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).

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

OBJECTIVE: Many physical models of biological processes including neural systems are characterized by parametric nonlinear dynamical relations between driving inputs, internal states, and measured outputs of the process. Fitting such models using experimental data (data assimilation) is a challenging task since the physical process often operates in a noisy, possibly non-stationary environment; moreover, conducting multiple experiments under controlled and repeatable conditions can be impractical, time consuming or costly. The accuracy of model identification, therefore, is dictated principally by the quality and dynamic richness of collected data over single or few experimental sessions. Accordingly, it is highly desirable to design efficient experiments that, by exciting the physical process with smart inputs, yields fast convergence and increased accuracy of the model. APPROACH: We herein introduce an adaptive framework in which optimal input design is integrated with square root cubature Kalman filters (OID-SCKF) to develop an online estimation procedure that first, converges significantly quicker, thereby permitting model fitting over shorter time windows, and second, enhances model accuracy when only few process outputs are accessible. The methodology is demonstrated on common nonlinear models and on a four-area neural mass model with noisy and limited measurements. Estimation quality (speed and accuracy) is benchmarked against high-performance SCKF-based methods that commonly employ dynamically rich informed inputs for accurate model identification. MAIN RESULTS: For all the tested models, simulated single-trial and ensemble averages showed that OID-SCKF exhibited (i) faster convergence of parameter estimates and (ii) lower dependence on inter-trial noise variability with gains up to around 1000 ms in speed and 81% increase in variability for the neural mass models. In terms of accuracy, OID-SCKF estimation was superior, and exhibited considerably less variability across experiments, in identifying model parameters of (a) systems with challenging model inversion dynamics and (b) systems with fewer measurable outputs that directly relate to the underlying processes. SIGNIFICANCE: Fast and accurate identification therefore carries particular promise for modeling of transient (short-lived) neuronal network dynamics using a spatially under-sampled set of noisy measurements, as is commonly encountered in neural engineering applications.

Hybrid Cubature Kalman filtering for identifying nonlinear models from sampled recording: Estimation of neuronal dynamics.

Kalman filtering methods have long been regarded as efficient adaptive Bayesian techniques for estimating hidden states in models of linear dynamical systems under Gaussian uncertainty. Recent advents of the Cubature Kalman filter (CKF) have extended this efficient estimation property to nonlinear systems, and also to hybrid nonlinear problems where by the processes are continuous and the observations are discrete (continuous-discrete CD-CKF). Employing CKF techniques, therefore, carries high promise for modeling many biological phenomena where the underlying processes exhibit inherently nonlinear, continuous, and noisy dynamics and the associated measurements are uncertain and time-sampled. This paper investigates the performance of cubature filtering (CKF and CD-CKF) in two flagship problems arising in the field of neuroscience upon relating brain functionality to aggregate neurophysiological recordings: (i) estimation of the firing dynamics and the neural circuit model parameters from electric potentials (EP) observations, and (ii) estimation of the hemodynamic model parameters and the underlying neural drive from BOLD (fMRI) signals. First, in simulated neural circuit models, estimation accuracy was investigated under varying levels of observation noise (SNR), process noise structures, and observation sampling intervals (dt). When compared to the CKF, the CD-CKF consistently exhibited better accuracy for a given SNR, sharp accuracy increase with higher SNR, and persistent error reduction with smaller dt. Remarkably, CD-CKF accuracy shows only a mild deterioration for non-Gaussian process noise, specifically with Poisson noise, a commonly assumed form of background fluctuations in neuronal systems. Second, in simulated hemodynamic models, parametric estimates were consistently improved under CD-CKF. Critically, time-localization of the underlying neural drive, a determinant factor in fMRI-based functional connectivity studies, was significantly more accurate under CD-CKF. In conclusion, and with the CKF recently benchmarked against other advanced Bayesian techniques, the CD-CKF framework could provide significant gains in robustness and accuracy when estimating a variety of biological phenomena models where the underlying process dynamics unfold at time scales faster than those seen in collected measurements.

Intracortical augmenting responses in networks of reduced compartmental models of tufted layer 5 cells.

Augmenting responses (ARs) are characteristic recruitment phenomena that can be generated in target neural populations by repetitive intracortical or thalamic stimulation and that may facilitate activity transmission from thalamic nuclei to the cortex or between cortical areas. Experimental evidence suggests a role for cortical layer 5 in initiating at least one form of augmentation. We present a three-compartment model of tufted layer 5 (TL5) cells that faithfully reproduces a wide range of dynamics in these neurons that previously has been achieved only partially and in much more complex models. Using this model, the simplest network exhibiting AR was a single pair of TL5 and inhibitory (IN5) neurons. Intracellularly, AR initiation was controlled by low-threshold Ca2+ current (I(T)), which promoted TL5 rebound firing, whereas AR strength was dictated by inward-rectifying current (I(h)), which regulated TL5 multiple-spike firing and also prevented excessive firing under high-amplitude stimuli. Synaptically, AR was significantly more salient under concurrent stimulus delivery to superficial and deep dendritic zones of TL5 cells than under conventional single-zone stimuli. Moreover, slow GABA-B-mediated inhibition in TL5 cells controlled AR strength and frequency range. Finally, a network model of two cortical populations interacting across functional hierarchy showed that intracortical AR occurred prominently upon exciting superficial cortical layers either directly or via intrinsic connections, with AR frequency dictated by connection strength and background activity. Overall, the investigation supports a central role for a TL5-IN5 skeleton network in low-frequency cortical dynamics in vivo, particularly across functional hierarchies, and presents neuronal models that facilitate accurate large-scale simulations.

Modeling the contribution of lamina 5 neuronal and network dynamics to low frequency EEG phenomena.

The Electroencephalogram (EEG) is an important clinical and research tool in neurophysiology. With the advent of recording techniques, new evidence is emerging on the neuronal populations and wiring in the neocortex. A main challenge is to relate the EEG generation mechanisms to the underlying circuitry of the neocortex. In this paper, we look at the principal intrinsic properties of neocortical cells in layer 5 and their network behavior in simplified simulation models to explain the emergence of several important EEG phenomena such as the alpha rhythms, slow-wave sleep oscillations, and a form of cortical seizure. The models also predict the ability of layer 5 cells to produce a resonance-like neuronal recruitment known as the augmenting response. While previous models point to deeper brain structures, such as the thalamus, as the origin of many EEG rhythms (spindles), the current model suggests that the cortical circuitry itself has intrinsic oscillatory dynamics which could account for a wide variety of EEG phenomena.