Theoretical Models of Neurovascular Coupling: Role of Potassium Ions

Abstract

The brain is a highly energetic organ that lacks an energy storage system and is dependent on continuous blood flow to provide oxygen and other nutrients needed for normal function. Local blood flow increases in response to neuronal activity, a phenomenon known as neurovascular coupling (NVC). In this response, active neurons send a signal to local capillaries, which in turn send a signal to upstream arterioles. The arterioles then dilate and increase blood flow specifically to the active area. While NVC has been studied extensively and multiple mechanisms have been proposed, the mechanisms regulating NVC remain incompletely understood. One potential mechanism is the diffusion of potassium ions released by neurons during activity through the extracellular space (ECS) to the capillaries. Changes in extracellular potassium concentration have been shown to cause changes in inward-rectifying potassium (KIR) channel conductance. As extracellular potassium concentration increases, KIR channel conductance increases, causing hyperpolarization of endothelial cells. The change in membrane potential can passively spread through the endothelial cells to arterioles via gap junctions in what is known as a conducted response. Testing this hypothesized mechanism experimentally with quantifiable results is technically difficult, due to the need to measure potassium concentrations in the ECS with high spatial and temporal resolution.Mathematical modeling of the proposed mechanism provides a means to predict changes in potassium concentration and membrane potentials with position and time, and thereby to test this hypothesis. To this end, mathematical models were created to analyze (i) changes in potassium concentration due to uptake and release of potassium by cells in the brain; (ii) the time course of diffusion of potassium in the ECS, including effects due to electrodiffusion; (iii) how geometry of brain microanatomy affects the rate of diffusion and maximum potassium concentration; and (iv) the spread and strength of the conducted response in a reconstructed vascular network. Model results show that diffusion of potassium to blood vessels can occur rapidly, within experimentally observed time frames of NVC, and that the potassium concentration at the blood vessels reaches levels sufficient to initiate a conducted response. Astrocytes in the brain have projections called endfeet that almost cover the outer surface of capillaries, potentially blocking diffusion of potassium. Results of models of astrocyte geometry suggest that these endfeet have small impact on the rate of diffusion and the maximum potassium concentration experienced by capillaries. The simulated spread of conducted responses in the reconstructed vascular network shows a dependence on the relative conductance of gap junctions in the upstream and downstream directions. Results are consistent with the proposed mechanism, in which potassium ions released by firing neurons diffuse through the ECS, reach the capillaries, and initiate conducted responses that spread upstream to arterioles. A brief discussion of the potential role of signaling by astrocytes in NVC is also provided.