Modeling and simulation of electrodiffusion in dense reconstructions of cerebral tissue

TL;DR

The paper presents a framework for simulating electrodiffusion in geometrically explicit brain tissue by coupling Kirchhoff-Nernst-Planck electrodiffusion with the Extracellular-Membrane-Intracellular model on high-resolution meshes derived from electron microscopy. It details a full computational pipeline—from dense image-based tissue reconstructions and conforming finite element meshing to operator-split time integration and a monolithic GMRES-AMG solver—validated on realistic cortical geometries and action-potential scenarios. Key contributions include the EMI-Meshing pipeline enabling geometry-aware simulations, a robust numerical strategy for solving the coupled KNP-EMI system in dense tissue, and insights into how cellular morphology shapes ion dynamics and potentials under low and high-frequency firing. The work demonstrates feasible, high-fidelity simulations of multiscale electrodiffusion in brain tissue, highlighting geometry as a critical factor and providing a platform for validating neurophysiological hypotheses and exploring pathological conditions.

Abstract

Excitable tissue is fundamental to brain function, yet its study is complicated by extreme morphological complexity and the physiological processes governing its dynamics. Consequently, detailed computational modeling of this tissue represents a formidable task, requiring both efficient numerical methods and robust implementations. Meanwhile, efficient and robust methods for image segmentation and meshing are needed to provide realistic geometries for which numerical solutions are tractable. Here, we present a computational framework that models electrodiffusion in excitable cerebral tissue, together with realistic geometries generated from electron microscopy data. To demonstrate a possible application of the framework, we simulate electrodiffusive dynamics in cerebral tissue during neuronal activity. Our results and findings highlight the numerical and computational challenges associated with modeling and simulation of electrodiffusion and other multiphysics in dense reconstructions of cerebral tissue.

Figures (14)

• Figure 1: A. The physical scales of the brain, from organ scale to subcellular scale. At the subcellular scale, ions are transported across the cellular membrane through ion channels. The ion channels illustrated on the membrane are, from left to right: open generic ion channel, $\mathrm{Na}^+/\mathrm{K^+}$-ATPase pump importing potassium ions, $\mathrm{Na}^+/\mathrm{K^+}$-ATPase pump exporting sodium ions, and a closed generic ion channel. The illustrations in this panel were created using https://BioRender.com/gc2jbqv. B. Plane illumination microscopy of macaque primary motor cortex tissue at centimeter scale glaser2025expansionC. Confocal microscopy image of a neuron (green) in rodent visual cortex tissue. Image spans half a millimeter lee2006dynamic. D. Light-microscopy based reconstructed cross section of mouse hippocampus tissue at the micrometer scale tavakoli2025light. E. 3D rendering of mouse hippocampus tissue, scale bar 3 $\mu$m tavakoli2025light. The images in panels B--E are reproduced under the terms of the https://creativecommons.org/licenses/by/4.0/.
• Figure 2: Illustration of the computational meshing pipeline. Segmented electron microscopy image data, here shown in the MICrONS explorer interface microns2025functional, is downloaded and processed into a voxel data array. The voxel data is next converted into triangulated surfaces representing the interfaces between the biological cells and extracellular space. These surfaces go through a sequence of morphological processing steps to ensure sufficient mesh quality downstream. Finally, a tetrahedral mesh is generated conforming to the interface surfaces.
• Figure 3: A sample of the computational meshes generated using the EMI-Meshing pipeline Causemann2024EMIMeshing of size $L \times L \times L$ containing $N$ biological cells surrounded by extracellular space.
• Figure 4: Statistics of cellular geometries of mouse visual cortex tissue. (A) Total number of computational cells in the mesh. (B) Total number of mesh vertices. (C) The ratio of total number of membrane vertices to total number of mesh vertices. (D) Percentage of the total mesh volume that is occupied by extracellular space. Common legend for all subfigures.
• Figure 5: Conceptual illustration of the geometry and meshes. Left: idealized geometry, illustrating the intracellular ($\Omega_i$) and extracellular ($\Omega_e$) spaces separated by a membrane $\Gamma$. The boundary of the domain is $\partial\Omega$. Right: The degree of freedom layout of the idealized cellular geometry when discretized with linear continuous Lagrange elements. The function spaces $V_i(\Omega_i)$ and $V_e(\Omega_e)$ share the degrees of freedom on $\Gamma$.