Capillary Density

by Maddison Marshalsea

Submitted : Spring 2013

The goal of this project is to estimate the maximum capillary spacing, RL, for which anoxic regions will not form. These regions will form when the concentration of oxygen in the tissue, at any point, is equal to zero. To estimate the maximum capillary spacing, an equation is derived for the concentration of oxygen in the tissue. By integrating the differential equation for the flux of oxygen in the tissue, and setting it equal to the differential equation for Fick's Law for concentration and integrating once again, an equation for concentration is produced. From which equation the integration constants can be solved for. Once these constants are solved for, and the variables are plugged in, the limit of the equation as c approaches zero is taken by graphing the concentration equation and y=0; the intersection of these two graphs gives the maximum value of the capillary spacing, RL.

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