Pharmacocinetic

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Pharmacocinetic

  1. 1. Basic Concepts of Pharmacokinetics Achiel Van Peer, Ph.D. Clinical Pharmacology Gent, 24 August 2007/avpeer 1
  2. 2. Some introductory Examples Gent, 24 August 2007/avpeer 2
  3. 3. 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 Gent, 24 August 2007/avpeer 3
  4. 4. 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% Gent, 24 August 2007/avpeer 4
  5. 5. Allometric Scaling Gent, 24 August 2007/avpeer 5
  6. 6. Pharmacokinetics: Time Profile of Drug Amounts Drug at absorption site Percent of dose Metabolites Drug in body Excreted drug Time (arbitrary units) Rowland and Tozer, Clinical Pharmacokinetics: Concepts and Applications, 3rd Ed. 1995 Gent, 24 August 2007/avpeer 6
  7. 7. 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 Gent, 24 August 2007/avpeer 7
  8. 8. 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 Gent, 24 August 2007/avpeer 8
  9. 9. The simplest approach … observational pharmacokinetics The Model-independent Approach Cmax : maximum observed concentration Tmax : time of Cmax AUC : area under the curve Gent, 24 August 2007/avpeer 9
  10. 10. 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%) Gent, 24 August 2007/avpeer 10
  11. 11. Absolute oral bioavailability flunarizine, J&J data on file Other example: nebivolol: 10% in extensive metabolisers; 100% in poor metabolisers Gent, 24 August 2007/avpeer 11
  12. 12. Area under the curve Trapezoidal rule: divide the plasma concentration-time profile to several trapezoids, and add the AUCs of these trapezoids Conc AUC t1 - t2 C1 + C 2 =( ).(t 2 − t1) 2 Units, e.g. ng.h/mL AUCextrapolated = 0 0 Time Gent, 24 August 2007/avpeer 12 Clast λz
  13. 13. Elimination half-life ? Half-life (t1/2) : time the drug concentration needs to decrease by 50% Gent, 24 August 2007/avpeer 13
  14. 14. Elimination half-life ? visual inspection Gent, 24 August 2007/avpeer 14
  15. 15. 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 Gent, 24 August 2007/avpeer 15
  16. 16. From Whole-Body Physiologically based Pharmacokinetics to Compartmental Models Poggesi et al., Nerviano Medical Science Gent, 24 August 2007/avpeer 16
  17. 17. 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 Gent, 24 August 2007/avpeer Drug Elimination 17
  18. 18. 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 Gent, 24 August 2007/avpeer 18
  19. 19. Intravenous dose of 0.2 mg Levocabastine (J&J data on file) Gent, 24 August 2007/avpeer 19
  20. 20. 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 Gent, 24 August 2007/avpeer 20
  21. 21. Zero-order rate drug administration and first-order rate drug elimination Amount A in blood, plasma Infusion rate mg/min Rate of elimination is proportional to the Amount in blood/plasma dA/dt = -k.A dDose/dt = Ko = mg/min [Often K=Kel=K10] Gent, 24 August 2007/avpeer 21
  22. 22. First-order rate of drug disappearance Rate of elimination is proportional to the Amount or Concentration in blood, plasma Amount A [or Concentration C] 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 Gent, 24 August 2007/avpeer 22
  23. 23. 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 C = C0. e-k10.t Gent, 24 August 2007/avpeer 23
  24. 24. A single iv dose of 5 mg C = C0 e-k10.t lnC = lnC0 - k10.t Remark for log10 scale: slope = k10/2.303 Gent, 24 August 2007/avpeer 24
  25. 25. A single iv dose of 5 mg ln C = lnC0 - k10.t k10 = ln C1 − ln C 2 0.693 = t 2 − t1 t 2 − t1 Slope=k10 = the elimination rate constant Half-life = 0.693/k10 C2 = half of C1 Gent, 24 August 2007/avpeer 25
  26. 26. A single iv dose of 5 mg dose 5000000ng Vd = = = 30.9 L Cpo 162ng / mL Vd = volume of distribution, relates the drug concentration to the drug amount in the body Gent, 24 August 2007/avpeer 26
  27. 27. 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 Gent, 24 August 2007/avpeer 27
  28. 28. Compartmental Approach after intravenous dosing Distribution Central compartment Peripheral 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 Gent, 24 August 2007/avpeer 28
  29. 29. Intravenous dose of 0.2 mg levocabastine K12= 0.84 h-1 V1 = 44 L V2 = 35 L K21= 1.05 h1 K10 = 0.4 h-1 Gent, 24 August 2007/avpeer 29
  30. 30. 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 Gent, 24 August 2007/avpeer 30
  31. 31. 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 Gent, 24 August 2007/avpeer 31
  32. 32. 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 t 1 / 2 term =t 1 / 2β = 0.693 β 0.693 = = 31h 0.0224h − 1 Vdβ = CL/β=Dose/(AUC. β)=Vdarea Gent, 24 August 2007/avpeer 32
  33. 33. Two-compartmental model Central K12 Compartment Peripheral Vc Compartment Vt K10 K21 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 Gent, 24 August 2007/avpeer 33
  34. 34. Compartmental approach after intravenous dosing Central compartment Shallow Peripheral 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 Gent, 24 August 2007/avpeer 34
  35. 35. Intravenous Sufentanil Gepts et al., Anesthesiology, 83:1194-1204, 1995 Gent, 24 August 2007/avpeer 35
  36. 36. Three compartmental model Sufentanil Pharmacokinetics Mixed-effects Population PK analysis (N =23) Population Average CV (%) 14.6 22 Rapidly equilibrating (V2) 66 31 Slowly equilibrating (V3) 608 76 At steady-state 689 Systemic (CL or CL1) 0.88 23 Rapid distribution (CL2) 1.7 48 Slow distribution (CL3) 0.67 78 Volume of distribution (L) Central (V1) Clearance (L/min) Gepts et al., Anesthesiology, 83:1194-1204, 1995 Gent, 24 August 2007/avpeer 36
  37. 37. Three compartmental model Sufentanil Pharmacokinetics Fractional Coefficients Rate constants (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 Gent, 24 August 2007/avpeer 37
  38. 38. Compartmental approach after intravenous dosing Central compartment Shallow Peripheral compartment Deep Peripheral compartment Central compartment Peripheral compartment Effect site Gent, 24 August 2007/avpeer 38
  39. 39. 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 Gent, 24 August 2007/avpeer 39
  40. 40. 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, brain poorly perfused : skin, fat, bone, muscle Permeability rate limitations or membrane barriers blood-brain barrier (BBB) blood-testis barrier (BTB) placenta Gent, 24 August 2007/avpeer 40
  41. 41. Unbound Fraction and Drug Disposition Cell membrane Plasma Tissue Receptor-bound drug Protein-bound drug Free drug (non-ionized) Free drug (non-ionized) Ionized drug (free) Protein-bound drug Ionized drug (free) Pka-pH, affinity for plasma and tissue proteins, permeability, … Gent, 24 August 2007/avpeer 41
  42. 42. Physicochemistry, PK and EEG PD of narcotic analgesics A lfe n ta n il F e n ta n y l S u fe n ta n il pKa 6 .5 8 .4 3 8 .0 1 % u n io n iz e d a t p H 7 .4 89 8 10 130 810 1750 8 16 8 23 358 541 0 .2 0 0 .6 2 1 .2 t1 /2 k e o E E G (m in ) 1 .1 6 .6 6 .2 C e 5 0 , E E G (n g /m l) 520 8 .1 0 .6 8 41 1 .2 0 .0 5 1 7 .9 0 .5 4 0 .0 3 9 P o c t/w a te r % u n b o u n d in p la s m a V d s s (L ) C l (L /m in ) C e50, unb K i (n g /m l) (n g /m l) Shafer SL, Varvel JR: Pharmacokinetics, pharmacodynamics, and rational opioid selection. Anesthesiology 1991; 74:53-63; DR Stanski, J Mandema (diverse papers) Gent, 24 August 2007/avpeer 42
  43. 43. Localisation and Role of Drug Transporters Zhang et al., FDA web site and Mol. Pharmaceutics 3, 62-69, 2006 Gent, 24 August 2007/avpeer 43
  44. 44. 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 body water 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 Gent, 24 August 2007/avpeer 44
  45. 45. Vd (L/kg) after iv dosing in rat and human (J&J data) Gent, 24 August 2007/avpeer 45
  46. 46. Multiple Dosing Concepts Gent, 24 August 2007/avpeer 46
  47. 47. 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 First-order rate - K.A; - CL.Cp mg/day 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 Gent, 24 August 2007/avpeer 47
  48. 48. 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 Gent, 24 August 2007/avpeer 48
  49. 49. 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 Gent, 24 August 2007/avpeer 49
  50. 50. Steady-state The amount in the body at steady-state (Ass) Ass = Ko Kel The plasma concentration at steady-state (Css,Cavgss) Cpss = Ko Ko = Kel.Vdss Cl Css is proportional to the dosing rate (zero-order input) and inversely proportional to the first-order elimination rate or clearance Gent, 24 August 2007/avpeer 50
  51. 51. Time to steady-state Half-life of 24 hr and dosing interval of 24 hrs Cmax Cavg,ss C=Css(1-e-k.t) Cmin 5-6 half-lives to reach steady-state Gent, 24 August 2007/avpeer 51
  52. 52. 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 Gent, 24 August 2007/avpeer 52
  53. 53. An effective half-life reflects drug accumulation Accumulation ratio = AUCss,τ 1 = AUC 0 − τ 1 − exp(− Keff .τ ) 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 Gent, 24 August 2007/avpeer 53
  54. 54. Mean residence time = MRT MRT is the time the drug, on average, resides in the body. MRT = Vdss/Cl Gent, 24 August 2007/avpeer 54
  55. 55. Loading and Maintenance Dose 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) Gent, 24 August 2007/avpeer 55
  56. 56. 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 Gent, 24 August 2007/avpeer 56
  57. 57. Physiological approach to Clearance Rate in Amount A or Concentration C in blood Q.Cpa Clearance = Rate out Q.Cpv Q(Cpa - Cpv) fu.Clint = Q. Cpa Q + fu.Clint Clearance = QE Low hepatic clearance if extraction ratio E <<1 High hepatic clearance if E ≅1 eg. Risperidone (Fabs 85%) eg. Nebivolol (Fabs 10%) Gent, 24 August 2007/avpeer 57
  58. 58. Bioavailability F After oral administration, not all drug may reach the systemic circulation The fraction of the administered dose that reaches the systemic circulation is called the bioavailability F Gent, 24 August 2007/avpeer 58
  59. 59. Oral drug absorption, Influx and Efflux Transporters, Drug Loss by First-pass Gut lumen Portal Uptake and effluxVein transporters Systemic circulation Tablet disintegration Drug dissolution Liver Gut wall Metabolism Hepatic Metabolism Biliary secretion Uptake and efflux transporters Into faeces F= Fabsorbed.(1-Egut).(1-Eliver) Gent, 24 August 2007/avpeer 59
  60. 60. Grapefruit inhibits gut-wall metabolism (J&J data on file) 140 Plasma cisapride conc. (ng/mL) Mean (N=13) 120 Cisapride 10 mg q.i.d./ GFJ Cisapride 10 mg q.i.d./ water 100 80 60 40 20 0 0 8 16 24 32 40 Time after morning dose on day 6 (hours) Gent, 24 August 2007/avpeer 48 60
  61. 61. 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 Gent, 24 August 2007/avpeer 61
  62. 62. Biopharmaceutical Classification Amidon et al., Pharm Res 12: 413-420, 1995; www.fda.gov High Permeability Low Solubility Class 1 Class 2 High Solubility High Permeability Rapid Dissolution Low Solubility High Permeability Low Permeability High Solubility Class 3 Class 4 High Solubility Low Permeability Low Solubility Low Permeability Gent, 24 August 2007/avpeer 62
  63. 63. Predicting Drug Disposition via BCS Wu and Benet, Pharm Res 22:11-23, 2005 High Permeability Low Solubility Class 1 Class 2 Transporter effects minimal Efflux transporter effects predominate Low Permeability High Solubility Class 3 Class 4 Absorptive transporter effects predominate Absorptive and efflux transporter effects could be important Gent, 24 August 2007/avpeer 63
  64. 64. Predicting Drug Disposition via BCS Wu and Benet, Pharm Res 22:11-23, 2005 High Permeability Low Solubility Class 1 Class 2 Metabolism Metabolism Low Permeability High Solubility Class 3 Class 4 Renal & Biliary Elimination of Unchanged Drug Renal & Biliary Elimination of Unchanged Drug Gent, 24 August 2007/avpeer 64
  65. 65. Biliary Excretion: Enterohepatic Recycling Excretion in urine Drug in blood Metabolism Conjugate in Liver Re-absorption The drug in the GI tract is depleted. Biliary excreted drug is reabsorbed Drug in Intestine Enzymatic breakdown of glucuronide Conjugate in bile Dumped from gall bladder Conjugate in intestine Excretion in feces Gent, 24 August 2007/avpeer 65
  66. 66. 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 Gent, 24 August 2007/avpeer 66
  67. 67. 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 medicines: Do not combine compound X with certain medicines called azoles that are given for fungal infections. Examples of azoles are ketoconazole, itraconazole, miconazole and fluconazole. You should not take compound X with grapefruit juice. …… Gent, 24 August 2007/avpeer 67
  68. 68. 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 Gent, 24 August 2007/avpeer 68
  69. 69. Thank for your attention ! Gent, 24 August 2007/avpeer 69
  70. 70. 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 rate of infusion: 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 Gent, 24 August 2007/avpeer 70
  71. 71. Rates of drug exchange Change of the drug amount in central compartment DAplasma/dt DAplasma/dt DAplasma/dt DCp/dt = - K10. Aplasma - K12. Aplasma + K21. Aperipheral = - K10.Vc.Cplasma - K12.Vc.Cplasma + K21.Vt.Cperipheral = - CL.Cplasma - CLd.Cplasma + CLd.Cperipheral = - K10.Cplasma - K12.Cplasma + K21.Cperipheral Change of the drug amount in peripheral compartment DAperipheral/dt DAperipheral/dt DCperipheral/dt = - K12.Vc.Cplasma + K21.Vt.Cperipheral = - CLd.Cplasma + CLd.Cperipheral = - K12.Cplasma + K21.Cperipheral Gent, 24 August 2007/avpeer 71

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