This paper develops a novel method to infer directional relationships between cortical areas of the brain based on simultaneously acquired EEG and fMRI data. Specifically, the fMRI activations are used to select ROIs related to the paradigm of interest. This information is used in a coupled state-space and forward propagation model to identify robust spatial sources and directional connectivity. The authors use a variational Bayesian framework to infer the latent posteriors and noise covariances. They demonstrate the power of joint EEG/fMRI analysis using two simulated experiments and a real-world dataset. Overall, this is a well-developed paper that presents an elegant new framework for directional EEG analysis, informed by an auxiliary data modality. I also appreciate the rigorous evaluation on both synthetic and real-world data. Directional connectivity is an increasingly popular topic of study in computational neuroscience, and the coupled state-space model is one of the more principled frameworks that I have seen. For these reasons, I would recommend this paper for acceptance. With that said, there were a few issues that dampened my enthusiasm for the paper. I would suggest that the authors address these points in a future iteration of this work. === Major Concerns === My main complaint is that even though the paper claims to develop a multimodal framework, the fMRI data is not well-integrated into the generative model. Practically speaking, the fMRI information is used to select the ROIs used in the Bayesian model. This process is done a priori, almost like a preprocessing step. However, fMRI has its own forward model (GLM) which mimics the form of Eq. (2). I would have liked to see the GLM folded into the Bayesian framework. For example, this joint analysis can mitigate cases when the fMRI activations are missing or unreliable by adding noise into the ROI boundaries. My second concern is the relatively small number of ROIs (5-6) assumed in the experimental section. While it may be appropriate for the chosen paradigm, ultimately, we would like to know more about information processing across distributed functional systems, analogous to resting-state data. Given the large number of parameters, it is unclear whether the inference procedure would be robust in the case of a larger state-space. If not, this would greatly limit the generalizability of this work to new applications. === Minor Points === 1) I would have preferred more details about the inference procedure (including update equations) and a much shorter discussion of the experimental setup and results. 2) The model initialization in Section 3.2 is very sophisticated. How do the final values differ from this initialization? Does the model produce reasonable results from a simple random intializaton? 3) The Discussion mentions that the ROIs are specific to each subject. While the spatial location may have been guided by the fMRI, as far as I can tell, all subjects had the same number of ROIs. Can this method be applied when the number of ROIs differs across subjects (as is often the case for fMRI activations)? ** UPDATE: The author response is good, in that it discusses a number of reviewer concerns. It solidifies my opinion that this is a good paper worthy of acceptance. With that said, using the fMRI as a precomputed spatial prior is not particularly innovative as far as multimodal approaches go.

This paper proposes a probabilistic model-based method for estimating effective connectivity among brain regions based on simultaneous EEG and fMRI recordings. The model is a linear state-space model for sensor-space EEG data, with the observation (forward) model pre-specified from a given lead-field matrix and task-based ROIs defined by fMRI. The technical idea sounds reasonable, although rather straightforward and the advance from previous studies like [7] appears to be quite small. Most crucially, the method does not seem to really exploit the advantage of simultaneous measurements because the task-based ROIs can actually be defined even from fMRI-only measurement during participants do the same task. The paper itself is very well-written, with high clarity. The simulation and real-data experiment are well conducted, although it is not easy to validate the method from the real-data result. As minor points, is it necessary to assume that Q_x is diagonal? Some comments will be useful on how the technical idea of this paper differs from previous uses of fMRI for spatial priors [12-14]. Comments after authors response: I still think that the method is not far beyond the previous work [7] because the key idea of reducing ROI-based source connectivity estimation into sensor-space AR model fitting has already been presented in that work and other modifications on the model is rather straightforward once the formulation is given. Some specific modeling and algorithmic details (e.g. modulatory connectivity, initialization scheme) are likely new and useful, which I initially overlooked.

In this work, the Authors propose a linear state-space model for estimating effective connectivity using EEG and fMRI data. The fMRI data is used to localize the ROIs and constraint the optimization of the model inferred from EEG data. The temporal dependence between latent variables is modeled as a first-order MVAR in the presence of external and context-dependent inputs. Such a model is complemented by a linear forward model for propagation. Variational-Bayes inference is used to estimate the model, adopting some strong assumptions, e.g. Q_s diagonal. Experiments on simulated data are conducted in order to characterize the importance of constraining sources to what fMRI data suggests, both in a block and in an event-related design. On real fMRI/EEG data, from a face, car, and house stimulation paradigm, the proposed method is used to study the connectivity patterns between FFA, PPA, SPL, ACC, FEF and PMC for face-house processing, suggesting that additional connectivity is required for recognizing a house relative to a face. The manuscript is very well written and the proposed method is very interesting and grounded. Issues: - The main issue is the absence of the code implementing the proposed method. The Authors do not commit even to publishing the code of the proposed method and simulations after acceptance. The Authors do not offer any explanation for this decision which, in 2019, is pretty difficult to accept. Same thing for the EEG/fMRI dataset. It is true that many practical details are present in the manuscript and the supplementary materials. Still, reproducibility of the results seems not a major concern for the Authors. But it is for me. - What about the time required by the entire method to be computed? No mention of that.