Daniel -
> We are trying to generate maps of the temporal delays of the hrf using the
> modeled temporal derivative. We are taking the ratio of the temporal
> derivative value to the beta value to derive an estimate of the time shift
> of the HRF relative to the assumed peak of the HRF of 6 seconds.
>
> Several problems arise.
>
> 1) When the beta value is small or near zero, we get VERY large values for
> this ratio. Should this type of analysis only be applied to voxels that
> have some minimum beta to avoid this problem?
Yes. In our paper, we restricted analysis to voxels that showed a significant
effect of the canonical HRF alone (F-test), for which the canonical beta is not
likely to be close to zero. See also Liao et al (2002), Neuroimage, for a proper
treatment using shrinkage estimators.
> 2) When the temporal derivative is very large, we get VERY small values for
> this ratio. Henson's paper warns that the ratio of temporal derivative to
> beta is a good estimate of the temporal shift only within a limited range
> of temporal derivative values. Should we exclude voxels whose temporal
> derivative values are too large?
The ratio is the derivative:canonical betas. So if the derivative beta is large,
the ratio should also be large (not small - so please check you are using
the correct ratio). Now the approximation only works well when the real
response is shifted by a small amount in time relative to the reference HRF
- about +/-1s with SPM's canonical HRF and derivative. We handled this by
using a sigmoidal squashing function to "saturate" subjects/voxels for
which the ratio is too large. I suggest you use this too (see paper). Simply
excluding voxels with a large derivative beta would not work, because
those voxels may also have a large canonical beta, and hence represent
perfectly valid (albeit shifted) responses. Put simply, a bigger canonical
needs a bigger derivative to shift it.
> 3) We have considered using just the temporal derivative value by itself,
> rather than taking the ratio. One problem we encountered is that the
> direction implied by the temporal derivative value (i.e., late or early
> relative to our assumed 6 second peak for the HRF) depends on whether the
> beta value is positive or negative. I believe that the temporal derivative
> value implies exactly opposite shifts for positive or negative betas. Does
> this mean we should further limit our search to voxels with positive beta
> values?
An important point made in the paper is that you can NOT simply compare
derivatives to infer differences in latency. You have to normalise by the
canonical HRF beta, ie compare ratios instead. Put again, a bigger canonical
needs a bigger derivative to shift it. There is also no problem of sign once you
take the ratio, though note that a positive ratio means an earlier response.
Note also that this sign is reversed using the sigmoidal function in the paper,
so that a positive ratio produces a negative latency value (which is more
intuitive). So again, I recommend that you use the sigmoid transform in
the paper.
> Are there alternatives to this method that provides a more stable (less
> susceptible to spuriously large or small values) estimate of the temporal
> delays of the hrf?
The ratio method can be thought of as a quick and dirty method.
Better methods include iterative fitting of an explicitly parameterised
reference HRF (see for example, Miezin et al 2000; Kruggel et al, 1999;
Henson & Rugg, 2001). However, these are computationally much
more expensive, and probably better restricted to regions of interest.
The ratio method is computationally trivial (eg in ImCalc), since it
uses normal OLS estimators within the GLM. The best strategy therefore
might be to use the ratio method to give SPMs of latency effects over
the whole brain, regions of interest in which could be examined in
more detail using iterative techniques.
Rik
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DR RICHARD HENSON
Institute of Cognitive Neuroscience
& Wellcome Department of Imaging Neuroscience
University College London
17 Queen Square
London, WC1N 3AR
England
EMAIL: [log in to unmask]
URL: http://www.fil.ion.ucl.ac.uk/~rhenson
TEL1 +44 (0)20 7679 1131
TEL2 +44 (0)20 7833 7472
FAX +44 (0)20 7813 1420
MOB +44 (0)794 1377 345
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