University of Jordan-Faculty of Pharmacy Department of Biopharmaceutics and Clinical Pharmacy Semester: First Course Title: Pharmacokinetics Course Code: 1203475 Prerequisite: Biopharmaceutics (1203471) Instructor: Dr. Mohammad Issa Name Office # Office Hours E - mail Dr. Mohammad Issa 230 Sun 12-1 Tue 11-12 Moh.saleh@ju.edu.jo

Course Objectives : 1) Understanding mathematical background for modeling of the concentration time relationships for the different routes of administration. 2) Designing dosing regimens by relating plasma concentration of drugs to their pharmacological and toxicological action, 3) Understanding the concept of therapeutic drug monitoring for drugs with narrow therapeutic range or high toxicity.

Learning Outcomes : A) Knowledge and understanding A1) Understanding mathematics of the time course of Absorption, Distribution, Metabolism, and Excretion (ADME) of drugs in the body. A2) Understanding Individualization of therapy and therapeutic drug monitoring. B) Intellectual skills (cognitive and analytical) B1) Utilization of mathematics of the time course of Absorption, Distribution, Metabolism, and Excretion (ADME) of drugs in the body for dosage optimization. B2) Developing dosing regimens for the individualization of therapy for the patient

C) Subject specific skills C1) Fitting concentration time profiles and estimating pharmacokinetic parameters. C3) Designing dosing regimens in case of renal and hepatic dysfunction. D) Transferable Skills D1) Communicating the dosage adjustment with physicians. D2) Suggesting therapeutic monitoring plans. Teaching Methods : 1) Lectures 2) Computer software (demo) 3) Case Studies

Tests & Evaluations : Midterm exam 40% Quizzes and HWs 10% Final exam 50%

1. Introduction 2. The one-compartment open model with an intravenous bolus dose. Plasma data; elimination rate constant, AUC, elimination half-life, volume of distribution and clearance Urinary data; excretion rate constant and half-life, elimination rate constant 3. The one-compartment open model with an intravenous infusion. Continues infusion, Infusion with a bolus dose, post infusion 4. The one-compartment open model with absorption and elimination; Absorption rate constant, calculation of F, method of residuals, flip-flop kinetics 5. The one-compartment open model with multiple dosing kinetics; Multiple dosing IV and oral, multiple dosing factor, accumulation factor, loading dose, and average concentration. 6. Designing dosing regimens 7. Dosage adjustment in renal failure. (Aminoglycosides) 8. The two-compartment open model with intravenous administration. 9. Non-linear pharmacokintics Michaels-Mention kinetics, methods to obtain Vmax and Km (Phenytoin). 10. Pharmacodynamics Linear models, E-max and time dependent response. 11. Therapeutic Drug Monitoring. 12. Bioequivalence revisited.

Textbook: Applied biopharmaceutics and pharmacokinetics Shargel and Yu, 5th edition, 2005 References: 1) Pharmacokinetics: processes, mathematics, and applications 2nd edition, Welling, P.G.., 1997 2) Handbook of Basic Pharmacokinetics Wolfgang Ritschel, 6th edition, 2004 3) Clinical pharmacokinetics: concepts and applications Rowland and Tozer, 3rd edition, 1995 Useful Web Sites 1) PHARMACOKINETICS LECTURE NOTES ONLINE http://www.healthsci.utas.edu.au/pharmacy/kinetics/main.htm 2) University of Alberta/ Dr. Jamali http://www.pharmacy.ualberta.ca/pharm415/contents.htm 3) A First Course in Pharmacokinetics and Biopharmaceutics http://www.boomer.org/c/p1/

Pharmacokinetics: Introduction Dr Mohammad Issa

What is pharmacokinetics?

What is pharmacokinetics? Pharmacokinetics is the study of kinetics of absorption, distribution, metabolism and excretion (ADME) of drugs and their corresponding pharmacologic, therapeutic, or toxic responses in man and animals’’ (American Pharmaceutical Association, 1972).

Review of ADME processes ADME is an acronym representing the pharmacokinetic processes of: A  Absorption D  Distribution M  Metabolism E  Excretion

Review of ADME processes Absorption is defined as the process by which a drug proceeds from the site of administration to the site of measurement (usually blood, plasma or serum) Distribution is the process of reversible transfer of drug to and from the site of measurement (usually blood or plasma)

Review of ADME processes Metabolism is the process of a conversion of one chemical species to another chemical species Excretion is the irreversible loss of a drug in a chemically unchanged or unaltered form Metabolism and excretion processes represent the elimination process

Applications of pharmacokinetics bioavailability measurements effects of physiological and pathological conditions on drug disposition and absorption dosage adjustment of drugs in disease states, if and when necessary correlation of pharmacological responses with administered doses evaluation of drug interactions clinical prediction: using pharmacokinetic parameters to design a dosing regimen and thus provide the most effective drug therapy

Applications of pharmacokinetics Bioavailability measurements: Blood sulfadiazine concentration in human following the administration of a 3 g dose. A comparison of the behavior of microcrystalline sulfadiazine with that of regular sulfadiazine in human

Applications of pharmacokinetics Effects of physiological and pathological conditions on drug disposition and absorption: plasma conc-time profile of cefepime after a 1000 mg IV infusion dose

Applications of pharmacokinetics Using pharmacokinetic parameters to design a dosing regimen and thus provide the most effective drug therapy

Rates and orders of reactions The rate of a chemical reaction of process is the velocity with which the reaction occurs. Consider the following chemical reaction: If the amount of drug A is decreasing with respect to time (that is, the reaction is going in a forward direction), then the rate of this reaction can be expressed as Since the amount of drug B is increasing with respect to time, the rate of the reaction can also be expressed as The rate of a reaction is determined experimentally by measuring the disappearance of drug A at given time intervals.

Zero-Order Reactions Consider the rate of elimination of drug A from the body. If the amount of the drug, A, is decreasing at a constant rate, then the rate of elimination of A can be described as: where k* is the zero-order rate constant. The reaction proceeds at a constant rate and is independent of the concentration of A present in the body. An example is the elimination of alcohol

Zero-Order Reactions The amount of a drug with zero order elimination is described according to the following equation: where A is the amount of drug in the body, A0 is the amount of the drug at time zero (equal to the dose in the case of IV bolus)

Drug with zero order PK A0 Slope = -K*

Zero-Order Reactions: example The administration of a 1000 mg of drug X resulted in the following concentrations: Time Conc. (mg/L) 100 4 90 6 85 10 75 12 70

Zero-Order Reactions: example What is the order of the elimination process (zero or first)? What is the rate constant?

Zero-Order Reactions: example

Zero-Order Reactions: example Since the decline in drug conc. Displayed a linear decline on normal scale, drug X has a zero order decline From the equation displayed on the figure (intercept = 100, slope = -2.5) The elimination rate constant is 2.5 mg/hr

First-order Reactions If the amount of drug A is decreasing at a rate that is proportional to A, the amount of drug A remaining in the body, then the rate of elimination of drug A can be described as: where k is the first-order rate constant The reaction proceeds at a rate that is dependent on the concentration of A present in the body It is assumed that the processes of ADME follow first-order reactions and most drugs are eliminated in this manner

First-Order Reactions The amount of a drug with first order elimination is described according to the following equation: where A is the amount of drug in the body, A0 is the amount of the drug at time zero (equal to the dose in the case of IV bolus) This equation is equivalent to:

Drug with first order PK

Drug with first order PK: log transformation

Nonlinear kinetics Nonlinear pharmacokinetics is also known as dose-dependent and concentration dependent pharmacokinetics because the pharmacokinetic parameters are dependent on the drug concentration or the drug amount in the body At least one of the absorption, distribution, and elimination processes, which affect the blood drug concentration—time profile, is saturable and does not follow first-order kinetics The change in drug dose results in disproportional change in the blood drug concentration— time profile after single- and multiple-dose administrations

Nonlinear kinetics

Nonlinear kinetics Nonlinear kinetics: Linear kinetics:

Linear vs nonlinear PK Linear PK Nonlinear PK 1-Known as dose-independent or concentration-independent PK. 1-Known as dose-dependent or concentration-dependent PK. 2-The absorption, distribution and elimination of the drug follow first-order kinetics 2-At least one of the PK processes (absorption, distribution or elimination) is saturable. 3-The pharmacokinetic parameters such as the half-life, total body clearance and volume of distribution are constant and do not depend on the drug conc 3-The pharmacokinetic parameters such as the half-life, total body clearance and volume of distribution are conc-dependant 4-The change in drug dose results in proportional change in the drug concentration. 4-The change in drug dose results in more than proportional or less than proportional change in the drug conc.

Laplace transformation Optional material

Laplace transformation The Laplace transform is a mathematical technique used for solving linear differential equations (apparent zero order and first order) and hence is applicable to the solution of many equations used for pharmacokinetic analysis.

Laplace transformation procedure Write the differential equation Take the Laplace transform of each differential equation using a few transforms (using table in the next slide) Use some algebra to solve for the Laplace of the system component of interest Finally the 'anti'-Laplace for the component is determined from tables

Important Laplace transformation (used in step 2) Expression Transform dX/dt K (constant) X (variable) K∙X (K is constant) where s is the laplace operator, is the laplace integral , and X0 is the amount at time zero

Anti-laplce table (used in step 4)

Anti-laplce table continued (used in step 4)

Laplace transformation: example The differential equation that describes the change in blood concentration of drug X is: Derive the equation that describe the amount of drug X??

Laplace transformation: example Write the differential equation: Take the Laplace transform of each differential equation:

Laplace transformation: example Use some algebra to solve for the Laplace of the system component of interest Finally the 'anti'-Laplace for the component is determined from tables

Laplace transformation: example The derived equation represent the equation for a zero order elimination