We are trying to deliver drugs to the walls of a blood vessel. The drug will be

Question

We are trying to deliver drugs to the walls of a blood vessel. The drug will be delivered using a catheter, which can be guided to the target site. The catheter has a cylindrical shaped tip loaded with drugs at concentration CW which comes in contact with the inner radius of the vessel rW. You can assume concentration at rW is CW and here are no chemical reactions and the primary method by which drug is moving across the vessel wall is diffusion. Once steady state is reached, the drug concentration at the outer wall of the vessel, radius ro is now Co .

1. Determine an expression or concentration profile C(r) at steady state.

2. Find an expression for the flux, using diffusion coefficient D in between rW and ro .

Explanation / Answer

JA= flux. From Ficks law, But JA=-D*dCA/dr, D = diffusion coefficient

JA= C1/r2

-D*dCA/dr = C1/r2

D*dCA= -C1dr/r2

when integrated

DAB*CA= C1/r + C2 (1), C2 is integration constant

At r= rw, C= Cw and r= ro, C=Co

Substituting the above boundary conditions

DAB*Cw= C1/rW+C2 (1)

D*Co = C1/rO+ C2 (2)

Subtracting C1*(1/rw-1/ro)= D*(Cw-Co)

C1= D*(Cw-Co)/ (1/rW-1/ro)

Hence JA*r2= D*(Cw-CO)/(1/rw-1/ro)

JA= D*(Cw-CO)/(1/rw-1/ro)/r2

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