Introduction Neuralfieldmodelsofferapowerfulframeworkforunderstandinglarge-scaleneuronaldynamics by encoding the underlying spatiotemporal processes as a system of integrodifferential equations. While early approaches modeled mean membrane potentials with a single quantity, modern methods [1] distinguish between postsynaptic and somatic potentials to provide a more nuanced description of synaptic interactions and their temporal dynamics. For this work, we consider the second-order neural field model (2ndNFM) introduced by Liley et. al. [2] and investigate how model parameters, governing both local activity and long-range connections, affect thetheta-band and alpha-bandpower of multi-leadEEGsignals as reported by [3].
Methods We propose a novel method for parameter estimation, utilizing recent developments in the characterization of nonlinear stochastic oscillators [4]. We implement the method to study~4Hz rhythms (2-5 Hz band) of EEG recordings that were found to correlate with cognition inParkinson’s disease (PD) [3]. We extract relevant features (e.g., the Q-function; see [4]) from the EEG data of PD patients and of healthy subjects performing an interval timing task [3], according to the algorithm proposed by [5]. We analyze these nonlinear dynamical features for significant differences between the groups, then perform parameter estimation andextendedKalmanfilteranalysis in the 2ndNFM to obtain a model that captures their characteristics.
Results We extended the results in [3] by analyzing the EEG signals recorded at the central leads C1 to C6. We found relevant changes in the 2-5 Hz frequency band activity for control and PD groups, like previous reports at Cz. Next, we parametrized the 2ndNFM to capture theattenuated2-5 HzrhythmsseeninPD patients, focusing on the functional coupling between a pair of leads placed on theleft (C3) and right (C4) brain hemispheres. We projected the dynamics of each 10-dimensionalsystem of differential equations perEEGchannel in 2ndNFM on a single variable via Q-function analysis [4, 5]. These projections were used for the model parameter estimation. The resulting 2ndNFM accurately fitted thepowerspectrumoftheEEGsignals at C3 and C4. Discussion To test the validity of 2ndNFMs for EEGs in an interval timing task, we performed parameter estimation using recordings at two central leads C3, C4. We also measured the performance of other methods [6] that assumed linearization of 2ndNFMs. We found them to fail to accurately fit the power spectrum of EEG signals due to nonlinear distortions. From our Kalman filter analysis, we detected anomalies in the subcortical and long-range inputs to the linear model that are inconsistent with previous assumptions of statistical independence. The nonlinear 2ndNFM parameterized on data-driven features guarantees an accurate fit for the power spectrum of EEG signals and could generate theoretical predictions.
Acknowledgements This work was funded by The Stanley-UI Foundation Support Organization (R.Curtu) and the Erwin and Peggy Kleinfeld Endowment (I.Ramsey). References 1. Cook, B.et al.(2022). Neural field models: a mathematical overview and unifying framework.Math. Neuro. and Appl., 2(2):1-67. 2. Liley, D.et al.(2002) A spatially continuous mean field theory of electrocortical activity.Network: Computation in Neural Syst., 13:67-113. 3. Singh, A.et al.(2021)https://doi.org/10.1038/s41531-021-00158-x 4. Perez-Cervera, A.et al.(2023)https://doi.org/10.1073/pnas.2303222120 5. Melland, P., & Curtu, R (2023)https://doi.org/10.1523/JNEUROSCI.1531-22.2023 6.Hartoyo, A.,et al.(2019)https://doi.org/10.1371/journal.pcbi.1006694
