The pill to deliver a particular drug has a solid spherical inner core of pure drug...

 

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The pill to deliver a particular drug has a solid spherical inner core of pure drug D and is surrounded by a spherical outer coating of A that makes the pill palat- able and helps to control the drug release. The outer coating and the drug dis- solve at different rates in the stomach due to their difference in solubilities. Let CAS = concentration of coating in the stomach in mg/cm³, CDs = concentration of drug in the stomach in mg/cm³, and CDB = concentration of drug in the body in mg/kg. Three different pill formulations are available: Pill 1 Diameter of A = 5 mm, Diameter of D = 3 mm Pill 2 Diameter of A = 4 mm, Diameter of D= 3 mm Diameter of A = 3.5 mm, Diameter of D = 3 mm Pill 3 Additional Information and Data Amount of drug in inner core of each pill = 20 mg Density of inner and outer layers = 1414.7 mg/cm³ Solubility of outer pill layer at stomach conditions = SA = 1.0 mg/cm³ Solubility of inner drug core at stomach conditions = SD = 0.4 mg/cm³ Volume of fluid in stomach = V = 1.2 liters Residence time in stomach = t = V/vo= 4 hours, where uo is the volumetric flow rate Typical body weight W = 75 kg Sherwood number = Nsh Dp KLDAB Effective Diffusivities of A and D in stomach DA = DD = 0.6 cm²/min = 2 (see Problem 10.3 for details) A person takes all three pills at the same time. Assume that the stomach is well mixed and that the pills remain in the stomach while they are dissolving. (a) Plot CAS and CDs as a function of time for up to 12 hours after the pills are taken. (b) If the drug is absorbed into the body (from solution in the stomach into the blood stream) by an effective mass transfer rate of 10×CDs in mg/ min, plot CAS and CDs under these conditions. (c) If the body metabolizes the drug with an effective first-order reaction rate of 1.0×CDB in mg/kg.min, plot CDB in the body under the condi- tions of (b). (d) Under the conditions of (c), what is the estimated time that CDB is greater than 2.0 x 103 mg/kg, which is the minimum effective concen- tration level for the drug? (e) Please suggest a more effective layering of the three pills with the drug placed only in the center to increase the time for the effective level con- centration of 2.0 x 103 mg/kg under the same conditions. The pill to deliver a particular drug has a solid spherical inner core of pure drug D and is surrounded by a spherical outer coating of A that makes the pill palat- able and helps to control the drug release. The outer coating and the drug dis- solve at different rates in the stomach due to their difference in solubilities. Let CAS = concentration of coating in the stomach in mg/cm³, Cps = concentration of drug in the stomach in mg/cm³, and CDB = concentration of drug in the body in mg/kg. Three different pill formulations are available: Pill 1 Diameter of A = 5 mm, Diameter of D = 3 mm Pill 2 Diameter of A = 4 mm, Diameter of D= 3 mm Diameter of A = 3.5 mm, Diameter of D = 3 mm Pill 3 Additional Information and Data Amount of drug in inner core of each pill = 20 mg Density of inner and outer layers = 1414.7 mg/cm³ Solubility of outer pill layer at stomach conditions = SA = 1.0 mg/cm³ Solubility of inner drug core at stomach conditions = SD = 0.4 mg/cm³ Volume of fluid in stomach = V = 1.2 liters Residence time in stomach = t = V/vo= 4 hours, where uo is the volumetric flow rate Typical body weight W = 75 kg Sherwood number = Nsh Dp KLDAB Effective Diffusivities of A and D in stomach DA DD = 0.6 cm²/min = 2 (see Problem 10.3 for details) A person takes all three pills at the same time. Assume that the stomach is well mixed and that the pills remain in the stomach while they are dissolving. (a) Plot CAS and CDs as a function of time for up to 12 hours after the pills are taken. (b) If the drug is absorbed into the body (from solution in the stomach into the blood stream) by an effective mass transfer rate of 10×CDs in mg/ min, plot CAS and CDs under these conditions. (c) If the body metabolizes the drug with an effective first-order reaction rate of 1.0×CDB in mg/kg.min, plot CDB in the body under the condi- tions of (b). (d) Under the conditions of (c), what is the estimated time that CDB is greater than 2.0 x 103 mg/kg, which is the minimum effective concen- tration level for the drug? (e) Please suggest a more effective layering of the three pills with the drug placed only in the center to increase the time for the effective level con- centration of 2.0 x 103 mg/kg under the same conditions. The pill to deliver a particular drug has a solid spherical inner core of pure drug D and is surrounded by a spherical outer coating of A that makes the pill palat- able and helps to control the drug release. The outer coating and the drug dis- solve at different rates in the stomach due to their difference in solubilities. Let CAS = concentration of coating in the stomach in mg/cm³, CDs = concentration of drug in the stomach in mg/cm³, and CDB = concentration of drug in the body in mg/kg. Three different pill formulations are available: Pill 1 Diameter of A = 5 mm, Diameter of D = 3 mm Pill 2 Diameter of A = 4 mm, Diameter of D= 3 mm Diameter of A = 3.5 mm, Diameter of D = 3 mm Pill 3 Additional Information and Data Amount of drug in inner core of each pill = 20 mg Density of inner and outer layers = 1414.7 mg/cm³ Solubility of outer pill layer at stomach conditions = SA = 1.0 mg/cm³ Solubility of inner drug core at stomach conditions = SD = 0.4 mg/cm³ Volume of fluid in stomach = V = 1.2 liters Residence time in stomach = t = V/vo= 4 hours, where uo is the volumetric flow rate Typical body weight W = 75 kg Sherwood number = Nsh Dp KLDAB Effective Diffusivities of A and D in stomach DA = DD = 0.6 cm²/min = 2 (see Problem 10.3 for details) A person takes all three pills at the same time. Assume that the stomach is well mixed and that the pills remain in the stomach while they are dissolving. (a) Plot CAS and CDs as a function of time for up to 12 hours after the pills are taken. (b) If the drug is absorbed into the body (from solution in the stomach into the blood stream) by an effective mass transfer rate of 10×CDs in mg/ min, plot CAS and CDs under these conditions. (c) If the body metabolizes the drug with an effective first-order reaction rate of 1.0×CDB in mg/kg.min, plot CDB in the body under the condi- tions of (b). (d) Under the conditions of (c), what is the estimated time that CDB is greater than 2.0 x 103 mg/kg, which is the minimum effective concen- tration level for the drug? (e) Please suggest a more effective layering of the three pills with the drug placed only in the center to increase the time for the effective level con- centration of 2.0 x 103 mg/kg under the same conditions. The pill to deliver a particular drug has a solid spherical inner core of pure drug D and is surrounded by a spherical outer coating of A that makes the pill palat- able and helps to control the drug release. The outer coating and the drug dis- solve at different rates in the stomach due to their difference in solubilities. Let CAS = concentration of coating in the stomach in mg/cm³, Cps = concentration of drug in the stomach in mg/cm³, and CDB = concentration of drug in the body in mg/kg. Three different pill formulations are available: Pill 1 Diameter of A = 5 mm, Diameter of D = 3 mm Pill 2 Diameter of A = 4 mm, Diameter of D= 3 mm Diameter of A = 3.5 mm, Diameter of D = 3 mm Pill 3 Additional Information and Data Amount of drug in inner core of each pill = 20 mg Density of inner and outer layers = 1414.7 mg/cm³ Solubility of outer pill layer at stomach conditions = SA = 1.0 mg/cm³ Solubility of inner drug core at stomach conditions = SD = 0.4 mg/cm³ Volume of fluid in stomach = V = 1.2 liters Residence time in stomach = t = V/vo= 4 hours, where uo is the volumetric flow rate Typical body weight W = 75 kg Sherwood number = Nsh Dp KLDAB Effective Diffusivities of A and D in stomach DA DD = 0.6 cm²/min = 2 (see Problem 10.3 for details) A person takes all three pills at the same time. Assume that the stomach is well mixed and that the pills remain in the stomach while they are dissolving. (a) Plot CAS and CDs as a function of time for up to 12 hours after the pills are taken. (b) If the drug is absorbed into the body (from solution in the stomach into the blood stream) by an effective mass transfer rate of 10×CDs in mg/ min, plot CAS and CDs under these conditions. (c) If the body metabolizes the drug with an effective first-order reaction rate of 1.0×CDB in mg/kg.min, plot CDB in the body under the condi- tions of (b). (d) Under the conditions of (c), what is the estimated time that CDB is greater than 2.0 x 103 mg/kg, which is the minimum effective concen- tration level for the drug? (e) Please suggest a more effective layering of the three pills with the drug placed only in the center to increase the time for the effective level con- centration of 2.0 x 103 mg/kg under the same conditions.

Answer rating: 100% (QA)

To solve this problem we can use the principles of mass transfer and diffusion Lets break down each part of the problem and solve them step by step a Plotting C AS and C DS as a function of time for u... View the full answer