Blood flow in the choriocapillaris

Abstract

The choriocapillaris is a capillary bed located in a thin layer adjacent to the outer retina and is part of the oxygen delivery system to the photoreceptors of the eye. The blood flow is approximately planar and is serviced by microvessels, which join the choriocapillaris through inlets perpendicular to its plane. Capillaries are densely organised and separated by avascular septal posts, which direct the blood flow. The capillary bed is composed of a juxtaposition of tessellating vascular units called lobules, which are filled and drained independently from each other. A theoretical analysis of the blood flow in an idealised model of a lobule of the choriocapillaris is developed and studied. Lobules are modelled as tessellating polygonal prisms, where the upper and lower surfaces correspond to planar parallel membranes. The septae are modelled as cylinders randomly distributed between the two membranes. Feeding arterioles and draining venules are modelled as inlets and outlets connecting at the lower surface of the prism perpendicularly to the plane of the lobule. An inlet is placed inside the lobule, while an outlet is placed at each of the vertices. The polygonal prism can be formally subdivided into a set of triangular prisms with one inlet and two outlets, each of them located at one of the vertices. The triangular prisms are taken to be isosceles, and are therefore characterised by a vertex angle ω at the inlet and a span L. The flow is viscously dominated, and is investigated in the lubrication limit, in which the characteristic thickness of the prism is much smaller than the diameter of the cylinders. As a result of the geometry, a stagnation point is located midway between the outlets. A separation streamline joins the inlet and the stagnation point. The pressure drop p and the average fluid particle residence time T are analysed as a function of the angle at the inlet ω and the septae volume fraction Φ. When no cylinders are present (Φ = 0), an analytical expression for the pressure field is calculated by conformal mapping. Close to the triangle walls, the flow is quasi-parallel and characterised by a shorter fluid particle residence time. In the vicinity of the stagnation point, the velocity decreases and the residence time diverges logarithmically with the distance to the stagnation streamline. The minimum in pressure drop corresponds to a maximum in residence time, and is obtained for ω = π/2. Asymptotic expressions for the pressure drop and average residence time are formulated in both the limits ω 1 and π − ω 1. The impact of Φ on the flow is characterised by solving the equations for the flow numerically and using the Darwin drift framework. We show that the pressure drop is approximately proportional to 1 + 2Φ for relatively small Φ, and that T is proportional to 1 − Φ regardless of the void fraction or shape of the septae. In the case Φ = 0, the average † Email address for correspondence: moussa.zouache.10@ucl.ac.uk 38 M. A. Zouache, I. Eames and P. J. Luthert residence time equals the volume of ...

A Revised Hemodynamic Theory of Age-Related Macular Degeneration

“…This causes blood entering from the arteriole to rapidly dissipate centrifugally towards collecting venules. This dissipation is observed in computational modeling [37, 38] and empirical observation in non-human primates [42, 43], which together suggest that the choriocapillaris exhibits substantial gradients in hemodynamic parameters as a function of distance to arteriolar and venule junctions. Although pending further validation, these findings suggest that shear stresses also vary significantly within the choriocapillaris, based on the relative distance from a feeding arteriole and draining venule.…”

“…Choroidal ischemia in hypertensive choroidopathy, where blood flow within the choroid is diminished or absent, and Alzheimer’s disease where choroidal thinning is observed [36], are distinct entities from AMD. Moreover, computational modeling predicts that within the healthy choriocapillaris, highly heterogeneous flow rates and pressures exist which can vary by orders of magnitude within tens of microns [37, 38]. In analogy to the effects of local hemodynamics of large arteries on atherosclerotic plaque development, we predict that local hemodynamics within choriocapillaris are critical determinants of the location, severity and progression of disease, but in isolation, are not sufficient to explain all manifestations of the complex disease that is AMD.…”

“…In the submacular choriocapillaris, the vascular lumen accounts for 80% of the volume of the tissue. The choriocapillaris has be computationally modeled as a thin (7–10 µm) sheet of blood interrupted by intercapillary pillars [37, 38]. Blood is supplied and drained from the choriocapillaris by small and mid-sized arterioles and venules that comprise Sattler’s layer (Figure 3).…”

“…For example, one would expect transport of oxygen, glucose and macromolecules from the choroid to the RPE layer to depend greatly on local blood flow. Computational modeling of choroidal geometry also predicts a strong interrelationship between anatomical parameters and blood residence time [37], a measure of the time which a substance remains within a unit system and a critical parameter in heat dissipation [44]. Another parameter affected by local blood flow is the magnitude of shear stress imparted on the vascular endothelium.…”

“…Computational modeling of choriocapillary blood flow predicts that local pressure and velocity are inextricably linked to anatomic architecture of the choroidal functional unit [37, 38]. The anatomy of the choroid is fundamentally transformed in aging and in AMD as described below.…”