Linear Model for FMRI Data — hemodynamicRF • ANTsR

Create the expected BOLD response for a given task indicator function. Borrowed from the fmri package.

hemodynamicRF(
  scans = 1,
  onsets = c(1),
  durations = c(1),
  rt = 3,
  times = NULL,
  mean = TRUE,
  a1 = 6,
  a2 = 12,
  b1 = 0.9,
  b2 = 0.9,
  cc = 0.35
)

Arguments

scans: number of scans
onsets: vector of onset times (in scans)
durations: vector of duration of ON stimulus in scans or seconds (if !is.null(times))
rt: time between scans in seconds (TR)
times: onset times in seconds. If present onsets arguments is ignored.
mean: logical. if TRUE the mean is substracted from the resulting vector
a1: parameter of the hemodynamic response function (see details)
a2: parameter of the hemodynamic response function (see details)
b1: parameter of the hemodynamic response function (see details)
b2: parameter of the hemodynamic response function (see details)
cc: parameter of the hemodynamic response function (see details)

Value

Vector with dimension c(scans, 1).

Details

The functions calculates the expected BOLD response for the task indicator function given by the argument as a convolution with the hemodynamic response function. The latter is modelled by the difference between two gamma functions as given in the reference (with the defaults for a1, a2, b1, b2, cc given therein):

$$\left(\frac{t}{d_1}\right)^{a_1} \exp \left(-\frac{t-d_1}{b_1}\right) $$$$- c \left(\frac{t}{d_2}\right)^{a_2} \exp $$$$\left(-\frac{t-d_2}{b_2}\right) $$

The parameters of this function can be changed through the arguments a1, a2, b1, b2, cc.

The dimension of the function value is set to c(scans,1).

If !is.null(times) durations are specified in seconds.

If mean is TRUE (default) the resulting vector is corrected to have zero mean.

References

Worsley, K.J., Liao, C., Aston, J., Petre, V., Duncan, G.H., Morales, F., Evans, A.C. (2002). A general statistical analysis for fMRI data. NeuroImage, 15:1-15.

Polzehl, J. and Tabelow, K. (2007) fmri: A Package for Analyzing fmri Data, R News, 7:13-17 .

Author

Karsten Tabelow tabelow@wias-berlin.de

Examples


# Example 1
hrf <- hemodynamicRF(107, c(18, 48, 78), 15, 2)
# Example 2: effect of varying parameter cc
cc <- round(seq(0, 1, length.out = 10), 2)
nlev <- length(cc)
cscale <- rgb(seq(0, 1, length.out = nlev), 
seq(1, 0, length.out = nlev), 0, 1)
mat <- matrix(NA, nrow = nlev, ncol = 20)
for (i in 1:nlev) {
  hrf <- ts(hemodynamicRF(scans = 20, onsets = 1, durations = 2, 
  rt = 1, cc = cc[i], a1 = 4, a2 = 3))
  mat[i, ] <- hrf
}
matplot(seq(1, 20), t(mat), "l", lwd = 1, col = cscale, xlab = "Time", 
ylab = "Response", main = "Parameter cc")
legend(x = "topleft", legend = cc, text.col = cscale)

# Example 3: effect of varying parameter a1
a1 <- seq(1, 10)
nlev <- length(a1)
cscale <- rgb(seq(0, 1, length.out = nlev), 
seq(1, 0, length.out = nlev), 0, 1)
mat <- matrix(NA, nrow = nlev, ncol = 20)
for (i in 1:nlev) {
  hrf <- ts(hemodynamicRF(scans = 20, onsets = 1, durations = 2, 
  rt = 1, a1 = a1[i], a2 = 3))
  mat[i, ] <- hrf
}
matplot(seq(1, 20), t(mat), "l", lwd = 1, col = cscale, xlab = "Time", 
ylab = "Response", main = "Parameter a1")
legend(x = "topleft", legend = a1, text.col = cscale)

# Example 4: effect of varying parameter a2
a2 <- seq(1, 10)
nlev <- length(a2)
cscale <- rgb(seq(0, 1, length.out = nlev), 
seq(1, 0, length.out = nlev), 0, 1)
mat <- matrix(NA, nrow = nlev, ncol = 20)
for (i in 1:nlev) {
  hrf <- ts(hemodynamicRF(scans = 20, onsets = 1, durations = 2, 
  rt = 1, a1 = 4, a2 = a2[i]))
  mat[i, ] <- hrf
}
matplot(seq(1, 20), t(mat), "l", lwd = 1, col = cscale, 
xlab = "Time", ylab = "Response", main = "Parameter a2")
legend(x = "topleft", legend = a2, text.col = cscale)

# Example 5: effect of varying parameter b1
b1 <- seq(0.4, 1.3, by = 0.1)
nlev <- length(b1)
cscale <- rgb(seq(0, 1, length.out = nlev), 
seq(1, 0, length.out = nlev), 0, 1)
mat <- matrix(NA, nrow = nlev, ncol = 20)
for (i in 1:nlev) {
  hrf <- ts(hemodynamicRF(scans = 20, onsets = 1, 
  durations = 2, rt = 1, a1 = 4, a2 = 3, b1 = b1[i]))
  mat[i, ] <- hrf
}
matplot(seq(1, 20), t(mat), "l", lwd = 1, col = cscale, 
xlab = "Time", ylab = "Response", main = "Parameter b1")
legend(x = "topleft", legend = b1, text.col = cscale)

# Example 6: effect of varying parameter b2
b2 <- seq(0.4, 1.3, by = 0.1)
nlev <- length(b2)
cscale <- rgb(seq(0, 1, length.out = nlev), 
seq(1, 0, length.out = nlev), 0, 1)
mat <- matrix(NA, nrow = nlev, ncol = 20)
for (i in 1:nlev) {
  hrf <- ts(hemodynamicRF(scans = 20, onsets = 1, 
  durations = 2, rt = 1, a1 = 4, a2 = 3, b2 = b2[i]))
  mat[i, ] <- hrf
}
matplot(seq(1, 20), t(mat), "l", lwd = 1, col = cscale, 
xlab = "Time", ylab = "Response", main = "Parameter b2")
legend(x = "topleft", legend = b2, text.col = cscale)