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  • br Discussion The model of a

    2022-06-29


    Discussion The model of a NVU described by Mathias et al. (2018) has been implemented on the macro scale (see Kenny et al. (2018b)) via a 2D cerebral tissue slice coupled to a vascular tree. In particular, further communication within the tissue slice has been implemented via extracellular ion electrodiffusion and astrocytic gap junctions. This state of the art model is able to simulate spatial phenomena such as CSD and astrocytic spatial buffering in a 2D tissue slice while also containing the full complex dynamics and multiple pathways of the NVU. Under pathological conditions our model shows that with extracellular electrodiffusion the medium (i.e. the ECS) is excitable and able to sustain a propagating K wave that travels at approximately 6.7 mm/min (based on block length of 124 µm); experiments usually show a velocity of around 2-5 mm/min (Ayata and Lauritzen, 2015) and our model estimate is considered within the bounds of experimental uncertainty. When using normal Fickian GNE-317 rather than electrodiffusion in the ECS, the medium is subexcitable and the wave of extracellular K is not able to travel further than two blocks in the tissue slice. This result still holds when both the stimulation area and duration are increased (results not shown). In our model, during CSD we observe a rise in extracellular K concentration and the vessel radius undergoes vasoconstriction followed by slight vasodilation in the absence of an astrocytic gap junction network. These results can be compared with the work of Chang et al. (2013) who utilised a simpler model containing a neuron, ECS and the vessel radius dynamics but did not include the astrocyte, SMC or EC compartments. They observed qualitatively similar results, namely a rise in extracellular K with vasoconstriction followed by vasodilation. The majority of CSD models do not consider the vascular dynamics so it is difficult to compare our results with a variety of other numerical models, however numerous experimental studies Cameron and Caronna (1976); Edwards et al. (1988); Golding et al. (2000); Kuschinsky et al. (1972); McCarron and Halpern (1990) have documented that small increases in extracellular K concentration can lead to vasodilation and high concentrations lead to vasoconstriction further supporting our results. Pathologies such as CSD can occur when the regulation of K via astrocytic gap junctions fails (Wallraff, 2006). Our model results support this fact, showing that when gap junctions are not present a neuronal stimulus during pathological conditions leads to vasoconstriction in both the stimulated area and in the area surrounding it via a propagating wave, with a corresponding decrease in blood flow through the vascular tree. The vasoconstrictive wave peaks after the extracellular K wave due to the delayed vascular response. However with astrocytic gap junctions the vasoconstrictive behaviour is unable to spread, instead inducing slight vasodilation outside the stimulation area (although the extracellular K still propagates as with the case without gap junctions) and the constriction remains localised. In addition the gap junctions are able to reduce the size of the initial area that is negatively affected by vasoconstriction by transporting astrocytic K outwards. CSD can be initiated experimentally by a number of methods: chemically, via direct application of depolarising substances such as concentrated KCl or NMDA glutamate receptor agonists; electrically, via direct tissue stimulation; or mechanically via pinprick, ultrasound or laser (Ayata and Lauritzen, 2015). In our model we observe a wave of high extracellular K concentration travelling outwards from the stimulation area which induces vasoconstriction (followed by slight vasodilation) in and around the stimulation area. This behaviour agrees with the experiment performed by Chen et al. (2006) as seen in Fig. 9. They used optical reflectance imaging to obtain high resolution images of CSD waves based on changes in blood perfusion. A normal rat cortex was induced by a pinprick, resulting in a wave of decreased perfusion (i.e. vasoconstriction) that propagated radially outward from the point of origin regardless of functional or vascular territories. This was followed by hyperperfusion (i.e. vasodilation) then a slow return to normal values. The wave travelled at approximately 5 mm/min which is comparable with the velocity of 6.7 mm/min found in our model simulations. Similar results were found in the experiment of Tomita et al. (2002) who induced CSD via a concentrated KCl solution microinjected into both rat and cat cortex.