P056 A numerical simulation of neural fields on curved geometries
Neekar Mohammed, David J. Chappell,Jonathan J. Crofts* Department of Physics and Mathematics, Nottingham Trent University, Nottingham, UK
*Email: jonathan.crofts@ntu.ac.uk
Introduction Brainwaves are crucial for information processing, storage, and sharing [1]. While a plethora of computational studies exist, the mechanisms behind their propagation remain unclear. Current models often simplify the cortex as a flat surface, ignoring its complex geometry [2]. In this study, we incorporate realistic brain geometry and connectivity into simulations to investigate how brain morphology influences wave propagation. Our goal is to leverage this approach to elucidate the relationship between increasing mammalian brain convolution, brain evolution, and its consequential impact on cognition.
Methods To achieve efficient modelling of large-scale cortical structures, we have extended isogeometric analysis (IGA) [3], a powerful tool for physics-based engineering simulations, to the complex nonlinear integro-differential equation models found in neural field models. IGA utilises non-uniform rational B-splines (NURBS), the standard for geometry representation in computer-aided design, to approximate solutions. Specifically, we will employ isogeometric collocation (IGA-C) methods, leveraging the high accuracy of NURBS with the computational efficiency of collocation. While IGA-C has proven effective for linear integral equations in mechanics and acoustics, its application to nonlinear NFMs represents a significant advancement. Results To enable more realistic brain simulations, we have developed a novel IGA-C method that directly utilises point cloud data and bypasses triangular mesh generation, allowing for the solution of partial integro-differential equation models of neural activity on complex cortical-like domains. Here, we demonstrate the method's capabilities by studying both localised and traveling wave activity patterns in a two-dimensional neural field model on a torus [4]. The model offers a significant computational advantage over standard mesh-dependent methods and, more importantly, provides a crucial framework for future research into the role of cortical geometry in shaping neural activity patterns via its ability to incorporate complex geometries. Discussion This work presents a novel numerical procedure for integrating neural field models on arbitrary two-dimensional surfaces, enabling the study of physiologically realistic systems. This includes, for example, accurate cortical geometries and connectivity functions that capture regional heterogeneity. Future research will focus on elucidating the influence of curvature on the nucleation and propagation of travelling wave solutions on cortical geometries derived from imaging studies.
Acknowledgements NM, DJC and JJC were supported through the Leverhulme Trust research project grant RPG-2024-114 References 1.https://doi.org/10.1038/nrn.2018.20 2.https://doi.org/10.1007/s00422-005-0574-y 3.https://doi.org/10.1016/j.cma.2004.10.008 4.https://doi.org/10.1007/s10827-018-0697-5
