I believe that you are correct that Dale & Buckner (1997) use the fixation
"trials" as a means to achieve the desired random distribution. The
selective averaging is done by averaging over task trials and fixation
trials to yield mean time-courses for each. These are extremely noisy
and not meaningful. The task-fixation difference does give a meaningful
time-course that can be cross-correlated with a model function to yield
an effect magnitude. Their method only works if the design is
counter-balanced, and I believe that this yields time-courses for the
fixation "trials" with the same artifacts as the task trials, so that they
cancel in the difference. You don't have to counter-balance if you are
using the general linear model (although it gives you a more homogeneous
variance across effects). Removing this constraint makes it possible to
analyze a wider range of experimental paradigms and also eliminates the need
to code fixation events explicitly.
You can think of the time-course in a given voxel in two ways. You can
think of the baseline as being a fixation state, and that the task responses
are a departure from this state, or you can think of the baseline as being
the task state, and that fixation is a departure from this state. The two
views are equivalent and will yield the same results if you use the
appropriate contrasts. When you code both task and fixation in the general
linear, you are trying to code both models at once. In fact, using delta
functions as a basis set to estimate time-courses will always yield a
singular design matrix for this reason. If you are
doing a study with a single control state, it is best to code only the task
and to implicitly account for fixation in the baseline. If there is more
than one fixation state in the experiment, you have a different, very
interesting,
can of worms.
John
--------------------------------------------------------------
John Ollinger
Washington University
Neuro-imaging Laboratory
Campus Box 8225
St. Louis, MO 63110
http://imaging.wustl.edu/Ollinger
On Thu, 20 Jan 2000, Rik Henson wrote:
>
> > In an event-related design like this, I would have thought that you
SHOULD
> > model the 'fixation' events explicitly. If they are not modelled, then
you
> > are asking of each voxel the question 'can a significant amount of the
> > variance be explained by the modelled covariate for event A' (with a
> > contrast 1 0 0), whereas I would rather model them explicitly and then
ask
> > the question 'is significantly more variance explained by the modelled
> > covariate for event A than for the modelled covariate for event D' (with
a
> > contrast 1 0 0 -1). I am assuming, though, that D is an actual event
(such
> > as the appearance of a fixation point or some other temporal cue) rather
> > than just an arbitrarily chosen moment between the real events.
>
> In our normal usage of the term "null events", we refer to imaginary
> events that are, in fact, no different from the interstimulus baseline
> (ie completely undetectable by subjects). If you like, they are used
> simply to achieve a particular random distribution of times between
> stimuli (ISIs). I think this is consistent with the original use of
> "fixation" trials by Dale & Buckner (1997) - though someone please
> correct me if I'm wrong!
>
> If you do include "fixation trials" that are different from baseline
> (as in Richard's example, the presentation of a fixation cross against
> an otherwise blank screen) then Richard is exactly right that they
> should be modelled. This potential confusion may be why "null event"
> is perhaps more suitable than "fixation trial".
>
> Rik
>
>
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