Accurate numerical simulation of electrodiffusion and water movement in brain tissue

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.

Reaction-diffusion models in weighted and directed connectomes

Connectomes represent comprehensive descriptions of neural connections in a nervous system to better understand and model central brain function and peripheral processing of afferent and efferent neural signals. Connectomes can be considered as a distinctive and necessary structural component alongside glial, vascular, neurochemical, and metabolic networks of the nervous systems of higher organisms that are required for the control of body functions and interaction with the environment. They are carriers of functional epiphenomena such as planning behavior and cognition, which are based on the processing of highly dynamic neural signaling patterns. In this study, we examine more detailed connectomes with edge weighting and orientation properties, in which reciprocal neuronal connections are also considered. Diffusion processes are a further necessary condition for generating dynamic bioelectric patterns in connectomes. Based on our high-precision connectome data, we investigate different diffusion-reaction models to study the propagation of dynamic concentration patterns in control and lesioned connectomes. Therefore, differential equations for modeling diffusion were combined with well-known reaction terms to allow the use of connection weights, connectivity orientation and spatial distances.

Three reaction-diffusion systems Gray-Scott, Gierer-Meinhardt and Mimura-Murray were investigated. For this purpose, implicit solvers were implemented in a numerically stable reaction-diffusion system within the framework of neuroVIISAS. The implemented reaction-diffusion systems were applied to a subconnectome which shapes the mechanosensitive pathway that is strongly affected in the multiple sclerosis demyelination disease. It was found that demyelination modeling by connectivity weight modulation changes the oscillations of the target region, i.e. the primary somatosensory cortex, of the mechanosensitive pathway.

In conclusion, a new application of reaction-diffusion systems to weighted and directed connectomes has been realized. Because the implementation were performed in the neuroVIISAS framework many possibilities for the study of dynamic reaction-diffusion processes in empirical connectomes as well as specific randomized network models are available now.

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.