Practice Problems
Medical Pharmacology

Please: In a Netscape^R browser, go to the Options/Font menu and change the print size to 9 or 10 to save paper!

"Multi-compartment" problems are not in this printout.. Answers are available via the web until a practical way is found to print them.

Medical Pharmacology
Practice Problems #1

Dose Adjust
Volume of Distribution & Loading Dose
Extraction Ratio & Clearance
Elimination Rate Constant & Half-life
One Compartment Model
Multi-Compartment Model
Unit Conversions (no problems)

Dose Adjust Problems

Theophylline:

Problem 01. You need to initiate a theophylline regimen via IV infusion in a 25 year old female who weighs 50 kg.

1. What loading dose would be required to produce an initial concentration of 10 mg/L?

Problem 02. A female patient to be given theophylline weighs 50 kg.

1. What is the predicted clearance rate in this patient?

Problem 03. Assume that you want to produce a 10 mg/L steady state concentration of theophylline in a 50 kg female.

1. What is the initial infusion rate in mg/h?

Problem 04. A patient has been receiving a theophylline infusion of 25 mg/h. The measured concentration at steady state was 23 mg/L.

1. What is the highest recommended concentration of theophyline?
2. What new dose of theophylline should be recommended?

Problem 05. Theophylline is supplied as hydrous aminophylline for infusion. Each mg of hydrous aminophylline contains 0.79 mg theophylline. The "core" drug molecule devoid of the salt or ester moiety is often called the drug base.

1. How much hydrous aminophylline should be infused per hour to produce an infusion rate of 20 mg/h of theophylline?

Problem 06. Theophylline is supplied in several forms for oral administration. One form is as enteric coated aminophylline tablets (0.79 mg theophylline/mg aminophylline) in sizes of 100 and 200 mg. An estimated dose rate of 25 mg /h is needed in a 50 kg patient. Oral F is approximately 1.

1. What is the estimated dose rate of aminophylline?
2. What is the estimated dose per 12 h?
3. What is a reasonable combination of tablets to produce this dose?
4. If CL in this patient is 1.95 L/h, what Css do you expect from this combination of tablets?

Problem 07. One speaks of a steady state concentration for an infusion of drug. When drug is given by oral administration, one must think of average concentration with oscillation. The average concentration (Css(ave))corresponds to the Css and can be computed from the following formula.

1. What is the average concentration of theophylline if one administers 316 mg of theophylline at a dose interval of 12h to a 50 kg patient? CL = 1.95 L/ 50 kg.

Problem 08. One should be concerned about the degree of oscillation of plasma drug concentrations when giving a drug by intermittent dosage. Given the following pieces of information: 316 mg theophylline per 12 h. Patient weight = 50 kg. CL = 1.95 L / 50 kg. Vd = 0.5 L/kg.

1. Is this enough information to calculate the oscillation?
2. What more does one need?

Problem 09. Given a dose interval of 12 hours and a Ke of 0.077/h. Also, a dose of 316 mg theophylline per 12 hours and a body weight of 50 kg and a Vd of 0.5 L/kg.

1. What is the oscillation factor?
2. What is the absolute degree of oscillation?
3. On what crucial assumption is this estimate of peak and trough based?
4. How will the peaks and troughs of drug given PO compare to those computed by the formulae used in this course?

Problems related to Vd & LD

Problem 01. Lidocaine has a Vd of 1.1 L/kg.

1. What is its Vd in a 70 kg human?

Problem 02. You find in a research project that a new drug has a Vd of 30 L. The subject weighd 50 kg.

1. What is the Vd per kg?

Problem 03. A drug was given IV to an experimental subject that weighed 70 kg. Dose of 2.5 mg/kg. Concentrations in the plasma were found to be as follows (mg/L): 2 hr = 7.07; 4 hr = 5.00; 6 hr = 3.54; 8 hr = 2.50.

1. What is the total dose?
2. What is the Cp(0)?
3. What is the Vd/kg?
4. What is the whole subject Vd?

Problem 04. A drug was given IV to a 60 kg subject at a dose of 5 mg/kg. The resulting Cp(0) was 20 mg/L. The same dose of drug was given 1 month later PO. The subject had no significant changes in weight or hydration status. The resulting Cp(0) was 17 mg/L.

1. What is the approximate F?
2. What formula did you use to calculate F?
3. How does it compare to the approach used in class?

Problem 05. A drug was given IV to a patient that had an estimated Vd of 0.9 L/kg. The dose was 4 mg/kg.

1. What is the estimated Cp(0)?
2. What is the estimated F?
3. How does this calculated Cp(0) correspond to the "A" in the one-compartment pharmacokinetic model?

Problem 06. You are preparing a dosage regimen for a 120 pound patient. The drug is listed as having a Vd of 0.4 L/kg.

1. How much drug should you give IV to produce an initial peak concentration of 15 mg/L? (i.e., what is the loading dose?)

Problems related to Ke & Half-life

Problem 01. Elimination half-life of a drug is 3 hours.

1. What is its Ke?
2. On a repeated dosage regimen, how long would be required for the peak plasma concentration to reach 97% of steady state? Hours? Half-lives?

Problem 02. Given an elimination rate constant of 0.07/h.

1. What is the elimination half-life?

Problems related to 1-COM

Problem 01. Given measured plasma concentrations of drug at the times noted, calculate the following:

• 2 hrs -- 5 mg/L
• 6 hrs -- 2 mg/L

1. Elimination half-life
2. Zero-time intercept concentration (Cp(0))
3. Can you calculate a Vd using the information given?

Problem 02. A plasma sample taken at 2 hours has a concentration of 22.7 mg/L. Your best estimate of a half-life of the drug in this patient is 5 h.

1. What concentration would you expect at 12 h?

Problem 03. A patient has been receiving a a drug on q12h schedule for 3 months. Plasma samples were taken at the time of drug administration and again 4 hours later for the PO administered drug. Concentrations were 24.4 and 28.0 mg/L. [help]

1. What is the estimated elimination half-life of this drug?
2. Has this drug reached its steady state concentration range?
3. What is the predicted "trough" concentration if one doubles the dose?

Problem 04. A drug is being given at a dosage of 3 mg/Kg q12h via IM injection. It is very rapidly absorbed. Its elimination half-life is 4 hours. Estimated Vd = 0.3 L/Kg.

1. What is the concentration of the initial peak?
2. What is the concentration of the peaks at steady state?
3. What is the concentration of the troughs at steady state?

Problem 05. no problem yet