Arterial Pulsations cannot Drive Intramural Periarterial Drainage: Significance for A β Drainage

Abstract

Alzheimer's Disease (AD) is the most common form of dementia and to date there is no cure or efficient prophylaxis. The cognitive decline correlates with the accumulation of amyloid-β (Aβ) in the walls of capillaries and arteries. Our group has demonstrated that interstitial fluid and Aβ are eliminated from the brain along the basement membranes of capillaries and arteries, the intramural periarterial drainage (IPAD) pathway. With advancing age and arteriosclerosis, the stiffness of arterial walls, this pathway fails in its function and Aβ accumulates in the walls of arteries. In this study we tested the hypothesis that arterial pulsations drive IPAD and that a valve mechanism ensures the net drainage in a direction opposite to that of the blood flow. This hypothesis was tested using a mathematical model of the drainage mechanism. We demonstrate firstly that arterial pulsations are not strong enough to produce drainage velocities comparable to experimental observations. Secondly, we demonstrate that a valve mechanism such as directional permeability of the IPAD pathway is necessary to achieve a net reverse flow. The mathematical simulation results are confirmed by assessing the pattern of IPAD in mice using pulse modulators, showing no significant alteration of IPAD. Our results indicate that forces other than the cardiac pulsations are responsible for efficient IPAD.

Keywords: Alzheimer's disease; cerebral blood flow; cerebral lymphatics; intramural periarterial drainage; perivascular drainage.

Figure 1

Geometry of the perivascular drainage pathways model. The length L of a typical artery in the brain can be assumed to be much greater than the width W of the perivascular drainage pathways. Therefore we can approximate the flow as a lubrication model. The pulsation of the capillary is described by the function h(z, t).

Figure 2

Inlet function for MCA simulations obtained from patient-specific measurements used to represent one period of 0.85 s of the pulse wave. The final 10 peaks of the velocity time series were averaged in the Fourier space and adjusted such that its range of values aligns with those reported in Olufsen et al. (2002). The resulting inlet function is smooth and serves as the inlet boundary condition for the MCA simulations using VaMpy (Diem and Bressloff, 2016).

Figure 3

Blood pressure (A), wall displacement (B), and the resulting ISF pressure (C) in the MCA. Simulations were performed using the VaMpy Python package (Diem and Bressloff, 2016) and the simulation parameters are listed in Table 2. Wall stiffness is high in small blood vessels, therefore pressure gradients in time are steep. Wall displacement was calculated from the linear elasticity approximation derived in Supplementary Material 2. The input function R_i(z, t) to the BM model Equation (6) is obtained by adding the radius at rest a (see geometry depiction in Figure 1).

Figure 4

BM width h_bm(z, t) at several time points during the cardiac cycle (A) and its gradient along the z-axis at the same time points (B). Pressure pulse driven variations of the BM width are small compared to the initial width of 200 m and thus flow through the BM is slow.

Figure 5

ISF flux (positive values in the direction of arterial flow) averaged over one cycle as a function of BM position η in the arterial wall. Here, the BM is at r = r₀ + ηh such that η = 0 represents a BM immediately adjacent to the lumen and η = 1 represents a BM on the outer wall of the artery. Note that reverse flow is only achieved by ratios of $K_0/K_1<2.74\times 10^{-2}$. The fastest net reverse drainage shown here (for $K_0/K_1=2.68\times 10^{-2}$ and on the arterial lumen η = 0) is −2.64 × 10⁻⁵ μm³ s⁻¹.

Figure 6

Composite tile scan of confocal images of the distribution of intracerebrally injected Aβ (a) in relation to collagen IV (b) and SMA (c). The image was taken at 400 mm anterior to the injection site in an atenolol (Ate) injected mouse, to avoid any artifacts induced by the injection tract, relying instead on the pattern of distribution of the fluorescently injected Aβ away from the direct injection. Arrows on merged image (d) indicate arteries with Aβ in the intramural perivascular drainage pathways. Scale bars = 400 μm.

Figure 7

Graphs showing the number of arteries, veins and capillaries with Aβ in their walls in atenolol treated mice compared to control mice. SEM: standard error of mean.