âPolymer beads 800 micrometer in diameter are used for timed released drug delivery. Initial uniform concentration of the drug in the beads is 5 micrograms/cm^3 and the diffusion coefficient for the drug through the polymer is 1x10^-8 cm^2/s. The beads are ingested and pass through the GI tract in your body in a period of 12 hours. Assume the concentration of the drug is zero in the GI tract.

a. Use divergence theorem to derive the partial differential equation that describes the drug concentration in a polymer sphere as a function of position and time.

b. What are the initial and boundary conditions for the equation in part a?

c. What is the drug concentration at the center of the bead after 4 hours?

d. How long does it take to release 50% of the drug?

e. What fraction of the drug is released during the 12-hour ingestion period?

2. Polymer beads 800 um in diameter are used for timed released drug delivery. The initial uniform the concentration of the drug in the beads is 5 ug/cms and the diffusion coefficient for the drug through polymer is l x 10 beads are and pass the gastrointestinal tract (GI) in period o cm/s. The ingested through 12 hours. Assume the concentration of the drug is zero in the GI tract. a) Use the divergence theorem to derive the partial differential equation that describes the drug concentration in a polymer sphere as a function of position and time b) What are the initial and boundary conditions for your equation in part a? c) What is the drug concentration at the center of the bead after 4 hours? d) How long does it take to release 50% of the drug? e) What fraction of the drug is released during the 12-hour ingestion period? The divergence operator for vectors in Cartesian V-ve i Vy j+V k), spherical (V-v, r, Va eo Ve and cylindrical (V- r, +V 0, V k) coordinates are given b V. V dz dy dV sin Va) r 0 V. V Sin 00 r sin B 1 d V. V r dz r dr extended source of infinite extent: CX, t) O.5 Coerfc constant concentration source: C(x, t) Coerfo htx extended source of finite extent: c 0.5 Co erf t er R- 0.08314 (L bar) (mol K)

Question

âPolymer beads 800 micrometer in diameter are used for timed released drug delivery. Initial uniform concentration of the drug in the beads is 5 micrograms/cm^3 and the diffusion coefficient for the drug through the polymer is 1x10^-8 cm^2/s. The beads are ingested and pass through the GI tract in your body in a period of 12 hours. Assume the concentration of the drug is zero in the GI tract. a. Use divergence theorem to derive the partial differential equation that describes the drug concentration in a polymer sphere as a function of position and time. b. What are the initial and boundary conditions for the equation in part a? c. What is the drug concentration at the center of the bead after 4 hours? d. How long does it take to release 50% of the drug? e. What fraction of the drug is released during the 12-hour ingestion period?  2. Polymer beads 800 um in diameter are used for timed released drug delivery. The initial uniform the concentration of the drug in the beads is 5 ug/cms and the diffusion coefficient for the drug through polymer is l x 10 beads are and pass the gastrointestinal tract (GI) in period o cm/s. The ingested through 12 hours. Assume the concentration of the drug is zero in the GI tract. a) Use the divergence theorem to derive the partial differential equation that describes the drug concentration in a polymer sphere as a function of position and time b) What are the initial and boundary conditions for your equation in part a? c) What is the drug concentration at the center of the bead after 4 hours? d) How long does it take to release 50% of the drug? e) What fraction of the drug is released during the 12-hour ingestion period? The divergence operator for vectors in Cartesian V-ve i Vy j+V k), spherical (V-v, r, Va eo Ve and cylindrical (V- r, +V 0, V k) coordinates are given b V. V dz dy dV sin Va) r 0 V. V Sin 00 r sin B 1 d V. V r dz r dr extended source of infinite extent: CX, t) O.5 Coerfc constant concentration source: C(x, t) Coerfo htx extended source of finite extent: c 0.5 Co erf t er R- 0.08314 (L bar) (mol K)

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