Dear Rajeev,
> Dear SPM list,
>
> I'd be very grateful for any help on the following question:
> I'm looking for activation that parametrically increases
> with four versions of a stimulus, i.e. a perfectly
> matching voxel would respond with strength 1 to stim1,
> strength 2 to stim2 etc.
>
> One way to look for this would be to have four conditions,
> [ stim1 ... stim4 ] and run a contrast [ 1 2 3 4 ].
>
> Another would be to make a parametrically modulated regressor
> with a 1 when stim1 onsets happen, 2 when stim2 onsets happen etc.,
> and then convolve that with an HRF before entering it into the
> model as a column in the design matrix.
> e.g. conv([0 0 0 1 0 0 ... 0 3 0 ... 2 0 ... 0 4 0 ...], hrf)
>
Firstly, (assuming we're talking ER design) I think you should be aware that
constructing your regressor as above would be slightly suboptimal. When SPM
creates the regressor for you it will "supersample" time for you such that
the "accuracy" of the timing of the event is 16 (by default) times higher
than that offered by you TR. You would be much better off using the method
supplied by the SPM bunch.
1. Before you start "specifying your design" create a vector with the number
1 to 4, e.g. mod = [1 2 4 2 3 1 ...]; where the nth number signifies the
type of the nth event.
2. Start specifying your design (specifying 1 trial type), and when you are
asked for "parametric modulation" answer "Other".
Then
Name of Parameter: Whatever
Expansion: Linear
Which Trials: The one you got
[no of events] Parameters for trial 1: Here you enter the name of the vector
you just created (e.g. mod)
This will give you a design with two regressors (provided you used hrf
only), and it is the second you are interested in. To test your "hypothesis"
simply enter the contrast weight vector [0 1].
>
> My question is: are these two methods mathematically equivalent?
> If so, how can one show that? If not, which is preferable,
> i.e. which method would do a better job of finding voxels
> whose activity really does increase with increasing stim-type?
>
They're "kind of" equivalent. I would tend to think that the former is a bit
more versatile. My choice of design here would be to have one regressor with
all events, and then four more regressors, one for each event type. Lets say
you use hrf only and put them in the order 1 2 3 4 in the design, then the
contrast [-1.5 -.5 .5 1.5] would answer much the same question as the [0 1]
contrast above.
In addition with this design you can look for "any" type of parametric
modulation, not just linear which is really a kind of hefty assumption. The
way to do this would be to use F-contrasts, which would in this case test
"was it really necessary to put those extra four regressors in?". Clearly if
the response to all four event-types was identical the data would be
adequately modelled by just the first regressor, right? So, you have your
design and you specify that you want to define an F-contrast. The easiest
way to do that is to use the little row saying "indexes of reduced model",
or something like that. There you enter the indicies of all columns EXCEPT
those four you want to test for.
Lets say now you have done that, and that you did get a nice little blob
somewhere. You then need to examine the nature of the modulation for that
blob. Place the little red arrow on the local maxima of that blob, press the
"Plot" button and choose "Contrast of parametes estimates". Just to clarify,
let us now assume the first regressor in the design is that for all events
lumped, followed by event-types 1, 2, 3 and 4. Let us further assume that
the first five "bars" have the following values
1 -1 -1 1 1 (just an example)
The first value being positive tells you that you are looking at activations
(as opposed to deactivations) over some baseline. The two next values tells
you that for event-types 1 and 2 there were no activation (the -1 cancels
the first 1) and the following two values tells you that for event-types 3
and 4 there were (equal size) activations. Hence, what you have found is a
region exhibiting some form of all or nothing behaviour with a rather high
threshold of stimulation (nice, ehh?).
Good luck Jesper
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