Posted: October 27th, 2022

# Drug delivery Math

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1. As shown in the figure, for the chemotherapeutic drug Doxorubicin to enter the tumor from the blood flow through passive diffusion, what would be the donor compartment and the receiver compartment? What is the driving force of this movement? What do you see as the potential limitation of this type of drug delivery to a solid tumor? (8 points)

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2. In a two-compartment system, donor and receiver compartments are separated by a semi-permeable membrane with surface area of 20.0 Cm2 that is 0.100 mm thick. The concentration of a small relatively hydrophobic molecule (partition coefficient of 2) in the donor and receiver phase is 2.00 mg/mL and 2.00 g/mL, respectively. If the diffusion coefficient of the molecule through the membrane is 4.35 x 10-7 Cm2/S, how many micrograms of the small molecule would diffuse to the receiver compartment in one minute? (10 Points)

3. What is the unit of K in zero, first and second order of reaction? Describe the relationship of initial concentration with the time to reach 90% remaining for each order of reaction. Explain why this relationship makes sense to you, based on what you know about the rate of reaction in each scenario. (12 points)

4. Complete the reaction (by drawing the resulting structures) that is the main cause of chemical instability for the following drugs. Write the name of the type of reaction (10 points):

a.

b.

5. A reaction follows the second order. If the initial concentration of drug is 5.00 mg/mL, and t90% is 180 days, how long does it take for the drug concentration to be 3.80 mg/mL? (10 points)

6. A combinational therapeutic approach is being evaluated in a clinical trial. This double-blind trial (neither patients nor nurses are aware of the group to which each patient is assigned) is designed to evaluate the therapeutic effect of 25 mg of drug A combined with 200 mg of drug B, administered orally twice a day. Patients participating in this clinical trial are assigned to four different groups:

· Control group: This group receives 225 mg total of lactose as placebo

· Group A: Patients in this group receive 25 mg of drug A plus 200 mg lactose as placebo

· Group B: This group receives 200 mg of drug B plus 25 mg lactose as placebo

· Group AB: Patients assigned to this group receive 25 mg of drug A and 200 mg of drug B

Drug A is available as a fine powder with a blue color, and drug B is a powder with a pale red color. Preliminary data shows that drugs A and B are chemically incompatible and trigger a chemical reaction that degrades both ingredients rapidly.

What is your suggestion for the dosage form to administer the proposed combinations to the four groups of patients? In your answer take the incompatibility issue, as well as the blind nature of study into consideration. Please explain your suggestion and specify the details in a few sentences. (10 points)

7. You are working on formulation for a tablet. The active ingredient is heat and moisture sensitive. What method of manufacturing do you recommend? Is granulation an option here? If yes, what type of granulation? (7 points)

8. Samples of a tablet being manufactured are not disintegrated in the standard time. They also show high friability (lose too much weight after friability test). What approaches we can take to fix both problems. (8 points)

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