Theoretical Model of Extracellular Potassium Diffusion as a Signaling Mechanism in Neurovascular Coupling

Abstract

Neurovascular coupling (NVC) is the process by which neuronal activity causes changes in cerebral blood flow within seconds of the onset of activity. The goal of this study is to explore the potential role of extracellular K+ diffusion as a mechanism for NVC. A mathematical model is used to simulate K+ kinetics in the extracellular space (ECS), including effects of K+release during neuronal activity, K+ uptake by astrocytic and neuronal Na+/K+ ATPase, and K+ diffusion in the ECS. The model consists of a partial differential equation in time and one spatial dimension. Parameter values are derived from experimental literature or from previous models. The effective K+ diffusivity is 937.5 μm2/s. Astrocytic and neuronal K+ uptake is assumed to have Michaelis‐Menten kinetics with maximum rate 84.7 mM/s and Michaelis constant 1.5 mM. The average distance from a neuron to the closest microvessel is 15 μm. A domain of length 15 μm is therefore assumed, with one end representing the neuron and the other the blood vessel. At rest, ECS K+ concentration is 3 mM. One spike is estimated to change the extracellular K+ concentration by 0.11 mM from rest. The neuron is assumed to fire continuously for 10 s at 100 Hz. Equilibrium values of K+ in the ECS are reached within 10 s, with values of 11 mM at the neuron and 9.6 mM at the vessel. The increase in extracellular K+ concentration at the vessel lags approximately 0.3 s behind the increase at the neuron. These results suggest that K+ diffuses fast enough to the vasculature to be a signal for NVC. Although uptake of K+ by Na+/K+ ATPase limits the concentration that reaches the vasculature, the increase in K+ concentration around the vasculature is sufficient to elicit a vascular response. Limitations of the model are that a simplified, one‐dimensional geometry is assumed and possible effects of K+ release at astrocytic endfeet are not included.