Quantifying the relationship between spreading depolarization and the glymphatic system

Spreading depolarization (SD) is an electro-chemical wave that propagates through the brain cortex due to ionic imbalances in the neurons following stroke, migraine, and traumatic brain injury (TBI). It has been recently discovered that SD leads to a large increase in cerebrospinal fluid (CSF) influx into the brain, which contributes to edema following stroke and TBI. We develop a novel computational model that couples SD and CSF fluid flow through perivascular spaces (PVSs) in the brain. PVSs are CSF-filled annular channels that line the brain's vasculature. We first use high order numerical simulations to solve a system of physiologically realistic reaction-diffusion equations which govern the spatiotemporal dynamics of K⁺ and Na⁺ ions in the extracellular and intracellular spaces of the brain cortex during SD. We then couple the SD wave with a 1D CSF flow model that captures the change of volume flow rate, pressure, and cross-sectional area of the PVSs. The coupling is modelled using an empirical relationship between K⁺ concentration in the extracellular space (which increases following SD) and vessel radius (which forms the inner boundary of the PVSs). We find that the CSF volume flow rate depends on the wavelength and wave speed of SD, as well as the domain size and width of the PVS. We also quantify the peak pressures and volume flow rates obtained when two SD waves collide. Our numerical approach is very general and offers novel, quantitative insights into pathological conditions which involve different forms of coupling between SD and CSF flow in the brain.