiple blocks
cond <- c("face", "scene", "tool", "object")
NSTIM <- length(cond)*4
## construct a design table with two blocks
design1 <- data.frame(stim=factor(sample(rep(cond, 4))),
ISI=sample(4:7, 16, replace=TRUE),
run=rep(1, NSTIM))
design2 <- data.frame(stim=factor(sample(rep(cond, 4))),
ISI=sample(4:7, 16, replace=TRUE),
run=rep(2, NSTIM))
design1$onset <- cumsum(design1$ISI+2) -2
design2$onset <- cumsum(design2$ISI+2) -2
design <- rbind(design1, design2)
## create a 'sampling_frame' describing the temporal outline of the scan consisting of 70 images collected every once every 2 seconds.
TR <- 2
sframe <- sampling_frame(blocklens=c(70,70), TR)
## create the event model d
emodel <- event_model(onset ~ hrf(stim), data=design, block = ~ run, sampling_frame=sframe)## [1] "onset" "hrf(stim)"
print(emodel)## 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 face ignore 6 1 20
## 4 object ignore 3 1 25
## 5 face ignore 3 1 30
## 6 tool ignore 4 1 36
## create a 'sampling_frame' describing the temporal outline of the scan consisting of 70 images collected every once every 2 seconds.
TR <- 2
sframe <- sampling_frame(blocklens=c(100,100), TR)
## create the event model d
emodel <- event_model(onset ~ hrf(stim, task), data=design, block = ~ run, sampling_frame=sframe)## [1] "onset" "hrf(stim, task)"
print(emodel)## 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[object]:task[attend] stim[scene]:task[attend] stim[tool]:task[attend] stim[face]:task[ignore] stim[object]:task[ignore] stim[scene]:task[ignore] stim[tool]:task[ignore]
## Term Types: event_factor event_factor
plot(emodel)
An event-related design with an amplitude-modulated variable
TR <- 2
sframe <- sampling_frame(blocklens=70, TR)
simple_design$RT <- scale(rnorm(nrow(simple_design), mean=700, sd=100))[,1]
## create the event model d
emodel <- event_model(onset ~ hrf(stim) + hrf(RT), data=simple_design, block = ~ run, sampling_frame=sframe)## [1] "onset" "hrf(stim)" "hrf(RT)"
print(emodel)## event_model
## onset ~ hrf(stim) + hrf(RT)
## Num Terms 2
## Num Events: 16
## Num Columns: 5
## Num Blocks: 1
##
## Term: 1 fmri_term: convolved_term
## Term Name: stim
## Formula: ~ (stim - 1)
## Num Events: 16
## Num Rows: 70
## Num Columns: 4
## Conditions: stim[face] stim[object] stim[scene] stim[tool]
## Term Types: event_factor
##
##
## Term: 2 fmri_term: convolved_term
## Term Name: RT
## Formula: ~ (RT - 1)
## Num Events: 16
## Num Rows: 70
## Num Columns: 1
## Conditions: RT
## Term Types: event_variable
plot(emodel, "RT")
An event-related design with an amplitude-modulated variable crossed with factor
TR <- 2
sframe <- sampling_frame(blocklens=70, TR)
simple_design$RT <- scale(rnorm(nrow(simple_design), mean=700, sd=100))
## create the event model d
emodel <- event_model(onset ~ hrf(stim) + hrf(stim, RT), data=simple_design, block = ~ run, sampling_frame=sframe)## [1] "onset" "hrf(stim)" "hrf(stim, RT)"
print(emodel)## event_model
## onset ~ hrf(stim) + hrf(stim, RT)
## Num Terms 2
## Num Events: 16
## Num Columns: 8
## 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
##
##
## Term: 2 fmri_term: convolved_term
## Term Name: stim:RT
## Formula: ~ (stim:RT - 1)
## Num Events: 16
## Num Rows: 70
## Num Columns: 4
## Conditions: stim[face]:RT stim[object]:RT stim[scene]:RT stim[tool]:RT
## Term Types: event_factor event_variable
plot(emodel, "stim:RT")
Trialwise event model to construct “beta-series” estimates
TR <- 2
sframe <- sampling_frame(blocklens=70, TR)
# create the event model d
emodel <- event_model(onset ~ trialwise(), data=simple_design, block = ~ run, sampling_frame=sframe)## [1] "onset" "trialwise()"
print(emodel)## 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[01] trialwise[02] trialwise[03] trialwise[04] trialwise[05] trialwise[06] trialwise[07] trialwise[08] trialwise[09] trialwise[10] trialwise[11] trialwise[12] trialwise[13] trialwise[14] trialwise[15] trialwise[16]
## Term Types: event_factor
plot(emodel, "trialwise")