J. Math. Biol. (1995) 33:281-294 ,Journal of MathemaUcal Molo2y © Springer-Verlag 1995 Transient transport across an inhomogeneous blood-retina barrier P. Dalgaard Department of Biostatistics, University of Copenhagen, 3 Blegdamsvej, DK-2200 Copenhagen N, Denmark Received 12 January 1994; received in revised form 4 April 1994 Abstract. A mathematical model for transport across the blood-retina barrier and diffusion into the vitreous body of the human eye is formulated. The eye is modeled as a sphere, the surface of which represents the blood-retina barrier. The equations of the model are solved analytically, using an expansion in spherical harmonics and inversion of the Laplace transform in the time variable. The numerical properties of the solution are investigated and the applicability of the model to the analysis of data from three-dimensional vitreous fluorometry is discussed. Key words: Diffusion - Blood-retina barrier - Ophthalmology 1 Introduction The blood-retina barrier separates the light-sensitive and nervous parts of the retina from the bloodstream. Similar to the blood-brain barrier, the barrier is normally very tight and allows only those water soluble substances that are necessary for the metabolism of the retina (glucose and certain amino acids) to pass in substantial quantity. Anatomically, the blood-retina barrier is not a single membrane. Rather, it is a complex system consisting of the retinal pigment epithelium and the endothelial linings of the retinal vessels. Breakdown of the blood-retina barrier is an element of several diseases of the human eye, notably diabetic retinopathy. Therefore, there is substantial interest in quantifying the permeability of the barrier (or, to be more precise, the permeability-surface product, since the surface of the barrier is ill-defined). Posterior vitreous fluorometry consists of injecting a fluorescent dye intravenously, allowing it to permeate the blood-retina barrier and enter the vitreous body (the gel-like substance occupying most of the interior of the eye)