Dear Pierre,

>Dear SPM users
>
>I am trying to understand the differences between modelling
>connectivity by the use of SEM or DCM. To date, I have only used SEM
>and I dread to make a wrong use of DCM.

Generally, you may find the following paper helpful in which we
directly compared SEM to DCM:

Penny WD, Stephan KE, Mechelli A, Friston KJ
Modelling functional integration: a comparison of structural equation
and dynamic causal models.
Neuroimage. 2004;23 Suppl 1:S264-74.
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=15501096&query_hl=1&itool=pubmed_docsum


>It seems to me that the first evidence is that SEM does not
>incorporate the time dimension in the model because the correlations
>are calculated without delays between the time series of different VOIs.

The lack of delays are not the critical point (DCM for fMRI does not
consider delays either). SEM does not take into account the time
series aspect of the data, i.e you could reshuffle the time series
(in all areas in the same fashion) without changing any of the
results. In DCM, your results would change as the model is based on
differential equations that represent the change of variables in time.


>In contrast DCM modelled the hemodynamic response and, if I have
>understood correctly SPM5 documentation, this response is modelled
>by some unknown parameters which are estimated during the model estimation.

Yes, this is the so-called Balloon model which was introduced by
Richard Buxton et al. and later extended by Karl.


>I have some questions concerning this point. What are these
>parameters (I have not found that in the documentation)?

See the following papers for details on the hemodynamic model and the
parameters therein:

Friston KJ, Mechelli A, Turner R, Price CJ
Nonlinear responses in fMRI: the Balloon model, Volterra kernels, and
other hemodynamics.
Neuroimage. 2000 Oct;12(4):466-77.
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=10988040&query_hl=6&itool=pubmed_docsum

Stephan KE, Harrison LM, Penny WD, Friston KJ
Biophysical models of fMRI responses.
Curr Opin Neurobiol. 2004 Oct;14(5):629-35.
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=15464897&query_hl=1&itool=pubmed_docsum


>Do they allow to get the hemodynamic response (I think yes because
>in the DCM results, SPM5 draws this response)

Yes.

>and is this response different from the hemodynamic response given
>by some dedicated software (as for an example the SPM HRF-toolbox)?

Do you mean the HDM tool in SPM? Yes, this is exactly the same
hemodynamic model as in DCM.


>If we have twoVOIs, A and B (with the input variable pointing on A
>and an intrinsic connection from A to B), the hemodynamic response
>observed in B will be always be later than the response in A because
>response in B has "to wait" for the response in A?

No - that is exactly the problem of models of effective connectivity
which do not have a forward model but operate on the BOLD data
directly: The neurovascular coupling can differ quite strongly across
the brain, leading to quite considerable differences in BOLD
latencies. In other words, it is perfectly possible that an area B
which, at the neuronal level, activates later than another area A,
nevertheless shows an earlier BOLD response.


>Finally, Kim et al. (Human Brain Mapping 2006, online in advance)
>proposes a SEM based method to take in account a time delay. I think
>that compared to DCM, this method is more powerful because it is a
>lower number of parameters to estimate (it is purely intuitive!) but
>is less precise because it take in account only the time t-1 and
>does not models the shape of the response. Is-it right?

I do not know this paper so I cannot really comment on this
issue. Just as a general remark: one has to be very specific what
one means by "more powerful" or "better" when comparing models. From
a Bayesian perspective, relative goodness of models is determined
through the model evidence, and this reflects both the fit of the
model to the data as well as its complexity (e.g. the number of free
parameters).


>Finally, can we submit a block paradigm to DCM

yes

>because it is a very little number of scans which allow to estimate
>the hemodynamic response (the transitions between blocks)?
>
>A second question concerns the input variables. In the example given
>in the SPM5 documentation and in some publications, the input
>variable is formed by short pulses (onsets of events). Is it
>possible to have an input variable which is formed by a function
>with long constant periods (as one modelling a block design)?

yes

>If it is possible, how does the model (in term of combining neural
>and hemodynamic state) account for "habituation"?

You can model habituation, for example, through a modulation of the
self-connections. See Fig. 1 in the SEM-DCM comparison paper mentioned above.


>Moreover, I tried to run models (in SPM5) which have no input
>variable and an error has occurred during model evaluation. Is-it
>particular case or does a model have to include at least one input variable?

You need at least one driving input, otherwise the modelled system is
silent forever, i.e. no activity is induced at all.


>Finally, when the input variable is a perceptual event (for an
>example, a visual or auditory object), it is easy to decide of the
>target VOI. But when the input variable is a complex cognitive task
>(for an example :"searching the significance of a complex movie"),
>how can we choose the target? Do we choose some integrative areas,
>as frontal cortex, or is-it possible to make the input variable
>pointing to all the VOIs included in the model?

This depends entirely on your experimental question and your
neurobiologically motivated hypothesis about the structure of the
neural system of interest.


>A third question (with some links with the precedent point) concerns
>the intrinsic connections. I think that these connections are
>similar to the path estimated in SEM models.

Well, kind of - the maths on which they rest is different and so is
their interpretation. In SEM, path coefficients are interpreted like
partial regression coefficients. In DCM, the connection strengths
correspond to the rate constants of the modelled processes
(first-order ordinary differential equations).


>However, it is not clear for me how connections which are estimated
>in a model including input variables can be independent of this input?

I assume you are referring to statements like the following one by
Karl in the original 2003 DCM paper: "The Jacobian or connectivity
matrix A represents the first-order connectivity among the regions in
the absence of input." (p. 1277). The reason for this statement
should become clear when you take the partial derivative of the
neural state equation with regard to the state z, and evaluate it at
u=0, i.e. when all inputs are off. Then you obtain the coupling
matrix A of the system.

I hope this is helpful. I will send you some more potentially useful
papers in a separate email off-list.

Best wishes,
Klaas