Consistent spectral predictors for dynamic causal models of steady-state responses.

Area of Science:

• Computational neuroscience
• Systems neuroscience
• Electrophysiology

Background:

• Dynamic Causal Modelling (DCM) for steady-state responses (SSR) infers mechanisms from electrophysiological spectra using generative models.
• Nonlinear conductance-based neural population models exhibit complex dynamics and phase transitions.

Purpose of the Study:

• To propose a generative model for power spectra of nonlinear neural population dynamics.
• To characterize phase transitions in neural population models and their spectral characteristics.
• To develop a predictor for spectral activity enabling gradient-based model inversion.

Main Methods:

• Developed a nonlinear Fokker-Planck model for interconnected excitatory and inhibitory neural populations.
• Explored mean-field and neural-mass formulations for neuronal state interactions.
• Utilized centre manifold theory and linear stability analysis to predict spectral activity.
• Employed gradient descent for inverting generative models using simulated data with phase transitions.

Main Results:

• The model reproduced spectral characteristics (2-100 Hz) of real electrophysiological data through fixed points and quasiperiodic dynamics.
• Phase transitions in neural dynamics were numerically characterized.
• A novel predictor for spectral activity demonstrated consistent behavior near phase transitions.
• Successful inversion of generative models (DCMs) for SSRs was achieved using simulated data.

Conclusions:

• The proposed generative model and spectral predictor offer a robust framework for analyzing neuronal dynamics and phase transitions.
• This approach facilitates gradient descent-based inversion, advancing the application of DCM for SSRs.
• The findings provide a powerful tool for inferring neural mechanisms from electrophysiological data, particularly in regions of dynamic change.