Basic Concepts of Pharmacokinetics Achiel Van Peer, Ph.D. Clinical Pharmacology 1 Gent, 24 August 2007/avpeer Some introductory Examples 2 Gent, 24 August 2007/avpeer 15 mg of Drug 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 concentrations before the first dose 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 metabolism excretion 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 Bioavailability Role of Pharmacokinetics 8 Gent, 24 August 2007/avpeer The simplest approach … observational pharmacokinetics The Model-independent Approach Cmax : maximum observed concentration Tmax : time of Cmax AUC : area under the curve 9 Gent, 24 August 2007/avpeer Cmax, Tmax and AUC in Bioavailability and Bioequivalence 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. tablet) 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 flunarizine, J&J data on file Other example: nebivolol: 10% in extensive metabolisers; 100% in poor metabolisers 11 Gent, 24 August 2007/avpeer Area under the curve rapezoidal ruleT: divide the plasma concentration-time profile trapezoids, and to several AUCs of these trapezoidsadd the Conc CC1+ 2 Units, e.g. ng.h/mL AUCt1 - t2= ().(t 2− t 1 ) 2 Clast AUCextrapolated = λz 0 0 Time 12 August 2007/avpeerGent, 24 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 blood 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-Tissue 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 volume of distribution 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 lnCC 1− ln0 . 2 693 k10 = = 2t − t 1 2t − t 1 Slope=k10 = the elimination rate constant Half-life = C2 0.693/k10 = half of C1 25 August 2007/avpeerGent, 24 A single iv dose of 5 mg dose 5000000ng Vd= = =30 .L 9 Cpo 162ng mL / = volume of distribution,Vd relates the drug concentration to the drug amount in the body 26 August 2007/avpeerGent, 24 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, liver, kidney, … 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 efflux 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 drugs; 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 0 . 693 t1 /term 2 =1 t /β 2 = = = 31h 0β . 0224h − 1 Vdβ = CL/β=Dose/(AUC. β)=Vdarea 32 August 2007/avpeerGent, 24 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 Clearance (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