I am working with resting state fMRI data acquired from rodents, have built a function to specify a DCM.mat structure with all the data necesary, and have run full and selected models for the Default Mode Network (DMN), extracting signals from preprocessed data for 4 ROIs. I am using spectral and stochastic DCM (from my own function, not using the GUI) for comparison but have a couple of questions ( in advance I apologize for the length of this, and the over-description, but I mean to be very specific):

1. Free-Energy  (F). F is supposed to be a bound on the log(evidence), and being the evidence a probability this log(evidence) should be negative (0, -Inf). Hoewever, for some subjects and models I get positive F and for others Negative (even with the same model). According to the Variational Laplace approach this should not happen right?  Also, it seems that F is very similar for every model family for a single subjects, but varies a lot between them for the same model. What values of F are acceptable and will post-hoc optimization correct this?

2. Variance Explained. Using spm_dcm_fmri_check.m I checked for the variance each model (per subject) explained and Free-Energy does not seem to play a role in this calculation. This explained variance is a measure of the model fit, but I assume it does not account for model complexity. In this sense, how can I check that a model is well balanced in terms of accuracy and complexity with the DCM results file?

3. Post-hoc. For the full model case, should I do post-hoc optimization for each subject and then Bayesian Parameter Averaging (BPA)? Or should I just run a joint (all subjects included) post-hoc analysis? I am trying to follow the methods used in Razi et al "Construct validation of a DCM for resting state fMRI" and this is not very clear to me.

4.Options. The "DCM.options" structure is particularly broad in terms of the information it contains. However, when defining the priors in spm_dcm_fmri_priors.m there are two values I don't completely understand which completely define the priors for the Effective Connectivity (EC) matrix, "pA" and "dA" namely precision and decay of connections. These values are described in Friston et al. original DCM paper "Dynamic Causal Modelling" as and in the priors program are set  (for one hidden state per node) by default to pA = 64, and dA = 1. Is there a specific reason for these values? 

5. Hemodynamic Priors. After the paper Stephan et al. "Comparing Hemodynamic Models with DCM", SPM uses the function spm_fx_fmri.m to compute the states (dynamic equation and hemodynamic equations) of the system, and spm_gx_fmri.m computes the corresponding modelled BOLD response. spm_fx fixes the hemodynamic parameters (vector H) corresponding to autoregulation (kappa); rate of elimination (gamma); grubb's exponent (alpha); and resting Ox. extraction (E0 or rho. It also leaves signal decay and transit time as free parameters. spm_gx on ly has as free parameter epsilon, as described in the mentioned paper. After performing spectral and stochastic DCM for resting state data, these parameters vary a lot between subjects and models. I was wondering if there is any recommendations for mice data and/or resting-state fMRI?

Also, there are some differences between how SPM12 by default sets priors. Since Stephan et al. these priors are set, however, subsequent papers such as Rosa et al. "Post-hoc optimization of DCMs" (appendix A); and Friston et al. "A DCM for resting state fMRI" have different ways of calculating them. 

6. Connectivity Priors. I inverted full and selected models for the DMN (4nodes) using spectral DCM with default priors; by modifying them according to Rosa et al.(post-hoc...); and then modifying them according to Friston et al. (DCM for rsfMRI). Default prior estimation yields shrinked (=0) intrinsic connections and 1/128 extrinsic, corresponding to slow modes in the system. Rosa et al. propose parameters priors based on the amount of nodes: A intrinsic = -1/2 with variance 1/8n, and A-extrinsic = 1/64n with variance (8/n) + (1/8n = 2.03. Finally, Friston et al. propose A-intrinsic = -1/2 with variance 1/256, and A-extrinsic = 1/128 with variance 1/64. After inverting models for many subjects, I saw that modifying these priors yielded models with different (even oposite sign) Free-Energies and much more accurate models with explained variances of over 50% and even some reaching 90% (oh, and with even less EM-algorithm iterations). This Compared to the default prior values, in which many models for the same subjects could not explain  more than 10% variance. Are there any recommendations on which approach to use? For mice?

In advance I deeply appreciate some guidance with this. I'm trying to test hypotheses of possible laterality in the DCM and want to be very sure of my results. If it helps, I am uploading a very raw and perhaps not so efficient program on how I prepared the data for future DCM inversion, for the three cases I just mentioned. I'm sure many people could use it as seen in previous posts.

Kind regards,

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