Principles of Pharmacokinetics Pharmacokinetics of IV Administration, 1-Compartment

1. Principles of PharmacokineticsPharmacokinetics of IV Administration, 1-Compartment Karunya Kandimalla, Ph.D kandimalla.karunya@mayo.edu

2. Objectives • Be able to: • To understand the properties of linear models • To understand assumptions associated with first order kinetics and one compartment models • To define and calculate various one compartment model parameters (kel, t½, Vd, AUC and clearance) • To estimate the values of kel, t½, Vd, AUC and clearance from plasma or blood concentrations of a drug following intravenous administration.

3. Recommended Readings • Chapter 3, p. 47-62 • IV route of administration • Elimination rate constant • Apparent volume of distribution • Clearance

4. Kinetics From the Blood or Plasma Data Pharmacokinetics of a drug in plasma or blood Absorption (Input) Disposition Distribution Elimination Excretion Metabolism

5. Disposition Analysis (Dose Linearity)

6. Disposition Analysis (Time Variance)

7. Linear Disposition • The disposition of a drug molecule is not affected by the presence of the other drug molecules • Demonstrated by: • Dose linearity Saturable hepatic metabolism may result in deviations from the dose linearity • Time invariance Influence of the drug on its own metabolism and excretion may cause time variance

8. Disposition Modeling • A fit adequately describes the experimental data • A model not only describes the experimental data but also makes extrapolations possible from the experimental data • A fit that passes the tests of linearity will be qualified as a model

9. One Compartment Model (IV Bolus) • Schematically, one compartment model can be represented as: Where Xp is the amount of drug in the body, Vd is the volume in which the drug distributes and kel is the first order elimination rate constant Drug Eliminated kel Drug in Body Xp = Vd• C

10. One Compartment Data (Linear Plot)

11. One Compartment Data (Semi-log Plot)

12. Two Compartment Model (IV Bolus) K 12 Drug in Central Compartment Blood, kidneys, liver Drug in Peripheral Compartment • For both 1- and 2-compartment models, elimination takes place from central compartment K 21 kel Fat, muscle Drug Eliminated

13. Two Compartment Data (Linear Plot)

14. Two Compartment Data (Semi-log Plot)

15. One Compartment Model-Assumptions • 1-Compartment—Intravascular drug is in rapid equilibrium with extravascular drug • Intravascular drug [C] proportional to extravascular [C] • Rapid Mixing—Drug mixes rapidly in blood and plasma • First Order Elimination Kinetics: • Rate of change of [C]  Remaining [C]

16. Derivation-One Compartment Model Bolus IV Kel Central Compartment (C)

17. C0 = Initial [C] C0 is calculated by back-extrapolating the terminal elimination phase to time = 0 IV Bolus Injection: Graphical Representation Assuming 1st Order Kinetics C0 = Dose/Vd C0 = Dose/Vd Slope = -Kel/2.303 Slope = -K/2.303 Concentration versus time, semilog paper

18. Elimination Rate Constant (Kel) • Kel is the first order rate constant describing drug elimination (metabolism + excretion) from the body • Kel is the proportionality constant relating the rate of change of drug concentration and the concentration • The units of Kel are time-1, for example hr-1, min-1 or day-1

19. Half-Life (t1/2) • Time taken for the plasma concentration to reduce to half its original concentration • Drug with low half-life is quickly eliminated from the body

20. Change in Drug Concentration as a Function of Half-Life

21. Apparent Volume of Distribution (Vd) • Vd is not a physiological volume • Vd is not lower than blood or plasma volume but for some drugs it can be much larger than body volume • Drug with large Vd is extensively distributed to tissues • Vd is expressed in liters and is calculated as: • Distribution equilibrium between drug in tissues to that in plasma should be achieved to calculate Vd

22. Area Under the Curve (AUC) • AUC is not a parameter; changes with Dose • Toxicology: AUC is used as a measure of drug exposure • Pharmacokinetics: AUC is used as a measure of bioavailability and bioequivalence • Bioavailability: criterion of clinical effectiveness • Bioequivalence: relative efficacy of different drug products (e.g. generic vs. brand name products) • AUC has units of concentration  time (mg.hr/L)

23. Calculation of AUC using trapezoidal rule

24. Clearance (Cl) • The most important disposition parameter that describes how quickly drugs are eliminated, metabolized and distributed in the body • Clearance is not the elimination rate • Has the units of flow rate (volume / time) • Clearance can be related to renal or hepatic function • Large clearance will result in low AUC

25. Clearance Concepts Cfinal Cinitial ORGAN elimination If Cfinal < Cinitial, then it is a clearing organ

26. Practical Example • IV bolus administration • Dose = 500 mg • Drug has a linear disposition

27. Linear Plot

28. Natural logarithm Plot ln (C0) Kel

29. Half-Lifeand Volume of Distribution t1/2 = 0.693 / Kel = 3.172 hrs Vd = Dose / C0 = 500 / 11.12 = 44.66 ln (C0) = 2.4155 C0 = Inv ln (2.4155) = 11.195 mg/L

30. Clearance Cl = D/AUC Cl = VdKel Cl = 44.66  0.218 = 9.73 L/hr

31. Home Work Determine AUC and Calculate clearance from AUC