Linear Model for FMRI Data

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 .

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)