GammaVar fits a single gamma variate curve of the form
A*(t-tzero)^b * exp(-(t-tzero)/c) * H(t)
to a time series, where {A,tzero,b,c} are the 4 parameters and H(t) is the Heaviside step function. Therefore, this would be useful for fitting an impulse response curve "-iresp" from 3dDeconvolve, for example. But it wouldn't be useful for many FMRI direct data fitting purposes, since it only has one "up and down" in the curve.

For fitting FMRI time series, you need a model that can allow for multiple "ups and downs" that go with the stimuli. The periodic functions that Doug Ward provided (e.g., SineWave_APF) allow for fitting periodic curves to data. This may be marginally useful for some block designs.

The ConvGamma model is an extension of the GammaVar model to allow for multiple onset times. These times are set by inputting a time series, whose name is given by the environment variable AFNI_CONVMODEL_REF. Suppose we call this time series r(n), where n is the time index. Then at each time point m, the ConvGamma model is the sum of a GammaVar-like sequence of functions starting at all previous times:
r(n) * A*(t(m)-t(n)-tzero)^b * exp(-(t(m)-t(n)-tzero)/c) * H(t(m)-t(n))
where we sum over all n < m. That is, we put a GammaVar response down at each time t(n), with amplitude r(n), and then add them up. This is convolution of GammaVar(t) with r(t).

The ConvGamma2a model is similar, but allows for 2 reference time series r1(n) and r2(n), which get the same {tzero,b,c} parameters but get different {A} parameters. This would be used to model 2 separate stimulus trains, which were expected to give different response strengths in each voxel.

As far as I know, I am the only one who has ever used the ConvGamma models. I know that Tom Ross and Elliot Stein of NIDA use 3dNLfim with some other models for FMRI data analysis. 3dNLfim is quite slow, and for many purposes it isn't clear that the power and complexity of nonlinear regression is needed. As regards slowness, I just finished parallelizing 3dNLfim (like 3dDeconvolve earlier this week), which will let it run faster on a multi-CPU machine.

bob cox