# A Blind Module Identification Approach for Predicting Effective Connectivity Within Brain Dynamical Subnetworks

## Abstract

Model-based network discovery measures, such as the brain effective connectivity, require fitting of generative process models to measurements obtained from key areas across the network. For distributed dynamic phenomena, such as generalized seizures and slow-wave sleep, studying effective connectivity from real-time recordings is significantly complicated since (i) outputs from only a subnetwork can be practically measured, and (ii) exogenous subnetwork inputs are unobservable. Model fitting, therefore, constitutes a challenging blind module identification or model inversion problem for finding both the parameters and the many unknown inputs of the subnetwork. We herein propose a novel estimation framework for identifying nonlinear dynamic subnetworks in the case of slowly-varying, otherwise unknown local inputs. Starting with approximate predictions obtained using Cubature Kalman filtering, residuals of local output predictions are utilized to improve upon local input estimates. The algorithm performance is tested on both simulated and clinical EEG of induced seizures under electroconvulsive therapy (ECT). For the simulated network, the algorithm significantly boosted the estimation accuracy for inputs and connections from noisy EEG. For the clinical data, the algorithm predicted increased subnetwork inputs during the pre-stimulus anesthesia condition. Importantly, it predicted an increased frontocentral connectivity during the generalized seizure that is commensurate with electrode placement and that corroborates the clinical hypothesis of increased frontal focality of therapeutic ECT seizures. The proposed framework can be extended to account for several input configurations and can in principle be applied to study effective connectivity within brain subnetworks defined at the microscale (cortical lamina interaction) or at the macroscale (sensory integration).

## Keywords

Model inversion Effective connectivity Kalman filtering Neuronal modeling Blind deconvolution Brain subnetworks## Notes

### Funding

This work has been supported by the Lebanese National Council for Scientific Research (LNCSR, Award No. 102630) and the following internal grant programs at AUB (1) the F Jabre Award for biomedical research, and (2) University Research Board award.

### Compliance with Ethical Standards

### Conflict of Interest

Fadi N. Karameh has no conflict of interest. Ziad Nahas has had research funding from MECTA Inc. in form of FEAST device loan.

### Ethical Approval

All procedures performed in studies involving human participants were approved by the institutional review board (IRB) at the American University of Beirut under a FDA investigation device exemption and in accordance with the 1964 Helsinki declaration and its later amendments.

### Informed Consent

Informed consent was obtained from all individual participants included in the study.

### Research Involving Human Participants and/or Animals

This article does not contain any studies with animals performed by any of the authors

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