A major problem in the successful design of implantable tissues is the availability of oxygen for respiring tissues, which is determined by the spatial access of tissues to blood capillaries that bring oxygen carrying red blood cells. A classic model in this field is the Krogh cylinder. Imagine a tissue space with cells surrounding a cylindrical capillary. Oxygen and other metabolites arriving into the capillary axially due to fresh flow of oxygenated blood will diffuse from the capillary radially towards the tissue, where they will be consumed by the cells. The solution of the Krogh cylinder problem yields an expression for the critical distance into the tissue, beyond which no more solute is available, denoted by :
Where
Parameters given are
DT=the metabolic tissue diffusivity = 8 x 10-6 cm^2/s
V = the blood plasma velocity =0.005cm/s
Rc=capillary radius =0.0005cm
Tm=capillary wall thickness = 5 x 10-5 cm
K0=overall metabolite mass transfer rate = 5.75 x 10-5 cm/s
C0 = 5 micromole/ cm^3
R0=0.01 micromole/cm^3/s
Using Newton Raphson method, solve the above equation for as a function of z. Vary z from 0.001 to 0.1 cm in increments of 0.01 cm. plot versus z.