Extracellular reaction–diffusion in the NEURON simulator: modeling ischemic stroke

The NEURON simulation platform, featured in over 1900 publications, traditionally focused on models of neurons and networks of neurons. NEURON's reaction–diffusion module (rxd) expanded support for 1D and 3D intracellular reaction–diffusion models [1]. This has been used to probe intracellular calcium dynamics in both physiological and pathological conditions. Originally rxd provided only limited extracellular support with an isolated space around each segment. We have extendedrxdto include coarse-grained macroscopic models of the extracellular space [2]. NEURON thus allows detailed neuron models to be embedded in a 3D macroscopic model of tissue. Extracellular diffusion is implemented using the Douglas-Gunn alternating direction implicit method, an efficient scheme which supports parallelization. Reactions are now implemented using Just-In-Time compilation, allowing numerical integration to use faster compiled code rather than slow interpreted code. The macroscopic tissue model is based on a volume averaging approach, allowing the user to specify both the free volume fraction (the proportion of space in which species are able to diffuse) and the tortuosity (the average multiplicative increase in path length due to obstacles). These tissue characteristics can be spatially dependent enabling the modeler to account for differences in brain region or pathological effects of injury. We applied the rxd simulation framework to develop a model of ischemic stroke, which required multiscale coupling of electrophysiology with intracellular molecular alterations, and consideration of network properties in the context of bulk tissue alterations mediated by extracellular diffusion [3]. We initially modeled spreading depression triggered by elevated potassium in a cube of tissue (Fig. 1). Occlusion of a blood vessel in the brain triggers a cascade of changes, including: (1) synaptic glutamate release, related to excitotoxicity; (2) elevated extracellular potassium, leading to spreading depression; (3) cell swelling, reducing the extracellular volume and increasing the tortuosity; (4) production of reactive oxygen species, which give rise to inflammation. These cascades occur over multiple time-scales, with the initial rapid changes in cell metabolism and ionic concentrations triggering several damaging agents that may ultimately lead to cell death.Fig. 1Spreading depression in a 1 cubic mm of tissue at 10, 20 and 30 s with 50,000 two compartment (soma, dendrite) neurons. (a) Extracellular potassium (b) Buffered concentration (based on a simple model of astrocyte buffering as an extracellular reaction) (c) The membrane potential of 1000 of the 50,000 neurons (positions shown in white in a & b)