Polymer implants have been used for the controlled release of drugs and genes in biological tissues. Consider a polymer membrane implanted in a tissue. To simplify the analysis of controlled drug release, we assume that the tissue is much larger than the thickness of the implant. In addition, we assume that the clearance of a drug in the tissue is very slow, so that the concentration of the drug at the tissue-implant interface is equal to the solubility C0 of the drug. Also, the transport of drug in the tissue is one dimensional and in the normal direction of the membrane. Finally, we assume that convection and drug clearance through blood and lymph vessels are negligible. Thus, drug transport in the tissues involves only diffusion. Given the following, calculate the effective diffusion coefficient with respect to the drug’s known diffusion coefficient in plasma (61 µm2 /s).

If the effective diffusion coefficient is Deff and there is no drug in the tissue initially, what is the concentration of the drug 50µm away the implant 24 hours after implantation?

Known: Ratio of the pore surface area to the polymer surface area = 0.01, the drug radius of gyration is 3 nm, the pore radius is 8 nm, the polymer thickness is 10 microns and the tortuosity is 1.5.