Probabilistic delay differential equation modeling of event-related potentials

Area of Science:

• Neuroscience
• Computational Neuroscience
• Cognitive Neuroscience

Background:

• Dynamic Causal Models (DCMs) offer biophysical interpretability for neuroimaging data analysis.
• Electroencephalography-DCM (ERP-DCM) integrates neural mass models with EEG forward models for scalp potential analysis.
• Existing ERP-DCM literature is fragmented, lacking a unified technical documentation.

Purpose of the Study:

• To provide a unified and coherent review of the mathematical machinery of ERP-DCM.
• To increase the technical accessibility of the ERP-DCM framework.
• To detail and validate the model estimation, focusing on variational free energy.

Main Methods:

• Formulation of ERP-DCM as a probabilistic latent delay differential equation model.
• Explicit derivation of the variational free energy function for Bayesian inversion.
• Application of a nonlinear optimization scheme for model parameter estimation.

Main Results:

• A unified mathematical framework for ERP-DCM is presented.
• The probabilistic nature and variational Bayesian inversion are emphasized and derived.
• Model estimation is detailed and validated, highlighting the variational free energy function.

Conclusions:

• This note enhances the technical accessibility of ERP-DCM.
• The unified framework facilitates a deeper understanding of neural underpinnings of cognitive phenomena.
• Future work should address identified computational challenges in ERP-DCM.