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Principles of Pharmacokinetics Pharmacokinetics of IV Administration, 1-Compartment Karunya Kandimalla, Ph.D Karunya Kandimalla, Ph.D

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2 Objectives Be able to: To understand the properties of linear models To understand assumptions associated with first order kinetics and one compartment models To define and calculate various one compartment model parameters (k el, t ½, V d, AUC and clearance) To estimate the values of k el, t ½, V d, AUC and clearance from plasma or blood concentrations of a drug following intravenous administration. Be able to: To understand the properties of linear models To understand assumptions associated with first order kinetics and one compartment models To define and calculate various one compartment model parameters (k el, t ½, V d, AUC and clearance) To estimate the values of k el, t ½, V d, AUC and clearance from plasma or blood concentrations of a drug following intravenous administration.

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3 Recommended Readings Chapter 3, p IV route of administration Elimination rate constant Apparent volume of distribution Clearance Chapter 3, p IV route of administration Elimination rate constant Apparent volume of distribution Clearance

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4 Kinetics From the Blood or Plasma Data Pharmacokinetics of a drug in plasma or blood Absorption (Input) Disposition Distribution Elimination Excretion Metabolism

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5 Disposition Analysis (Dose Linearity)

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6 Disposition Analysis (Time Variance)

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7 Linear Disposition The disposition of a drug molecule is not affected by the presence of the other drug molecules Demonstrated by: a) Dose linearity Saturable hepatic metabolism may result in deviations from the dose linearity b) Time invariance Influence of the drug on its own metabolism and excretion may cause time variance The disposition of a drug molecule is not affected by the presence of the other drug molecules Demonstrated by: a) Dose linearity Saturable hepatic metabolism may result in deviations from the dose linearity b) Time invariance Influence of the drug on its own metabolism and excretion may cause time variance

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8 Disposition Modeling A fit adequately describes the experimental data A model not only describes the experimental data but also makes extrapolations possible from the experimental data A fit that passes the tests of linearity will be qualified as a model A fit adequately describes the experimental data A model not only describes the experimental data but also makes extrapolations possible from the experimental data A fit that passes the tests of linearity will be qualified as a model

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9 One Compartment Model (IV Bolus) Schematically, one compartment model can be represented as: Where X p is the amount of drug in the body, V d is the volume in which the drug distributes and k el is the first order elimination rate constant Schematically, one compartment model can be represented as: Where X p is the amount of drug in the body, V d is the volume in which the drug distributes and k el is the first order elimination rate constant Drug in Body Drug Eliminated X p = V d C k el

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10 One Compartment Data (Linear Plot)

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11 One Compartment Data (Semi-log Plot)

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12 Two Compartment Model (IV Bolus) For both 1- and 2-compartment models, elimination takes place from central compartment Drug in Central Compartment Drug Eliminated Drug in Peripheral Compartment kel Blood, kidneys, liver Fat, muscle K 12 K 21

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13 Two Compartment Data (Linear Plot)

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14 Two Compartment Data (Semi-log Plot)

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15 One Compartment Model-Assumptions 1-CompartmentIntravascular drug is in rapid equilibrium with extravascular drug Intravascular drug [C] proportional to extravascular [C] Rapid MixingDrug mixes rapidly in blood and plasma First Order Elimination Kinetics: Rate of change of [C] Remaining [C] 1-CompartmentIntravascular drug is in rapid equilibrium with extravascular drug Intravascular drug [C] proportional to extravascular [C] Rapid MixingDrug mixes rapidly in blood and plasma First Order Elimination Kinetics: Rate of change of [C] Remaining [C]

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16 Derivation-One Compartment Model Bolus IV K el Central Compartment (C)

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17 IV Bolus Injection: Graphical Representation Assuming 1 st Order Kinetics C 0 = Initial [C] C 0 is calculated by back-extrapolating the terminal elimination phase to time = 0 C 0 = Dose/Vd Slope = -K/2.303 Slope = -K el /2.303 Concentration versus time, semilog paper

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18 Elimination Rate Constant (K el ) K el is the first order rate constant describing drug elimination (metabolism + excretion) from the body K el is the proportionality constant relating the rate of change of drug concentration and the concentration The units of K el are time -1, for example hr -1, min -1 or day -1 K el is the first order rate constant describing drug elimination (metabolism + excretion) from the body K el is the proportionality constant relating the rate of change of drug concentration and the concentration The units of K el are time -1, for example hr -1, min -1 or day -1

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19 Half-Life (t 1/2 ) Time taken for the plasma concentration to reduce to half its original concentration Drug with low half-life is quickly eliminated from the body Time taken for the plasma concentration to reduce to half its original concentration Drug with low half-life is quickly eliminated from the body t/t 1/2 % drug remaining

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20 Change in Drug Concentration as a Function of Half-Life

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21 Apparent Volume of Distribution (V d ) V d is not a physiological volume V d is not lower than blood or plasma volume but for some drugs it can be much larger than body volume Drug with large V d is extensively distributed to tissues V d is expressed in liters and is calculated as: Distribution equilibrium between drug in tissues to that in plasma should be achieved to calculate V d V d is not a physiological volume V d is not lower than blood or plasma volume but for some drugs it can be much larger than body volume Drug with large V d is extensively distributed to tissues V d is expressed in liters and is calculated as: Distribution equilibrium between drug in tissues to that in plasma should be achieved to calculate V d

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22 Area Under the Curve (AUC) AUC is not a parameter; changes with Dose Toxicology: AUC is used as a measure of drug exposure Pharmacokinetics: AUC is used as a measure of bioavailability and bioequivalence Bioavailability: criterion of clinical effectiveness Bioequivalence: relative efficacy of different drug products (e.g. generic vs. brand name products) AUC has units of concentration time (mg.hr/L) AUC is not a parameter; changes with Dose Toxicology: AUC is used as a measure of drug exposure Pharmacokinetics: AUC is used as a measure of bioavailability and bioequivalence Bioavailability: criterion of clinical effectiveness Bioequivalence: relative efficacy of different drug products (e.g. generic vs. brand name products) AUC has units of concentration time (mg.hr/L)

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23 Calculation of AUC using trapezoidal rule

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24 Clearance (Cl) The most important disposition parameter that describes how quickly drugs are eliminated, metabolized and distributed in the body Clearance is not the elimination rate Has the units of flow rate (volume / time) Clearance can be related to renal or hepatic function Large clearance will result in low AUC The most important disposition parameter that describes how quickly drugs are eliminated, metabolized and distributed in the body Clearance is not the elimination rate Has the units of flow rate (volume / time) Clearance can be related to renal or hepatic function Large clearance will result in low AUC

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25 Clearance Concepts ORGAN C initial C final elimination If C final < C initial, then it is a clearing organ

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26 Practical Example IV bolus administration Dose = 500 mg Drug has a linear disposition IV bolus administration Dose = 500 mg Drug has a linear disposition Time (hr) Plasma Conc. (mg/L) ln (Plasma Conc.)

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27 Linear Plot

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28 Natural logarithm Plot K el ln (C 0 )

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29 Half-Life and Volume of Distribution t 1/2 = / K el = hrs V d = Dose / C 0 = 500 / = ln (C 0 ) = C 0 = Inv ln (2.4155) = mg/L t 1/2 = / K el = hrs V d = Dose / C 0 = 500 / = ln (C 0 ) = C 0 = Inv ln (2.4155) = mg/L

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30 Clearance Cl = D/AUC Cl = V d K el Cl = = 9.73 L/hr Cl = D/AUC Cl = V d K el Cl = = 9.73 L/hr

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31 Home Work Determine AUC and Calculate clearance from AUC Determine AUC and Calculate clearance from AUC

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