A mathematical model to understand structure and function of the choriocapillaris

The choriocapillaris is a 10-30µm layered meshwork of capillaries lying externally to Bruch’s membrane and internally to the arteries and veins from the inner and outer choroid. Sole supplier of metabolites to the photoreceptors, it has evolved into a remarkable architecture. Choriocapillaris vessels are approximately planar, and densely organised. They are separated by round avascular septae, which direct the blood flow, and are serviced by vessels travelling under the choriocapillaris and inserting into it at approximately a right angle relative to the plane of the capillaries. The remaining controversies concerning choriocapillaris structure and function, which are largely caused by the anatomical complexity of the capillary bed, have historically hindered the analysis of the role played by the choriocapillaris in the onset and progression of pathologies of the back of the eye. The aim of this thesis is to build a mathematical framework, in which choriocapillaris structure and function can be investigated using physical principles. Methods based on immunohistochemistry and confocal microscopy are first developed to image, identify and quantify the anatomical characteristics of the human choriocapillaris. A mathematical model for the blood flow through the choriocapillaris inspired by these anatomical observations is thereafter formulated. Based on the modelling assumptions, it is shown that the blood flow and the passive transport are segmented, which corroborates in vivo angiographic observations published in the literature, and significantly heterogeneous. These heterogeneities may be responsible for the high degree of selective localisation of various pathologies of the back of the eye. Local and geographical variations in the density of the capillaries and in the relative distribution of arteriolar and venular insertions allow for a mechanical tuning of the characteristics of the blood flow to arteriolar flow conditions. Based on the model, novel methods relevant to the diagnosis and monitoring of pathologies of the choriocapillaris are proposed