# Karunya Kandimalla, Ph.D

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Karunya Kandimalla, Ph.D
Principles of Pharmacokinetics Pharmacokinetics of IV Administration, 1-Compartment Karunya Kandimalla, Ph.D CP Clarke,L FD/MB

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 (kel, t½, Vd, AUC and clearance) To estimate the values of kel, t½, Vd, AUC and clearance from plasma or blood concentrations of a drug following intravenous administration. CP Clarke,L FD/MB

Elimination rate constant Apparent volume of distribution Clearance CP Clarke,L FD/MB

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

Disposition Analysis (Dose Linearity)

Disposition Analysis (Time Variance)

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

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

One Compartment Model (IV Bolus)
Schematically, one compartment model can be represented as: Where Xp is the amount of drug in the body, Vd is the volume in which the drug distributes and kel is the first order elimination rate constant kel Drug Eliminated Drug in Body Xp = Vd • C The rate of change in systemic drug level is dependent on the balance between the rates of drug absorption and elimination For both zero and first order processes, the net rate of drug accumulation is equal to the rate of drug absorption minus the rate of drug elimination The absorption (ka) and elimination (kel) rate constants describe how quickly serum concentrations rise (ka) or decline (kel) after administration. The elimination rate of a drug can be computed by taking the product of the elimination rate constant (kel) and the amount of drug in the body (Xp) In general, low molecular weight, high lipid solubility and lack of charge encourage absorption. CP Clarke,L FD/MB

One Compartment Data (Linear Plot)

One Compartment Data (Semi-log Plot)

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

Two Compartment Data (Linear Plot)

Two Compartment Data (Semi-log Plot)

One Compartment Model-Assumptions
1-Compartment—Intravascular drug is in rapid equilibrium with extravascular drug Intravascular drug [C] proportional to extravascular [C] Rapid Mixing—Drug mixes rapidly in blood and plasma First Order Elimination Kinetics: Rate of change of [C]  Remaining [C] Notice here that the log-transformed equation represents the equation of a straight line CP Clarke,L FD/MB

Derivation-One Compartment Model
Bolus IV Central Compartment (C) Kel This is the simplest of the intravascular administration models The entire dose enters the systemic circulation immediately and the body is depicted as a single homogenous unit Plasma concentrations are not necessarily equal to tissue concentrations, but they are proportional The advantage of this model is that it permits calculation of drug concentrations at any time (no absorption phase, no distribution phase) The disadvantage is that the kinetic parameters do not have physiologic meaning CP Clarke,L FD/MB

Concentration versus time, semilog paper
IV Bolus Injection: Graphical Representation Assuming 1st Order Kinetics C0 = Initial [C] C0 is calculated by back-extrapolating the terminal elimination phase to time = 0 C0 = Dose/Vd C0 = Dose/Vd Slope = -K/2.303 Slope = -Kel/2.303 Note that half-life can also be read from the graph Concentration versus time, semilog paper CP Clarke,L FD/MB

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

Half-Life (t1/2) Time taken for the plasma concentration to reduce to half its original concentration Drug with low half-life is quickly eliminated from the body t/t1/2 % drug remaining 1 50 2 25 3 12.5 4 6.25 5 3.125

Change in Drug Concentration as a Function of Half-Life

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

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)

Calculation of AUC using trapezoidal rule

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

Clearance Concepts Cinitial Cfinal ORGAN
elimination If Cfinal < Cinitial, then it is a clearing organ

Practical Example Time (hr) Plasma Conc. (mg/L) ln (PlasmaConc.) 1
9.46 2.25 2 7.15 1.97 3 5.56 1.71 4 4.74 1.56 6 3.01 1.10 10 1.26 0.23 12 0.83 -0.19 IV bolus administration Dose = 500 mg Drug has a linear disposition

Linear Plot

Natural logarithm Plot
Kel ln (C0)

Half-Life and Volume of Distribution
t1/2 = / Kel = hrs Vd = Dose / C0 = 500 / = 44.66 ln (C0) = C0 = Inv ln (2.4155) = mg/L

Clearance Cl = D/AUC Cl = VdKel Cl =  = 9.73 L/hr

Home Work Determine AUC and Calculate clearance from AUC