Macro scale modelling of cortical spreading depression and the role of astrocytic gap junctions

Neuronal activity evokes a localised increase in cerebral blood flow in a response known as neurovascular coupling (NVC), achieved through communication between a group of cells known as a neurovascular unit (NVU). Dysfunctional NVC can lead to pathologies such as cortical spreading depression (CSD), characterised by a slow moving wave of neuronal depolarisation and high extracellular K+ levels. This phenomenon can be affected by the presence of an astrocytic gap junction network which is able to transport K+ away from areas of high concentrations, however the precise role of these gap junctions remains controversial. In this study, a large scale numerical NVC model of a vascular tree coupled with multiple NVUs comprising a two-dimensional cerebral tissue slice is extended through extracellular K+ and Na+ electrodiffusion and K+ transport via an astrocytic gap junction network. An updated NVU model has been utilised that contains complex neuronal and extracellular dynamics and is able to simulate various pathologies such as CSD and the effect on the vascular response. Under pathological conditions (determined by model parameters) and with extracellular electrodiffusion the model is able to simulate a propagating wave of high extracellular K+ travelling at 6.7 mm/min as can occur in CSD. This wave travels outward from the neuronally stimulated area and is followed by a wave of vasoconstriction (with corresponding decreased blood flow) then slight vasodilation in agreement with multiple experimental results. The vasoconstrictive wave peaks after the K+ wave due to the delayed vascular response. Increasing the density of astrocytic gap junctions reduces the duration and amplitude of the vasoconstrictive wave and for high enough density the vasoconstrictive behaviour outside the stimulated area is eliminated. Gap junctions also reduce the area that is initially affected by vasoconstriction. This in silico model provides a complex and experimentally validated test bed for a variety of neurological phenomena.