A mathematical model of recurrent spreading depolarizations

Abstract

A detailed biophysical model for a neuron/astrocyte network is developed in order to explore mechanisms responsible for the initiation and propagation of recurrent cortical spreading depolarizations. The model incorporates biophysical processes not considered in the earlier models. This includes a model for the Na-glutamate transporter, which allows for a detailed description of reverse glutamate uptake. In particular, we consider the specific roles of elevated extracellular glutamate and K in the initiation, propagation and recurrence of spreading depolarizations.

Using NEURON for Reaction-Diffusion Modeling of Extracellular Dynamics

“…We consider the case of excess potassium in the ECS, which is primarily taken up by astrocytes (MacAulay and Zeuthen, 2012 ). A wide variety of modeling options are available for explicitly modeling these cells at various levels of complexity (Wei et al, 2014 ; Conte et al, 2018 ). Here we demonstrate the phenomenological model of astrocytic buffering from (Bazhenov et al, 2004 ; Krishnan and Bazhenov, 2011 ).…”

“…To produce this positive feedback between ECS and cellular physiology, we simulate a realistic density of 90,000 cells/mm 3 embedded in 1mm 3 of ECS with diffusion of both K + and Na + . Each neuron has a soma and dendrite with the Hodgkin-Huxley complement of channels (naf, kdr, gleak) as well as kleak and nap (persistent Na + channel) with parameters based on Conte et al ( 2018 ). This initial simplified model omits several mechanisms likely to contribute to spreading depolarization, including slow Ca 2+ -dependent K + currents.…”

A computational study on the role of glutamate and NMDA receptors on cortical spreading depression using a multidomain electrodiffusion model

“…Indeed, the review article [6] asserts that, at least in normoxic tissue, NMDAR activation serves as the crucial link that allows SD initiation and propagation. On the other hand, most computational models of SD do not include glutamate dynamics (but see [16]), and have often relied on the activation of persistent Na (NaP) current for SD initiation and propagation [17, 18]. Here, we incorporate glutamate dynamics into our model, and examine the relative importance of NaP and NMDAR currents in SD activation.…”

“…We further extend our model to 2D. While several detailed models have investigated recurrent SD in either 1D or 0D [16, 20], none have investigated recurrence in 2D (however, there have been phenomenological models [4]). Recurrence in 2D is significantly more complex than 1D, as the recurrence can arise from the geometry of the wave (spirals).…”

“…Glutamate dynamics and NMDAR have long been known to play an important role in SD [15, 19], but modeling in this area has been sparse [16, 17, 26]. As is well-known, NMDAR is gated both by glutamate and voltage [27], and thus serves a coincidence detector thought to play an important role in memory formation [28].…”