Nonlinear properties of multistable states of intracranial EEG
Poster No:
1339
Submission Type:
Abstract Submission
Authors:
Ying Wang1, Min Li2, Ronaldo García Reyes3, Jorge Bosch-Bayard4, Maria Bringas-Vega1, Ludovico Minati1, Pedro Valdes-Sosa1
Institutions:
1University of Electronic Science and Technology of China, Chengdu, China, 2Hangzhou Dianzi University, Hangzhou, China, 3Cuban Center for Neurocience, La Habana, Cuba, 4Universidad Autónoma de Madrid, Madrid, Spain
First Author:
Co-Author(s):
Introduction:
Multistability, the presence of multiple stable states (attractors) in dynamical systems, is crucial in neuroscience, especially for EEG studies[1–5]. It reflects transitions between distinct modes of brain activity. Linear models, with their single global attractor, fail to capture these complex multistable dynamics.
Threshold autoregressive (TAR) models [6,7] have been used for neural dynamics [8]. While TAR approximates attractors using piecewise linear models, it struggles with threshold determination in high-dimensional systems and often requires multiple models per attractor. Parametric nonlinear AR (NAR) such as NARMAX [9] depend heavily on order selection and parameter fitting, making them unrobust for complex, high-dimensional data with unknown structure.
Nonparametric approaches, such as nonparametric NAR (NNAR) with Nadaraya-Watson estimators, overcome these limitations by directly modeling dynamics from data, with bandwidth as the only key parameter [10,8]. Although NNAR effectively captures phenomena such as spiking wave limit cycles, their performance declines in multistable systems due to the inherent variability in attractors' intrinsic dimensions and scales. A global bandwidth fails to account for local properties, leading to poor representation of dynamics. And Implicit multistability is not conducive to interpretability.
To address these challenges, we propose a nonlinear clustering-based approach inspired by microstates[11]. By clustering states in high-dimensional embedding spaces, we enable localized modeling within each cluster, improving accuracy and interpretability. This method captures each attractor's local features and provides a robust framework for understanding their domains of attraction. Additionally, our findings align with frequency domain nonlinear characteristics identified by the HOXiAlpha (Higher Order XiAlpha) model[12].
Threshold autoregressive (TAR) models [6,7] have been used for neural dynamics [8]. While TAR approximates attractors using piecewise linear models, it struggles with threshold determination in high-dimensional systems and often requires multiple models per attractor. Parametric nonlinear AR (NAR) such as NARMAX [9] depend heavily on order selection and parameter fitting, making them unrobust for complex, high-dimensional data with unknown structure.
Nonparametric approaches, such as nonparametric NAR (NNAR) with Nadaraya-Watson estimators, overcome these limitations by directly modeling dynamics from data, with bandwidth as the only key parameter [10,8]. Although NNAR effectively captures phenomena such as spiking wave limit cycles, their performance declines in multistable systems due to the inherent variability in attractors' intrinsic dimensions and scales. A global bandwidth fails to account for local properties, leading to poor representation of dynamics. And Implicit multistability is not conducive to interpretability.
To address these challenges, we propose a nonlinear clustering-based approach inspired by microstates[11]. By clustering states in high-dimensional embedding spaces, we enable localized modeling within each cluster, improving accuracy and interpretability. This method captures each attractor's local features and provides a robust framework for understanding their domains of attraction. Additionally, our findings align with frequency domain nonlinear characteristics identified by the HOXiAlpha (Higher Order XiAlpha) model[12].
Methods:
We applied Gaussian Mixture Modeling (GMM) to high-dimensional iEEG embeddings to identify clusters corresponding to distinct attractor states. Nonparametric NAR was applied within each cluster to estimate local nonlinear dynamics. The embedding dimension was optimized using AICc (Corrected Akaike information criteria) from linear AR model, while the number of clusters was guided by established bistability in EEG [1–3]. The CNAR (cluster NAR) model iteratively refines cluster assignments and model parameters using an Expectation-Maximization (EM) algorithm. We validated the approach on 1772 channels of sEEG and ECoG recordings from 106 patients [13]. Spectral dynamics of the reconstructed time series were evaluated using higher-order spectrum-bicoherence, to identify phase coupling and nonlinear frequency interactions in the full model and within each attractor.
Results:
The CNAR model successfully partitioned the state space into distinct clusters, each representing a localized dynamical regime. Simulated time series accurately replicated the temporal structure and nonlinear interactions observed in the original data, including the harmonic contributions of individual attractors. Bicoherence revealed robust phase coupling, with significant bicoherence peaks indicative of nonlinear frequency interactions specific to each attractor. The spectra and bicoherence of the limit cycle corresponding to the alpha process we spilite with our previous study with HOXiAlpha model. PCA projections showed well-preserved attractor-like geometry structures.
Conclusions:
The CNAR model provides a powerful framework for characterizing multistability in iEEG data, offering both interpretability and precision in modeling complex nonlinear dynamics. Its ability to simulate realistic time series and uncover higher-order spectral interactions makes it a valuable tool for advancing our understanding of brain dynamics. This approach has potential applications in clinical and cognitive neuroscience, particularly for investigating pathophysiological conditions characterized by disrupted multistability.
Modeling and Analysis Methods:
EEG/MEG Modeling and Analysis 1
Methods Development 2
Task-Independent and Resting-State Analysis
Keywords:
Computational Neuroscience
Data analysis
Electroencephaolography (EEG)
Machine Learning
Modeling
Other - Multistability
1|2Indicates the priority used for review
Abstract Information
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