Neural activity induces strongly coupled electro-chemo-mechanical interactions and fluid flow in astrocyte networks and extracellular space-A computational study.

The complex interplay between chemical, electrical, and mechanical factors is fundamental to the function and homeostasis of the brain, but the effect of electrochemical gradients on brain interstitial fluid flow, solute transport, and clearance remains poorly quantified. Here, via in-silico experiments based on biophysical modeling, we estimate water movement across astrocyte cell membranes, within astrocyte networks, and within the extracellular space (ECS) induced by neuronal activity, and quantify the relative role of different forces (osmotic, hydrostatic, and electrical) on transport and fluid flow under such conditions. We find that neuronal activity alone may induce intracellular fluid velocities in astrocyte networks of up to 14µm/min, and fluid velocities in the ECS of similar magnitude. These velocities are dominated by an osmotic contribution in the intracellular compartment; without it, the estimated fluid velocities drop by a factor of ×34-45. Further, the compartmental fluid flow has a pronounced effect on transport: advection accelerates ionic transport within astrocytic networks by a factor of ×1-5 compared to diffusion alone.

Validating a Computational Framework for Ionic Electrodiffusion with Cortical Spreading Depression as a Case Study.

Cortical spreading depression (CSD) is a wave of pronounced depolarization of brain tissue accompanied by substantial shifts in ionic concentrations and cellular swelling. Here, we validate a computational framework for modeling electrical potentials, ionic movement, and cellular swelling in brain tissue during CSD. We consider different model variations representing wild-type (WT) or knock-out/knock-down mice and systematically compare the numerical results with reports from a selection of experimental studies. We find that the data for several CSD hallmarks obtained computationally, including wave propagation speed, direct current shift duration, peak in extracellular K+ concentration as well as a pronounced shrinkage of extracellular space (ECS) are well in line with what has previously been observed experimentally. Further, we assess how key model parameters including cellular diffusivity, structural ratios, membrane water and/or K+ permeabilities affect the set of CSD characteristics.

Accurate numerical simulation of electrodiffusion and water movement in brain tissue.

Mathematical modelling of ionic electrodiffusion and water movement is emerging as a powerful avenue of investigation to provide a new physiological insight into brain homeostasis. However, in order to provide solid answers and resolve controversies, the accuracy of the predictions is essential. Ionic electrodiffusion models typically comprise non-trivial systems of non-linear and highly coupled partial and ordinary differential equations that govern phenomena on disparate time scales. Here, we study numerical challenges related to approximating these systems. We consider a homogenized model for electrodiffusion and osmosis in brain tissue and present and evaluate different associated finite element-based splitting schemes in terms of their numerical properties, including accuracy, convergence and computational efficiency for both idealized scenarios and for the physiologically relevant setting of cortical spreading depression (CSD). We find that the schemes display optimal convergence rates in space for problems with smooth manufactured solutions. However, the physiological CSD setting is challenging: we find that the accurate computation of CSD wave characteristics (wave speed and wave width) requires a very fine spatial and fine temporal resolution.

Finite Element Simulation of Ionic Electrodiffusion in Cellular Geometries.

Mathematical models for excitable cells are commonly based on cable theory, which considers a homogenized domain and spatially constant ionic concentrations. Although such models provide valuable insight, the effect of altered ion concentrations or detailed cell morphology on the electrical potentials cannot be captured. In this paper, we discuss an alternative approach to detailed modeling of electrodiffusion in neural tissue. The mathematical model describes the distribution and evolution of ion concentrations in a geometrically-explicit representation of the intra- and extracellular domains. As a combination of the electroneutral Kirchhoff-Nernst-Planck (KNP) model and the Extracellular-Membrane-Intracellular (EMI) framework, we refer to this model as the KNP-EMI model. Here, we introduce and numerically evaluate a new, finite element-based numerical scheme for the KNP-EMI model, capable of efficiently and flexibly handling geometries of arbitrary dimension and arbitrary polynomial degree. Moreover, we compare the electrical potentials predicted by the KNP-EMI and EMI models. Finally, we study ephaptic coupling induced in an unmyelinated axon bundle and demonstrate how the KNP-EMI framework can give new insights in this setting.