A.U.C. (Area Under Curve) Dr Jayesh Vaghela

A.U.C. (Area Under Curve) Dr Jayesh Vaghela

1. Area Under Curve Dr. Jayesh Vaghela

2. Pharmacokinetics Definition : “ Study of the time course of – - the drug & its metabolite levels in different body fluids, tissues & excreta of body and, - the mathematical relationships required to develop models to interpret such data. ”

3. Drug is given by Intravenous bolus It follows First order kinetic Single compartment open model

4. Area Under Plasma Concentration-Time Curve Linear Plot of Cp versus Time showing AUC and AUC segment

5. Importance of AUC Toxicology : - Measure of drug exposure Biopharmaceutics : - Comparison of drug products in BABE studies Pharmacokinetics : - Measure of Pharmacokinetic parameters e.g. Clearance, BA.

6. Elimination Rate Constant, kel Definition : “ The fraction of the total amount of drug in the body which is removed per unit time . ” An overall elimination rate constant Describes removal of the drug by all the elimination processes including excretion and metabolism.

7. Equation for kel Proportionality constant relating, - The rate of change in drug plasma concentration, & - Plasma concentration. kel = - dCp / dt Cp

8. kel as Slope

9. Calculation of kel

10. Unit of kel kel = - dCp / dt Cp 1 / hour Or Hr -1

11. Example Drug kel (1 / hour) Acetaminophen 0.28 Diazepam 0.021 Digoxin 0.017 Gentamycin 0.35 Lidocaine 0.43 Theophylline 0.063

12. Relation Between Cp & Time

13. Steps Dividing whole AUC into trapezoidal segments ⇓ Counting the area of each segments separately ⇓ Summation of all the area ⇓ Total area

14. Calculation of AUC Planimeter : - M echanically measuring the area of plain figures Cut & Weigh method : - Cutting area on rectilinear graph paper & weighing it by analytical method Mathematical : - Trapezoidal rule

15. Trapezoidal Rule

16. Trapezoid Four sided figure with two parallel sides

17. We can calculate the AUC of each segment if we consider the segments to be trapezoids

18. Calculation of a segment AUC 2-3 = Cp 2 + Cp 3 x ( t 3 – t 2 ) 2

19. The area from the first to last data point can then be calculated by adding the areas together

20. Calculation of First Segment The first segment can be calculated after determining the zero plasma concentration Cp by extrapolation AUC 0-1 = C p + C p 1 x t 1 2

21. Calculation of Last Segment Final segment can be calculated from t last to t infinity

22. Total AUC

23. Example of calculation of AUC Time ( hr ) Concentration (mg / L) ????? 1 71 2 50 3 35 4 25 6 12 8 6.2 10 3.1

24. AUC

25. Calculation of kel ln (x) = 2.303 . log(x ) Time Concentration ( ln ) 1 71 ( 4.26 ) 2 50 ( 3.91) 3 35 ( 3.55 ) 4 25 ( 3.21 ) 6 12 ( 2.48 ) 8 6.2 ( 1.82 ) 10 3.1 ( 1.13 )

26. ln Concentration-Time Curve Slope = kel = - 0.34 / time

27. Extrapolation of Cp - kel . t Cp0 = Cp / e Cp = 71 kel = 0.34 Cp0 = 100

28. Calculation of First Segment AUC 0-1 = Cp + Cp 1 x t 1 2 = ( 100 + 71 ) . 1 2 = 85.5

29. Calculation of Observed Segments AUC 2-3 = Cp 2 + Cp 3 . ( t 3 – t 2 ) 2 Time Concentration AUC 100 1 71 85.5 2 50 60.5 3 35 42.5 4 25 30 6 12 37 8 6.2 18.2 10 3.1 = Cp last 9.3 ??? ??? ???

30. Calculation o f Last Segment = 3.1 / 0.34 = 9.11

31. Total AUC Time Concentration AUC 100 1 71 85.5 2 50 60.5 3 35 42.5 4 25 30 6 12 37 8 6.2 18.2 10 3.1 9.3 ?? ?? 9.1 = AUC last Total 292.1

32. Unit of AUC Conc . time mass . time / volume mg . hr / litre

33. So, in our example, Total AUC = 292.1 mg . hr / L

34. References Gibaldi , M. and Perrier, D. 1975 Pharmacokinetics, Marcel Dekker, page v . Atkinson et al 2007, Principles of Clinical Pharmacology ,Elsevier-2 nd edition David Bourne, Ph.D., A First Course in Pharmacokinetics and Biopharmaceutics