Neural Field Modelling of Cortico-Hippocampal Interactions

Understanding the complex dynamics of cortico-hippocampal interactions is essential for exploring cognitive processes and their disruptions in neurological disorders. This section of the educational course provides a practical introduction to neural field modeling, focusing on the cortico-hippocampal interactions. More specifically, we focus on how to derive and apply eigenmodes—a mathematical framework that captures the intrinsic oscillatory patterns of any geometric surface.

To achieve this, we go through a step-by-step implementation of the following:

1 - Preparing Anatomical Surfaces
We begin by learning techniques to import and preprocess 2-D anatomical meshes of cortical and hippocampal surfaces. Preprocessing would involve ensuring a smooth medial wall boundary for the cortical mesh and a smooth outer boundary for the hippocampal mesh.

2 - Computing Eigenmodes for Spatial Activity Patterns
Eigenmodes will be computed by solving the Helmholtz equation for the cortical and hippocampal meshes. Hands-on exercises will be provided, covering eigenmode computation, visualization, and decomposition of neural activity.

3 - Integrating Eigenmodes into the Neural Field Theory Framework

After the first two steps, we will integrate eigenmodes into the Neural Field Theory (NFT) framework by decomposing cortical and the hippocampal NFT equations into eigenmode domain. We will briefly detail the mathematical steps to transform NFT equations into eigenmode-specific dynamics, including the derivation of temporal evolution equations for each eigenmode. With these equations, we will simulate the spatio-temporal dynamics of eigenmode evolution on these surfaces. Some of these dynamical behaviours involve looking at mode-mixing, and pathological states (e.g., epileptogenic activity) using hands-on examples. The specific effects of a proximity preserving coupling between cortical and hippocampal surfaces on the dynamics across these two surfaces would be subsequently discussed.

In summary, this section of the course will bridge theoretical concepts with practical, hands-on techniques, equipping attendees with tools to model and interpret cortico-hippocampal dynamics.