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  • Experiments show that CSD propagation

    2022-01-26

    Experiments show that CSD propagation can be slowed or interrupted by pre-existing lesions or areas of high astrocytic density (Chen et al., 2006), and reduced expression of astrocytic gap junctions significantly increases the size of ischemic infarcts (Nakase et al., 2003). By decreasing the gap junction diffusion rate to 20% of its original value (in order to simulate reduced gap junction density) we observed a propagating wave of slight vasoconstriction shortly followed by slight vasodilation, whereas with reduced to 40% of its original value we observed only slight vasodilation. This suggests that increasing astrocytic density or gap junction expression reduces the duration of the vasoconstrictive wave prior to vasodilation, and for high enough density (over 40%) the vasoconstrictive behaviour outside of the stimulation area is eliminated. By increasing the extracellular electrodiffusion rates D and D we can increase the velocity and wave width of the propagating K wavefront, as the area in front of the wave takes less time to reach the excitation threshold. Whereas decreasing the diffusion rates by 5% produced a propagating K wave that is subexcitable and dies after propagating through a few blocks. Decreasing the diffusion rates further resulted in a nonexcitable medium where an extracellular K wave could not propagate at all (results not shown).
    Limitations and future work Different diffusion rates can occur physiologically as they depend on the tortuosity of the ECS (which can vary) (Nicholson et al., 2008), and they can also change depending on the curvature of the medium (Kenny, David, Plank, 2016, Kneer, Schöll, Dahlem, 2014). Areas of negative curvature (e.g. a concave lens) have a higher diffusion rate, whereas areas of positive curvature (e.g. a convex lens) have a lower diffusion rate. The orexin receptor is composed of tightly folded grey matter and as such contains areas of strongly negative and positive curvature. Hence it is possible to simulate the effect of curvature on CSD propagation by spatially varying the extracellular diffusion rates, creating areas of propagation and cessation; this is an area for possible future research. The large K efflux from the neuron into the ECS that occurs during CSD is reciprocated by Na and Cl influx that also pulls in water, leading to neuronal swelling and in turn decreases the volume of the ECS (Ayata and Lauritzen, 2015). In our model the volume ratio of the ECS to the neuron is given by the parameter taken from the model of Kager et al. (2000). During CSD neuronal swelling is observed leading to a decreased volume ratio of 0.05 (Jing et al., 1994). In our model decreasing the parameter to 0.05 amplifies extracellular K changes, meaning the K concentration reaches a higher peak and decreases more quickly following stimulation, but does not qualitatively alter the behaviour. However in reality the volume ratio would not be constant, instead decreasing during the CSD wave as the neurons swell then returning to baseline following the wave. Hence to further study the effects of cell swelling on CSD would require dynamic rather than constant volumes, and is an area of possible future research. Astrocytic gap junctions are generally known to aid in spatial buffering, where astrocytes take up large amounts of K from the ECS and move it away via gap junctions with neighbouring astrocytes (Bellot-Saez et al., 2017). In our simulations the astrocytic K does spread out from the stimulated area via gap junctions, but this has little effect on the extracellular K as there is no direct link between the astrocyte and ECS present in our model. Instead there are multiple channels and pumps connecting the astrocyte with the synaptic cleft, modelled as a subspace of the ECS. Rather than affecting the extracellular K directly, the decrease in astrocytic K lowers the perivascular K concentration leading to slight vasodilation rather than vasoconstriction. This behaviour is not directly predicted by experiments, although to date no study has fully described the relative contribution of gap junctions to the phenomenon of CSD (Rovegno and Sáez, 2018). KIR channels are highly expressed on astrocytic endfeet adjacent to the synaptic cleft, and K channels, Na/K/2Cl transporters and Na/K ATPase pumps are also expressed on astrocytes (Dallérac, Chever, Rouach, 2013, Higashi, Fujita, Inanobe, Tanemoto, Doi, Kubo, Kurachi, 2001). These channels and pumps may provide further uptake of K+ from the ECS and their inclusion in the model is a possible area of future research.