Chapter 2. Mathematical Fundamentals in Pharmacokinetics

Because pharmacokinetics and biopharmaceutics have a strong mathematical basis, a solid foundation in mathematical principles in algebra, calculus, exponentials, logarithms, and unit analysis are critical for students in these disciplines. A self-exam is included in this chapter to provide a self-assessment of possible weaknesses in one's basic math skills. Difficulties with questions in the self-exam indicate that a review of mathematical essentials is necessary. Mathematical fundamentals are summarized here for review purposes only. For a more complete discussion of fundamental principles, a suitable textbook in mathematics should be consulted.

1. What are the units for concentration, mass, and volume?

2. A drug solution has a concentration of 50 mg/mL. What amount of drug is contained within 20.5 mL of the solution? In 0.4 L? What volume of the solution will contain 30 mg of drug?

3. Convert the units in the above solution from mg/mL to g/L and μg/uL. If the molecular weight of the drug is 325 Da, what are the units in M?

4. If 20 mg of drug are added to a container of water and result in a concentration of 0.55 mg/L, what volume of water was in the container?

5. For the following equation:

   

   1. Sketch a plot of the equation.

   2. Describe the relevance of each part of this equation.

   3. If x = 0.6, what is y?

   4. If y = 4.1, what is x?

6. Solve the following equations for x:

   1. log x = 0.95

   2. ex = 0.44

   3. ln x = 1.22

7. What is the slope of the line that connects the following two points?

   • Point 1:? x = 2 y = 5.6
   • Point 2:? x = 0.6 y = 2.38

8. For the following graph, determine C if x = 2, if x = 12.

   

9. Plot the following data on rectangular coordiantes and semilog graph paper. Pick two points on each graph and determine the slope of the line. Compare the slopes; are they the same? What is the initial concentration when time equals “0”?

Most of the mathematics needed for pharmacokinetics and other calculations presented in this book may be performed with pencil, graph paper, and logical thought processes. A scientific calculator or computer software program with logarithmic and exponential functions will make the calculations less tedious. Special computer software (see Appendix B) is available for disease state calculations in clinical pharmacokinetics. Spreadsheet software, such as EXCEL® (Microsoft), can also be used for many pharmacokinetic calculations and for graphing data. A small manual scientific calculator can also be used for many pharmacokinetic calculations.

Students often ask why they should learn to calculate pharmacokinetic problems manually if software is available. Computer software is a tool that allows one to solve more complex pharmacokinetic problems rapidly, but efficient use requires a thorough understanding of the subject. Many different pharmacokinetic ...