Purpose
To calculate the rate of change in the size of a devise.
Material
Calculator and graph paper
Paper
Background
You are studying devices for drug delivery. From the readings you found that the administration of medication to a specific part of the body can be done in many ways, but the most efficient way would be to get the drug to the site where it is needed. You found that if the drug is taken orally its passage through the digestive system to the circulatory system is not efficient because
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a) the required amount of drug does not reach the targeted area
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b) the drug could cause undesired effects in different areas of the body.
You realized that a local delivery system would be best but realized that there are constraints on the system;
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a) time
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b) constant drug concentration vs time variation
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c) Number of application (one time or repeated administration).
You also found that there exist the following types of devices
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1. Membrane device: a polymeric membrane encapsulates the drug, which is then carried in the form of a saturated aqueous solution that consists of undissolved particle of the drug. The membranes are usually spherical in shape, and consist of an outer membrane and an inner reservoir that holds the drugs.
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2. The Matrix device: This can be compared to a sponge that is loaded with drugs. When the matrix is implanted the drug molecules in the solution diffuse across the body surface of the matrix.
Activities
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1. Under certain conditions, the movement of a diffused substance across a cell's membrane is given by the equation dy/dt = k(A/V)(c-y). In the equation y is the concentration of the substance inside the cell, and dy/ dt is the rate with which y changes over time. The letters k, A, V and c are constants. K is the permeability coefficient of the membrane and A is the surface area of the membrane, v is the cell's volume and c is the concentration of the substance outside the cell.
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The equation says that the rate at which the concentration changes within the cell is proportional to the difference between it and the outside concentration.
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a) Solve the equation for y(t) using y0 = y(0)
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b) find the steady state concentration, lim t -> ∞ y (t).
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2. You designed a spherical drug delivery system that has an inner and outer shell. The radius of the outer shell is 4 nanometer and the radius of the inner shell is 1.5 nanometer. Find the volume of this device.
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3. Suppose a membrane type device containing drug was implanted. The membrane will dissolve at a rate y = y0 e -0.18t with t in days.
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a) About how long will it take for the membrane to dissolve?
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b) How long before it is 90% of its original size?
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4. If you design a rectangular wafer with dimension l = b = 5 mm and h = 0.5 mm, and it dissolve at the given rate. Graph the remaining size of the wafer for ten days.
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5. You designed a spherical matrix devise with radius r = 2mm. The dissipation rate is given by y = y0 e - 0. 005 t
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a) Find the half life of the device.
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b) After how many days will the devise disintegrate?