Multidomain Model for Optic Nerve Potassium Clearance: Roles of Glial Cells and Perivascular Spaces

Abstract

The accumulation of potassium in the extracellular space surrounding nerve cells is a fundamental aspect of biophysics that has garnered significant attention in recent research. This phenomenon holds implications for various neurological conditions, including spreading depression, migraine, certain types of epilepsy, and potentially, learning processes. A quantitative analysis is essential for understanding the dynamics of potassium clearance following a series of action potentials. This clearance process involves multiple structures along the nerve, including glia, the extracellular space, axons, and the perivascular space, necessitating a spatially distributed systems approach akin to the cable equations of nerve physiology. In this study, we propose a multi-domain model for the optic nerve to investigate potassium accumulation and clearance dynamics. The model accounts for the convection, diffusion, and electrical migration of fluid and ions, revealing the significant roles of glia and the perivascular space in potassium buffering. Specifically, our findings suggest that potassium clearance primarily occurs through convective flow within the syncytia of glia, driven by osmotic pressure differences. Additionally, the perivascular space serves as a crucial pathway for potassium buffering and fluid circulation, further contributing to the overall clearance process. Importantly, our model's adaptability allows for its application to diverse structures with distinct channel and transporter distributions across the six compartments, extending its utility beyond the optic nerve.

Figures (29)

• Figure 1: Optic nerve structure. (a) Longitudinal section of the optic nerve; (b) cross section of the optic nerve.
• Figure 2: The optic nerve $\Omega_{OP}$ consists of axon compartment, glial compartment, extracellular space, perivascular space. The subarachnoid space $\Omega_{SAS}$ only has cerebrospinal fluid.
• Figure 3: In the optic nerve $\Omega_{OP}$ region, the ECS exchanges fluid and ions with the axon, glial, the pvsA, the pvsV and the pvsC; glial exchanges fluid and ion with the ECS, the pvsA, the pvsV and the pvsC; CSF exchanges fluid and ions with the ECS, the pvsA, the pvsV, and the pvsC by across the pia mater in $\Gamma_{7}$, see Fig. \ref{['fig:Op_structure_model']}.
• Figure 4: Stimulated and non-stimulated regions in the optic nerve ($\Omega_{OP}$). The stimulus is applied to the axon membrane within the region $R_{a}<r<r_{sti}$ at a specified location $z=z_{0}$.
• Figure 5: Numerical results. Panels a-h: Average transmembrane ion flux in the stimulated region. Panels i-l: Average sum of all ion transmembrane source terms for each compartment, with positive values indicating increased osmotic concentration and negative values indicating decreased osmotic concentration.