tissue Tissue Patch Impermeable boundary 6. (23 pts) Unsteady State. After a heart attack, the delivery of drugs into the tissue can be accomplished by a myocardial patch applied to the surface of the heart. The HeartSaver patch is composed of a hydrogel matrix containing a drug (A) that forms solid aggregates that slowly dissolve into the hydrogel. The hydrogel therefore contains a constant concentration of drug A, equal to the saturated concentration (ca'=0.1M). The drug partitions from the patch into the tissue (Kv=0.176), with preferential solubility in the hydrogel. Within the tissue, DA- e=1x109cm /sec. Ignore convective mass transfer that may result from the heart beating (a) (3 pts) What is the concentration of drug in the tissue immediately outside of the patch membrane? (b) (5 pts) Provide the differential expressions (the symbolic GDE, no calculations needed) for the concentration of the drug as a function of distance into the heart tissue relevant to early timescales after the patch is applied. Please state your assumptions. (e) (10 pts) Desirable drug effects in the tissue require a local drug concentration of 1 mM. Assuming the tissue can be treated as a semi-infinite medium, how long will it take to reach these concentrations at a depth of 2 mm into the heart? (d) (5 pts) Based on your calculated time, does this case meet the conditions for application of the semi-infinite approximation? Here, the characteristic length scale (L) is the thickness of the heart wall which is 1 cm. a