```Markus -

First, you might want to check this archived message:

https://www.jiscmail.ac.uk/cgi-bin/wa.exe?A2=ind0904&L=SPM&D=0&X=1B29E63F8DCB1C3993&Y=rik.henson%40mrc-cbu.cam.ac.uk&P=196039

where Donald McLaren identified a problem with using the precise
sigmoidal equation in Henson et al (2002) for data analysed in SPM5+,
because the scaling in spm_get_bf.m changed (that paper was based on SPM2).

> I am refering to the paper of Henson et al 2002 NeuroImage 15, 83-95,
>
> I would like to use this technique.
>
> I am right when I proceed as follows?
>
> a) integrate temporal derivatives into my first level model
Yes. Note however that you can only separate estimation of latency from
estimation of height of an HRF if you have long or jittered SOAs (eg
null events); with rapid, fixed-SOA event-related designs (eg SOA<~2s,
randomised event-types), the temporal derivative for one event-type will
be correlated with the difference in (ie contrast of) canonical HRFs
across event-types. This is just an example of the more general point
that you need to estimate each regressor (temporal basis function) with
high statistical efficiency - ie the distinction between estimating an
HRF *shape* and simply detecting the *amplitude* of an assumed shape
(e.g, relative efficiencies of a canonical HRF vs an FIR basis set; see
Henson, 2004, HBF book chapter).

> b) calculate the beta for the hrf_<each condition> as a [1 0]
>
> c) calculate the beta for the td_<each condition> as a [0 1]
>
> d) use the image calculator to create the latency_image_<each condition>
> using the formula
>
> 2C/(1+exp(D beta2/beta1)) - C;
>
> where C=1.78, D=3.1 (Henson et al 2002, Neuroimage 15, p86).
Yes to points b-d, except that you might need to restimate the
parameters C and D in you are using SPM5+, as Donald found.

Note that these parameters only matter if you want to estimate the
precise latency (eg in seconds), which is only really valid in the
linear regime where the Taylor approximation holds (ie +/-1s of the
canonical latency). Furthermore, precise latency differences in the BOLD
impulse response may not be easily interpretable, because they do not
necessarily reflect latency differences in the underlying neural
activity (which is what I assume you are really interested in) - given
the time integration (see Discussion in Henson et al, 2002) and that the
neural-BOLD coupling is likely to have appreciable nonlinearities. (This
is perhaps one reason that the various published methods for estimating
BOLD latencies have not been used extensively for neuroscientific
conclusions.)

If you don't care about precise latency, then you can view the sigmoidal
function just as a statistical transform that prevents the
derivative:canonical ratio from exploding beyond the linear regime (or
when the canonical estimate is close to zero - ie for voxels where there
is no basic impulse response in the first place). Then the precise
parameters don't matter: you are just conditioning the data so that it
becomes more Gaussian (the ratio won't be precisely Gaussian, even after
transformation (you could use a log transform for that), though with
enough Gaussian smoothing, the parametric stats should be reasonably
robust). It also helps to only analyse voxels where there is a
significant loading on the canonical HRF as well (ie use an inclusive
mask, as in Henson et al, 2002), where the ratio only really makes sense
(as mentioned above).

> e) enter these latency_images into the second level stats (ANOVA).
Yes

> f) And the last question: Is the above formula correctly entered into
> the ImageCalculator when doing:
>
> f =  '(2*1.78./(1+exp(3.1*i2./i1))) - 1.78' ( I mean, I do get some
> imges, but are they correct??)
Should be. I can send you a function that writes latency images offline
if you want. But only if you are sure you want to proceed with latency
analyses.... ;-)

Rik

--

-------------------------------------------------------
Dr Richard Henson
MRC Cognition & Brain Sciences Unit