A control mechanism for intra-mural peri-arterial drainage via astrocytes: How neuronal activity could improve waste clearance from the brain

Abstract

The mechanisms behind the clearance of soluble waste from deep within the parenchyma of the brain remain unclear. Experimental evidence reveals that one pathway for clearance of waste, termed intra-mural peri-arterial drainage (IPAD), is the rapid drainage of interstitial fluid along basement membranes (BM) of the smooth muscle cells of cerebral arteries; failure of IPAD is closely associated with the pathology of Alzheimer's disease (AD), but its driving mechanism remains unclear. We have previously shown that arterial pulsations generated by the heart beat are not strong enough to drive IPAD. Here we present computational evidence for a mechanism for clearance of waste from the brain that is driven by functional hyperaemia, that is, the dilatation of cerebral arterioles as a consequence of increased nutrient demand from neurons. This mechanism is based on our model for the flow of fluid through the vascular BM. It accounts for clearance rates observed in mouse experiments, and aligns with pathological observations and recommendations to lower the individual risk of AD, such as mental and physical activity. Thus, our neurovascular hypothesis should act as the new working hypothesis for the driving force behind IPAD.

Fig 1. Schematic diagram of a cross-section of a cerebral artery demonstrating the geometry and location of the IPAD pathway.

The artery lumen is surrounded by an endothelium (yellow), which forms a BM (dark green). Several layers of SMC, which express their own type of BM (light green) surround the artery. A pial or leptomeningeal sheath (pink), which is derived from the pia mater, surrounds the outside of the artery. Arteries are covered tightly by astrocyte end-feet (grey), forming the pial-glial BM (glia limitans) [11, 14, 15].

Fig 2. Effect of the release of K⁺ and Glu into the synaptic space of a neuron and an astrocyte process.

Glu here refers to the ratio of bound/unbound Glu receptors (dimensionless). The arterial radius is modelled using a system of ODE [18] with corrections to the equations listed in [24]. The model shows dilatation of the artery of 20%. This figure only shows the input (a) and result (b) of the functional hyperaemia model. We refer the reader to the original and reimplementation publications for the full details of the chemical cascade implemented in the model and the source code.

Fig 3. IPAD inside a cerebral arteriole.

(a) Displacement and stress of the arteriole wall due to U(t) at t = 20 s of a single astrocyte end-foot. Because displacement is fixed to u = 0 at the ends, stresses at the ends are high. Thus, all following results are presented for 10 μm ≤ z ≤ 190 μm. (b) IPAD velocity at various time points over the length of the arteriole wall using K₀/K₁ = 0.1. The average velocity over time and space is −8.37 μm s⁻¹. (c) IPAD flow rate at various time points over the length of the arteriole wall using K₀/K₁ = 0.1. The average flow rate over time and space is −7.24 × 10⁻⁸ μl/min for a single arteriole. Extrapolated over 6.5 billion arterioles estimated for the human brain it would take 9.92 h to process the total amount of ISF in the brain (280 ml). (d) IPAD velocity for k = 1 × 10⁻³ (blue), 1 × 10⁻⁴ (orange), 1 × 10⁻⁵ μm² (green) over the strength of the valve mechanisms K₀/K₁. Values are always negative, except at K₀/K₁ = 1.0. The effect of the valve mechanism is decreased with decreasing k.

Fig 4. Comparison of IPAD velocities in an arteriole for varying numbers of astrocytes acting on the wall and strength of the valve-like mechanism.

An astrocyte end-foot is modelled with a width of 10 μm and gap between astrocytes 1 μm. Length has a negative effect on IPAD whilst the number of astrocytes acting on the arteriole simultaneously has a positive effect. k = 1 × 10⁻³ μm², arteriole length l = 309 μm, number of astrocytes: 10 (black), 5 (white), 2 (gray), 1 (dotted).