Finite Element Simulation of Ionic Electrodiffusion in Cellular Geometries

Area of Science:

• Computational neuroscience
• Mathematical biology
• Biophysics

Background:

• Cable theory models homogenize domains and assume constant ionic concentrations, limiting their ability to capture effects of altered ion concentrations or detailed cell morphology on electrical potentials.
• Existing models struggle to represent the complex interplay between ion dynamics, cell geometry, and electrical signaling in neural tissue.

Purpose of the Study:

• To introduce and numerically evaluate a novel mathematical model, the KNP-EMI model, for detailed electrodiffusion in neural tissue.
• To develop and assess a new finite element-based numerical scheme for the KNP-EMI model.
• To investigate the impact of detailed morphology and ion concentrations on electrical potentials and ephaptic coupling.

Main Methods:

• Developed the KNP-EMI model by combining the electroneutral Kirchhoff-Nernst-Planck (KNP) model with the Extracellular-Membrane-Intracellular (EMI) framework.
• Implemented a new, finite element-based numerical scheme for the KNP-EMI model, designed for arbitrary dimensions and polynomial degrees.
• Compared KNP-EMI model predictions with the EMI model and studied ephaptic coupling in unmyelinated axon bundles.

Main Results:

• The KNP-EMI model successfully describes ion concentration distribution and evolution in geometrically explicit intra- and extracellular domains.
• The finite element scheme efficiently handles complex geometries and provides accurate numerical evaluations.
• The KNP-EMI model offers new insights into ephaptic coupling in unmyelinated axon bundles, which are not captured by simpler models.

Conclusions:

• The KNP-EMI model provides a more comprehensive approach to modeling electrodiffusion in neural tissue by incorporating detailed geometry and ion dynamics.
• The developed finite element method offers a flexible and efficient computational tool for simulating complex biological systems.
• This framework enhances our understanding of electrical signaling and interactions, such as ephaptic coupling, in neural environments.