COMPARTMENTAL ANALYSIS OF DRUG DISTRIBUTION

Transcription

1 COMPARTMENTAL ANALYSIS OF DRUG DISTRIBUTION Juan J.L. Lertora, M.D., Ph.D. Director Clinical Pharmacology Program September 13, 2012 Office of Clinical Research Training and Medical Education National Institutes of Health Clinical Center 1

2 DRUG DISTRIBUTION The post-absorptive transfer of drug from one location in the body to another. Compartmental Models (ordinary differential equations) Distributed Models (partial differential equations) 2

3 Pharmacokinetic Models Using Ordinary Differential Equations* MODEL NUMBER OF COMPARTMENTS MATHEMATICAL CHARACTERISTICS NONCOMPARTMENTAL 0 CURVE FITTING TO DATA COMPARTMENTAL 1 3 PHYSIOLOGICAL 4-20 MODEL PARAMETERS FIT TO DATA MODEL PARAMETERS FIXED A PRIORI * From Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12:

4 Mathematical vs. Physical Models* MATHEMATICAL MODEL: Functions or differential equations are employed without regard to the physical characteristics of the system. PHYSICAL MODEL: Implies certain mechanisms or entities that have physiological, biochemical or physical significance. * Berman M: The formulation and testing of models. Ann NY Acad Sci 1963;108:

5 Goals of Drug Distribution Lecture Significance of Drug Distribution Volumes Physiological Basis of Multi-Compartment Pharmacokinetic Models Clinical Implications of Drug Distribution Kinetics 5

6 DIGOXIN DISTRIBUTION VOLUME V d DOSE C μg 1.4μg/L 536 L 6

7 Body Fluid Spaces Catenary 3-Compartment Model cell membranes 7

8 Apparent Volume of Distribution and Physiological Fluid Spaces Intravascular Space: No drug is restricted to this fluid space Extracellular Fluid Space: Inulin Proteins and other Macromolecules Neuromuscular Blocking Drugs (N + ) Aminoglycoside Antibiotics (initially) 8

9 Apparent Volume of Distribution and Physiological Fluid Spaces Total Body Water Urea Ethyl alcohol Antipyrine (some protein binding) Caffeine 9

10 Factors Affecting Volume of Distribution Estimates Binding to Plasma Proteins Thyroxine Theophylline Tissue Binding (partitioning) Lipophilic Compounds Digoxin (Na + - K + ATPase) 10

11 Effect of Plasma Protein Binding on Drug Distribution Cell Membranes ECF ICF BINDING PROTEINS Elimination 11

12 Effect of Plasma Protein Binding on Apparent Volume of Distribution* V d ECF f u TBW - ECF f u is the free fraction, the fraction of drug in plasma that is not bound to plasma proteins. * Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12:

13 Impact of Protein Binding on Thyroxine Distribution Volume* f u = 0.03% V d = V ECF * From Larsen PR, Atkinson AJ Jr, et al. J Clin Invest 1970;49:

14 Impact of Protein Binding on Theophylline Distribution Volume* f u = 60% V d = V ECF + f u V ICF * From Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12:

15 Basis for Increased Theophylline Volume of Distribution in Pregnancy* PREGNANT WEEKS WEEKS f U (%) FLUID SPACE ESTIMATES (L) V d(ss) (L) ECF TBW EST. MEAS TOTAL V d POSTPARTUM 6-8 WEEKS >6 MONTHS * From Frederiksen MC, et al. Clin Pharmacol Ther 1986;40;

16 Effect of Plasma Protein and Tissue Binding on the Volume of Distribution of Most Drugs* V d ECF Φf u TBW - ECF Ф is the ratio of tissue/plasma drug concentration. * Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12:

17 Log Φ LIPID SOLUBILITY(D oct ) and 6 5 Amiodarone 4 Loratidine 3 Chlorpromazine 2 Propranolol Imipramine Diazepam Clozapine 1 Clonidine Digoxin Carbamazepine Omeprazole 0 Cimetidine Log D oct 17

18 Apparent Volume of Distribution for Digoxin V ECF d V V 11.2 TBW - ECF ECF 11.2 L, TBW 45.5 L, f d d 536 L Φf u u , Φ 20.4 L Φ includes binding to Na + -K + ATPase. 18

19 mµci/gm Tissue vs. Plasma Digoxin Levels HOURS 19

20 GOALS OF DRUG DISTRIBUTION LECTURE Significance of drug distribution volumes Physiologic basis of multi-compartment pharmacokinetic models Clinical implications of drug distribution kinetics 20

21 First Multicompartmental Analysis of Drug Distribution* * From Teorell T. Arch Intern Pharmacodyn 1937;57:

22 Analysis of Experimental Data How many compartments? Number of exponential phases in plasma level vs. time curve determines the number of compartments. 22

23 TECHNIQUE OF CURVE PEELING A β α 23

24 COMPARTMENTAL ANALYSIS Data Equation: C = A e -αt + B e -βt Dose Central k 21 Periph. Model Equation: k 01 V 1 k 12 V 2 dx 1 /dt = -(k 01 + k 21 )X 1 + k 12 X 2 24

25 TWO-COMPARTMENT MODEL Dose Central V 1 CL I Periph. V 2 CL E V d(ss) = V 1 + V 2 25

26 3 DISTRIBUTION VOLUMES V V V d (extrap.) d (area) d (ss) DOSE t V 1 1/2 CL V 2 C E 0... V n 26

27 TWO-COMPARTMENT MODEL Dose Central V 1 CL I Periph. V 2 CL E k 01 CL E = k 01 V 1 27

28 TWO-COMPARTMENT MODEL Dose Central V 1 k 21 CL I k 12 Periph. V 2 CL E CL I = k 21 V 1 = k 12 V 2 28

29 INTERCOMPARTMENTAL CLEARANCE* Volume-Independent Parameter Characterizing the Rate of Drug Transfer Between Compartments of a Kinetic Model * From Saperstein et al. Am J Physiol 1955;181:

30 Is Central Compartment Intravascular Space? Usually not identified as such unless drug is given rapidly IV. NEED TO CONSIDER: - If distribution is limited to ECF, compare the central compartment volume with plasma volume. - If distribution volume exceeds ECF compare central compartment with blood volume.* *(account for RBC/Plasma partition if [plasma] measured) 30

31 Analysis of Procainamide and NAPA Central Compartment Volumes* DRUG V C (L) RBC/P INTRAVASCULAR SPACE (L) PREDICTED OBSERVED PA NAPA * From Stec GP, Atkinson AJ Jr. J Pharmacokinet Biopharm 1981;9:

32 If Central Compartment Volume is Based on Plasma Concentration Measurements V C(corr.) V / C(meas.) 1 Hct Hct RBC P RBC/P = red cell/plasma partition ratio Hct = hematocrit 32

33 [INULIN] (mg/dl) Analysis of Inulin Kinetics with a 2-Compartment Model* AFTER INFUSION AFTER BOLUS MINUTES * Gaudino M. Proc Soc Exper Biol Med 1949;70:

34 3-Compartment Model of Inulin Kinetics EXTRACELLULAR FLUID CELL MEMBRANES Dose V F V C CL E V S 34

35 Kinetic Heterogeneity of IF Space The interstitial fluid (IF) comparment is kinetically heterogeneous with regard to rate of drug distribution. Splanchnic vascular bed Fenestrated capillaries - large pores Somatic tissues vascular beds Continuous capillaries small pores 35

36 UREA- 15 N 2 KINETICS IN A NORMAL SUBJECT 36

37 Multicompartment Model of Inulin and Urea Kinetics* INULIN UREA * From Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12:

38 ROLE OF TRANSCAPILLARY EXCHANGE The central compartment for both urea and inulin is the intravascular space. Therefore, transcapillary exchange is the ratelimiting step in the distribution of urea and inulin to the peripheral compartments of the mammillary 3-compartment model. 38

39 RENKIN EQUATION* Cl Q (1 e P/Q ) Q = capillary blood flow P = capillary permeability coefficient-surface area product (sometimes denoted P S). * From Renkin EM. Am J Physiol 1953;183:

40 SIMULTANEOUS ANALYSIS OF INULIN AND UREA- 15 N 2 KINETICS SUBJECT 1 UREA INULIN 40

41 3-COMPARTMENT MODEL Dose V F V C CL E V S 41

42 For Each Peripheral Compartment 3 UNKNOWNS: 3 EQUATIONS: P P P U I U U = urea; I = inulin Q, P U, P I I U Q ln Q Q - Cl Q ln Q Q - Cl P D D D = free water diffusion coefficient I U I 42

43 SIMULTANEOUS ANALYSIS OF INULIN AND UREA- 15 N 2 KINETICS SUBJECT 1 UREA INULIN How does Q F + Q S compare with C.O.? 43

44 CARDIAC OUTPUT AND COMPARTMENTAL BLOOD FLOWS* Q F Q S Q F + Q S L/min L/min L/min % CO MEAN MEAN OF 5 SUBJECTS * From Odeh YK, et al. Clin Pharmacol Ther 1993;53;

45 TRANSCAPILLARY EXCHANGE Mechanisms TRANSFER OF SMALL MOLECULES (M.W. < 6,000 Da): Transfer proportional to D - Polar, uncharged (urea, inulin) Transfer rate < predicted from D - Highly charged (quaternary compounds) - Interact with pores (procainamide) Transfer rate > predicted from D - Lipid soluble compounds (anesthetic gases) - Facilitated diffusion (theophylline) 45

46 Urea and Theophylline Diffusion Coefficients* MOLECULAR WEIGHT (DALTONS) CORRECTED STOKES- EINSTEIN RADIUS (Å) D 37º C (x 10-5 cm 2 /sec) UREA THEOPHYLLINE * From Belknap SM, et al. J Pharmacol Exp Ther 1987;243;

47 PRESUMED CARRIER-MEDIATED TRANSCAPILLARY EXCHANGE O H O H NH 2 H H 3 C N N H N N H N N O N N N N N N CH 3 THEOPHYLLINE HYPOXANTHINE ADENINE 47

48 GOALS OF DRUG DISTRIBUTION LECTURE Significance of drug distribution volumes Physiologic basis of multi-compartment pharmacokinetic models Clinical implications of drug distribution kinetics 48

49 SIGNIFICANCE OF DRUG DISTRIBUTION RATE 1. Affects toxicity of IV injected drugs Theophylline, lidocaine 2. Delays onset of drug action Insulin, digoxin 3. Terminates action after IV bolus dose Thiopental, lidocaine 49

50 PK Model of THEOPHYLLINE Distribution CNS HEART CL E IV Dose IVS SPLANCHNIC SOMATIC CO = Q F + Q S 50

51 PK-PD Study of INSULIN Enhancement of Skeletal Muscle Glucose Uptake* GLUCOSE INFUSION RATE * From Sherwin RS, et al. J Clin Invest 1974;53:

52 DISTRIBUTION TERMINATES EFFECT BOLUS LIDOCAINE DOSE* THERAPEUTIC RANGE * From Atkinson AJ Jr. In: Melmon KL, ed. Drug Therapeutics: Concepts for Physicians, 1981:

53 CONSEQUENCES OF VERY SLOW DRUG DISTRIBUTION Flip-Flop Kinetics Effective Half-Life Pseudo Dose Dependency 53

54 GENTAMICIN Elimination Phase Preceeds Distribution Phase* ELIMINATION PHASE DISTRIBUTION PHASE * From Schentag JJ, et al. JAMA 1977;238:

55 GENTAMICIN ELIMINATION Nephrotoxic vs. Non-Toxic Patient* NEPHROTOXIC NON-TOXIC * From Coburn WA, et al. J Pharmacokinet Biopharm 1978;6:

56 CONSEQUENCES OF VERY SLOW DRUG DISTRIBUTION Flip-Flop Kinetics Effective Half-Life Pseudo Dose Dependency 56

57 TOLRESTAT Cumulation with Repeated Dosing* *From Boxenbaum H, Battle M: J Clin Pharmacol 1995;35:

58 CUMULATION FACTOR CF 1-1 e -k τ 58

59 TOLRESTAT CUMULATION Predicted C.F. from T ½ = 31.6 hr: 4.32 Observed C.F.:

60 EFFECTIVE HALF- LIFE* k eff 1 τ CF ln CF obs 1 obs t 1/2eff ln2 k eff * From Boxenbaum H, Battle M. J Clin Pharmacol 1995;35:

61 EFFECTIVE HALF-LIFE OF TOLRESTAT* Since τ = 12 hr and Observed CF = 1.29: k t eff 1/2eff 1 12 ln ln hr hr 1 * From Boxenbaum H, Battle M. J Clin Pharmacol 1995;35:

62 CONSEQUENCES OF VERY SLOW DRUG DISTRIBUTION Flip-Flop Kinetics Effective Half-Life Pseudo Dose Dependency 62

63 [DRUG] (mcg/ml) AREA UNDER THE CURVE Measure of Dose Proportionality CL = ABSORBED DOSE/AUC PLASMA LEVEL VS. TIME CURVE AUC HOURS 63

64 HYPOTHETICAL Phase I Trial Results DOSE 1 DOSE 2 INCREASE DOSE (mg) AUC (μg hr/ml) x x 64

65 Dependency of PK Estimates on Identified Terminal Phase C 0 = 2.1μg/mL, V d = 47.6 L, CL = 5.6 L/hr C 0 = 1.8μg/mL, V d = 13.9 L, CL = 18.9 L/hr 65

66 DISTRIBUTION VOLUME Representative Macromolecules MACROMOLECULE MW (kda) V 1 (ml/kg) V d(ss) (ml/kg) INULIN FACTOR IX (FIX) INTERLEUKIN-2 (IL-2) INTERLEUKIN-12 (IL-12) GRANULOCYTE COLONY STIMULATING FACTOR (G-CSF) RECOMBINANT TISSUE PLASMINOGEN ACTIVATOR (RT-PA)

67 CLOTTING FACTOR PHARMACOKINETICS* The V d(ss)... always exceeds the actual plasma volume, implying that no drug, not even large molecular complexes as F-VIII, is entirely confined to the plasma space. A too short blood sampling protocol gives flawed results not only for terminal T1/2 but also for the model independent parameters. * Berntorp E, Björkman S. Haemophilia 2003;9: