The transport of plasma-derived, atherogenic macromolecules such as low-density lipoprotein (LDL) in the artery wall is one of the initiating, fundamental events in the prelesional stages of atherosclerosis. A typical theoretical, two-dimensional (2D) transport model consists of two boundary value problems, one, a porous media (potential) flow problem for water filtration and the other for the convective-diffusive transport of a solute, here LDL, into the tissue. The tissue's thickness is far smaller than any curvature that it might have, e.g., the curvature of a vessel wall, and one can therefore treat the tissue as being flat. The typical model employed is of a cylindrical slab of tissue whose axis is perpendicular to the tissue, assumed, despite abuse of geometry, to be periodic and to tile fill the plane, consisting of various layers of tissue. Such models have has been widely applied in the blood vessel walls and heart valves. Although, the tissue structure varies among arteries, veins, and heart valves, they all share the feature that the top of the cylinder represents a monolayer of cells, called the endothelium, that separates the blood from the subsequent layers of the tissue and generally acts as a barrier that keeps large molecules out of the tissue interior. Just beneath the endothelium in the subendothelial intima, comprised of collagen and extracellular matrix, whose thickness is small compared with the radius ξ of the periodic tissue cylinder. This is generally followed by various layers that are much thicker and denser than the intima. Macromoleculles tend to cross the endothelium and enter these tissues not uniformly, but rather via rare, small isolated regions that generally appear to correspond to temporarily widened or otherwise leaky junction that surrounds one or a small number of endothelial cells. Some of these leaks have been associated with cells that are either dying or dividing. These junctions are much thinner than either the radius of an endothelial cell or the thickness of the intima. Typical numbers are 20-100nm for the junction thickness, 200-1000nm for the intima thickness and hundreds of microns for ξ. There is typically an overall pressure gradient from the lumen side across the tissue and this drives a water flow across the tissue. Water, being a small molecule, penetrates all of the junctions, both normal and leaky, and can advect large molecules through leaky junctions with it into the subendothelial intima. Interestingly, this region, being far sparser than the subsequent layers, has very different physiology properties, e.g., it presents far less flow resistance (the fluid viscosity divided by the tissue layer's Darcy permeability) than those other layers, and the flow and transport in the intima is often interesting and non-trivial, and is a strong focus of the overall transport calculation. Given the scales mentioned, i.e., that the intima is far thinner than ξ, several authors have simplified the intima calculation based on this separation of scales by simply asserting that the dynamic variables do not vary in the intima in the short direction and it is therefore adequate to simply treat the transport equation integrated across the subendothelial intima. Given the scale of the leaky junction relative to the subendotheial intima thickness, one might question the uniform validity of this approach to such a problem. The present study mathematically analyzes these filtration and convection diffusion models in the subendothelial intima (SI). We begin by formally deriving the separation of scales for the intima problem to all orders and see how it dramatically simplifies the axisymmetric 2D transport models there. We then numerically investigate the SI region near the leaky junction (modeled as a ring source), show that this approach breaks down there, calculate accurate numerical solutions there and investigate the factors that influence the size of the region over which the separation of scales solution breaks down.