Drug is being delivered using spherical polymers of radius R. These spherical po

Question

Drug is being delivered using spherical polymers of radius R. These spherical polymers are saturated with the drug such that concentration at the surface is Co . Once they are implanted inside a tissue, the drugs diffuse out, assuming homogenous condition throughout and there was no drug inside the body already.
(A) After reaching steady state, what is the concentration C(r)?

(B) Find an expression for the flux, using diffusion coefficient D.

(C) What is the steady-state drug release rate (mass/sec) per sphere at the polymer surface?

Explanation / Answer

The release rate of drug in a non-eroding sphere of surface area, Ni (4 R2). If we now consider polymer, we can assume that will be similar, Np (4 R2), where p denotes polymer and i denotes drug. Taking the volume of a sphere, V = 43 R3, we can write an expression for the changing volume of the polymer sphere in time,

If we multiply this by the concentration of solid polymer, we get change in material per time. Thus we can write the relationship between the change in geometry to the release rate,

The flux, we can assume steady state diffusion of polymer into the solvent

Where concentration of the polymer in the solvent is Cp and B and A are integration constants.

Then we need to apply the boundary conditions.We know that a boundary condition is Cp = 0.

Applying these, we can say that B = 0 and A = pCpR. Thus,

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