sign in sign up
<<
Home , ADME, Bioavailability, Bioequivalence, Clearance (pharmacology), Loading dose, Pharmacokinetics

Basic Concepts of

Achiel Van Peer, Ph.D. Clinical

1 Gent, 24 August 2007/avpeer Some introductory Examples

2 Gent, 24 August 2007/avpeer 15 mg of X in a slow release OROS capsule administered in fasting en fed conditions in comparison to 15 mg in solution fasting

3 Gent, 24 August 2007/avpeer Prediction of drug plasma before the first in a human

NOAEL in female rat

NOAEL in female dog

NOAEL in male dog NOAEL in male rat

First dose 5 mg Fabs 100% Fabs 50% Fabs 20%

4 Gent, 24 August 2007/avpeer Allometric Scaling

5 Gent, 24 August 2007/avpeer Pharmacokinetics: Time Profile of Drug Amounts

Drug at absorption site

Metabolites

Drug in body

Percent of dose Excreted drug

Time (arbitrary units) Rowland and Tozer, Clinical Pharmacokinetics: Concepts and Applications, 3rd Ed. 1995 6 Gent, 24 August 2007/avpeer Definition of Pharmacokinetics ?

Pharmacokinetics is the science describing drug

absorption from the administration site distribution to „ tissues, „ target sites of desired and/or undesired activity

PK= ADME

7 Gent, 24 August 2007/avpeer We will cover

Some introductory Examples Model-independent Approach Compartmental Approaches Drug Distribution and Elimination Multiple-Dose Pharmacokinetics Drug Absorption and Oral Role of Pharmacokinetics

8 Gent, 24 August 2007/avpeer The simplest approach … observational pharmacokinetics The Model-independent Approach

Cmax : maximum observed

Tmax : time of Cmax AUC : area under the curve

9 Gent, 24 August 2007/avpeer Cmax, Tmax and AUC in Bioavailability and Studies Absolute bioavailability (Fabs) „ compares the amount in the systemic circulation after intravenous (reference) and extravascular (usually oral) dosing

Fabs = AUCpo/AUCiv for the same dose

„ between 0 and 100% (occasionally >100%)

Relative bioavailability (Frel) „ compares one drug product (e.g. ) relative to another drug product (solution)

Bioequivalence (BE): a particular Frel Two drug products with the same absorption rate (Cmax, Tmax) and the same extent (AUC) of absorption (90% confidence intervals for Frel between 80-125%) 10 Gent, 24 August 2007/avpeer Absolute oral bioavailability , J&J data on file

Other example: : 10% in extensive metabolisers; 100% in poor metabolisers

11 Gent, 24 August 2007/avpeer Area under the curve

Trapezoidal rule: divide the plasma concentration-time profile to several trapezoids, and add the AUCs of these trapezoids Conc

+ CC 21 Units, e.g. ng.h/mL t2-t1 = (AUC − tt )12).( 2

Clast AUCextrapolated = λz

0 0 Time 12 Gent, 24 August 2007/avpeer Elimination half-life ?

Half-life (t1/2) : time the drug concentration needs to decrease by 50%

13 Gent, 24 August 2007/avpeer Elimination half-life ? visual inspection

14 Gent, 24 August 2007/avpeer Elimination half-life ? visual inspection or alternatives ?

Half-life (t1/2) : time to decrease by 50%

T1/2 = 6 hrs Derived from a semilog plot

T1/2 = 0.693/λz

15 Gent, 24 August 2007/avpeer From Whole-Body Physiologically based Pharmacokinetics to Compartmental Models

Poggesi et al., Nerviano Medical Science

16 Gent, 24 August 2007/avpeer Compartmental Approach

drug distributes very rapidly to all tissues via the systemic circulation an equilibrium is rapidly established between the and the tissues, the body behaves like one (lumped) compartment does not mean that the concentrations in the different tissues are the same

One-compartment PK model

Drug Absorption Body compartment Drug Elimination

17 Gent, 24 August 2007/avpeer One compartment behaviour more often observed after oral drug intake

1000

100

Poor metabolisers

10

Extensive metabolisers 1 0 8 16 24 32 40 48 Time, hours

18 Gent, 24 August 2007/avpeer Intravenous dose of 0.2 mg Levocabastine (J&J data on file)

19 Gent, 24 August 2007/avpeer Depending on rate of equilibration with the systemic circulation, lumping tissues together, and simplification is possible

Multi- or Multi-Compartment Whole Body Pharmacokinetic model

Tri-compartment model

Two-compartment model

One-compartment model

20 Gent, 24 August 2007/avpeer Zero-order rate drug administration and first-order rate drug elimination

Amount A in blood, plasma

Infusion rate Rate of elimination is mg/min proportional to the Amount in blood/plasma dDose/dt = Ko = mg/min dA/dt = -k.A

[Often K=Kel=K10]

21 Gent, 24 August 2007/avpeer First-order rate of drug disappearance

Rate of elimination Amount A is proportional to [or Concentration C] the Amount or in blood, plasma Concentration in blood, plasma

dA/dt = -k.A = -k.Vd.C Intravenous bolus

If A = Amount in plasma, then V= Plasma volume If A = Remaining amount in the body, then Vd= Total

22 Gent, 24 August 2007/avpeer A single iv dose of 5 mg for a drug with immediate equilibration (one compartment behaviour)

dA/dt = -k10.A = -k10.V.C

dA/dt = -k10.A = -CL.C

dC/dt = -k10.C -k10.t C = C0. e

23 Gent, 24 August 2007/avpeer A single iv dose of 5 mg

-k10.t C = C0 e

lnC = lnC0 -k10.t

Remark for log10 scale: slope = k10/2.303 24 Gent, 24 August 2007/avpeer A single iv dose of 5 mg

ln C = lnC0 -k10.t

− CC 2ln1ln 693.0 k10 = = t − t12 t − t12

Slope=k10 = the elimination rate constant

Half-life = C2 0.693/k10 = half of C1

25 Gent, 24 August 2007/avpeer A single iv dose of 5 mg

dose 5000000ng Vd == = 9.30 L Cpo /162 mLng

Vd = volume of distribution, relates the drug concentration to the drug amount in the body

26 Gent, 24 August 2007/avpeer One-Compartment model after intravenous administration

Vd = volume of distribution, relates the drug concentration at a particular time to the drug amount in the body at that time

k10= (first-order) elimination rate constant

Clearance (CL) = Vd.K10 The volume of drug in the body cleared per unit time

Half-life = 0.693 . Vd/CL

27 Gent, 24 August 2007/avpeer Compartmental Approach after intravenous dosing Distribution

Central Peripheral compartment compartment Re-distribution

Elimination

Rapidly equilibrating tissues: plasma, red blood cells, , , …

Slower equilibrating: adipose tissues, muscle, … Usually peripheral compartment Slowly redistribution reason for long terminal half-life

28 Gent, 24 August 2007/avpeer Intravenous dose of 0.2 mg levocabastine

-1 K12= 0.84 h

V1 = 44 L V2 = 35 L

K = 1.05 h- 21 1

-1 K10 = 0.4 h

29 Gent, 24 August 2007/avpeer Intravenous dose of 0.2 mg levocabastine

Cld= k12.V1= 36.7 L/h

V1 = 44 L V2 = 35 L

Cld= k21.V2= 36.7 L/h

Cl=K10 .V1=Dose/AUC= 1.77 L/h=30 mL/min

Vdss = V1 + V2

30 Gent, 24 August 2007/avpeer Rates of drug exchange

DAp/dt = - K10.Vc.Cp - K12.Vc.Cp + K21.Vt.Ct

DAt/dt = K12.Vc.Cp - k12.Vt.Ct

Initially very fast decay due to distribution to tissues and elimination (“distribution phase”) until equilibrium is reached (influx into and from tissue is equal)

After a pseudo-equilibrium is reached, there is only loss of drug from the body (“elimination phase”), but is in fact combination of redistribution from tissues and elimination

Rate of redistribution may differ significantly across ; long terminal half-life is compounds sticks somewhere

31 Gent, 24 August 2007/avpeer Intravenous dose of 0.2 mg levocabastine

Cp=A.e-α.t+B.e-β.t

Cp=2.1.e-1.91 .t+2.5.e- 0.0224.t

0.693 693.0 2/1 term tt 2/1 β == = = 31h β h −10224.0

Vdβ = CL/β=Dose/(AUC. β)=Vdarea

32 Gent, 24 August 2007/avpeer Two-compartmental model

Central K12 Compartment Peripheral Vc Compartment K21 Vt K10

K10, K12, K21 are first order rate constants

hybrid first-order rate constants α and β for the so-called distribution phase and elimination phases, T1/2α and T1/2β

Vc, Vdss, Vdβ or Vdarea are Vd of central compartment, at steady-state, during elimination phase

33 Gent, 24 August 2007/avpeer Compartmental approach after intravenous dosing

Shallow Peripheral Central compartment compartment

Deep Peripheral compartment

Compartments serve as reservoirs with different drug amounts (concentrations), different volumes, and different rates of exchange of drug with the central compartment.

The shape of the plasma concentration-time profile empirically defines the number of compartmentsl

34 Gent, 24 August 2007/avpeer Intravenous Sufentanil

Gepts et al., Anesthesiology, 83:1194-1204, 1995

35 Gent, 24 August 2007/avpeer Three compartmental model Sufentanil Pharmacokinetics Mixed-effects Population PK analysis (N =23) Population CV (%) Average Volume of distribution (L) Central (V1) 14.6 22 Rapidly equilibrating (V2) 66 31 Slowly equilibrating (V3) 608 76 At steady-state 689 (L/min) Systemic (CL or CL1) 0.88 23 Rapid distribution (CL2) 1.7 48 Slow distribution (CL3) 0.67 78

Gepts et al., Anesthesiology, 83:1194-1204, 1995

36 Gent, 24 August 2007/avpeer Three compartmental model Sufentanil Pharmacokinetics

Fractional Rate constants Coefficients (min-1) A 0.94 K10 0.06 B 0.058 K12 0.11 C 0.0048 K13 0.05 K21 0.025 K31 0.0011 Exponents (min-1) Half-lives (min) α 0.24 t1/2 α 2.9 β 0.012 t1/2 β 59 γ 0.0006 t1/2 γ 1129

Gepts et al., Anesthesiology, 83:1194-1204, 1995

37 Gent, 24 August 2007/avpeer Compartmental approach after intravenous dosing

Central Shallow Peripheral compartment compartment

Deep Peripheral compartment

Central Peripheral compartment compartment

Effect site

38 Gent, 24 August 2007/avpeer Time profile of opioid concentrations in plasma and the predicted concentrations at the effect site based upon an effect compartment PK-PD model (expressed as percentage of the initial plasma concentration)

Effect site concentration profile reflect difference in onset time of analgesia

Shafer and Varvel, Anesthesiology 74:53-63, 1991

39 Gent, 24 August 2007/avpeer Rate of Drug Distribution

perfusion-limited tissue distribution

„ immediate equilibrium of drug in blood and in tissue

„ only limited by blood flow

„ highly perfused : liver, kidneys, lung,

„ poorly perfused : skin, fat, bone, muscle

Permeability rate limitations or membrane barriers

„ blood-brain barrier (BBB)

„ blood-testis barrier (BTB)

„ placenta

40 Gent, 24 August 2007/avpeer Unbound Fraction and Drug Disposition

Plasma Cell Tissue membrane -bound drug

Protein-bound Free drug Free drug Protein-bound drug (non-ionized) (non-ionized) drug

Ionized drug Ionized drug (free) (free)

Pka-pH, affinity for plasma and tissue proteins, permeability, … 41 Gent, 24 August 2007/avpeer Physicochemistry, PK and EEG PD of narcotic analgesics Sufentanil pKa 6.5 8.43 8.01 % unionized at pH 7.4 89 8 10

P oct/water 130 810 1750

% unbound in plasma 8 16 8

Vdss (L) 23 358 541

Cl (L/m in) 0.20 0.62 1.2 t1/2 keo EEG (m in) 1.1 6.6 6.2

Ce50, EEG (ng/ml) 520 8.1 0.68

Ce50, unb (ng/m l) 41 1.2 0.051 Ki (ng/ml) 7.9 0.54 0.039

Shafer SL, Varvel JR: Pharmacokinetics, , and rational opioid selection. Anesthesiology 1991; 74:53-63; DR Stanski, J Mandema (diverse papers) 42 Gent, 24 August 2007/avpeer Localisation and Role of Drug Transporters Zhang et al., FDA web site and Mol. Pharmaceutics 3, 62-69, 2006

43 Gent, 24 August 2007/avpeer Apparent Volume of Distribution

Vd = Amount of drug in body/concentration in plasma Minimum Vd for any drug is ~3L, the plasma volume in an adult, for ethanol: equal to For most basic drugs very high due to sequestering in specific organs (liver, muscle, fat, etc.)

Rowland and Tozer, Clinical Pharmacokinetics: Concepts and Applications, 3rd Ed., 1995

44 Gent, 24 August 2007/avpeer Vd (L/kg) after iv dosing in rat and human (J&J data)

45 Gent, 24 August 2007/avpeer Multiple Dosing Concepts

46 Gent, 24 August 2007/avpeer Dosing to Steady-state On continued drug administration, the amount in the body will initially increase but attain a steady-state, when the rate of elimination (drug loss per unit time) equals the amount administered per unit time

Amount A in body Cplasma.Vdss

Fractional loss of A or Cp mg/day First-order rate -K.A; -CL.Cp

1. Initial increase when ko > -K10.Abody

2. Steady state when ko = K.Abody= CL.C

3. Ass or Css constant as long ko constant and CL constant

47 Gent, 24 August 2007/avpeer Time to steady-state Half-life of 24 hr and dosing interval of 24 hrs

Steady-state when drug loss per day equals drug intake per day

48 Gent, 24 August 2007/avpeer Time to steady-state Half-life of 24 hr and dosing interval of 24 hrs

Cmax

Cavg,ss

Cavg,ss = AUCssτ/ τ Cmin AUCτ at steady state = AUC∞ single dose AUCτss/ AUCτfirst dose= Accumulation Index

49 Gent, 24 August 2007/avpeer Steady-state

The amount in the body at steady-state (Ass)

Ko Ass = Kel

The plasma concentration at steady-state (Css,Cavgss)

Ko Ko Cpss = = Kel.Vdss Cl

Css is proportional to the dosing rate (zero-order input) and inversely proportional to the first-order elimination rate or clearance

50 Gent, 24 August 2007/avpeer Time to steady-state Half-life of 24 hr and dosing interval of 24 hrs

Cmax

Cavg,ss

Cmin C=Css(1-e-k.t)

5-6 half-lives to reach steady-state

51 Gent, 24 August 2007/avpeer An effective half-life reflects drug accumulation

Drug A: A=20 ng/mL; B=80 ng/mL; T1/2α=3 h; T1/2β=24 h

Drug B: A=80 ng/mL; B=20 ng/mL; T1/2α=3 h; T1/2β=24 h

52 Gent, 24 August 2007/avpeer An effective half-life reflects drug accumulation AUCss,τ 1 Accumulati ratioon = = AUC0 −τ −− Keff τ ).exp(1

Drug A: T1/2eff= 20 h Drug B: T1/2eff= 10 h

C=Css(1-e-keff.t)

Boxenbaum, J Clin Pharmcol 35:763-766, 1995 53 Gent, 24 August 2007/avpeer Mean = MRT

MRT is the time the drug, on average, resides in the body.

MRT = Vdss/Cl

54 Gent, 24 August 2007/avpeer Loading and

Maintenance Dose = desired Css x CL

Loading Dose = desired Css X Vd

Loading dose can be high for drugs with large Vd, then LD divided over various administrations

(J&J data on file)

55 Gent, 24 August 2007/avpeer Total body clearance (CL)

A measure of the efficiency of all eliminating organs to metabolize or excrete the drug Volume of plasma/blood cleared from drug per unit time

CL = k10.Vc = λz.Vdz=MRT.Vdss

CL= Dose / AUCplasma

56 Gent, 24 August 2007/avpeer Physiological approach to Clearance

Amount A or Concentration C Rate in in blood Rate out Q.Cpv Q.Cpa

a Cpv)-Q(Cp fu.Clint Clearance = = .Q Cpa + fu.ClintQ

Clearance = QE

Low hepatic clearance High hepatic clearance if E <<1 if E ≅1 eg. Risperidone (Fabs 85%) eg. Nebivolol (Fabs 10%)

57 Gent, 24 August 2007/avpeer Bioavailability F

After , not all drug may reach the systemic circulation

The fraction of the administered dose that reaches the systemic circulation is called the bioavailability F

58 Gent, 24 August 2007/avpeer Oral drug absorption, Influx and Efflux Transporters, Drug Loss by First-pass Gut lumen

Portal Uptake and effluxVein transporters Systemic Tablet circulation disintegration Drug Liver dissolution Gut wall Hepatic Metabolism Metabolism Biliary secretion Uptake and efflux Into transporters faeces F= Fabsorbed.(1-Egut).(1-Eliver)

59 Gent, 24 August 2007/avpeer Grapefruit inhibits gut-wall metabolism (J&J data on file)

140 Mean (N=13) 120 10 mg q.i.d./ GFJ 100 Cisapride 10 mg q.i.d./ water

80

60

40 Plasma cisapride conc. (ng/mL) Plasma cisapride 20

0 0 8 16 24 32 40 48 Time after morning dose on day 6 (hours)

60 Gent, 24 August 2007/avpeer Total body clearance (CL)

Intravenous clearance

Cl = k10.Vc = λz.Vdz = MRT.Vdss

CL= Dose / AUCiv

Apparent oral clearance

Oral clearance CL/F= Dose / AUCoral

61 Gent, 24 August 2007/avpeer Biopharmaceutical Classification Amidon et al., Pharm Res 12: 413-420, 1995; www.fda.gov High Low Solubility Class 1 Class 2 High Solubility Low Solubility High Permeability High Permeability High Rapid Dissolution Permeability Class 3 Class 4 High Solubility Low Solubility Low Permeability Low Permeability Low Permeability

62 Gent, 24 August 2007/avpeer Predicting Drug Disposition via BCS Wu and Benet, Pharm Res 22:11-23, 2005

High Solubility Low Solubility Class 1 Class 2 Transporter Efflux transporter effects minimal effects High predominate Permeability Class 3 Class 4 Absorptive Absorptive and transporter efflux transporter Low effects effects could be

Permeability predominate important

63 Gent, 24 August 2007/avpeer Predicting Drug Disposition via BCS Wu and Benet, Pharm Res 22:11-23, 2005

High Solubility Low Solubility Class 1 Class 2 Metabolism Metabolism High Permeability Class 3 Class 4 Renal & Biliary Renal & Biliary Elimination of Elimination of Low Unchanged Drug Unchanged Drug Permeability

64 Gent, 24 August 2007/avpeer Biliary Excretion: Enterohepatic Recycling

Excretion Drug The drug in the GI tract in in blood is depleted. Re-absorption Biliary excreted drug is reabsorbed Metabolism Drug in Intestine Conjugate in Liver Enzymatic breakdown of glucuronide

Conjugate Conjugate Excretion in bile in intestine Dumped in feces from gall bladder

65 Gent, 24 August 2007/avpeer Highly variable drugs and drug products

Drugs with high within-subject variability in Cmax and AUC (> 30% coefficient of variation) are called “highly-variable drugs”

Highly-variable drug products are pharmaceutical products in which the drug is not highly variable, but the product is of poor pharmaceutical quality

66 Gent, 24 August 2007/avpeer From PK to relevant information for the patient

Compound X ® Tablets and oral solution …… Pharmacokinetics: The estimated mean ± SD half-life at steady-state of compound X after intravenous infusion was 35.4 ± 29.4 hours. Renal impairment: The oral bioavailability of compound X may be lower in patients with renal insufficiency. A dose adjustment may be considered. Other : Do not combine compound X with certain medicines called azoles that are given for fungal infections. Examples of azoles are , , and . You should not take compound X with grapefruit juice. ……

67 Gent, 24 August 2007/avpeer Useful Material Handbooks Pharmacokinetics, 2nd Ed., by Milo Gibaldi Clinical Pharmacokinetics, Concepts and Applications, 3rd Ed., by Malcolm Rowland and Thomas N. Tozer Pharmacokinetic & Pharmacodynamic Data Analysis: Concepts and Applications, 4th Ed., by Johan Gabrielsson and Dan Weiner

WinNonLin software™, Pharsight® Noncompartmental and Compartmental analysis Pharmacokinetic-pharmacodynamic analysis Statistical Bioequivalence analysis In vitro-in vivo Correlation for drug products

68 Gent, 24 August 2007/avpeer Thank for your attention !

69 Gent, 24 August 2007/avpeer Rates and Orders of pharmacokinetic processes

The rate of a process is the speed at which it occurs The rate of drug elimination represents the amount (A) of drug absorbed, distributed or eliminated per unit time

Zero-order process or rate: constant amount per unit time Input : mg per h „ dA/dt = ko = zero order rate constant

First-order process or rate: rate is proportional to the amount of drug available for the process „ dA/dt = - k.A = -k.Volume.Concentration

70 Gent, 24 August 2007/avpeer Rates of drug exchange Change of the drug amount in central compartment

DAplasma/dt = -K10. Aplasma - K12. Aplasma + K21. Aperipheral DAplasma/dt = -K10.Vc.Cplasma - K12.Vc.Cplasma + K21.Vt.Cperipheral DAplasma/dt = -CL.Cplasma - CLd.Cplasma + CLd.Cperipheral DCp/dt = -K10.Cplasma - K12.Cplasma + K21.Cperipheral

Change of the drug amount in peripheral compartment

DAperipheral/dt = -K12.Vc.Cplasma + K21.Vt.Cperipheral DAperipheral/dt = -CLd.Cplasma + CLd.Cperipheral DCperipheral/dt = -K12.Cplasma + K21.Cperipheral

71 Gent, 24 August 2007/avpeer