Appendix B: Design Matrix Rules

This section describes the rules which are followed in order to take the FEAT setup and produce a design matrix, for use in the FILM GLM processing.

Here HTR model means "high temporal resolution" model - a time series of values that is used temporarily to create a model and apply the relevant HRF convolution before resampling down in time to match the temporal sampling of the FMRI data.

Note that it is assumed that every voxel was captured instantaneously in time, and at the same time, exactly halfway through a volume's time period, not at the beginning. This minimises timing errors, if slice-timing correction has not been applied.

No constant column is added to the model - instead, each EV is demeaned, and each voxel's time-course is demeaned before the GLM is applied.

for each EV
(
  if ( square waveform )
    fill HTR model with 0s or 1s
  else if ( sinusoidal waveform )
    fill HTR model with sinusoid scaled to lie in the range 0:1
  else if ( custom waveform )
    fill HTR model with custom information, with 0s outside of
    specified periods

  demean

  create "triggers" i.e. record the start and end of event or block

  create blurring+delaying HTR HRF convolution kernel, normalised so
  that the sum of values is 1 (in the case of basis functions, several
  related kernels are created)

  convolve HTR model with HRF convolution kernel (values in HTR model
  for t<0 are set to 0 to allow simple convolution)
     OR
  in the case of sinusoidal original waveform; create harmonics (if
  requested)

  subsample HTR model to match the temporal resolution of the data;
  take the value in the centre of each volume's time period

  add motion parameters as confound EVs if requested on the command
  line

  do two passes
  (
    take model produced by subsampling step above

    if pass=2 then apply high-pass temporal filtering

    re-demean

    instead of all the above - if this EV is an "interaction"
    (nonlinear interaction between other EVs);
    model = PRODUCT(other EVs, after subtracting the min value from
    each)

    orthogonalise current EV wrt earlier EVs if requested (form
    temporary matrix from selected EVs, carry out SVD, and subtract
    projection of current EV onto each vector in SVD output)

    orthogonalise main model wrt motion parameter EVs if requested

    if requested, create a new EV, calculated as the temporal derivative
    of the current EV

    re-demean

    if pass=1 then estimate peak-peak model heights
    if pass=2 then estimate contrast estimability information
  )
)