Hi Piers,
A sinusoid at period T, of arbitrary amplitude A, with arbitrary phase
shift p,
A*sin(x+p) = A*cos(p)*sin(x)+A*sin(p)*cos(x)
where
x=2*pi*t/T, and t is the time variable.
I.e. it can be modelled as a weighted combination of two pure sine and
cosine terms. In other words, I think if you include sin(x) and cos(x)
variables in your design (evaluated at 2*pi*t/15 at the appropriate
t), then you'll be able to recover the phase at each voxel from the
magnitudes of the two betas (S and C), since
p = atan2(C, S)
(that way round, since the cosine beta corresponds to A*sin(p))
Sound good?
Ged
Piers Howe wrote:
> Dear SPM community
>
> I am having troubing analyzing fMRI data generated by a particular visual
> stimulus and would appreciate any tips people may have.
>
> The stimulus consists of a wedge with its point centered on the origin. The
> wedge continuously rotates around the origin, completing a revolution every
> 15 seconds.
>
> I am interested in analyzing the BOLD signals from V1 (the primary visual
> cortex) using SP5. Because V1 is topographically organized the region of
> activity caused by the wedge should slowly move across the surface of V1. I
> would like to show this movement. I think that the easiest way to do this
> would be to fit a peridodic funciton (e.g. a sin wave) to the activity at
> each voxel in V1 and then plot a map of the phase at each voxel. This phase
> should change in a gradual manner and so illustrate the topography of V1.
>
> My question: How can I fit a cyclical function to the bold signal at each
> voxel, extract the phase for each voxel, and then plot these phases on a map
> of the brain?
>
> Many thanks for any help you may be able to give.
>
> Piers
> Piers Howe, PhD
> Harvard Medical School
> Boston, MA 02115, USA
>
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