Question

Consider a drug-eluting balloon catheter deployed into a blood vessel. The balloon is inflated to perfectly adhere to the vessel walls. Drug is released from the outer surface of the balloon and diffuses radially through the endothelial tissue only in the r-direction. Let the outside radius of the balloon be r = R_0, where the drug has a constant concentration c_0. The drug diffuses into the tissue as far as r = R, where the concentration of the drug becomes zero.

Assume cylindrical geometry, steady state conditions and no chemical reaction involving the drug. The drug diffusion coefficient in tissue is D.
(a) Find an expression for the profile c(r) inside the tissue (i.e. from R_0 to R).
(b) Determine the diffusive flux at the outer surface of the balloon.

Answer 1

a) Cr = Co - Fx / D

b) ΔC / Δx = ( CR - Cr ) / ( xR - xRo )

Step-by-step explanation:

A) Derive an expression for the profile c(r) inside the tissue

F = DΔC / X = D ( Co - Cr ) / X ------ 1

where : F = flux , D = drug diffusion coefficient

X = radial distance between Ro and R

Hence : Cr = Co - Fx / D

B) Express the diffusive flux at outer surface of the balloon

Diffusive flux at outer surface = ΔC / Δx = CR - Cr / xR - xRo