Calculate and Interpret Pharmacokinetic Parameters of a Given Drug

Pharmacokinetic Exercises for Practice

1. Calculate and Interpret Pharmacokinetic Parameter of a Drug from Given Data Dr. Shivankan Kakkar , MD

2. Learning Objectives After completing this lecture each student should:- understand the one compartment model, rapid IV bolus dosing and linear elimination understand the properties of first order kinetics, linear models be able to define, use, and calculate the parameters: V d (apparent volume of distribution) CL (clearance ) K E (elimination rate constant ) t 1/2 (half-life ) Cp (Plasma drug conc. at zero time after administration) {as they apply to a one compartment linear model} be able to use the integrated equations for a one compartment linear model to perform various dose and dosing regimen calculations Clinical Pharmacokinetics by DrShivMD 2

3. Important Formulas : Arithmetic Vs Graphical V d = Dose / Cp CL = 0.693 * V d / t 1/2 K E = CL / V d t 1/2 = 0.693 / K E Cp t = Cp * e – K E * t Common Log Natural Log Slope of the straight line of Log C vs t graph is : Slope = Y 2 – Y 1 / X 2 – X 1 or Slope = Log Cp t1 – Log Cp t2 / t 1 – t 2 K E = – Slope * 2.303 Slope of the straight line of ln C vs t graph is : Slope = Y 2 – Y 1 / X 2 – X 1 or Slope = ln Cp t1 – ln Cp t2 / t 1 – t 2 K E = – Slope y = mx + b where m = slope and b = y-intercept Cp = Antilogarithm (10^y-intercept ) y = mx + b where m = slope and b = y-intercept Cp = Exponential Function ( e ^y-intercept ) Clinical Pharmacokinetics by DrShivMD 3

4. Instructions Using a scientific calculator for logarithmic and exponential calculations Logarithm (log base 10): To find the logarithm of a number "N," press the "Log and N" buttons. Antilogarithm (10^N): To find the antilogarithm (10^N) of a number "N," press the "Shift" button, then press the "Log and N" buttons. Natural Logarithm (ln): To find the natural logarithm (ln) of a number "N," press the "Ln and N" buttons. Exponential Function ( e^N ): To find "e" raised to the power of "N," press the "Shift" button, then press the "Ln and N" buttons. Clinical Pharmacokinetics by DrShivMD 4

5. Question What is the concentration of a drug at , 2 and 4 hours after a dose of 500 mg ? Known pharmacokinetic parameters are apparent volume of distribution, V d is 30 L itre and the elimination rate constant , K E is 0.2 hr -1 Problem Set 1 Hint : Use formulas V d = Dose / Cp Cp t = Cp * e – K E * t Clinical Pharmacokinetics by DrShivMD 5

6. Answers Cp is 16.7 mg/ Litre Cp 2 is 11.2 mg/ Litre Cp 4 is 7.5 mg/ Litre Clinical Pharmacokinetics by DrShivMD 6

7. Question If Cp 2 at 2 hours is 4.5 mg/ Litre and Cp 6 at 6 hours is 3.7 mg/ Litre after a 400 mg IV bolus dose, what are the values of K E , Cp , V d and CL? Problem Set 2 Hint: Use formulas Slope = ln Cp t1 – ln Cp t2 / t 1 – t 2 K E = – Slope Cp t = Cp * e – K E * t V d = Dose / Cp K E = CL / V d Clinical Pharmacokinetics by DrShivMD 7

8. Clinical Pharmacokinetics by DrShivMD 8

9. Answers K E is 0.05 hr -1 Cp is 5 mg/ Litre V d is 80 Litres CL is 4 Litre / hr Clinical Pharmacokinetics by DrShivMD 9

10. Data Provided Plasma concentration of viomycin after i.v . bolus administration: 10 μg /ml at 2 hours 5.5 μg /ml at 4 hours Dose administered: 300 mg Problem Set 3 Clinical Pharmacokinetics by DrShivMD 10

11. Questions Calculate the half-life of the drug (t 1/2 ). Calculate the concentration of drug in plasma at zero time (Cp ). Calculate the volume of distribution ( V d ). Calculate the total systemic clearance ( CL T ). Clinical Pharmacokinetics by DrShivMD 11

12. Important Formulas : Arithmetic Vs Graphical V d = Dose / Cp CL = 0.693 * V d / t 1/2 K E = CL / V d t 1/2 = 0.693 / K E Cp t = Cp * e – K E * t Common Log Natural Log Slope of the straight line of Log C vs t graph is : Slope = Y 2 – Y 1 / X 2 – X 1 or Slope = Log Cp t1 – Log Cp t2 / t 1 – t 2 K E = – Slope * 2.303 Slope of the straight line of ln C vs t graph is : Slope = Y 2 – Y 1 / X 2 – X 1 or Slope = ln Cp t1 – ln Cp t2 / t 1 – t 2 K E = – Slope y = mx + b where m = slope and b = y-intercept Cp = Antilogarithm (10^y-intercept ) y = mx + b where m = slope and b = y-intercept Cp = Exponential Function ( e ^y-intercept ) Clinical Pharmacokinetics by DrShivMD 12

13. Answers The half-life of the drug is 2.32 hours. The concentration of drug in plasma at zero time, Cp is 18.2 μg /ml. The V d is 16.5 litres . The total systemic clearance, CL T is 82.23 ml/min. Clinical Pharmacokinetics by DrShivMD 13

14. Clinical Pharmacokinetics by DrShivMD 14

15. Alternatively Clinical Pharmacokinetics by DrShivMD 15

16. Calculate the half-life of the drug Data given: Cp t1 = 10 mcg/ml at t 1 = 2 hours Cp t2 = 5.5 mcg/ml at t 2 = 4 hours Formula to be used: t 1/2 = 0.693/K E where K E = Elimination rate constant So, to calculate t 1/2 we have to first determine K E with the help of given data. K E can be determined from the slope of a line obtained by plotting log conc. on y-axis vs time on x-axis or by plotting ln conc. on y-axis vs time on x-axis (first order kinetics) Clinical Pharmacokinetics by DrShivMD 16

17. Clinical Pharmacokinetics by DrShivMD 17

18. Clinical Pharmacokinetics by DrShivMD 18

19. Calculate the half-life of the drug K E = – slope * 2.303 Log Cp t1 = Log 10 = 1 Log Cp t2 = Log 5.5 = 0.74 Slope of the straight line of Log C vs t is: Slope = Y 2 – Y 1 / X 2 – X 1 = 1 – 0.74 / 2 – 4 = – 0.26 / 2 = – 0.13 K E = – slope * 2.303 = – (– 0.13) * 2.303 = 0.299 hr -1 t 1/2 = 0.693 / K E = 2.32 hours Common Log- Log Concentration Vs Time Graph Clinical Pharmacokinetics by DrShivMD 19

20. Calculate the concentration of drug in plasma at zero time Cp is the plasma drug concentration at zero time after administration or initial plasma drug concentration. This can be obtained from the graph (Log conc. Vs time) by extrapolating the straight line and finding the Y-intercept which is equal to log Cp From the graph, log Cp = 1.26 (Also, we can use the formula: y = mx + b where m = slope and b = y-intercept and by plugging in the given point and the slope and we can solve for b.) Therefore, Cp = Anti-log 1.26 = 18.2 mcg/ml Graphical Method: Common Log- Log Concentration Vs Time Graph Clinical Pharmacokinetics by DrShivMD 20

21. Calculate the half-life of the drug K E = – slope Ln Cp t1 = Ln 10 = 2.3 Ln Cp t2 = Ln 5.5 = 1.7 Slope of the straight line of Ln C vs t is: Slope = Y 2 – Y 1 / X 2 – X 1 = 2.3 – 1.7 / 2 – 4 = - 0.6 / 2 = – 0.3 K E = – slope = -(- 0.3) = 0.3 hr -1 t 1/2 = 0.693 / K E = 2.31 hours Alternatively : Natural Log - Ln Concentration Vs Time Graph Clinical Pharmacokinetics by DrShivMD 21

22. Alternatively Clinical Pharmacokinetics by DrShivMD 22

23. Calculate the concentration of drug in plasma at zero time Cp is the plasma drug concentration at zero time after administration or initial plasma drug concentration. This can be obtained from the graph ( Ln conc. Vs time) by extrapolating the straight line and finding the Y-intercept which is equal to ln Cp We can use the formula: y = mx + b where m = slope and b = y-intercept and by plugging in the given point and the slope and we can solve for b.) Therefore, Cp = e^ 2.9 = 18.2 mcg/ml Graphical Method: Natural Log - Ln Concentration Vs Time Graph Clinical Pharmacokinetics by DrShivMD 23

24. Calculate the concentration of drug in plasma at zero time Use formula Cp t = Cp * e – K E * t 10 = Cp * e – 0.3 * 2 10 = Cp * e – 0.6 10 = Cp * 0.54 Cp = 10 / 0.54 = 18.5 mcg/ml Arithmetic Method Clinical Pharmacokinetics by DrShivMD 24

25. Calculate the volume of distribution ( V d ) Vd = Dose / Cp where: Dose = Dose administered intravenously and Cp = Plasma drug conc. at zero time after administration Therefore, Vd = 300 * 1000 mcg / 18.2 mcg per ml = 16,500 ml or 16.5 litres Clinical Pharmacokinetics by DrShivMD 25

26. Calculate the total systemic clearance ( CL T ) CL T = K E * V d = 0.299 hr -1 * 16.5 litres = 0.299/60 mins *16.5*1000 ml = 82.23 ml/min Clinical Pharmacokinetics by DrShivMD 26