Form, shape and function: segmented blood flow in the choriocapillaris

Abstract

The development of fluid transport systems was a key event in the evolution of animals and plants. While within vertebrates branched geometries predominate, the choriocapillaris, which is the microvascular bed that is responsible for the maintenance of the outer retina, has evolved a planar topology. Here we examine the flow and mass transfer properties associated with this unusual geometry. We show that as a result of the form of the choriocapillaris, the blood flow is decomposed into a tessellation of functional vascular segments of various shapes delineated by separation surfaces across which there is no flow, and in the vicinity of which the transport of passive substances is diffusion-limited. The shape of each functional segment is determined by the distribution of arterioles and venules and their respective relative flow rates. We also show that, remarkably, the mass exchange with the outer retina is a function of the shape of each functional segment. In addition to introducing a novel framework in which the structure and function of the metabolite delivery system to the outer retina may be investigated in health and disease, the present work provides a general characterisation of the flow and transfers in multipole Hele-Shaw configurations.

Figure 1. Vascular geometry of the choriocapillaris in man.

Portions of human choriocapillaris in the posterior pole are shown from the retinal side in (a,b,e) and from the scleral side in (c,d). Shown in (b,c,d) are three-dimensional reconstructions of portions of choriocapillaris obtained by serially imaging the vascular plexus at different depths. The capillaries are separated by collagenous pillars spanning the thickness of the choriocapillaris (arrow, a, b). In (c), two venules are seen inserting into the plane of the capillaries at approximately a right angle (arrows). (d) Arterioles and venules inserting into the plane of the choriocapillaris may be differentiated by the morphology of their endothelial cells, which is characteristically more elongated in arterioles (red arrows) and more rhombic in venules (blue arrow). Shown in (e) is the distribution of arteriolar (red dots) and venular (blue dots) openings, which correspond to insertions of respectively feeding arterioles and draining venules into the outer surface of the choriocapillaris, over an extended portion of tissue taken from the posterior pole. The number of arteriolar openings is here N_a = 73; the number of venular openings is N_v = 59.

Figure 2. Geometrical segmentation of the choriocapillaris blood flow and its visualisation.

A schematic of the streamline pattern in the mid-plane of the choriocapillaris is shown in (a). Arteriolar and venular openings are represented as respectively red and blue dots. Streamlines of the blood flow in the mid-plane of the choriocapillaris set by a random distribution of arteriolar and venular openings are plotted in (b). The separation surfaces of the flow field, which delineate functional vascular segments, are plotted as a series of connected black lines. Stagnations points are represented as asterisks. An individual functional vascular segment taken from (b) is represented in (c) and parameters of the model are indicated. The number of sides of the functional vascular segment is here . The vicinity of the separation surfaces takes a comparatively prolonged time to be reached by a passive dye filling the flow domain, as shown in (d) (Video S2). This property may be harnessed to visualise the segmentation of the blood flow.

Figure 3. Fluorescent dye angiography of the choriocapillaris, taken with permission from Hayreh.

The scale bars are missing from the original publication. The mosaic pattern observed during the filling of the choriocapillaris with a passive fluorescent dye is shown in (a). Images (b–d) show the segmentation pattern at different time points as the passive dye fills (b,c) and drains (d) the choriocapillaris within the area delineated in (a). The fluorescent units forming the mosaic displayed in (a) have been described as ‘functional lobules’, and consist of one or a group of functional vascular segments as defined in the present work.

Figure 4. Relation between the shape of functional vascular segments, the corpuscle travel time and mass extraction.

Shown in (a,c) is the probability density function (pdf) of the travel time of a corpuscle (here denoted ) calculated for ten adjacent functional vascular segments of a randomly generated distribution of arteriolar and venular openings (plotted in (b)). In (d), the evolution of the mass extraction η is plotted as a function of the angle ω between an arteriolar opening and two consecutive venular openings feeding and draining the same functional vascular segment (see Methods). Regular polygons associated with certain angles are indicated. The shaded area corresponds to 0.2 × 10⁵ s ≤ τ ≤ 10⁵ s, which concurs with an extraction rate of between 1 and 5% per volume of blood.