The general concept of pharmacokinetics

Transcription

1 The general concept of pharmacokinetics Hartmut Derendorf, PhD University of Florida

2 Pharmacokinetics the time course of drug and metabolite concentrations in the body

3 Pharmacokinetics helps to optimize drug therapy: dose dosage regimen dosage form

4 What happens to a drug after its administration? ("Fate of drug") Liberation Absorption Distribution Metabolism Excretion

5 Goal to produce a desired drug concentration in the body using the optimum dosage regimen and dosage form Problem What is the optimum target concentration?

6 Pharmacokinetics in "normal" subjects Biological variability! Therapeutic drug level monitoring in individual patients

7 Pharmacokinetic Parameters Clearance Volume of distribution Half-life Bioavailability

8 Clearance! quantifies ELIMINATION! is the volume of body fluid cleared per time unit (L/h, ml/min)! is usually constant

9 Clearance Eliminating Organ CL = Q E Blood Flow Extraction Ratio

10 Clearance Clearance can be calculated from! Excretion rate / Concentration e.g. (mg/h) / (mg/l) = L/h! Dose / Area under the curve (AUC) e.g. mg / (mg h/l) = L/h

11 Clearance Total body clearance is the sum of the individual organ clearances CL = CL ren + CL hep + CL other

12 Volume of Distribution Vd = X / Cp - quantifies DISTRIBUTION - relates drug concentration (Cp) to amount of drug in the body (X) - gives information on the amount of drug distributed into the tissues

13 Apparent Volume of Distribution X X V C1 V C2 C1 = X / V V = X / C1 C1 > C2 V < Vd C2 = X / Vd Vd = X / C2

14 Volume of Distribution Ibuprofen Gentamicin (ECF) Antipyrine (TBW) Diazepam Digoxin Azithromycin 0.15 L/kg 0.25 L/kg 0.60 L/kg 1.1 L/kg 7.3 L/kg 31 L/kg

15 Half-Life t 1/ 2 = CL Vd Half-life is the time it takes for the concentration to fall to half of its previous value Half-life is a secondary pharmacokinetic parameter and depends on clearance and volume of distribution

16 Half-Life ln 2 t = = 1 / 2 k k CL = k Vd k CL Vd elimination rate constant clearance volume of distribution

17 Zero order kinetics First order kinetics C = Co - ko t Co = 100 ng/ml ko = 10 ng/ml/h t [h] C [ng/ml] C = Co exp(-k t) t [h] C [ng/ml] Co = 100 ng/ml k = /h C [ng/ml] C [ng/ml] t [h] t [h]

18 Bioavailability f = AUC AUC po iv - quantifies ABSORPTION f is the fraction of the administered dose that reaches the systemic circulation

19 Bioavailability Rate and Extent of Absorption 70 Cmax Cmax tmax tmax Time (hours)

20 Models in Pharmacokinetics Compartment Models Physiological Models Statistical Models

21 Compartment Models Parameters: Rate constants, intercepts Linear and nonlinear regression Complete concentration-time-profiles Steady-state and non-steady-state

22 Physiological Models Q E = C i C i C o C i Eliminating Organ C o CL CL = = Q E Q Q + f u f u CL CL int int Parameters: Blood Flow, intrinsic clearance, protein binding Good prediction of changes in clearance Steady state

23 High-extraction drugs CL = Q << Q f Q + f u u f u CL CL CL int int int CL = Q Low-extraction drugs CL = Q >> Q f Q + f u u f u CL CL CL int int int CL = f u CL int

24 Statistical Models MRT AUMC = = AUC 0 Cp t dt 0 Cp dt Parameters: Mean residence time, mean absorption time Area calculation by trapezoidal rule Calculation of clearance and volume of distribution Additivity of parameters Steady state

25 Drug Input Intravenous Bolus First-Order Absorption Zero-Order Absorption

26 Intravenous bolus One compartment model D X k E D X E Dose Drug in the body Drug eliminated

27 Intravenous bolus Plasma concentration (single dose) C C = 0 e k t 10 2 C0 C (ng/ml) k/2.3 D 10 0 C = 0 Vd Time (hours)

28 Intravenous bolus Multiple Dose

29 Intravenous bolus Plasma concentration (multiple dose, steady state) C = C 0 e kt ( 1 e k ) τ Peak Trough C C e 0 ( 1 e k τ ) Cmin = 0 ( 1 e k τ ) Cmax = k τ

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31 The AUC within a dosing interval at steady state is equal to the total AUC of a single dose.

32 Intravenous bolus Average concentration (multiple dose, steady state) C = D CL τ

33 First-order absorption One compartment model D f A k a X k E Dose Drug at absorption site Drug in the body Drug eliminated

34 Oral administration Plasma concentration (single dose) C = F D k ( ) a k k Vd a ( e kt e k t) a

35 Oral administration

36 Oral administration Multiple Dose

37 Oral administration Average concentration (multiple dose, steady state) C = F CL D τ

38 Zero-order absorption One compartment model D f A R 0 X k E Dose Drug at absorption site Drug in the body Drug eliminated

39 Constant rate infusion Plasma concentration (during infusion) C R = 0 1 CL ( e kt )

40 Constant rate infusion

41 Constant rate infusion Plasma concentration (steady state) C = R0 CL

42 Two-compartment model D Xc k 10 E k 12 k 21 Xp Dose Xc Drug in the central compartment Xp Drug in the peripheral compartment Drug eliminated

43 Two-compartment model 10 3 C a C (ng/ml) C (ng/ml) 10 2 b 10 1 β α Time (hours) Time (hours)

44 Two-compartment model Plasma concentration (single i.v. bolus dose) α t β t C = a e + b e α-phase: β-phase: distribution phase elimination phase

45 Two-compartment model Volume of distribution Xc Xc Xc Xp Xp Xp initially steady state elimination phase V c = D C 0 Vd ss = 1 + k k V c CL Vd = area β

46 Two-compartment model Amount of drug in tissue X T = k D 12 ( ) ( e α t e β t ) β α Free concentration in tissue C f T = ( ) k D f 21 1 V c ( β α) b ( e α t e β t )

47 Two-compartment model C (ng/ml) Time (hours)

48 Three-compartment model d Xp D k 31 k 13 Xc k 10 E k 12 k 21 D E Dose Drug eliminated Xp s Xc Drug in the central compartment Xps Drug in the shallow peripheral compartment Xpd Drug in the deep peripheral compartment

49 Significance of Pharmacokinetic Parameters for Dosing Maintenance Dose Loading Dose R 0 = C F D = τ LD = C desired C CL desired desired CL Vd Fluctuation Dosing Interval F = τ = C C max( desired ) min( desired ) 0 1/ t ln( F)

50 Drug Delivery? Biopharmaceutics Pharmacokinetics? PK-PD-Modeling Pharmacodynamics

51 Conclusion Pharmacokinetic data is only therapeutically useful if there is a known relationship between drug concentration and drug effect or side effect.