Progression of Diabetic Capillary Occlusion: A Model
Fig 4
Schematic of conveyor-belt model of oxygen advection.
The schematic shows a small capillary network with five segments and two junctions. Along the blood flow direction, marked as arrow with empty triangular head, the first junction has merging blood flow and the second branching blood flow. Blocks in red are CAPs, building blocks, or structural elements (visually present in model configuration), of capillary segments. Blocks in yellow are CBs, functional elements for advection. Size of a CAP is fixed throughout a simulation, so each capillary segment has fixed number of CAPs. In contrast, the size of a CB is always proportional to flow velocity on the capillary segment, so flow velocity and accordingly the number of CBs on a patent capillary segment can vary following an occlusion elsewhere as flows in the network are adjusted to the changed network resistance structure. During each time step of advection, a CB passes its oxygen volume to the next CB. Importantly, the size of a CB is equal to flow velocity of host capillary segment multiplied by time step of advection, which means the “conveying” speed of oxygen from one CB to next is exactly equivalent to the flow velocity in that capillary segment. At a merging junction, the upstream capillary segments add the oxygen volumes in their last CBs and pass the total to the first CB of the down stream capillary segment. At a branching junction, the parent capillary segment distributes the oxygen volume in its last CB into the first CBs of the daughter segments according to conservation of blood flow volume. Mathematical descriptions were detailed as equations (9)-(11) in S1 Text. Each CB is associated with, or mapped to, a host CAP. The modules of advection (involving CBs) and diffusion (involving CAPs) are connected with processes that convert oxygen volumes between the host CAP and its associated CBs. (see Fig 5).