BIO E425/625

Spring 20004

Homework 3

Due: Feb 19

Topics Constant rate delivery systems, repetitive dosing, nonlinear kinetics

1. (5 pts) Write the differential equation for Xu and then integrate it using Laplace transforms. You are told that ke and km are the first order excretion and metabolism rate constants, respectively, and k0 represents a zero order infusion.

2. ( 30 pts) You are developing an oral controlled release dosage form with a zero order release rate. The volume of distribution of the drug is 50 L in at 70 kg person. The absorption rate constant, ka = 0.8 h^-1and the elimination rate constant ke= 0.5 h^-1. Assume there is 1st order absorption and elimination and that there is no metabolism of your drug.

1. For therapeutic reasons, it is important to hit the minimum effective plasma concentration of 10mg/ml at 3 hours. What release rate do you need to design your drug to be released at, if you want to reach at plasma concentration of 10 mg/ml at 3 hours (this is not the steady state concentration)? Hint: draw the schematic, write the DE’s and integrate, then remember that it takes time to establish equilibrium.

2. What is the steady state plasma concentration and how long did it take to reach 99% of the steady state concentration?

3. You have just conducted your first animal studies (shown below). How well did your model predict the experimental results?

Time (hours)	Cp ug/ml *hr
1	2.0
2	6
4	12.5
6	14.9
12	16.8
24	17.1

3. (20pt) A patient is being infused with a cardiac drug at a constant rate of 0.1 mg/min (pump1). Because of an acute episode, a higher level of drug is needed. So, 2 hours after the initial infusion began, a second infusion line is started. It delivers at a rate of 0.25 mg/min (pump2) for 2 hours and then it is turned off while pump 1 remains on.



Draw the graph that would represent the plasma level of drug in the patient for the first 6 hours (starting when the 1st pump starts infusing) if the drug is eliminated via a 1st order process with a rate constant of 0.2 min^-1. The volume of distribution is 5000ml.

4. (20 points) For your in vivo drug development study, you must give your animal 800 mg IV bolus dose of an experimental drug every 8 hours. After steady state is achieved, you determined that the peak plasma concentration was 30 mg/ml. The concentration 5 hours after this peak, the plasma concentration was 8 mg/ml. You would like to maintain a steady state plasma concentration in the range of 4- 20 mg/ml.

A Estimate the elimination rate constant for this drug in this animal. What are your assumptions?

2. Calculate this drugs volume of distribution in this animal.
3. What is the animal’s average plasma concentration at steady state?
4. Determine an appropriate dose and dosing interval the will maintain the plasma concentration of this antibiotic within the therapeutic range of 4- 20 mg/ml.

5 (25 pts) Two friends are drinking whisky at a constant rate. Dan is drinking at a rate of 1 drink/hour and Steve is drinking ½ drink/hour. Compare their blood alcohol concentrations assuming the amount of alcohol in a full drink is 14 grams. Show this graphically using a maximum rate of metabolism (Vm) of 10 g/hr and the Michaelis constant (Km) of 100 mg/L. When would the pharmacological affects of alcohol consumption be noticeable (the average blood concentration of alcohol where intoxication becomes noticeable is 200mg/L)? How many drinks can each guy drink and for how long could they drink at their fixed rates before reaching the toxic concentration of alcohol 5000mg/L, which can result in coma or death? Assume Vd alcohol in each man = 42L

6. Not due this week – Will be on homework 4. Read Gentamicin dosing in critically ill patients paper. Write a summary ( < 1 page) of their study. You should be able to give an overview of their work (purpose, experiential procedure, findings) and point out the strengths and weaknesses of their research. The Nicolau paper, reference (12), is here if you are interested.