Comparison of different Kalman filter approaches in deriving time varying connectivity from EEG data

SEED-G: Simulated EEG Data Generator for Testing Connectivity Algorithms

EEG signals are widely used to estimate brain circuits associated with specific tasks and cognitive processes. The testing of connectivity estimators is still an open issue because of the lack of a ground-truth in real data. Existing solutions such as the generation of simulated data based on a manually imposed connectivity pattern or mass oscillators can model only a few real cases with limited number of signals and spectral properties that do not reflect those of real brain activity. Furthermore, the generation of time series reproducing non-ideal and non-stationary ground-truth models is still missing. In this work, we present the SEED-G toolbox for the generation of pseudo-EEG data with imposed connectivity patterns, overcoming the existing limitations and enabling control of several parameters for data simulation according to the user's needs. We first described the toolbox including guidelines for its correct use and then we tested its performances showing how, in a wide range of conditions, datasets composed by up to 60 time series were successfully generated in less than 5 s and with spectral features similar to real data. Then, SEED-G is employed for studying the effect of inter-trial variability Partial Directed Coherence (PDC) estimates, confirming its robustness.

Altered Functional Connectivity in Children with ADHD Revealed by Scalp EEG: An ERP Study

Attention deficit hyperactivity disorder (ADHD) is one of the most common neurodevelopmental brain disorders in childhood. Despite extensive researches, the neurobiological mechanism underlying ADHD is still left unveiled. Since the deficit functions, such as attention, have been demonstrated in ADHD, in our present study, based on the oddball P3 task, the corresponding electroencephalogram (EEG) of both healthy controls (HCs) and ADHD children was first collected. And we then not only focused on the event-related potential (ERP) evoked during tasks but also investigated related brain networks. Although an insignificant difference in behavior was found between the HCs and ADHD children, significant electrophysiological differences were found in both ERPs and brain networks. In detail, the dysfunctional attention occurred during the early stage of the designed task; as compared to HCs, the reduced P2 and N2 amplitudes in ADHD children were found, and the atypical information interaction might further underpin such a deficit. On the one hand, when investigating the cortical activity, HCs recruited much stronger brain activity mainly in the temporal and frontal regions, compared to ADHD children; on the other hand, the brain network showed atypical enhanced long-range connectivity between the frontal and occipital lobes but attenuated connectivity among frontal, parietal, and temporal lobes in ADHD children. We hope that the findings in this study may be instructive for the understanding of cognitive processing in children with ADHD.

Modeling time-varying brain networks with a self-tuning optimized Kalman filter

Brain networks are complex dynamical systems in which directed interactions between different areas evolve at the sub-second scale of sensory, cognitive and motor processes. Due to the highly non-stationary nature of neural signals and their unknown noise components, however, modeling dynamic brain networks has remained one of the major challenges in contemporary neuroscience. Here, we present a new algorithm based on an innovative formulation of the Kalman filter that is optimized for tracking rapidly evolving patterns of directed functional connectivity under unknown noise conditions. The Self-Tuning Optimized Kalman filter (STOK) is a novel adaptive filter that embeds a self-tuning memory decay and a recursive regularization to guarantee high network tracking accuracy, temporal precision and robustness to noise. To validate the proposed algorithm, we performed an extensive comparison against the classical Kalman filter, in both realistic surrogate networks and real electroencephalography (EEG) data. In both simulations and real data, we show that the STOK filter estimates time-frequency patterns of directed connectivity with significantly superior performance. The advantages of the STOK filter were even clearer in real EEG data, where the algorithm recovered latent structures of dynamic connectivity from epicranial EEG recordings in rats and human visual evoked potentials, in excellent agreement with known physiology. These results establish the STOK filter as a powerful tool for modeling dynamic network structures in biological systems, with the potential to yield new insights into the rapid evolution of network states from which brain functions emerge.

During normal behavior, brains transition between functional network states several times per second. This allows humans to quickly read a sentence, and a frog to catch a fly. Understanding these fast network dynamics is fundamental to understanding how brains work, but up to now it has proven very difficult to model fast brain dynamics for various methodological reasons. To overcome these difficulties, we designed a new Kalman filter (STOK) by innovating on previous solutions from control theory and state-space modelling. We show that STOK accurately models fast network changes in simulations and real neural data, making it an essential new tool for modelling fast brain networks in the time and frequency domain.

Time-varying effective EEG source connectivity: the optimization of model parameters

Adaptive estimation methods based on general Kalman filter are powerful tools to investigate brain networks dynamics given the non-stationary nature of neural signals. These methods rely on two parameters, the model order p and adaptation constant c, which determine the resolution and smoothness of the time-varying multivariate autoregressive estimates. A sub-optimal filtering may present consistent biases in the frequency domain and temporal distortions, leading to fallacious interpretations. Thus, the performance of these methods heavily depends on the accurate choice of these two parameters in the filter design. In this work, we sought to define an objective criterion for the optimal choice of these parameters. Since residual- and information-based criteria are not guaranteed to reach an absolute minimum, we propose to study the partial derivatives of these functions to guide the choice of p and c. To validate the performance of our method, we used a dataset of human visual evoked potentials during face perception where the generation and propagation of information in the brain is well understood and a set of simulated data where the ground truth is available.

Layer 3 Dynamically Coordinates Columnar Activity According to Spatial Context

To reduce statistical redundancy of natural inputs and increase the sparseness of coding, neurons in primary visual cortex (V1) show tuning for stimulus size and surround suppression. This integration of spatial information is a fundamental, context-dependent neural operation involving extensive neural circuits that span across all cortical layers of a V1 column, and reflects both feedforward and feedback processing. However, how spatial integration is dynamically coordinated across cortical layers remains poorly understood. We recorded single- and multiunit activity and local field potentials across V1 layers of awake mice (both sexes) while they viewed stimuli of varying size and used dynamic Bayesian model comparisons to identify when laminar activity and interlaminar functional interactions showed surround suppression, the hallmark of spatial integration. We found that surround suppression is strongest in layer 3 (L3) and L4 activity, where suppression is established within ∼10 ms after response onset, and receptive fields dynamically sharpen while suppression strength increases. Importantly, we also found that specific directed functional connections were strongest for intermediate stimulus sizes and suppressed for larger ones, particularly for connections from L3 targeting L5 and L1. Together, the results shed light on the different functional roles of cortical layers in spatial integration and on how L3 dynamically coordinates activity across a cortical column depending on spatial context.SIGNIFICANCE STATEMENT Neurons in primary visual cortex (V1) show tuning for stimulus size, where responses to stimuli exceeding the receptive field can be suppressed (surround suppression). We demonstrate that functional connectivity between V1 layers can also have a surround-suppressed profile. A particularly prominent role seems to have layer 3, the functional connections to layers 5 and 1 of which are strongest for stimuli of optimal size and decreased for large stimuli. Our results therefore point toward a key role of layer 3 in coordinating activity across the cortical column according to spatial context.

Directed functional connections underlying spontaneous brain activity

Neuroimaging studies have shown that spontaneous brain activity is characterized as changing networks of coherent activity across multiple brain areas. However, the directionality of functional interactions between the most active regions in our brain at rest remains poorly understood. Here, we examined, at the whole-brain scale, the main drivers and directionality of interactions that underlie spontaneous human brain activity by applying directed functional connectivity analysis to electroencephalography (EEG) source signals. We found that the main drivers of electrophysiological activity were the posterior cingulate cortex (PCC), the medial temporal lobes (MTL), and the anterior cingulate cortex (ACC). Among those regions, the PCC was the strongest driver and had both the highest integration and segregation importance, followed by the MTL regions. The driving role of the PCC and MTL resulted in an effective directed interaction directed from posterior toward anterior brain regions. Our results strongly suggest that the PCC and MTL structures are the main drivers of electrophysiological spontaneous activity throughout the brain and suggest that EEG-based directed functional connectivity analysis is a promising tool to better understand the dynamics of spontaneous brain activity in healthy subjects and in various brain disorders.

A Time-Varying Connectivity Analysis from Distributed EEG Sources: A Simulation Study

Time-varying connectivity analysis based on sources reconstructed using inverse modeling of electroencephalographic (EEG) data is important to understand the dynamic behaviour of the brain. We simulated cortical data from a visual spatial attention network with a time-varying connectivity structure, and then simulated the propagation to the scalp to obtain EEG data. Distributed EEG source modeling using sLORETA was applied. We compared different dipole (representing a source) selection strategies based on their time series in a region of interest. Next, we estimated multivariate autoregressive (MVAR) parameters using classical Kalman filter and general linear Kalman filter approaches followed by the calculation of partial directed coherence (PDC). MVAR parameters and PDC values for the selected sources were compared with the ground-truth. We found that the best strategy to extract the time series of a region of interest was to select a dipole with time series showing the highest correlation with the average time series in the region of interest. Dipole selection based on power or based on the largest singular value offer comparable alternatives. Among the different Kalman filter approaches, the use of a general linear Kalman filter was preferred to estimate PDC based connectivity except when only a small number of trials are available. In the latter case, the classical Kalman filter can be an alternative.

Cortical Correlates of Human Balance Control

Balance control is a fundamental component of human every day motor activities such as standing or walking, and its impairment is associated with an increased risk of falling. However, in humans the exact neurobiological mechanisms underlying balance control are still unclear. Specifically, although previous studies have identified a number of cortical regions that become significantly activated during real or imagined balancing, the interactions within and between the relevant cortical regions remain to be investigated. The working hypothesis of this study is that cortical networks contribute to an optimization of balance control, and that this contribution can be revealed by partial directed coherence—a time-variant, frequency-selective and directed functional connectivity analysis tool. Electroencephalographic activity was recorded in 37 subjects during single-leg balancing on a stable as well as an unstable surface. Results of this study show that in the transition from balancing on a stable surface to an unstable surface, two topographically delimitable connectivity networks (weighted directed networks) are established; one associated with the alpha and one with the theta frequency band. The theta network sequence can be described as a set of subnetworks (modules) comprising the frontal, central and parietal cortex with individual temporal and spatial developments within and between those modules. In the alpha network, the occipital electrodes O1 and O2 act as a source, and the interactions propagate predominantly in the directions from occipital to parietal and to centro-parietal areas. These important findings indicate that balance control is supported by at least two functional cortical networks.