## Hw4.doc

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

The bioavailability of drugs delivered orally is often low. Following absorption from the
digestive tract into the blood, many drugs are quickly converted by the liver to an inactive form
before they can reach the rest of the circulation. One way to circumvent this difficulty is to
implant a device that will release the drug at a constant rate into the systemic circulation. This
type of device can also improve the efficacy of the drug because patients often forget to take
drugs at the proper times. Norplant is an implantable device that releases the steroid hormone
Norgestrel into the blood when implanted under the skin of the arm. It consists of a silicone
rubber cylinder surrounding a core matrix containing the drug, as shown below. The silicone
rubber serves as a diffusion barrier to control the release rate of the steroid.
(a) Derive an equation for the rate of steroid release from the device in terms of
cb = concentration of drug in the body fluid at the surface of the device (assume const.)
cs = drug concentration in the core (assume const. and equal to max. solubility in silicone)
R1, R2 = inner and outer radii of the cylindrical membrane
Dm = diffusion coefficient of the steroid in the membrane
S = cmembrane/cbody fluid (partition coefficient)
(b) It is desired to deliver 76 µg of the drug per day to the patient using a device that is 2 cm long with an inside diameter of 1.57 mm. The desired steady-state concentration in the plasma of the patient is 1 ng/ml. What should the wall thickness be to give the correct dosage? Data: S = 50; cs = 0.2 mg/ml; Dsteroid-silicone = 2 x 10-7 cm2/s
Problem 8 (continuation of Problem 7)
In clinical trials of the device described in the preceding problem, it is noted that the release rate
is much slower in some patients than in others. This difference is attributed to the formation of
scar tissue around the device, which adds a resistance to transport from the device to the blood.
In one patient, a capsule of scar tissue 0.75 mm thick was found surrounding the device. Assume
that the scar capsule acts as a 0.75 mm thick coating of the device and that the surface of the scar
is in contact with body fluid. The body metabolizes the drug according to
-rA = m
where cb is the concentration of drug in the body fluid outside the capsule and α =0.88 cm3/s. If the solubility of the drug in the scar tissue is the same as tha t in body fluids and if the diffusion coefficient in tissue is 6 x 10-7 cm2/s, (a) what is the expected plasma concentration of the drug in this patient? What is the rate of (b) When the release of drug from these devices is measured in the laboratory, a “burst” effect is usually noted. The initial rate of release is very high but decays rapidly to steady-state, constant behavior. What is a reasonable physical explanation for this behavior? The vapor pressure of the drug at the storage conditions of the devices is negligible.

Source: http://www-unix.ecs.umass.edu/~jmdavis/che334/hw4.pdf

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