Numerical Twin with Two Dimensional Ornstein--Uhlenbeck Processes of Transient Oscillations in EEG signal
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914288569942016 |
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| author | Michel, P. O. Sun, C. Jaffard, S. Longrois, D. Holcman, D. |
| author_facet | Michel, P. O. Sun, C. Jaffard, S. Longrois, D. Holcman, D. |
| contents | Stochastic burst-like oscillations are common in physiological signals, yet there are few compact generative models that capture their transient structure. We propose a numerical-twin framework that represents transient narrowband activity as a two-dimensional Ornstein-Uhlenbeck (OU) process with three interpretable parameters: decay rate, mean frequency, and noise amplitude. We develop two complementary estimation strategies. The first fits the power spectral density, amplitude distribution, and autocorrelation to recover OU-parameters. The second segments burst events and performs a statistical match between empirical spindle statistics (duration, amplitude, inter-event interval) and simulated OU output via grid search, resolving parameter degeneracies by including event counts. We extend the framework to multiple frequency bands and piecewise-stationary dynamics to track slow parameter drifts. Applied to electroencephalography (EEG) recorded during general anesthesia, the method identifies OU models that reproduce alpha-spindle (8-12 Hz) morphology and band-limited spectra with low residual error, enabling real-time tracking of state changes that are not apparent from band power alone. This decomposition yields a sparse, interpretable representation of transient oscillations and provides interpretable metrics for brain monitoring. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_21768 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical Twin with Two Dimensional Ornstein--Uhlenbeck Processes of Transient Oscillations in EEG signal Michel, P. O. Sun, C. Jaffard, S. Longrois, D. Holcman, D. Neurons and Cognition 92-08, J.3 Stochastic burst-like oscillations are common in physiological signals, yet there are few compact generative models that capture their transient structure. We propose a numerical-twin framework that represents transient narrowband activity as a two-dimensional Ornstein-Uhlenbeck (OU) process with three interpretable parameters: decay rate, mean frequency, and noise amplitude. We develop two complementary estimation strategies. The first fits the power spectral density, amplitude distribution, and autocorrelation to recover OU-parameters. The second segments burst events and performs a statistical match between empirical spindle statistics (duration, amplitude, inter-event interval) and simulated OU output via grid search, resolving parameter degeneracies by including event counts. We extend the framework to multiple frequency bands and piecewise-stationary dynamics to track slow parameter drifts. Applied to electroencephalography (EEG) recorded during general anesthesia, the method identifies OU models that reproduce alpha-spindle (8-12 Hz) morphology and band-limited spectra with low residual error, enabling real-time tracking of state changes that are not apparent from band power alone. This decomposition yields a sparse, interpretable representation of transient oscillations and provides interpretable metrics for brain monitoring. |
| title | Numerical Twin with Two Dimensional Ornstein--Uhlenbeck Processes of Transient Oscillations in EEG signal |
| topic | Neurons and Cognition 92-08, J.3 |
| url | https://arxiv.org/abs/2512.21768 |