onventional chemotherapeutic drugs are delivered to the tumor by either oral

administration or IV injection. This necessitates the usage of high doses since the

route of administration to the tumor is through the blood stream. This results in

significant toxicity to the rest of the non$-$tumor tissues in the body which is one of the

reasons for the severe adverse side effects patients undergoing chemotherapy

experience. Possible solutions include local delivery of drugs in cases of localized

solid tumors by encapsulating the drug in polymer hydrogels $($implant$)$ and affixing

them directly to the tumor using minimally invasive surgical techniques.

In order to construct a mathematical model of such a drug delivery system, consider

the following. Drug concentration at the implant surface is p$0($mg$/$ml$)$ and at a

distance of $1\mathrm{.}3$ cm from the surface it is zero $(0).$ The drug diffusivity in the target

tissue is estimated to be $1\mathrm{.}4$ x $10-8$ cm$2/$s$.$ The surface area of the biopolymer

implant is $1\mathrm{.}8$ cm$2.$ Model the system at steady state $($assume large drug reservoir in

the hydrogel$)$ and only be concerned with unidirectional transport.

a$.$ Write the appropriate governing differential equation describing mass transfer of

drug for this system. State the general assumptions and apply them to produce

a simplified differential equation. $(4$ points$)$

b$.$ What is the solution for the drug concentration profile as a function of position $($x$)$

from the implant surface? Sketch and label the diffusion process indicating the

boundary conditions employed. $(2$ points$)$

b$.$ Find the distance from the implant surface $($cm$)$ at which the drug concentration

becomes $15\%$ of its value at the implant surface. $(2$ points$)$

d$.$ Using this model, would increasing the concentration at the surface increase the

treatment volume? Explain why or why not. $(2$ points$)$