Basic Pharmacokinetics.pdf

8/21/2019 Basic Pharmacokinetics.pdf

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Basic Pharmacokinetics REV. 99.4.25 -1Copyright 1996-1999 Michael C. Makoid All Rights Reserved http://kiwi.creighton.edu/pkinbook/

F I R S T E D I T I O N

Basic Pharmacokinetics

Michael C. Makoid, Ph.D.

Professor of Pharmaceutical Sciences

Creighton University School of Pharmacy

and Allied Health Sciences,

Omaha, Nebraska

Phillip J. Vuchetich

Pharm.D. Candidate

Creighton University School of Pharmacy

and Allied Health Sciences,

Omaha, Nebraska

Umesh V. Banakar, Ph.D.

Professor of Pharmaceutical Sciences

St. Louis College of Pharmacy

St. Louis, Missouri


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Copyright 1996-1999 The Virtual University Press

All rights reserved.

ISBN 0-000-000000-0

ABCDEFGHIJ-DO-89


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Acknowledgement

When I first started teaching, I had the good fortune to work with another newPh.D., John Cobby. We struggled through our first five years on the otherside o

the podium together and learned many of the tenents upon which this book isbased, not content but process. First and formost, it was his belief that students arebright, enthusiastic and hardworking. We should tell them what to do and get outof their way. We both prepared extensive handouts complete with even moreextensive practice problems so that the student could experience the scientificmethod as a detective might solve a murder mystery. The idea was to make learn-ing pharmaceutical science interesting and fun. Through the years, as the methodsbecame more refined, student perceptions and performance improved dramatically

John ultimately abandoned academe to go to work in the real world of industry,clearly their gain and our loss. I approached him some years ago to co-author this

text. He declined believing himself to be too far removed from the cutting edge othis discipline. That may be true (I doubt it!), but what can not be argued is that hewas a major contributor to this book in his philosophy and class notes. Over theyears, the explainations were rewritten and revised. Many new problems wereadded and some were suplanted. These teaching aides have evolved but their origins are clear. Using the industry standard regarding authorship, which defines anauthor as one whose contributions significantly alters the content of the paper, DrCobby is an author of this book.


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CHAPTER 1 Introduction

Basic Pharmacokinetics 1-2

Course Objectives: 1-3Course Arrangement: 1-3

Learn the tools; get the pharmacokinetic parameters from patient information. 1-3

Learn the modifications of the pharmacokinetic parameters which result from illness. 1-5

Apply the tools; use the pharmacokinetic parameters to develop dosage regimens. 1-5

Apply the tools in specialized drug classes. 1-5

Exams 1-7Library Assignment in Pharmacokinetics 1-7

Blooms taxonomy for the Hierarchy of Educational Objectives 1-9

Course Contract 1-10

Computers in the course 1-14

Survival Kit 1-15Things for your Survival Kit! 1-15

What you will gain: (your goals) 1-16

Tentative Schedule 1-17Study Group 1: Learn the tools - obtain pharmacokinetic parameters from data. 1-17

Study group 2: Learn how the parameters are modified. 1-19

Study Group 3: Apply the tools in compromised patients. 1-20

Study Group 4: Apply the tools in special cases. 1-20

Competency Statements Related To Pharmacokinetics 1-22Specific Competency Statements addressed in this course 1-22

Pharmacokinetic Symbolism 1-25Amount Terms (unit: mass) 1-25

Concentration terms (units mass/volume) 1-26

Volume Terms (unit: volume) 1-26

Time Terms (unit: time) 1-27

Rate Constant Terms (unit: reciprocal time (*), mass/time (**) 1-27Clearance Terms (units: volume/time) 1-28

Rate Terms (units: mass/time (*), mass/time, volume (**), volume/time (***) 1-28

Other Terms 1-29

Subscripts 1-30

Superscripts 1-30

First Lesson in Pharmacokinetics 1-32

CHAPTER 2 Mathematics Review

Concepts of Mathematics 2-2

Mathematical Preparation 2-3Zero and Infinity 2-3

Expressing Large and Small Numbers 2-3

Significant Figures 2-4

Rules of Indices 2-4

Logarithms 2-6

Natural Logarithms 2-6

Negative Logarithms 2-9


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Using Logarithmic and Anti-logarithmic Tables 2-10

Dimensions 2-11

Dimensional Analysis 2-12

Calculus 2-14Differential Calculus 2-14

Non-linear Graphs 2-14

Slope of Non-linear Graph 2-15

Value of the Slope 2-15

Differentiation from First Principles 2-16

Rule of Differentiation 2-17

Three Other Derivatives 2-17

A Seeming Anomaly 2-18

Integral Calculus 2-19

Rule of Integration 2-19

The Constant of Integration 2-20

The Exception to the Rule 2-20

A Useful Integral 2-20

Example Calculations 2-21

Graphs 2-24Graphical Conventions 2-25

Straight Line Graphs 2-26

The Slope of a Linear Graph (m) 2-28

Linear Regression: Obtaining the slope of the line 2-29

Parallel lines 2-31

Graphical Extrapolations 2-32

Significance of the Straight Line 2-32

Graphical Honesty 2-32

Axes with Unequal Scales 2-33

Graphs of Logarithmic Functions 2-34

Semilogarithmic Coordinates 2-34

Log - Log Coordinates 2-38Pitfalls of Graphing: Poor Technique 2-38

Graphical analysis 2-40

Pharmacokinetic Modeling 2-44Making a Model 2-45

One Compartment Open Model 2-47

The LaPlace Transform 2-48Table of LaPlace Transforms 2-49

Symbolism 2-49

Conventions used in drawing pharmacokinetic schema. 2-50

Steps for Integration Using the LaPlace Transform 2-53

Example Integration Using the LaPlace Transform 2-54

Second Example Integration Using the LaPlace Transform 2-56

Third Example Integration Using the LaPlace Transform 2-57

Conclusions 2-58

Table of LaPlace Transforms 2-60

LaPlace Transform Problems 2-62

LaPlace Transform Solutions 2-63


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CHAPTER 3 Pharmacological Response

Pharmacological Response 3-2The Hyperbolic Response Equation 3-2

Interrelationships between concentration, time and response 3-3

Change in Response with Time 3-4One-Compartment Open Model: Intravenous Bolus Injection 3-4

One-Compartment Open Model: Oral Administration 3-4

Duration of Effective Pharmacological Response 3-4

Pharmacokinetic Parameters from Response Data 3-5

Delayed Response 3-5

Response of active metabolite: 3-6

Therapeutic Drug Monitoring 3-7Therapeutic monitoring: Why do we Care? 3-9

Problems 3-11Answers: Oxpranolol 3-18

Answers: Minoxidil 3-21

Answers: Propranolol 3-23

CHAPTER 4 I.V. Bolus Dosing

I.V. Bolus dosing of Parent compound 4-2Plasma 4-2

Iv bolus, parent compound, plasma Problems 4-7

Urine 4-47

Metabolite 4-51Plasma 4-51

Urine 4-56

CHAPTER 5 I.V. Infusion

Parent compound 5-2Plasma 5-2

Problems 5-10

CHAPTER 6 Biopharmaceutical Factors

CHAPTER 7 Oral Dosing

Oral dosing 7-3 Valid equations: ( oral dosing, plasma) 7-3

Utilization 7-3

CHAPTER 8 Bioavailability, Bioequivalence, and Drug Selection

Bioavailability, Bioequivalence and Drug Product Selection 8-2


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Relative and Absolute Bioavailability 8-2

Factors Influencing Bioavailability 8-4

Methods of Assessing Bioavailability 8-11

Study Design 8-15

In-vitro Dissolution and Bioavailability 8-15

In-vitro / in-vivo correlation studies- 8-18

Bioequivalence 8-20Bioequivalence Regulations 8-23

Study Design 8-26

Assessment of bioequivalence 8-29

Controversies and Concerns in Bioequivalence 8-31

Generic Drugs and Product Selection 8-35

The Orange Book 8-38

Therapeutic equivalence 8-38

Therapeutic equivalence evaluation codes- 8-39

Drug Product Selection 8-44Considerations in selecting a manufacturer 8-45

Special Cases 8-50Summary 8-54

Questions 8-55

Answers to Questions 8-57

Bioavailibility Equations 8-58

Problems 8-60

Solutions 8-80Caffeine on page 61 8-80

Cefetamet Pivoxil on page 62 8-83

Cefixime on page 63 8-86

Ceftibuten on page 64 8-87

Cimetidine on page 65 8-88

Diurnal Variability in Theophylline Bioavailability on page 66 8-89

cis-5-Fluoro-1-[2-Hydroxymethyl-1,3-Oxathiolan-5-yl] Cytosine (FTC) on page 67 8-90

Hydromorphone on page 68 8-91

Isosorbide Dinitrate on page 69 8-92

Ketanserin on page 70 8-93

Methotrexate on page 71 8-94

Moclobemide on page 72 8-95

Nalbuphine on page 73 8-96

Nefazodone on page 74 8-97

Ondansetron on page 75 8-98

Omeprazole on page 76 8-99

Paroxetine on page 77 8-100

Ranitidine on page 78 8-101

Sulpiride on page 79 8-102References 8-103

CHAPTER 9 Clearance

Equations 9-2

Definitions and Terms 9-3


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Measurement of Creatinine Clearance 9-4

Model Correlations 9-5Renal Clearance 9-5

Systemic Clearance and Metabolic Clearance 9-5

Use in Pharmacokinetic Equations 9-6

Physiological Factors Affecting Clearance 9-7Intrinsic Clearance 9-7

Extraction Ratio (E) 9-8

Hepatic Function and Clearance 9-10Alterations in Hepatic blood Flow 9-10

Alterations in Hepatic Intrinsic Clearance 9-10

Tabulated or Graphical Alterations 9-11

Renal Function and Clearance 9-12

General Equations for Changes in Clearance 9-14Plasma/Blood ratio 9-14

Half life and elimination rate constant in relationship to clearance 9-16

Effects of alterations in protein binding on clearance 9-16

Problems 9-17

CHAPTER 10 Dosage Regimen (Healthy, Aged, and Diseased Patients)

Therapeutic Drug Monitoring 10-2Therapeutic Range 10-2

Therapeutic monitoring: Why do we Care? 10-4

Steady State 10-5

Diseases - Dosing the Compromised Patient 10-10

Problems 10-12

Answers 10-36

CHAPTER 11 Multicompartment Modeling

Executive Summary 11-2

Equations 11-3

PHARMCOKINETICS: MAMMILLARY MODELS 11-4

Begin 11-90

Problems 11-91Two-compartment Model Equations 11-119

Answers 11-120

CHAPTER 12 Protein Binding

CHAPTER 13 Nonlinear (Michaelis-Menton) Kinetics

Problems 13-2

Nonlinear Equations 13-14


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Answers 13-14

CHAPTER 14 Practice Exams: Section 1

Nifedipine - Section 1 3Nifedipine Data 3Nifedipine Questions 4

Nifedipine Solutions 6

Enalapril - Section 1 11enalapril data 11

Enalapril Questions 13

enalapril Solutions 14

Ciprofloxacin Section 1 19Ciprofloxacin data 19

Ciprofloxacin Questions 20

Ciprofloxacin Solutions 21

Methylphenidate Section 1 23methylphenidate data 23

MethylPhenidate Questions: 24

methylPhenidate Solutions 25

Adinazolam - Section 1 27ADINAZOLAM DATA 27

Adinazolam Questions 28

Adinazolam Solutions 30

Labetalol - Section 1 32labetalol data 32

labetalol Questions 33

labetalol Solutions 34

Zidovudine Section 1 36zidovudine data 36

Zidovudine Questions 38

Zidovuldine Solutions 40

Fosinopril Section 1 42fosinopril data 42

Fosinopril Questions 44

Fosinopril Solutions 46

Omeprazole 49Omeprazole Data 49

Omeprazole Questions 50

Omeprazole solutions 53

EXP3312, an Experimental Drug 57

EXP3312 DATA 57EXP3312 & M1 Questions: 59

Graph Paper 62

CHAPTER 15 Practice Exams: Exam 2

Nifedipine: Exam 2 2


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Nifedipine Questions: 3

Valproate: Exam 2 6Valproate Questions 7

Valproate Solutions 10

Methyl phenidate 11Methyl phenidate Questions: 12

Methyl phenidate Solutions: 13

Verapamil 15Verapamil Questions 16

Verapamil Solutions 17

Hydromorphone hydrochloride 19Hydromorphone hydrochloride Questions 20

Fosinopril Sodium 23Fosinopril Questions 24

Fosinopril Sodium Solutions 26

Remoxipride 28Remoxipride Questions 29

Remoxipride Solutions 31

Naproxen 33Naproxen Questions 34

Naproxen Solutions 36

38

CHAPTER 16 Exam 3

Pharmacokinetics Final Exam 16-2


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Basic Pharmacokinetics REV. 99.4.25 1-1Copyright 1996-1999 Michael C. Makoid All Rights Reserved http://kiwi.creighton.edu/pkinbook/

CHAPTER 1 Introduction

Author: M ichael M akoid and John Cobb

Reviewer: Phi ll ip Vuchetich

OBJECTIVES

At the completion of this chapter, the successful student shall be able to:

1. define pharmacokinetics

2. state the overall objectives of the course

3. state the major themes of the course

4. state the course organizational structure with respect to study sections

5. state the objectives of each study section

6. state the examination structure and objectives

7. state student performance expectations

8. state the schedule and timeline


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1.1 Basic Pharmacokinetics

What is pharmacokinet-

ics?

Pharmacokinetics is the mathematics of the time course of Absorption, Distribu-

tion, Metabolism, and Excretion (ADME) of drugs in the body. The biological,physiological, and physicochemical factors which influence the transfer processesof drugs in the body also influence the rate and extent of ADME of those drugs inthe body. In many cases, pharmacological action, as well as toxicological action, isrelated to plasma concentration of drugs. Consequently, through the study ofpharmacokinetics, the pharmacist will be able to individualize therapy for thepatient.


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1.2 Course Objectives:

The Roman numerals refer to the cognitive complexity as described in Bloom's

Taxonomy of Educational Objectives described elsewhere in this document. At thecompletion of this course, the successful student will be able to:

What will you be able to

do?

Calculate (III)patient and drug specific pharmacokinetic parameters from patient data,

Predict (calculate - III) the changes in relevant pharmacokinetic parameters in the patient withselected diseases,

Utilize the above parameters to individualize patient therapy (devise a dosage regimen - V),

Communicate his/her therapy recommendations to another competent health professional (writea consult - V).

1.2.1 COURSE ARRANGEMENT:

Two courses are described below. The first, a two credit (Creighton Universityrequired) and the second, a three credit (CU optional) version. The two creditcourse will consist of major themes one through three and exams one and two,while the three credit course will add theme four and exam three. The four majorthemes are entitled:

How is the course

arranged?

Learn the tools; get the pharmacokinetic parameters from patient information.

Learn the modifications of the pharmacokinetic parameters which result from illness.

Apply the tools; use the pharmacokinetic parameters to predict patient response and developdosage regimens for the normal as well as for the compromised patient.

Apply the tools in specialized drug classes.

Each major theme of the course is further broken down into study sections, eachwith their own set of general objectives as shown below:

1.2.2 LEARN THE TOOLS; GET THE PHARMACOKINETIC PARAMETERS

FROM PATIENT INFORMATION.

A. Basic Mathematical skills objectives:What will I be required

to be able to do? How

will examination ques-

tions be written for this

material?

1. Given a data set containing a pair of variables, the student will properly construct (III) various graphs of the data.

2. Given various graphical representations of data, the student will calculate (III) the slopeand intercept by hand as well as using linear regression.

3. The student shall be able to interpret (V) the meaning of the slope and intercept for thevarious types of data sets.

4. The student shall demonstrate (III) the proper procedures of mathematical and algebraicmanipulations.


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5. The student shall demonstrate (III) the proper calculus procedures of integration and dif-ferentiation.

6. The student shall demonstrate (III) the proper use of computers in graphical simulationsand problem solving.

7. Given the assumptions for the model, the student will construct (III) models of the ADME

processes using Laplace Transforms.8. The student shall develop (V) integrated equations associated with the above models.9. The student shall generate a pharmacokinetic model based on given information.10. The student shall interpret a given model mathematically.11. The student shall predict changes in the final result based on changes in variables through

out the model.

B. Pharmacological Response objectives:1. Given patient data of the following types, the student will be able to properly construct

(III) a graph and compute (III) the slope: response (R) vs. concentration (C), response (R)vs. time (T), concentration (C) vs. time (T)

2. Given any two of the above data sets, the student will be able to compute (III) the slope of

the third.

C. IV one compartment model, plasma and urine objectives:1. Given patient drug concentration and/or amount vs. time profiles, the student will calcu-

late (III) the relevant pharmacokinetic parameters available ( , K, , , , Clear-

ance, MRT) from IV data.2. Given the appropriate pharmacokinetic parameters, the student shall simulate (III)

I.V. bolus/infusion dosing for parent compounds

Plasma concentration vs. time profile analysis

Rate vs. time profile analysis3. Given patient specific pharmacokinetic parameters, the student shall provide professional

communication regarding IV bolus/infusion information4. The student shall utilize computer aided instruction and simulation5. Given patient drug concentration and/or amount vs. time profiles, the student will calcu-

late (III) the relevant metabolite (active vs. inactive) pharmacokinetic parameters avail-able ( , K, , , , Clearance, MRT) from IV data.

D. Biopharmaceutical factor objectives: the student shall be able to discuss:1. physiology and mechanisms of absorption2. effects of diffusion, cardiac output / blood perfusion, physical properties of the drug and

body on distribution3. biotransformation, first pass effect, and clearance4. renal, biliary, mammary, salivary, other forms of excretion.5. the effects of physiological changes with age, sex, and disease on the absorption, distribu

tion, metabolism, and excretion of a drug.

E. Oral one compartment model objectives:1. Given patient drug concentration and/or amount vs. Time profiles, the student will calcu-

late (III) the relevant pharmacokinetic parameters ( , K, , , , , Clearance,

MRT, MAT) available from oral data.

Vd km kr AUC

Vd km kr AUC

Vd km kr ka AUC


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F. Bioavailability objectives:1. Given sufficient data to compare an oral product with another oral product or an IV prod-

uct, the student will estimate (III) the bioavailability (compare AUCs) and judge (VI) pro

fessional acceptance of the product with regard to bioequivalence (evaluate (VI) AUC,

and ).2. The student will write (V) a professional consult using the above calculations.

1.2.3 LEARN THE MODIFICATIONS OF THE PHARMACOKINETIC

PARAMETERS WHICH RESULT FROM ILLNESS.

G. Clearance objectives:1. Given patient information regarding organ function, the student will calculate (III)

changes in clearance and other pharmacokinetic parameters inherent in compromisedpatients.

1.2.4 APPLY THE TOOLS; USE THE PHARMACOKINETIC PARAMETERS

TO DEVELOP DOSAGE REGIMENS.

H. Dosage regimens objectives:1. Given population average patient data, the student will devise (V) dosage regimens which

will maintain plasma concentrations of drug within the therapeutic range.2. Given specific patient information, the patient will justify (VI) dosage regimen recom-

mendations.3. Given patient information regarding organ function, the student will devise (V) and justify

(VI) dosage regimen recommendations for the compromised patient.

4. The student will write (V) a professional consult using the above calculations

1.2.5 APPLY THE TOOLS IN SPECIALIZED DRUG CLASSES.

I. Two Compartment Model objectives:1. Given patient Concentration and/or Amount of Drug vs. Time, profiles the student will

calculate (III) the relevant pharmacokinetic parameters( , Alpha, , Beta, ,

, , , , Clearance, compartmental amount ratios) available from two com-

partment data.2. Given population average patient data, the student will devise (V) a dosage regimen which

will maintain plasma concentrations of drug within the therapeutic range.3. Given specific patient information, the patient will justify (VI) the optimal dosage regi-men.

4. Given patient information regarding organ function, the student will devise (V) and justify(VI) the optimal dosage regimen for the compromised patient.

5. The student will write (V) a professional consult using the above calculations.

Tp

Cp( )max

Vd1 A1 B1

k10 k12 k21 AUC


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J. Protein Binding objective:1. Given population average patient data, the student will devise (V) dosage regimens which

will maintain plasma concentrations of unbound drug within the therapeutic range.2. Given specific patient information, the patient will justify (VI) the optimal dosage regi-

men.

3. Given patient information regarding organ function, the student will devise (V) and justify(VI) dosage regimens for the compromised patient.

4. The student will write (V) a professional consult using the above calculations.

K. Non-linear kinetics objective:1. Given population average patient data, the student will devise (V) a dosage regimen which

will maintain plasma concentrations of drug within the therapeutic range.2. Given specific patient information, the patient will justify (VI) the optimal dosage regi-

men.3. Given patient information regarding organ function, the student will devise (V) and justify

(VI) dosage regimens for the compromised patient.4. The student will write (V) a professional consult using the above calculations.


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1.3 Exams

How are the exams

made?

Exams will consist of problems which will be linked directly back to an objective

(above) and a library assignment in which you will be asked to evaluate a researcharticle with the tools available to you by the time of the exam as discussed below.

1.3.1 LIBRARY ASSIGNMENT IN PHARMACOKINETICS

L. Library Assignment ObjectivesWhat do I have to do in

the library?

1. Given a suitable primary research article in the area of pharmacokinetics, the student shallcalculate the pharmacokinetic parameters from the data using the tools learned in class.

2. The student shall communicate in writing the results of such calculations with suitablecommentary regarding differences and interpretations.

Format of the paper:How should the paper

look?

1. Tell me what type of paper you have chosen to evaluate:

The problem sets show what data you need for each of these.

First Exam

What content should I

look for in the paper and

what is its relative

worth?

IV Bolus Parent compound 10 pts

IV Bolus Parent metabolite 12.5 pts

IV Infusion 12.5 pts

Pharmacological Response 15 pts

Second Exam

Oral Dosing / Bioavailability 10 pts

Third Exam (2 credit course)

Multiple dosing 10 pts

Clearance and disease 12.5 pts

Dosage Regimen 15 pts

Third Exam (3 credit course)

Two compartment model 10 pts

Protein Binding and Disease 12.5 pts

Non-linear kinetics and disease 15 pts

2. Include a Xerox copy of the entire paper. I need to evaluate it, too.


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3. Enlarge the graph by successive Xeroxes so that you can accurately evalu-ate the data.

4. Do analysis of data by hand and by PKAnalyst, or Scientist.

5. Compare your work with the authors (short paragraph).

6. Comment on any differences of parameter calculation or interpretation. Seeobjectives above (Paragraph).

7. Write an exam question to obtain pharmacokinetic parameters. You knowfrom the first exam what they should look like.

Why do I need to do this

library assignment?

Each of the above sections is designed to bring the student an understanding of theinformation and the processes necessary to operate as a competent professional inthe area of pharmacokinetic evaluation and consulting. Consequently, the

course will evolve from a quantitative, manipulative mathematics course to acourse which stresses communication skills. Consults will be graded not only oncontent (the proper dosage regimen for the patient) but also grammar, punctuationspelling, organization and neatness. You may have the best medical information inthe world, but if it is poorly executed, it will be ignored.

Can I cram the night

before?

This course will probably be one of the more rigorous ones that you will haveexperienced in your college career to date. It will be one of the first ones whichattempt to show some clinical relevance. The course can be successfully completed with your current skills and background. It is not difficult IF (and that is abig IF) taken slowly, in small bites. Its just like eating an elephant - you can't do i

all in one sitting. Some of you may try to get it all the night before the examregardless of my admonitions and those of your upper-class friends (ask them!). Inmany cases, that has been more than sufficient to get A's and B's on exams in pre-vious courses. Past experience tells many of you that you can do it. I suggest thatthe requirements and expectations of a professional school are considerably morethan your undergraduate experience and it most likely will not work in manycourses which require assimilation of the information presented, as is expected in aprofessional program.


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Introduction


1.4 Blooms taxonomy for the Hierarchy of Educational Objectives

Blooms taxonomy for the Hierarchy of Educational Objectives describes the

expectations of a course in increasing order of complexity as:What is cramming good

for? Lowest level of cog-

nitive skills.

I. To Know: means to memorize (recognize, recall) (Many college coursesrequire only this level of cognitive effort, hence the extensive experience withmultiple guess exams).

II. To Comprehend: means to translate; to be able to put information into yourown words. (Essay exams routinely call for this level of effort on the part of thestudent).

This is where we begin. III. To Apply: means to be able to use knowledge, rules and principles in anunfamiliar situation. (This is the lowest level of skill necessary to function at a

technician level).This is where we need

to be in school.

IV. To Analyze: means to be able to critically examine a body of knowledgeand to be able to identify the relationships. (This is where a B.S. graduate shouldoperate. Education obviates the need for teachers.)

This is where we need

to be as graduates.

V. To Synthesize: means to put together information, not necessarily previously so organized, in order to get a new piece of information. (This is the begin-ning level of professional judgment).

VI. To Evaluate: means to be able to judge the worth of an idea, form hypothe-ses and do problem solving, research, invent new knowledge. (This is the doctoralevel of participation in the area).

Cant I just do it the

same way that I have

always studied?

A professional routinely operates at level IV and V with occasional forays intolevel VI. This is where you will operate in this course and in most subsequentcourses in the professional curriculum. You will note that each of the objectives forthe course contains specific action words followed by the level in the taxonomy atwhich you will operate. These are the standard descriptive terms for use in instruc-tional objectives. You will be asked to do critical thinking, not simply recite orrecognize the right answer. Problems challenge thinking skills and demand thesynthesis of material into concepts. To facilitate this transition we both must workvery hard.


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1.5 Course Contract

I Will:

What will the teacher do

in this class? Act as a

facilitator.

1. Provide individualized learning methods: Some students learn by hearingand others by seeing (auditory or visual learners). I have designed the course toaccommodate both types of learners. In class, I will provide you with executivesummaries of what you read. I will provide group leaders with detailed reviews ofmaterials for which they are responsible. I will tell you what I'm going to say, sayit, and then tell you what I said. I will also attempt to write it out and draw appro-priate graphs, charts and pictures as well as appropriate visual aids in class andwith the homework problems. I will provide you with ample examples of the typesof manipulations that you will be expected to do. I will provide you with ampleproblem sets so that you may practice those manipulations. I will provide youwith computer simulations so that you may see these manipulations in action andbegin to get a feel for the numbers and their magnitude. Feedback and interactionis encouraged. If I am not meeting your perceived needs, you must tell me. Somestudents might feel too intimidated to ask questions. To obviate this problem, youwill elect a group team leader, an ombudsman, whose job it will be to carry yourquestions, concerns, and comments to me. It is your job and his responsibility tosee that the group interaction facilitates the learning process. This is not to preventyou coming to see me but offered as another avenue of communication.

Will I learn anything rel-

evant in this course?

2. Provide clinical relevance to the practice of pharmacy. This will be stressedat all times. I will also relate real clinical experiences; virtually all of the problemscome from real patients. Some educators believe examples must fit the theory

exactly. This gives the student a false set of reality parameters. Consequentlywhen the data does not fall on the line the student rejects relevant informationYou will become familiar with real data, and the problems associated with realdata.

How will I know how Im

doing?

3. Give adequate feedback: Evaluation of your performance will be availableto you at all times. A running evaluation, updated weekly will be on my door foryour review. You may check any thing with me at any time. I expect that you willsee me outside of class time either individually if you need help or in supervisedreview sessions. You must see me for assistance if your performance is unsatis-factory.

What will the teacher bedoing? Engaging you in

an active learning pro-

cess.

4. Teach: As an operational definition this means: clarifying what you readdemonstrating how and why things work as they do, and unifying the material -attempting to generate the A - HA! syndrome. The correlate of teach from the stu-dent view is learn. Neither is a passive process. I can not open your head and pourthe knowledge in. A saying in education is: Knowledge maketh a bloodyentrance. You must expend the effort necessary for you to learn.


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What must I do in this

active learning process?

You MUST participate in

class and in your

assigned groups!!!

5. Facilitate Learning. You received objectives (above) and a summary foreach study section (chapters in this text), of exactly what is expected of you withexamples in the problem sets at the end of each chapter. We will have ample timeduring class to field questions generated by the correlated reading and problem

sets, as well as homework assignments. I will not be duplicating any book's effortsStudent participation in class is required. You will answer (as well as ask) ques-tions, do problems in class. You will sound things out and get feedback from meand your fellow colleagues. Remember - the class is to help you learn. It is not thesole means of learning, nor am I the source of all knowledge. Its only reason forbeing is to help you organize and summarize what you learn. It has a relativelysimple plan with multiple examples. From these examples you will develop con-cepts which will obviate the need for memorizing individual facts (or actually meentirely). I will assist you in the formation of these concepts. It is patently obviousthat I can not give you every possible example of every type of question that youwill be asked during your professional career. For one thing I don't know what

questions you will be asked nor problems you will encounter. Going from the spe-cific to the general forms concepts which will allow you to go from the general tothe specific, even if you have never been there before. The total medical knowl-edge is now doubling at a rate of every 4 years. I can not teach you the content nec-essary to operate 5 years in the future, let alone 40. You must learn to learnHence, if you plan to become a competent professional, you must operate at leastin Bloom's level V.

How do I get in touch

with the teacher?

6. Be available: I do not have office hours. I believe them to be restrictivefrom your view point. What I do have is a schedule prepared two weeks in advanceof when I am NOT available. You may set an appointment, at least a 1/2 day inadvance to guarantee that I see it, any other time. Of course, appointments are not

necessary if I'm in my office, but you take the chance of my not being there orsomeone else being there ahead of you if you do not sign up. You may contact meby e-mail: [email protected], or by phone: 402-280-2952.

How can I tell the

teacher how things are

going?

7. Be responsive: After each study section, you will be asked to provide mewith a one minute summary of the topic consisting answering the following ques-tions:

a. What was the main thrust of the study section?

b. What was clear about the study section? What was done well?

c. What was unclear? How could it be done better?

This will provide me with a running monitor of my effectiveness as well as aframework of what to stress and what to change.


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Introduction


Do I have any say in the

examination questions?

After each exam, in addition to working out the problems, we will decide whetherany individual question was not covered by the objectives. Note: Not that it wastough, not that you got it wrong, not that it didn't allow you to tell me what youknew, but did I tell you that I was going to ask you to do it? (Was it covered by the

objectives?)How are the exams

graded?

8) Evaluate your performance fairly and honestly: Quite simply, I'm going to tellyou what I expect that you will do. I will show you how to do it. I will provide youwith practice in doing it. I will provide you with an exam which tests your abilityto do it. The exams, as well as the whole course, will use real data and/or pharma-cokinetic parameters for real drugs in real patient settings, much like the stateboard exams (and hopefully real life). Like both of these situations, all answers areinterconnected. What that means is, if you improperly calculate a parameter whichis needed to make another calculation which is used to make a third, etc. ALL arewrong. Conversely, if you can't get a particular calculation by one method or equa-tion, try another. That's simply the way it is. You probably wouldn't get much sym-

pathy if you calculated a dosage regimen properly based on a wrong eliminationrate constant and ended up killing your patient.

You Will:

What do I have to do?

How much work is really

expected?

1) Come prepared to participate in class. This is your full time job. If you areworking full time, it is usually 40 to 60 hours per week. If you go to college 15 to18 credits and prepare/study 2 hours for each credit, you work 45 to 55 hour perweek - you have a full time job. Your commitment is the 45 to 50 hour week notjust the contact hours and a night for each exam. This specifically means for each 1hour class, I expect no less than 2 hours of preparation on your part. Each of you

will be assigned to a study group. You will work the problems together and teacheach other both in and out of class. We will have group discussion of class as wellas group problem solving. It will be your responsibility that every member ofyour group be adequately prepared to answer for the group during recitation. Therewill be a grade for group participation. Part of your grade will be based on quizzeshow well your group performed both on the material for which you were responsi-ble as well as overall and your peer evaluation.

Do I have to read the

text?

2) Read the text. When you read, read critically. Do you understand each idea?Place a (in pencil) in the left side of each paragraph after you read and under-stand it. If you don't get it, place a and come prepared to ask about it in class.

Why do I have to do theproblem sets? 3) Work the problems. Check the answers. These come from old exams, so theyare the type that you are likely to see. Work them in your study groups so thaeveryone can see your thought processes. Bring them to class if you can not dothem or come and see me privately. Be prepared to show me your attempts at solv-ing the problem. I will show you how to get started and give direction to yourthought. I will not work the problem for you. You would not learn if I did it foryou. It is crucial that you work the problems. Each has a specific objective. Over-


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Introduction


all, they contribute to your gaining facility in the processes that a pharmacokineti-cist must know how to do.

Can I just coast

through?

4) Do not delude yourself with respect to your performance. If you received agrade that was less than satisfactory for you, do not simply console yourself by

saying I knew the stuff, I just made a little error. Can you get it right consis-tently? That's when you know the stuff. That is not a laudable goal. That's what aprofessional does. There have been several students in the past that knew thatstuff right up till the time that they had to repeat the course (and sometimesbeyond).


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Introduction


1.6 Computers in the course

Can I get through with

just paper and pencil?

Computer literacy is necessary in this field. Consequently computers will pervade

the course. The homework problems (above) are to done both by hand andchecked with the computer. This will help your understanding of pharmacokineticsin general and that homework objective in particular. Computers are naturaadjunctive tools in the teaching of pharmacokinetics. The are able to simulate theconcentration vs. time profiles and do difficult repetitive calculations which allowthe student to get a broad view of the processes involved.

What are the programs

that I will be using?

Programs that are currently being used in the course are The Scientist and PKAna-lyst both from MicroMath Scientific Software, P.O. Box 71550, Salt Lake City, UT84171-0550; or http://www.micromath.com. A working student version of the software is available free for the downloading for your own work at home. A ful

working version is on the Pharmacy Server.

In addition to the above course objectives, there are specific objectives for the useof computers in the course. They are:

What will I be expected

to do with the comput-

ers?

1. Simulation. The student will construct a graph of the drug time courseusing classical pharmacokinetics. The student will demonstrate effects of changesin pharmacokinetic parameters on the ADME processes and correlated pharmaco-logical / therapeutic response.

2. The student shall statistically evaluate models with regard to fit of datausing both linear and nonlinear regression analysis. The student will calculate

pharmacokinetic parameters which best describe the processes of ADME.How can I use the com-

puters in the homework

and library questions?

These objectives will be met in a variety of ways. Clearly, the most direct methodis the solution of the problem sets by computer. First, I expect that you would dothe problem by hand, complete with graphs and other supporting calculations fol-lowed by computer simulation and data analysis. Just how close did you come tothe best fit? Next, a portion of each exam will be a library exercise in which youwill find and evaluate a published article according to the principles that youlearned in class utilizing the computer facilities. How close did you come theauthors numbers? Do you, in fact, even agree with the authors? You will prepare ashort consult in which you describe the patient and what the authors did along withyour support (or non-support) of the authors conclusions.


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Introduction


1.7 Survival Kit

1.7.1 THINGS FOR YOUR SURVIVAL KIT!What do I need to buy

RIGHT NOW?

1. You will need a good calculator - One with and functions. You mushave it ASAP. You will use it in class.

2. You will also need 2 cycle semilog paper and a clear straight edge ruler foruse in class. These are available in the book store or at an office supply store.

3. You will need access to a computer (486 DX or higher). Micromath hasmade available a student version of the programs for a nominal fee (This softwareis pre-loaded in the Criss computer lab; you may purchase a copy for home use)

4. You will need a 3 D three-ring binder for collecting and maintaining althe pages in this book as well as your class notes.

What do I need to do in

and out of class?

Work in your study groups. You never learn it so well as when you teach it tosomeone else. Everyone benefits from a well run prepared study group. You arenot in competition with your fellow classmates. If everyone earns an A, theneveryone will receive one.

How can I organize this

material?

Organize and label your study notes. This is basic survival. This is one strategythat I find works well. I recommend it highly. Good study notes are formatted onloose-leaf in a three ring binder. The individual pages have a line drawn downabout 1/3 the way in. The notes are taken on the right (2/3) of the page, while

labels go in the left. The labels on the left are often written as questions, which areanswered in the text on the right. Loose leaf binders allow for the incorporation ofreading summaries as well as relevant problems and homework to be organizedwith a divider all in one place. You should write intelligently, with proper punctua-tion and spelling as if you were preparing a consult for a physician. Organization isthe key.

Remember: you may have all the information in the world at your fingertips; beable to solve the most difficult therapy problem and no one will listen to you if youcan't communicate intelligently. Chapters in the book will be organized as above.

ex

xln


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Introduction


1.7.2 WHAT YOU WILL GAIN: (YOUR GOALS)

How is the course to be

graded?

1. At the lowest level, a decent grade for a significant course. Specific gradeswill be earned by attaining the following averages:

A 90 and above B+ 85 to 89

B 80 to 84

C+ 75 to 79

C 70 to 74

D 60 to 69

F 59 and below

The number of exams and point distribution will be determined in class.

2. At the next higher level, I will guarantee that if you comprehend this mate-rial at level V, you will have no trouble passing any state board anywhere withregard to pharmacokinetics.

3. You will gain a useful skill that will make you an integral part of the healthcare team.

Do I really need a

teacher to learn?

4 You will learn to learn. There is an old proverb which goes: Give a man afish and you feed him for a day. Teach a man to fish and you feed him for a life-time. The B.S. Degree is designed to eliminate teachers. An educated man is onewho has learned to how to learn, not one who memorized a page in a book. Thatis what you need to be a professional. The total medical knowledge is doubling at a

rate of every 3-4 years. That means that you will be out of date shortly after gradu-ation (if not before) if you simply memorized content and don't learn to learn andcontinue to learn throughout your career.

What about cheating? One last piece of information: Neither you nor I will not tolerate any academicmisconduct. Anyone caught will minimally receive an F for their efforts and Iwill recommend dismissal from the program. The profession has no room forunprofessional behavior. I will prosecute.


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Introduction


1.8 Tentative Schedule

1.8.1 STUDY GROUP 1: LEARN THE TOOLS - OBTAIN PHARMACOKINETICPARAMETERS FROM DATA.

A: Introduction1. Texts2. Literature3. Grading Policy4. Course Philosophy

B: Math review1. Numbers and exponents

2. Graphs and reaction order3. Calculus4. Laplace transform5. Computer Introduction6. Computer simulation and problem sets

C: Pharmacokinetic modeling1. What a model is and what it isn't.2. Why we model3. Philosophy of modeling

D: Pharmacological Response1. Michaelis - Menton Mass balance equation2. Interrelationships between Concentration, time and response.

E: I.V. Bolus dosing1. Parent compound

I. Plasmaa. Plasma concentration vs. time profile analysisb. Computer aided instruction and simulationc. Problem setsd. Professional communication.

II Urinea. Amount vs. time profile analysisb. Rate vs. time profile analysisc. Computer aided instruction and simulationd. Problem setse. Professional communication.

2. Metabolite


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Introduction


I. Plasmaa. Plasma concentration vs. time profile analysisb. Computer aided instruction and simulationc. Problem sets

d. Professional communication.II. Urinea. Rate vs. time profile analysisb. Computer aided instruction and simulationc. Problem setsd. Professional communication.

F: I.V. infusion1. Parent compound

I. Plasmaa. Plasma concentration vs. time profile analysisb. Computer aided instruction and simulation

c. Problem setsd. Professional communication.

II. Urinea. Amount vs. time profile analysisb. Rate vs. time profile analysisc. Computer aided instruction and simulationd. Problem setse. Professional communication.

1. MetaboliteI. Plasma

a. Plasma concentration vs. time profile analysis

b. Computer aided instruction and simulationc. Problem setsd. Professional communication.

II. Urinea. Amount vs. time profile analysisb. Rate vs. time profile analysisc. Computer aided instruction and simulationd. Problem setse. Professional communication.

End of Material for first exam (six weeks for semester, two weeks for summer ses-

sion)


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Introduction


1.8.2 STUDY GROUP 2: LEARN HOW THE PARAMETERS ARE MODIFIED.

G: Biopharmaceutical factors

1. Absorption

I. PhysiologyII. MechanismsIII. Physiological changes with age, sex, disease

2. DistributionI. DiffusionII. Cardiac output / blood perfusionIII. Physical properties of the drugIV. Physical properties of the bodyV. Physiological changes with age, sex, disease

3. MetabolismI. Biotransformation methods

II. First pass effectIII. ClearanceIV. Physiological changes with age, sex, disease

4. ExcretionI. RenalII. BiliaryIII. MammaryIV. SalivaryV. Misc.VI. Physiological changes with age, sex, disease

H: Oral dosing1. Parent compound

I. Plasmaa. Plasma concentration vs. time profile analysisb. Computer aided instruction and simulationc. Problem setsd. Professional communication.

II. Urinea. Amount vs. time profile analysisb. Rate vs. time profile analysisc. Computer aided instruction and simulation

d. Problem setse. Professional communication.

2. MetaboliteI. Plasma

a. Plasma concentration vs. time profile analysisb. Computer aided instruction and simulation


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Introduction


c. Problem setsd. Professional communication.

II. Urinea. Amount vs. time profile analysis

b. Rate vs. time profile analysisc. Computer aided instruction and simulationd. Problem setse. Professional communication.

I: Bioavailability, Bioequivalence, Drug product selection1. Relative and Absolute Bioavailability2. Factors Influencing Bioavailability3. Methods of Assessing Bioavailability

I. in vivoII. in vitroIII. Correlation

4. Bioequivalence5. Bioavailability6. Drug Product Selection

1.8.3 STUDY GROUP 3: APPLY THE TOOLS IN COMPROMISED PATIENTS.

J: Dosage regimen (Healthy, aged and diseased patients)1. Multiple dose kinetics2. Optimization of dosage regimen3. Computer aided instruction4. Computer simulation and problem sets

5. Computer aided consultation6. Professional consultation process

End of Material for two credit course (six weeks semester - 2 weeks summer)

1.8.4 STUDY GROUP 4: APPLY THE TOOLS IN SPECIAL CASES.

K: Multicompartment Modeling1. Parent compound plasma vs. time profile analysis2. Multiple dose considerations

3. Computer aided instruction4. Computer simulation and problem sets5. Computer aided consultation6. Professional consultation process

L: Protein Binding (healthy, aged and diseased patients)1. Mass balance considerations / drug interactions2. Effects of protein binding on pharmacokinetic parameters


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Introduction


3. Computer aided instruction4. Computer simulation and problem sets5. Computer aided consultation6. Professional consultation process

M: Non - linear (Michaelis - Menton) kinetics1. Computer aided instruction2. Computer simulation and problem sets3. Computer aided consultation4. Professional consultation process

End of material for three credit course (4 weeks semester, 2 weeks summer)


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Introduction


1.9 Competency Statements Related To Pharmacokinetics

The profession of pharmacy has determined that there are minimum, entry level

abilities necessary for a pharmacist. These form the Standards of Practice for theprofession of pharmacy, as written by The National Association of Boards of Pharmacy (who make the NAPLEX, coincidentally). It is important to note that theseabilities are not thought up by some faculty member who sits in his ivory towersaying what he thinks is important. These are what pharmacists do. They havebeen promulgated as competency statements They are also the basis for the stateboard exams as well as the basis far your coursework while in the School of Phar-macy. They are broken down into three general areas:

Area 1: Manage Drug Therapy to Optimize Patient Outcomes (Approximately50% of Test)

Area 2:Assure the Safe and Accurate Preparation and Dispensing of Medications(Approximately 25% of Test)

Area 3: Provide Drug Information and Promote Public Health (Approximately25% of Test)

For a complete listing of competency statements please refer to the National Asso-ciation of Boards of Pharmacys web site, www.nabp.net

1.9.1 SPECIFIC COMPETENCY STATEMENTS ADDRESSED IN THISCOURSE

Area 1: Manage Drug Therapy to Optimize Patient Outcomes (Approxi-

mately 50% of Test)

1.1.0 Evaluate the patient and/or patient information to determine the presence of adisease or medical condition, to determine the need for treatment and/or referral,and to identify patient-specific factors that affect health, pharmacotherapy, and/ordisease management.

1.1.1 Identify and/or use instruments and techniques related to patient assessmentand diagnosis.

1.1.2 Identify and define the terminology, signs, and symptoms associated withdiseases and medical conditions.


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Introduction


1.1.4 Identify patient factors, biosocial factors, and concurrent drug therapy thatare relevant to the maintenance of wellness and the prevention or treatment of adisease or medical condition.

1.2.0 Assure the appropriateness of the patient's specific pharmacotherapeuticagents, dosing regimens, dosage forms, routes of administration, and delivery sys-tems.

1.2.1 Identify drug products by their generic, trade, and/or common names.

1.2.3 Evaluate drug therapy for the presence of pharmacotherapeutic duplicationsand interactions.

1.2.5 Identify physicochemical properties of drug substances that affect their solu-bility, pharmacokinetics, pharmacologic actions, and stability.

1.2.6 Interpret and apply pharmacokinetic principles to calculate and determineappropriate drug dosing regimens.

1.2.7 Interpret and apply biopharmaceutic principles and the pharmaceutical char-acteristics of drug dosage forms and delivery systems, to assure bioavailability andenhance patient compliance.

1.3.0 Monitor the patient and/or patient information and manage the drug regimento promote health and assure safe and effective pharmacotherapy.

1.3.2 Evaluate patient information to determine the safety and effectiveness ofpharmacotherapy.

1.3.5 Identify and remedy interactions or contraindications with diagnostic ormonitoring tests or procedures.

Area 2: Assure the Safe and Accurate Preparation and Dispensing of Medica-

tions (Approximately 25% of Test)

2.1.0 Perform calculations required to compound, dispense, and administer medi-cation.

2.1.1 Calculate the quantity of medication to be compounded or dispensed; reduceand enlarge formulation quantities and calculate the quantity or ingredients neededto compound the proper amount of the preparation.

2.1.3 Calculate the rate of drug administration.


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Introduction


2.1.4 Calculate or convert drug concentrations, ratio strengths, and/or extent ofionization.

2.2.0 Select and dispense medications.

2.2.3 Interpret and apply pharmacokinetic parameters and quality assurance data todetermine equivalence among manufactured drug products, and identify productsfor which documented evidence of inequivalence exists.

2.2.5 Identify and describe the use of equipment and apparatus required to admin-ister medications.

Area 3: Provide Drug Information and Promote Public Health (Approxi-

mately 25% of Test)

3.1.0 Access, evaluate, and apply information to promote optimal health care.

3.1.1 Identify the typical content and organization of specific sources of drug andhealth information.

3.1.2 Interpret and evaluate data presented in textual, tabular, or graphic form.

3.1.3 Evaluate the suitability, accuracy, and reliability of information from refer-ence sources by explaining and evaluating the adequacy of experimental designand by applying and evaluating statistical tests and parameters.


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Introduction


1.10 Pharmacokinetic Symbolism

Pharmacokinetics was developed in several locations simultaneously. Because of

this, the symbols used in the literature are not consistent. Provided each symbol isrigorously defined prior to use, this inconsistency should not prove an insurmount-able difficulty when assessing the literature. In this book, the symbolism belowwill be generally used, though, as an illustration of the variety, some deviation maybe anticipated on occasions.

1.10.1 AMOUNT TERMS (UNIT: MASS)

amount remaining to be eliminated (excreted)

dose (or maintenance dose)

loading dose

amount of drug remaining to be absorbed at any time

amount of unchanged drug in body at any time

amount of metabolite in body at any time

cumulative amount of unchanged drug excreted into urine up to any time

cumulative amount of metabolite excreted into urine up to any time

maximum amount of unchanged drug in body

minimum amount of unchanged drug in body

average amount of unchanged drug in body (also Laplace transform)

minimum amount of unchanged drug in body necessary for pharmacologi-

cal response

ARE

D

DL

Xa

X

Xm

Xu

Xmu

Xmax

Xmin

X

Xef f


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Introduction


1.10.2 CONCENTRATION TERMS (UNITS MASS/VOLUME)

concentration of drug in blood at any time

concentration of drug in plasma at any time

Concentration of metabolite in plasma (or blood) at any time

average steady-state concentration of drug in plasma during a dosing

interval

maximum concentration of drug in plasma

minimum concentration of drug in plasma

average concentration of drug in plasma

dissociation constant of drug-protein complex

Michaelis-Menton rate constant

dissociation constant of drug-receptor complex

minimum effective concentration of drug or metabolite

minimum toxic concentration of drug or metabolite

1.10.3 VOLUME TERMS (UNIT: VOLUME)

apparent volume of unchanged drug distribution in compartment

apparent volume of metabolite distribution in compartment

physiological volume of plasma water

Cb

Cp

Cm

Cp( )ss

Cp( )max

Cp( )min

Cp

KA

KM

KR

MEC

MTC

Vd

Vm

Vw


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Introduction


1.10.4 TIME TERMS (UNIT: TIME)

time since administration of dose

duration of zero-order input

time since cessation of zero-order input

lag time

mean time during sampling interval

elimination half-life (biological half-life)

time for 50% removal

time when maximum amount or concentration occurs

duration of effective pharmacological response

dosing interval (greek theta)

time variable used in association with zero-order input

1.10.5 RATE CONSTANT TERMS (UNIT: RECIPROCAL TIME (*), MASS/TIME

(**)

apparent first-order rate constant for elimination, Summation of all

the ways the drug is eliminated (*)

apparent first-order rate constant for absorption (*)

apparent first-order rate constant for urinary (renal) excretion of unchanged

drug (*)

apparent first-order rate constant for metabolism of unchanged drug (*)

t

T

t'

t0

t

t

t0.5

tmax

tdur

b

K keKdK, i,,

ka

ku k, r

km


38/802

Introduction


apparent first-order rate constant for excretion of metabolite (*)

apparent first-order transfer rate constant (*)

zero-order input rate constant (**)

zero-order infusion rate constant (**)

rate constant for decline in pharmacological effect (usual units:%/time)

hybrid first-order rate constant (*) (greek alpha)

hybrid first-order rate constant (*) (greek beta)

1.10.6 CLEARANCE TERMS (UNITS: VOLUME/TIME)

total body clearance (TBC)

renal clearance (RC)

metabolic clearance (MC)

creatinine clearance

hepatic clearance (HC)

1.10.7 RATE TERMS (UNITS: MASS/TIME (*), MASS/TIME, VOLUME (**),

VOLUME/TIME (***)

instantaneous rate of change of amount of unchanged drug (*)

measured rate of change of amount of unchanged drug (*)

rate of plasma flow through the liver (***)

kmu

kij

k0

Q

R

Cl

Clr

Clm

Clcr

ClH

dXdt-------

Xt----

RH


39/802

Introduction


rate of plasma flow through the kidney (***)

theoretical maximum rate of a process (**)

1.10.8 OTHER TERMS

area under the plasma concentration-time curve (units: time * mass/vol-ume)

area under the first moment of the plasma concentration-time curve (units

)

Mean Residence Time (units: )

Mean Absorption Time (units: )

Mean Dissolution Time (units: )

intensity of pharmacological effect

steady-state hepatic extraction ratio

steady-state renal extraction ratio

maximum intensity of pharmacological effect

fraction of administered dose ultimately absorbed

fraction remaining to be eliminated (excreted)

hematocrit (fractional volume of erythrocytes in whole blood)

number of elimination half-lives in a dosing interval

accumulation factor

intercept

Rr

VM

AUC

AUMC

time2

mass volume

MRT time

MAT time

MDT time

E

EH

Er

Emax

F

FRE

H

N

R

b


40/802

Introduction


fraction of drug that is free (unbound)

fraction of steady-state

slope (sometimes specifically for log dose-response plot)

number of doses

Laplace operator

indicates molar concentration

1.10.9 SUBSCRIPTS

at time zero

at time infinity

during steady-state

at time t

at time T

following dose n

difference between extrapolated and observed

intrinsic

index (i.e., 1,2,3)

index (i.e., 1,2,3)

1.10.10 SUPERSCRIPTS

extrapolated

ss

m

n

s

[ ]

0

ss

t

T

n

diff

int

i

x


41/802

Introduction


last measured valuex


42/802

Introduction


1.11 First Lesson in Pharmacokinetics

It should be intuitively obvious to the most casual observer that the relative bioavailability of 2simultaneous I.V. bolus doses of a drug is equal to the following: (EQ 1-1

(EQ 1-2

given that 100% bioavailability of a single I.V. bolus dose is equal to 1, and bothdoses contain an equal mass of active drug.

For the struggling pharmacokinetics student, we would like to show the veracity ofthis statement. Of course, it is obvious that; the reverse of the transpose is equal tothe transpose of the inverse in matrix theory. i.e.:

(EQ 1-3

Also, it should be obvious that:

(EQ 1-4

Consequently,

(EQ 1-5

which means that:

(EQ 1-6

By definition,

(EQ 1-7

and

(EQ 1-8

Thus:

x1[ ]

1x

1[ ]1

( )! 1---+

lim

ln qsin( )2 qcos( )2+ + p 1 ptanh( )2

cosh

2n

--------------------------------------------------

n 0=

=

x1[ ] 1 x 1[ ]1=

0! 1=

x1[ ]

1x

1[ ]1

( )! 1=

1 1---+

lim

ln qsin( )2 qcos( )2++ p 1 ptanh( )2

cosh

2n

--------------------------------------------------

n 0=

=

e 1 1---+

=

1 p 1 ptanh( )2cosh=


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Introduction


(EQ 1-9

Also,

(EQ 1-10

and

(EQ 1-11

and

(EQ 1-12

So, as we observed in equation 1,

(EQ 1-13

under the stated conditions, two I.V. bolus doses given simultaneously will havetwice as much available drug as a single I.V. bolus dose.

You will agree, however, equation 1-1 is obvious and therefore is more easilyunderstood by a pharmacokineticist!

eln qsin( )2 qcos( )2+ + 1

2n

-----

n 0=

=

2 1

2n

-----

n 0=

=

1 eln=

1 qsin( )2 qcos( )2+=

1 1+ 2=


44/802


CHAPTER 2 Mathematics Review

Author: M ichael M akoid, Phill ip Vuchetich and John Cobb

Reviewer: Phi ll ip Vuchetich

BASICMATHEMATICALSKILLSOBJECTIVES

1. Given a data set containing a pair of variables, the student will properly construct(III) various graphs of the data.

2. Given various graphical representations of data, the student will calculate (III) theslope and intercept by hand as well as using linear regression.

3. The student shall be able to interpret (V) the meaning of the slope and interceptfor the various types of data sets.

4. The student shall demonstrate (III) the proper procedures of mathematical and

algebraic manipulations.

5. The student shall demonstrate (III) the proper calculus procedures of integrationand differentiation.

6. The student shall demonstrate (III) the proper use of computers in graphical simu-lations and problem solving.

7. Given information regarding the drug and the pharmacokinetic assumptions forthe model, the student will construct (III) models and develop (V) equations of theADME processes using LaPlace Transforms.

8. The student will interpret (IV) a given model mathematically.

9. The student will predict (IV) changes in the final result based on changes in vari-ables throughout the model.

10. The student will correlate (V) the graphs of the data with the equations and mod-els so generated.


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Mathematics Review


2.1 Concepts of Mathematics

Pharmacokinetcs is a challenging field involving the application of mathematical

concepts to real situations involving the absorbtion, distribution, metabolism andexcretion of drugs in the body. In order to be successful with pharmacokinetics, acertain amount of mathematical knowledge is essential.

This is just a review.

Look it over. You should

be able to do all of these

manipulations.

This chapter is meant to review the concepts in mathematics essential for under-standing kinetics. These concepts are generally taught in other mathematicalcourses from algebra through calculus. For this reason, this chapter is presented asa review rather than new material. For a more thorough discussion of any particu-lar concept, refer to a college algebra or calculus text.

Included in this section are discussions of algebraic concepts, integration/differen-tiation, graphical analysis, linear regression, non-linear regression and the LaPlacetransform. The Scientist and PKAnalyst are the computer programs used in thiscourse.

Something new -

LaPlace transforms.

Useful tool.

A critical concept introduced in this chapter is the LaPlace transform. The LaPlacetransform is used to quickly solve (integrate) ordinary, linear differential equa-

tions. The Scientistby Micromath Scientific Software, Inc.1is available for work-ing with the LaPlace transform for problems throughout the book.

1. MicroMath Scientific Software, Inc., P.O. Box 21550, Salt Lake City, UT 84121-0550,

http://www.micromath.com


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2.2 Mathematical Preparation

2.2.1 ZERO AND INFINITY

Any number multiplied by zero equals zero. Any number multiplied by infinity

equals infinity. Any number divided by zero is mathematically undefinedAny number divided by infinity is mathematically undefined.

2.2.2 EXPRESSING LARGE AND SMALL NUMBERS

Large or small numbers can be expressed in a more compact way using indices.

How Does Scientific

Notation Work?

Examples: 316000 becomes

0.00708 becomes

In general a number takes the form:

Where Ais a value between 1 and 10, and nis a positive or negative integer

The value of the integer n is the number of places that the decimal point must bemoved to place it immediately to the right of the first non-zero digit. If the decimalpoint has to be moved to its left then n is a positive integer; if to its right, n is anegative integer.

Because this notation (sometimes referred to as Scientific Notation) uses indi-ces, mathematical operations performed on numbers expressed in this way are sub-ject to all the rules of indices; for these rules see Section 2.2.4.

A shorthand notation (AEn) may be used, especially in scientific papers. This may

be interpreted as , as in the following example:

2.28E4 =

( )

3.16 105

7.08310

A 10n

A 10n

2.28410 22800=


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2.2.3 SIGNIFICANT FIGURES

A significant figure is any digit used to represent a magnitude or quantity in theplace in which it stands. The digit may be zero (0) or any digit between 1 and 9

For example:

How do I determine the

number of significant

figures?

Examples (c) to (e) illustrate the exceptions to the above general rule. The value 10raised to any power, as in example (c), does not contain any significant figureshence in the example the four significant figures arise only from the 10.65. If oneor more zeros immediately follow a decimal point, as in example (e), these zerossimply serve to locate the decimal point and are therefore not significant figuresThe use of a single zero preceding the decimal point, as in examples (d) and (e), isa commendable practice which also serves to locate the decimal point; this zero istherefore not a significant figure.

What do significant fig-

ures mean?

Significant figures are used to indicate the precision of a value. For instance, a

value recorded to three significant figures (e.g., 0.0602) implies that one can reli-ably predict the value to 1 part in 999. This means that values of 0.0601, 0.0602and 0.0603 are measurably different. If these three values cannot be distinguished,they should all be recorded to only two significant figures (0.060), a precision of 1part in 99.

After performing calculations, always round off your result to the number of sig-nificant figures that fairly represent its precision. Stating the result to more signifi-cant figures than you can justify is misleading, at the very least!

2.2.4 RULES OF INDICES

What is an index? An index is the power to which a number is raised.

Example: where Ais a number, which may be positive or negative, and nisthe index, which may be positive or negative.

TABLE 2-1. Significant Figures

ValueSignificant

Figures

Number of

SignificantFigures

(a) 572 2,5,7 3

(b) 37.10 0,1,3,7 4

(c) 10.65 x 104 0,1,6,5 4

(d) 0.693 3,6,9 3

(e) 0.0025 2,5 2

An


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Sometimes nis referred to as the exponent, giving rise to the general term, Rulesof Exponents. There are three general rules which apply when indices are used.

(a) Multiplication

(b) Division

(c) Raising to a Power

There are three noteworthy relationships involving indices:

(i) Negative Index

As n tends to infinity then .

(ii) Fractional Index

(iii) Zero Index

An

Am

A=n m+

An

Bm A

B---

n Bn m+

=

An

Am

------- An m

=

An

Bm

------- AB---

n Bn m

=

An( )

mA

nm=

An 1

An

------= n ( ) A n 0

A

1n---

An

=

A0

1=


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2.2.5 LOGARITHMS

What is a logarithm? Some bodily processes, such as the glomerular filtration of drugs by the kidney,are logarithmic in nature. Logarithms are simply a way of succinctly expressing anumber in scientific notation.

In general terms, if a number (A) is given by

then

where log signifies a logarithm to the base 10, and is the value of the logarithmof (A).

Example: 713000 becomes ,

and , thus 713000 becomes

and

Logarithms to the base 10 are known as Common Logarithms. The transformation

of a number (A) to its logarithm (n) is usually made from tables, or on a scientificcalculator; the reverse transformation of a logarithm to a number is made usinganti-logarithmic tables, or on a calculator.

What is the characteris-

tic? the mantissa?

The number before the decimal point is called the characteristic and tells the place-ment of the decimal point (to the right if positive and to the left if negative). Thenumber after the decimal is the mantissa and is the logarithm of the string of num-bers discounting the decimal place.

2.2.6 NATURAL LOGARITHMS

What is a natural loga-

rithm?

Instead of using 10 as a basis for logarithms, a natural base (e) is used. This naturalbase is a fundamental property of any process, such as the glomerular filtration of adrug, which proceeds at a rate controlled by the quantity of material yet to undergothe process, such as drug in the blood. To eight significant figures, the value of thetranscendental function, e, is

....

A 10n

=

A( )log n=

n

7.13 105

7.13 100.85

= 100.85

105 10 5 0.85+( ) 105.85= =

713000( )log 5.85=

e 2.7182818=


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Strictly speaking,

Where is an integer ranging from 1 to infinity ,

denotes the summation from , and

! is the factorial (e.g., 6! = 6x5x4x3x2x1= 720)

In general terms, if a number (A) is given by , then by definition

Where, ln signifies the natural logarithm to the base , and is the value of the

natural logarithm of .

Natural logarithms are sometimes known as Hyperbolic or Naperian Logarithmsagain tables are available and scientific calculators can do this automatically. Theanti-logarithm of a natural logarithm may be found from exponential tables, which

give the value of for various values of n.

How are natural loga-

rithms and common

logarithms related?

Common and natural logarithms are related as follows:

, and

Because logarithms are, in reality, indices of either 10 or , their use and manipu-lation follow the rules of indices (See Section 2.2.4).

(a) Multiplication:

To multiply , where and ; .

By definition,

e 1 1x!----

x 1=

+=

x ( )

x 1=

x 1 tox = =

A e

n

=A( )ln n=

e n

A

en

xln

xlog A( )ln 2.303 A( )log=

A( )log 0.4343 A( )ln=

e

N M N en= M em= NM en em en m+= =


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;

but

and

,

hence

Thus, to multiply two numbers (N and M) we take the natural logarithms of each,add them together, and then take the anti-logarithm (the exponent, in this case) ofthe sum.

(b) Division

(c) Number Raised to a Power

There are three noteworthy relationships involving logarithms:

(i) Number Raised to a Negative Power

As tends to infinity , then

(ii) Number Raised to a Fractional Power

NM( )ln n m+=

n N( )ln=

m M( )ln=

NM( )ln N( )ln M( )ln+=

N

M-----

ln N( )ln M( )ln=

Nm( )ln m N( )ln=

Nm( )ln m N( )ln m 1

N----

ln= =

m m ( ) N m( )ln


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(iii) Logarithm of Unity

2.2.7 NEGATIVE LOGARITHMS

The number 0.00713 may be expressed as:

, or

, or

.

Hence, , which is the result generated by most calculators.

However, another representation of a negative logarithm (generally used by refer-encing a log table):

log (0.00713) = 3.85

The 3 prior to the decimal point is known as the characteristicof the logarithm; itcan be negative (as in this case) or positive, but is never found in logarithmictables. The .85 following the decimal point is known as the mantissaof the loga-rithm; it is always positive, and is found in logarithmic tables.

In fact 3 is a symbolic way of writing minus 3 (-3) for the characteristic. In everycase the algebraic sum of the characteristic and the mantissa gives the correctvalue for the logarithm.

Example: log (0.00713) = 3.85

Add -3 and 0.85

Result is -2.15, which is the value of

Nm( )ln N1m----

ln 1m---- N( )ln= =

1( )ln 1( )log 0= =

7.13310

100.85

103

102.15

0.00713( )log 2.15=

0.00713( )log


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The reason for this symbolism is that only positive mantissa can be read from anti-logarithmic tables, and hence a positive mantissa must be the end result of any log-arithmic manipulations. Note that while there are negative logarithms (when N We want to get pharmacokinetic data (elimination rate con-

stant) from pharmacological response data (Response vs concontration andResponse vs time graphs) .

Response vs Time Graph

1. Plot Response vs Time on Cartesian (regular) Graph Paper.

2. Use Response data between 20 and 80 percent of maximum (Pick the straight part) to do the lin-ear regression on. (Rule of thumb: Connect first and last data point with a straight line. If allthe points fall on one side of the line, its not straight!

3. Find the slope of the straight line, , (eyeball the rise over the run or use linear regression as

required). Important: you must determine the best fit line through all of the points that you will

use. Eyeball method: Get the line as close to the points as possible placing as many pointsabove the line as below the line. Take two points on the line (not data points) to calculate thechange in Y over the change in X.

Response vs Ln(Concentration) Graph

1. Turn semi-log paper on its side so that the numbers are on the top.

What we are attempting to do is get the logarithm part of the paper on the x axis and have thenumbers get bigger as you go from left to right.

2. Plot concentration on the x axis and response on the y.

3. Find the slope of the line plotted this way by the rise over the run method.

Run is change in ln(C).

If you take any two concentrations such that C2 = 2*C1 then the run is (ln(C2) - ln(C1)).

Using rules of logs, when two logs are subtracted, the numbers are devided, thus: = ln(C2/C1).

If C2 = 2*C1 then ln(C2/C1) = ln(2) = 0.693.

0.0

0.2

0.4

0.6

0.8

1.0

10 10 10 10 10 10

Response

Time

dRdT-------

10-810-710-610-510-410-310-210-1

Conc.

0.0

0.2

0.4

0.6

0.8

1.0

Respons

e

1

10

10

10

0

1

10

100

1

10

10

10

0

100

1 10

Concentration

Response


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Documents

Basic Pharmacokinetics.pdf