Adaptive optimal input design and parametric estimation of nonlinear dynamical systems: application to neuronal modeling

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

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).