COMPARTMENTAL ANALYSIS OF DRUG DISTRIBUTION Arthur J. Atkinson, Jr., M.D. Senior Advisor in Clinical Pharmacology Clinical Center, NIH DRUG DISTRIBUTION THE POST-ABSORPTIVE TRANSFER OF DRUG FROM ONE LOCATION IN THE BODY TO ANOTHER GOALS OF DRUG DISTRIBUTION LECTURE SIGNIFICANCE OF DRUG DISTRIBUTION VOLUMES PHYSIOLOGIC BASIS OF MULTI- COMPARTMENT PHARMACOKINETIC MODELS CLINICAL IMPLICATIONS OF DRUG DISTRIBUTION KINETICS DIGOXIN DISTRIBUTION VOLUME BODY FLUID SPACES (CONVENTIONAL VIEW) cell membranes DRUGS WITH V d CORRESPONDING TO PHYSIOLOGICAL FLUID SPACES INTRAVASCULAR SPACE: NONE EXTRACELLULAR FLUID SPACE: INULIN PROTEINS & OTHER MACROMOLECULES NEUROMUSCULAR BLOCKING DRUGS (N + ) AMINOGLYCOSIDE ANTIBIOTICS (initially) TOTAL BODY WATER: UREA CAFFEINE ETHYL ALCOHOL ANTIPYRINE (some protein binding) DISTRIBUTION VOLUME OF REPRESENTATIVE MACROMOLECULES FACTORS AFFECTING V d ESTIMATES OF MOST DRUGS BINDING TO PLASMA PROTEINS: THYROXINE THEOPHYLLINE TISSUE BINDING (PARTITIONING): DIGOXIN (Na + - K + ATPase) LIPOPHILIC COMPOUNDS PHYSIOLOGICAL SPACES FOR DRUG DISTRIBUTION ECF ICF ELIMINATION CELL MEMBRANES EFFECT OF BINDING CHANGES ON V d OF THYROXINE & THEOPHYLLINE* * Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12: f u is the free fraction, the fraction of drug in plasma that is not bound to plasma proteins. IMPACT OF PROTEIN BINDING ON THYROXINE DISTRIBUTION VOLUME* * From Larsen PR, Atkinson AJ Jr, et al. J Clin Invest 1970;49: f u = 0.03% V d = V ECF IMPACT OF PROTEIN BINDING ON THEOPHYLLINE DISTRIBUTION VOLUME* * From Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12: f u = 60% V d = V ECF + f u V ICF BASIS FOR INCREASED THEOPHYLLINE V d IN PREGNANCY * From Frederiksen MC, et al. Clin Pharmacol Ther 1986;40;321-8. EFFECT OF BINDING CHANGES ON V d OF MOST DRUGS* * Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12: is the ratio of tissue/plasma drug concentration. LIPID SOLUBILITY & V D (L/kg) f U OCTANOL/WATER PARTITION COEF. = 10 100* PHENYTOIN DIAZEPAM OCTANOL/WATER PARTITION COEF. = >1000* PROPRANOLOL NORTRIPTYLINE *measured at pH 7 APPARENT V d OF DIGOXIN represents binding to Na + -K + ATPase. TISSUE VS. PLASMA DIGOXIN LEVELS m C/gm HOURS GOALS OF DRUG DISTRIBUTION LECTURE SIGNIFICANCE OF DRUG DISTRIBUTION VOLUMES PHYSIOLOGIC BASIS OF MULTI- COMPARTMENT PHARMACOKINETIC MODELS CLINICAL IMPLICATIONS OF DRUG DISTRIBUTION KINETICS BASIC PHARMACOKINETIC MODELS* * From Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12: MONES BERMAN MATHEMATICAL VS. PHYSICAL MODELS* MATHEMATICAL MODEL: FUNCTIONS OR DIFFERENTIAL EQUATIONS ARE EMPLOYED WITHOUT REGARD TO ANY MECHANISTIC ASPECTS 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;108:182-94 FIRST MULTICOMPARTMENTAL ANALYSIS OF DRUG DISTRIBUTION* * From Teorell T. Arch Intern Pharmacodyn 1937;57: IS CENTRAL COMPARTMENT INTRAVASCULAR SPACE? USUALLY NOT IDENTIFIED AS SUCH UNLESS DRUG GIVEN RAPIDLY IV NEED TO CONSIDER: - IF DISTRIBUTION LIMITED TO ECF, COMPARE V C WITH PLASMA VOLUME. - IF LARGER DISTRIBUTION VOLUME, COMPARE V C WITH BLOOD VOLUME ACCOUNTING FOR RBC/ PLASMA. IF V C IS BASED ON PLASMA CONCENTRATION MEASUREMENTS RBC/P = red cell/plasma partition ratio Hct = hematocrit ANALYSIS OF PA & NAPA CENTRAL COMPARTMENT VOLUMES* * From Stec GP, Atkinson AJ Jr. J Pharmacokinet Biopharm 1981;9: DRUGV C (L) RBC/P INTRAVASCULAR SPACE (L) PREDICTED OBSERVED PA NAPA ANALYSIS OF EXPERIMENTAL DATA HOW MANY COMPARTMENTS? DESPITE AVAILABILITY OF COMPUTER PROGRAMS FOR PK ANALYSIS, STILL NEED TO MAKE INITIAL ESTIMATES. TECHNIQUE OF CURVE PEELING A COMPARTMENTAL ANALYSIS k 01 Central V 1 Periph. V 2 Dose k 21 k 12 DATA EQUATION: C = A e -t + B e -t MODEL EQUATION: dX 1 /dt = -(k 0 + k 12 )X 1 + k 21 X 2 TWO-COMPARTMENT MODEL Central V 1 Periph. V 2 Dose CL E CL I V d(ss) = V 1 + V 2 3 DISTRIBUTION VOLUMES TWO-COMPARTMENT MODEL CL E = k 01 V 1 Central V 1 Periph. V 2 Dose CL E CL I k 01 INTERCOMPARTMENTAL CLEARANCE* A VOLUME-INDEPENDENT PARAMETER CHARACTERIZING THE RATE OF ANALYTE TRANSFER BETWEEN COMPARTMENTS OF A KINETIC MODEL * From Saperstein et al. Am J Physiol 1955;181:330-6. TWO-COMPARTMENT MODEL CL I = k 21 V 1 = k 12 V 2 CL I Central V 1 Periph. V 2 Dose CL E k 21 k 12 3-COMPARTMENT MODEL OF PA PHARMACOKINETICS [PROCAINAMIDE] (g/mL) HOURS CATENARY 3-COMPARTMENT MODEL cell membranes MINUTES [INULIN] (mg/dL) ANALYSIS OF INULIN KINETICS WITH A 2-COMPARTMENT MODEL* AFTER BOLUS AFTER INFUSION * Gaudino M. Proc Soc Exper Biol Med 1949;70:672-4. 3-COMPARTMENT MODEL OF INULIN KINETICS VSVS CL F VFVF CL S VCVC Dose CL E CELL MEMBRANES EXTRACELLULAR FLUID BASIS FOR KINETIC HETEROGENETIY ENDOTHELIAL FENESTRAE IN HEPATIC SINUSOIDS INTERENDOTHELIAL CELL JUNCTION IN CONTINUOUS CAPILLARY PK-PD STUDY OF INSULIN ENHANCEMENT OF SKELETAL MUSCLE GLUCOSE UPTAKE* * From Sherwin RS, et al. J Clin Invest 1974;53: UREA- 15 N 2 KINETICS IN A NORMAL SUBJECT MULTICOMPARTMENTAL MODEL OF INULIN AND UREA KINETICS* * From Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12: ROLE OF TRANSCAPILLARY EXCHANGE THE CENTRAL COMPARTMENT FOR BOTH UREA AND INULIN IS INTRAVASCULAR SPACE. THEREFORE, TRANSCAPILLARY EXCHANGE IS THE RATE-LIMITING STEP IN THE DISTRIBUTION OF BOTH COMPOUNDS TO THE PERIPHERAL COMPARTMENTS OF THE MAMMILLARY 3-COMPARTMENT MODEL. RENKIN EQUATION* * From Renkin EM. Am J Physiol 1953;183: Q = capillary blood flow P = capillary permeability coefficient-surface area product (sometimes denoted PS). 3-COMPARTMENT MODEL VSVS VCVC Dose CL E CL F = Q F (1 e P F/Q F ) VFVF CL S = Q S (1 e P S/Q S ) SIMULTANEOUS ANALYSIS OF INULIN AND UREA- 15 N 2 KINETICS SUBJECT 1 INULIN UREA How does Q F + Q S compare with C.O.? FOR EACH COMPARTMENT 3 UNKNOWNS: 3 EQUATIONS: U = urea; I = inulin D = free water diffusion coefficient CARDIAC OUTPUT AND COMPARTMENTAL BLOOD FLOWS* * From Odeh YK, et al. Clin Pharmacol Ther 1993;53; MECHANISMS OF TRANSCAPILLARY EXCHANGE DIFFUSIVE TRANSFER: M.W. < 6,000 DALTONS CONVECTIVE TRANSFER: M.W. > 50,000 DALTONS CAPILLARY PERMEABILITY VS. M.W. * * From Dedrick RL, Flessner MF. Immunity to Cancer 1989;II: MECHANISMS OF TRANSCAPILLARY EXCHANGE TRANSFER OF SMALL MOLECULES (M.W. < 6,000 Da): TRANSFER PROPORTIONAL TO D - POLAR, UNCHARGED (urea, inulin) - FACILITATED DIFFUSION (theophylline) TRANSFER RATE > PREDICTED FROM D - LIPID SOLUBLE COMPOUNDS (anesthetic gases) TRANSFER RATE < PREDICTED FROM D - HIGHLY CHARGED (quaternary compounds) - INTERACT WITH PORES (procainamide) THEOPHYLLINE KINETICS REFERENCED TO INULIN AND UREA THEOPHYLLINE UREA INULIN THEOPHYLLINE I.C. CLEARANCE AND COMPARTMENTAL BLOOD FLOWS* * From Belknap SM, et al. J Pharmacol Exp Ther 1987;243:963-9. UREA & THEOPHYLLINE DIFFUSION COEFFICIENTS* * From Belknap SM, et al. J Pharmacol Exp Ther 1987;243; MOLECULAR WEIGHT (DALTONS) CORRECTED STOKES- EINSTEIN RADIUS () D 37 C (x cm 2 /sec) UREA THEOPHYLLINE PRESUMED CARRIER-MEDIATED TRANSCAPILLARY EXCHANGE SIGNIFICANCE OF DRUG DISTRIBUTION RATE AFFECTS TOXICITY OF IV INJECTED DRUGS THEOPHYLLINE DELAYS ONSET OF DRUG ACTION DIGOXIN INSULIN TERMINATES ACTION AFTER BOLUS DOSE THIOPENTAL LIDOCAINE EARLY BENEFITS & LATER RISKS OF INITIAL IV THEOPHYLLINE DOSES 1937 THEOPHYLLINE 1st USED SUCCESSFULLY TO TREAT STATUS ASTHMATICUS Herrman G, Aynesworth MB. J Lab Clin Med 1937;23: 3 CASES OF ARRHYTHMIC DEATH AFTER SLOW IV INJECTION OF 200 mg THEOPHYLLINE Merrill GA. JAMA 1943;123: 3 CASES OF CONVULSIVE CARDIORESPIRATORY DEATH AFTER SLOW BUT UNMEASURED INJECTION OF mg THEOPHYLLINE Bresnick E, et al. JAMA 1948;136: IV INJECTION OF 250 750 mg THEOPHYLLINE OVER min RESULTS IN 60% OF DRUG-RELATED CARDIAC ARRESTS IN LA COUNTY SHOCK WARD Camarata, et al. Circulation 1971;44: SAFETY LINKED TO RATE OF THEOPHYLLINE ADMINISTRATION THE TOTAL DOSE ..DOES NOT SEEM TO BE IMPORTANT, WITHIN THERAPEUTIC LIMITS, THE FATAL DOSE HAVING VARIED FROM 0.1 Gm TO 0.36 Gm. IT IS QUITE POSSIBLE THAT THE SPEED OF INJECTION IS MORE IMPORTANT. Bresnick E, et al. JAMA 1948;136: CURRENT RECOMMENDATION: IV THEOPHYLLINE LOADING DOSE SHOULD BE 5 mg/kg INFUSED OVER 20 40 min. PK MODEL OF THEOPHYLLINE DISTRIBUTION SOMATIC IVS IV Dose CL E CL F = Q F SPLANCHNIC CL S = Q S CNS HEART CO = Q F + Q S SIGNIFICANCE OF DRUG DISTRIBUTION RATE AFFECTS TOXICITY OF IV INJECTED DRUGS THEOPHYLLINE DELAYS ONSET OF DRUG ACTION DIGOXIN INSULIN TERMINATES ACTION AFTER BOLUS DOSE THIOPENTAL LIDOCAINE DIGOXIN IS NOT THE 1ST DRUG GIVEN TO PATIENTS WITH ACUTE PULMONARY EDEMA VASOCONSTRICTIVE EFFECTS MYOCARDIAL EFFECTS PLASMA VS. MYOCARDIAL DIGOXIN LEVELS EFFECTS ON CNS VOMITING CENTER SIGNIFICANCE OF DRUG DISTRIBUTION RATE AFFECTS TOXICITY OF IV INJECTED DRUGS THEOPHYLLINE DELAYS ONSET OF DRUG ACTION DIGOXIN INSULIN TERMINATES ACTION AFTER BOLUS DOSE THIOPENTAL LIDOCAINE DISTRIBUTION TERMINATES EFFECT OF BOLUS LIDOCAINE DOSE* * From Atkinson AJ Jr. In: Melmon KL, ed. Drug Therapeutics: Concepts for Physicians, 1981: THERAPEUTIC RANGE ANALYSIS OF LIDOCAINE DISTRIBUTION KINETICS* * From Benowitz N, et al. Clin Pharmacol Ther 1974;16:87-98. CONSEQUENCES OF VERY SLOW DRUG DISTRIBUTION FLIP-FLOP KINETICS EFFECTIVE HALF-LIFE PSEUDO DOSE DEPENDENCY GENTAMICIN ELIMINATION PHASE PRECEEDS ITS DISTRIBUTION PHASE* * From Schentag JJ, et al. JAMA 1977;238:327-9. GENTAMICIN ELIMINATION IN A NEPHROTOXIC VS. NON-TOXIC PATIENT* * From Coburn WA, et al. J Pharmacokinet Biopharm 1978;6: NON-TOXIC NEPHROTOXIC CONSEQUENCES OF VERY SLOW DRUG DISTRIBUTION FLIP-FLOP KINETICS EFFECTIVE HALF-LIFE PSEUDO DOSE DEPENDENCY TOLRESTAT CUMULATION WITH REPEATED DOSING* *From Boxenbaum H, Battle M: J Clin Pharmacol 1995;35:763-6. CUMULATION FACTOR TOLRESTAT CUMULATION OBSERVED C. F. ( = 12 hr):1.29 PREDICTED (T = 31.6 hr):4.32 EFFECTIVE HALF- LIFE* * From Boxenbaum H, Battle M. J Clin Pharmacol 1995;35: EFFECTIVE HALF-LIFE OF TOLRESTAT* * From Boxenbaum H, Battle M. J Clin Pharmacol 1995;35: PSEUDO DOSE DEPENDENCY DISTRIBUTION VOLUME OF REPRESENTATIVE MACROMOLECULES COMPARTMENTAL ANALYSIS OF DRUG DISTRIBUTION PARAMETERS OF COMPARTMENTAL MODELS THREE DIFFERENT DISTRIBUTION VOLUMES TECHNIQUE OF CURVE PEELING TWO-COMPARTMENT MODEL Central V 1 Periph. V 2 Dose CL E CL I k 21 k 12 k 01 3 DISTRIBUTION VOLUMES TECHNIQUE OF CURVE PEELING A