The effects of cerebral curvature on cortical spreading depression

Neuronal activity evokes a localised increase in cerebral blood flow through neurovascular coupling (NVC), a communication system 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 slowly propagating wave of neuronal depolarisation and high extracellular potassium (K⁺) levels. CSD is associated with several neurological disorders such as migraine, stroke, and traumatic brain injury. Insight into the spatial dynamics of CSD in humans is mainly deduced from animal experiments on the smooth lissencephalic brain (in particular murine experiments), however the human cortex is gyrencephalic (highly folded) and is considered likely to exhibit different and more complex patterns of CSD. In this study a large scale numerical NVC model of multiple NVUs is coupled to a vascular tree simulating a two-dimensional cerebral tissue slice. This model is extended with a spatial Gaussian curvature mapping that can simulate the highly folded nature of the human cortex. For a flat surface comparable to a lissencephalic cortex the model can simulate propagating waves of high extracellular K⁺ travelling radially outwards from a stimulated area at approximately 6.7 mm/min, corresponding well with multiple experimental results. The high K⁺ concentration induces a corresponding wave of vasoconstriction (with decreased blood flow) then slight vasodilation, achieved through cellular communication within the NVU. The BOLD response decreases below baseline by approximately 10% followed by an increase of 1%. For a surface with spatially varied curvature comparable to a section of gyrencephalic cortex, areas of positive Gaussian curvature inhibit wave propagation due to decreased extracellular diffusion rate. Whereas areas of negative curvature promote propagation. Consequently extracellular K⁺ is observed travelling as wave segments (as opposed to radial waves) through flat or negatively curved "valleys" corresponding to folds (sulci) in the cortex. If the wave size (defined as the activated area of high K⁺ concentration) is too small or diffusion rate too low then wave segments can cease propagation. If the diffusion rate is high enough the wave segments can grow from open ends forming loose spiral waves. These results may provide some insight into the differences seen between human and animal experiments.