BasicPKworkbook1

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Making the connections

Francis A. Ndemo, PharmD.MRPharmS.

Doctor of Pharmacy Program

Creighton University

Medical Center

School of Pharmacy and Health profession

ProfessionCompetency

InstitutionILO

CourseILO

UnitILO

LessonILO


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In order for the Pharmacist to ensure desirable therapeutic outcomes thefollowing drug-related problems must be addressed.

sub-therapeutic dosage*

over-dosage *

drug-drug interactions* improper drug product selections*

untreated indications

failure to receive medications

adverse drug reactions

medication use without indications

*Pharmacokinetics discipline addresses these.

The Pharmacist as a professional entrusted to assure the safe and effective useof medicines has to have some minimum or entry-level abilities ( competencies)

that will enable him/her carry out these functions.

The professional bodies and the examining boards have established minimumrequirements that a Pharmacist must meet before being allowed to practicelegally. These minimum requirements are presented as competency statements.(Ref:NAPLEX or Basic Pharmacokinetic text Makoid et al).

In summary these statements have been categorized in three main areas:

manage drug therapy to optimize patient outcomes assure safe and accurate preparation and dispensing of medications provide drug information and promote public health

The Pharmacokinetics course is a subset of these statements: managing drugtherapy to optimize patient outcomes.

How important is the discipline of Pharmacokinetics in optimizing drug therapy?Prior to Pharmacokinetics drug therapy was a matter of hit or miss. Therapyconsisted of a best guess based on Physician experience. In many cases it wasnot necessary to be precise as every patient was expected to respond to drugs

similarly. Population data was more often used than individualized data. Therewere no tools either to optimize drug therapy even in cases where precision wasfound necessary.

It soon became apparent that when a standard dose of certain drugs was givento a population of patients they exhibited varying Pharmacological responses.This response ranged from having no therapeutic effect (under-dose) to showingovert toxic effect (over-dose).This led to the thinking that specific patient factors


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must be responsible for these outcomes since all the patients received the sameamount of drug. It also indicated that the amount of drug reaching the respectivereceptors responsible for the Pharmacologic effect could be varying betweenpatients.

The study of these specific patient factors and the use of such knowledge inoptimizing drug therapyin individual patients is the basis of Pharmacokineticsdiscipline. The most important uses of Pharmacokinetic principles in optimizingdrug therapy are to determine:

how much drug is to be given to an individual patient( optimum dose) when to the most appropriate time to give the dose (dosing

interval) evaluating differences in the rate or extent of physiological availability

between formulations (bioequivalence)

There are, however, other uses of Pharmacokinetics that include:

Predicting plasma, tissue, and urine drug levels Estimating possible accumulation of drugs or metabolites Explaining drug interactions. Diagnosing drug toxicity related to drug overdose

Pharmacokinetic discipline thus gives the Pharmacist the major tools inoptimizing drug therapy and indeed it is the basis of Modern Clinical Pharmacy.It has eliminated the guesswork approach to drug therapy and replaced it with amore objective and rational approach.

The rationale for the discipline is based on the demonstration that the intensity ofthe pharmacological action of many drugs correlates better with plasmaconcentration than with dosage.

It should be noted , however, that the application of Pharmacokinetic principles isjust one of the tools available for optimizing drug therapy and only applies tocertain class of drugs whose concentration-pharmacologic response relationshipis well established. By characterizing the pharmacokinetics of a drug in a specificpatient one can predict individual dosage requirements. The pharmacokineticparameters used for such characterization are determined using drug

concentrations in biological fluids such as plasma ,serum etc.

It should be noted, however, that a number of drugs may be monitored directlywithout indirect use of concentration. This is done by using thepharmacodynamic response. Good examples are antiarrythmics where heart rateis monitored, antihypertensives where blood pressure is monitored andanticougulants where the bleeding time is monitored.


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Finally, it is important to note that Pharmacokinetic discipline uses concepts tooptimize drug therapy .Since pharmacokinetics is a quantitative science,theseconcepts are used to develop theories or equations that can be used to predictthe dose, dosing interval etc.

Pharmacokinetic course is divided into two parts: The Basic Pharmacokinetics(PHA 443) which addresses the development of these concepts (tools) andClinical Pharmacokinetics(PHA 464) which addresses the application of theseconcepts.

This workbook is intended to be a companion to the electronic text; BasicPharmacokinetics,Makoid et al , hence the hyperlinks or references imbendedthroughout the book.

The instructional goals in this course are to:

Develop problem-solving skills Develop analytic skills

Develop ability to synthesize and integrate information and ideas

Develop creative thinking skills

Develop ability to draw reasonable inferences from observations.

Given that these are higher-order thinking skills the best known methods toachieve them is through comprehending the concepts through engaged-learningand masteryof the skills through quizzes.

The workbook is intended to further help in problem-solving and with lots of

simulations of the concepts it is hoped that the necessary connections forcomprehension will be made. The overriding philosophy in this workbook is thatall the students expectations are duly spelled out and that the Intended LearningOutcomes(ILO) for the lessons, the course ,the institution(Creighton University)and the Profession of Pharmacy competency Statements are all connected,hence the title: making the connections.

In order to appreciate the clinical application of the pharmacokinetic principlesthe pharmacokinetic concepts have been matched with the criteria used tooptimize drug therapy in the table below.


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Criteria for effective & Safe use Pharmacokinetic Principles

Selecting the right Chemical Entity T1/2,Ka,tmaxSelecting the right dosage form BioavailabilitySelecting the rightProduct BioequivalenceSelecting the right dose(start& MD) Vd, Cl ,MEC,MTC,MIC

Selecting the rightFrequency Kd,t1/2,tdur,MRT,CL,MICSelecting the right duration Time to Cpss(t1/2), Abx course, Washoutperiods(t1/2)

Ensuresafety& Diagnose Drug Toxicity Plasma Level, PK-PD relationship.Establish Compliance Plasma level


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A. Study GuideB. Course outline and syllabus...C. Course Schedule and topicsD. Pre-quiz (Pharmacokinetic terminologies)E. Introduction to Pharmacokinetic Concepts....F. Unit objectives.

1. Basic Mathematical Skills2. Pharmacological response

3. IV One compartment model ( Plasma, Urine)..4. Oral One Compartment Model.5. Two Compartment Model6. Biopharmaceutical factors..7. Bioavailability8. Multiple dosing.9. Organ Clearance10.Multi compartment Models..11.Non-Linear Kinetics.

G. Lesson Format

H. Pharmacokinetic Model(simulation)(Hyperlink to Animation& Games)I. Learning experiences J. Practice ProblemsK. Worked out answers to Practice Problems.L. Frequently Asked Questions(FAQ)M .Assessment 1-Quizzes..

N. Assessment 2-Library Assignment.O. Assessment 3-Case studies/Recitation..P. Assessment 4-Classroom(CQI, Discussion board)

Q. Assessment 5- ExaminationU. Newsletter..V. Glossary of terminologiesW. Summary of Pharmacokinetic Equations


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Pharmacokinetics may be defined as the quantitative study of the rateprocesses of drug absorption, distribution, and elimination (i.e excretion andmetabolism),ADME. In order to optimize drug dosage for a specific patient

pharmacokinetic parameters must be established. The results are theninterpreted according to how the physiological factors and the formulationcharacteristics of the drug (biopharmaceutics) affect ADME.

In this course there will be a focus on the development of the basic tools andtheir use in designing drug dosage regimens. The factors that affect that theinterpretation a pharmacokinetic study in an individual patient will be

addressed under Clinical Pharmacokinetics course.

What are the expectations of the students in this course?1. As a pre-requisite to this course students are expected to have aknowledge

of Algebra, differential and integral calculus, physiology andpharmacology. An overview of math skills is covered in chapter 1 of therecommended text (Basic Pharmacokinetics by Makoid).Printed copiesare available. Contact Dr Francis Ndemo.

2. Mastery of the necessary computer skills especially use of the excelspreadsheet.

3. Following the written course objectives as presented under courseschedule and topics.

4. Attempt pre-quiz problems before coming to class.5. Ensure that post-quiz problems are completed before the deadlines.

6. Ensure all library assignments are completed and submitted before thedeadline

7. The post-quizzes may be repeated as many times as necessary until adesirable mastery of the skills is achieved.


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8. Ability to select an appropriate pharmacokinetic theory

This workbook is intended to supplement the recommended text. Therelevant chapters are provided in the course schedule. The main approachused in this workbook is the linking of the given objectives to the body oftext. Explanations of the basic pharmacokinetic concepts are given wherefound necessary.By following the objectives, learning the concepts, appreciating the workedout problem, solving the pre-quiz and post-quiz problems mastery of

pharmacokinetic skills necessary to design optimal dosage regimen wouldnot be difficult.Because the pharmacokinetic theories are based on certain basic concepts.understanding of the latter is therefore paramount. These theories are builton each other. Therefore there should be no rushing through the course

material .Attempts have been made to clarify these concepts througheveryday models.The approach here is NOT to cram the material but ratheruse to understand the concepts in the subsequent sections.They have beenseparated from the body of the text so as to allow for better arrangement ofcalculations.Finally, a stepwise approach to learning and solving pharmacokinetic

problems is recommended.

Any difficulties encountered while solving the pre-quiz problems may be

directed to Dr Francis A. Ndemo .These problems will then be compiled fordiscussion in the scheduled lectures.


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COURSE TITLE: Basic Pharmacokinetics

COURSE NUMBER: PHA 443

SEMESTER HOURS: 2 credits

REQUIRED: YES

PREREQUISITES: PHA 313

BULLETIN

DESCRIPTION: Pharmacokinetics is the mathematics of the time course of

Absorption, Distribution, Metabolism, and Excretion (ADME) of

drugs in the body. The biological, physiological, and

physicochemical factors which influence the transfer processes of

drugs in the body thus influence the rate and extent of ADME of

those drugs in the body. In many cases, pharmacological and

toxicological actions are related to plasma concentration of drugs.

Consequently, through the study of pharmacokinetics, the

pharmacist will be able to individualize therapy for the patient.

JUSTIFICATION: Pharmacokinetics is a necessary step toward rational, optimal drugtherapy, preventing toxicity and assuring maintenance of therapeutic

concentrations of active ingredient. Modification of the dosing

regimen, which consists of the dose and the dosing interval, using

patient specific parameters, is the method of dosing optimization.

The pharmacist is the only health professional extensively educated

in the area of pharmacokinetics. The profession of Pharmacy has

determined that there are minimum entry level abilities necessary

for a pharmacist. These have been promulgated as competency

statements in the NABPLEX Candidate's Review Guide. This

course deals with a specific subset of those competency statements.

COURSE

OBJECTIVES:

Course Objective

(number objectives)Pharmaceutical Care

Abilities

(Ability Based Outcome)

Blooms Taxonomy Level

(refer to BloomTaxonomy Flip

1) Given a patient pharmacokinetic profile, the student 3, 8 III


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shall calculate the pharmacokinetic parameters.

2) Given an appropriate patient assessment, the student will

calculate the modifications of the pharmacokinetic

parameters which result from illness.

1, 8 IV

3) Given the modifications of pharmacokinetic parameters

which result from illness, the student shall justifyappropriate dosage regimens.

2,3,4,8 VI

ACTIVE LEARNING

METHODS: Activiy 1) Group based case study format with recitation of

problem sets and discussion of selected topics from prearranged

reading as well as student participation in problem solving.

Activiy 2) Group based evaluation of current pharmacokinetic

literature applying the tools learned in the course will be an integral

part of the teaching process as well as the examination procedure.


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GRADING: The School of Pharmacy and Health Professions default gradingsystem will NOT be utilized in this course.The assessment will be as follows:

Activity WeightPrequizes (1 / lesson) (0)One minute paper (1 / lesson) (0)

Quizes (16) 10%Library Assignments (2) 10%Exam 1 (course objective 1) 30%Exam 2 (course objectives 2,3) 50%

Each activity must be completed to a minimum passing score of70% to successfully complete the course.

Prequizzes must be completed prior to attemptingappropriate section quiz. They are designed to assess ifmaterials were read and are group activities.

One minute post lecture assessment.

Quizzes are individual formative assessment tools which

may be taken as often as needed to attain a minimally

passing grade.

Library Assignments are student evaluations of current

pharmacokinetic research literature utilizing the tools

learned in the course and are group activities. The

assignments may be redone once to attain a minimally

passing grade.

Exams are individual activities and are cumulative,

formative and summative assessments available to the

students on-line using QuestionMark software. They are

formative in the sense the students may practice on any of

several thousand exam versions as often as needed to

attain mastery. They are summative in that the studentmust take the exams during specified times for a grade

assignment.

Grades: Successful completion of all activities with a minimum

score of 70% AND an average of: equal to or greater

than:

92% A

88% B+

84% B

79% C+

75% C70% D

Unsuccessful completion of any activity (failure to attain a

minimally passing score of 70%) will result in failure (F).

Academic misconduct in any activity will minimally result in

course failure and the faculty reserve the right to pursue

additional sanctions as discussed in the school misconduct

policy.


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INSTRUCTOR: Michael Makoid and Francis Ndemo

TEXT(S): The Text is Basic Pharmacokinetics available on the course

website for downloading and through Kappa Psi in hardcopy at

the PSAG agreed upon price.

The latest policies, including those regarding students with disabilities and misconduct can be

found on the School's web site at http://spahp.creighton.edu/Acad_SAffairs/policies.asp. Each

student is responsible for becoming familiar with all of the latest policies.

Faculty reserve the right to make changes in a course as necessary and those

changes must be submitted to the Curriculum Committee within 30 days.


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The course syllabus is a topic by topic outline as follows:

Course Objective 1) Given a patient pharmacokinetic profile, the student shall calculate the

pharmacokinetic parameters.

Lecture Topic

1 Basic Mathematical skills objectives:

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

graphs of the data.

i. Given various graphical representations of data, the student will

calculate (III) the slope and intercept by hand as well as using linear

regression.ii. The student shall demonstrate (III) the proper procedures of

mathematical and algebraic manipulations.

iii. The student shall demonstrate (III) the proper calculus procedures of

integration and differentiation.

2,3 Pharmacological Response objectives:

i. Given patient data of the following types, the student will be able to

properly construct (III) a graph and compute (III) the slope.

1. response (R) v. concentration (C)

2. response (R) v. time(T))

3. concentration (C) v. time (T)

ii. Given any two of the above data sets, the student will be able to compute

(III) the slope of the third.

iii. Given a literature article, the student will evaluate (V) it with respect to

the tools learned.

4-7 IV one compartment model, plasma and urine objectives:

i. The student shall define all pharmacokinetic parameters discussed in

each lesson.

ii. Given a pharmacokinetic profile, the student shall state the assumptions

of the model used to develop the theory used to describe the profile.

iii. Given patient drug concentration and/or amount v. time profiles, thestudent will calculate (III) the relevant pharmacokinetic parameters

available (Vd , K, km , kr , AUC, Clearance, MRT) from IV data.

iv. Given a pharmacokinetic profile, the student shall demonstrate therelationship between the model and the ADME processes.

v. Given a literature article, the student will evaluate (V) it with respect to

the tools learned.

8-11 Oral one compartment model objectives:

i. The student shall define all pharmacokinetic parameters discussed in each lesson.




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iii. Given patient drug concentration and/or amount v. Time profiles, thestudent will calculate (III) the relevant pharmacokinetic parameters (Vd ,

K, km , kr , ka , AUC, Clearance, MRT, MAT) available from oral

data.

iv. Given a literature article, the student will evaluate (V) it with respect to the tools learned.

12- 13 Bioavailability objectives:

i. The student shall define all pharmacokinetic parameters discussed in each

lesson.



iii. Given sufficient data to compare an oral product with another oralproduct or an IV product, the student will estimate (III) the

bioavailability (compare AUCs) and judge (VI) professional acceptance

of the product with regard to bioequivalence (evaluate (VI) AUC, Tpand Cpmax ).

iv. Given a literature article, the student will evaluate (V) it with respect to the

tools learned.

Mid-term Exam

Course Objective 2) Given an appropriate patient assessment, the student will

calculate the modifications of the pharmacokinetic parameters which result from

illness.

Lecture Topic

15-22 Clearance objectives:

i. The student shall define all pharmacokinetic parameters discussed in

each lesson.

ii. Given a pharmacokinetic profile, the student shall state the assumptionsof the model used to develop the theory used to describe the profile.

iii. Given patient information regarding organ function, the student will

calculate (III) changes in clearance and other pharmacokinetic

parameters inherent in compromised patients.

iv. Given patient information regarding organ function, the student will

devise (V) and justify (VI) the optimal dosage regimen for the

compromised patient.


the tools learned.

Course Objective 3) Given the modifications of pharmacokinetic parameters which

result from illness, the student shall justify appropriate dosage regimens.

Lecture Topic

23-29 Multiple dosing objective:


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i. Given population average patient data, the student will devise (V)

dosage regimens which will maintain plasma concentrations of drug

within the therapeutic range.

ii. Given specific patient information, the patient will justify (VI) dosage

regimen recommendations.

iv. Given patient information regarding organ function, the student willdevise (V) and justify (VI) dosage regimen recommendations for the

compromised patient


the tools learned.

30 Final Examity-Based Educational Outcomes for GraduatesSeehttp://pharmacy.creighton.edu/programs/goals_obj.aspfor more detailed explanations of

outcomes.

Pharmaceutical Care Abilities1. Patient Assessment - The student shall contribute to the database of information about the

patient.2. Pharmaceutical Care Plan Development - The student shall develop pharmaceutical care

plans.3. Drug Therapy Evaluation - The student shall assess and monitor the patients drug

therapy4. Pharmacotherapy Decision-Making - The student shall make pharmacotherapy decisions

and support those decisions.5. Medication Preparation, Distribution, and Administration The student shall

compound and/or dispense drug products consistent with patient needs and in harmonywith the law.

6. Systems Management - The student shall use and evaluate acquisition, inventory controland distribution systems.

General Education Abilities

7. Communication Skills - The student shall read, write, speak, listen and use multimedia tocommunicate effectively.

8. Critical Thinking - The student shall acquire, comprehend, apply, analyze, synthesize,and evaluate information.

9. Professional Ethics and Responsibility - The student shall represent the profession in anethical manner. The student shall identify, analyze, and resolve ethical problems.

10. Social Interaction, Citizenship, Leadership, Professionalism - The student shalldemonstrate appropriate interpersonal behaviors.

11. Life-long Learning - The student shall continuously strive to expand his or her knowledgeto maintain professional competence.

12. Information Management The student shall apply technology to pharmacypractice and scienc
http://pharmacy.creighton.edu/programs/goals_obj.asphttp://pharmacy.creighton.edu/programs/goals_obj.asphttp://pharmacy.creighton.edu/programs/goals_obj.asphttp://pharmacy.creighton.edu/programs/goals_obj.asp


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BASIC PHARMACOKINETICS PHA443

(CAMPUS BASED CLASS: SPRING SEMESTER , 2003)Venue: Criss 258

Days: Monday (Section CA)Wednesday (Section CB)Friday (Section CC)

Time: 9.30 11.20 AM

DATE:

WEEK

ENDING

LEC TOPIC OBJECTIVE QUIZ NO BASICPK

CHAPT

01/17 1 Basic Math Skill 1.Calculate slope & intercept2.Demonstrate proper

procedures of math &algebraic manipulations

3 Demonstrate proper calculus

None 2

01/17 2 Pharmacological

Response

1. Response Vs Conc.

2. Response Vs Time

01 3

01/24 3 PharmacologicalResponse

3. Conc Vs Time4. Computing slope of third

when given two other slopes

01

4 questions

Due by

midnight

2/02/03

3

01/24 4 IV bolus dosingone compartmentModel(Plasma)

1. Describe PK model2. Relationship between model

and ADME3.1 Define & calculate Vd3.2 Define & calculate K

3.3 Define & calculate t1/2

02 4

01/31 5 IV bolus dosingone compartmentModel(Plasma)for Parent drugand metabolite

3.4 Define & calculate AUC3.5 Define & calculate MRT3.6 Define & calculate CL3.7 Given Patient data

calculate above PKparameters

02

11 questions

Due by

midnight

2/9/03

4


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01/31 6 IV bolus dosingone compartmentModel(urine)for parent drugand metabolite

1.Calculate K2.Calculate Kr3.Calculate Km4.Calculate% metab/excret

04 & 05

8 questions in

each

Due

midnight

2/16/03

4

02/07 7 IV InfusiondosingOne Compart.

1.Calculate:Vd,t1/2,Km,Kr,AUCCL,MRT using infusion data

2.Utilize rate Vs time tocalculate K and Vd

3. Calculate infusion rate fordesired steady state.

4.Calculate dose for desired

Cpss5. Calculate time to reach steadystate

6.Calculate conc. at end ofinfusion

7. Calculate conc. at any timeafter discontinuation ofinfusion.

03

8 questions

Due

midnight

2/16/03

02/07 8 Oral one

compartmentmodel

1.Calculate Ka from oral

data(plasma)2. Calculate K from oraldata(plasma)

06

16 questionsdue

midnight

3/06/03

7

02/14 9 Oral onecompartmentmodel

3.Calculate Kr from oraldata(urine)

4.Calculate Km from oral data

07

16 questions

due

midnight

3/13/03

7

02/21 10 Oral onecompartment

model

5. Calculate Vd from oral data6.Calculate AUC from oral data

7

02/21 11 Oral onecompartmentmodel

7. Calculate CL from oral data8. Calculate MRT from oral data

7

02/28 12 Bioavailability 1.Define PK parameters used inbioavalability studies

2. Describe PK model thatdescribe profile

8


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3. Estimate absolutebioavailability

02/28 13 Bioavailability 4. Estimate bioavailability usingbioequivalence

08, 09, &10

10 questions

Due

Midnight3/23/03

Quizes 11- 15

65

Conceptual

questions

Due

Midnight

3/23/03

8

03/07 14 MID-TERMEXAM

Exam1

Due between

12:01 A.M.

3/21/03 and

11:59 P.M.

3/23/03

9

03/10-03/14

SPRING

BREAK

03/21 15 Clearance 1.Define and show relationshipto ADME2.Describe PK model used to

describe profile (model-dependent approach toestimating CL)

9

03/21 16 Clearance 3.State importance of CL toclinical practice

4.Show how creatinine clearanceis related to organ clearance

9

03/28 17 Clearance 5. Estimate total clearance basedon dose and AUC

9

03/28 18 Clearance 6. Estimate clearance of anorgan based on dose,AUC,andfraction eliminated by organ

9


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5/10/03 until

11:59 P.M.

5/12/03

THE BIG PICTURE- DIAGRAM 1

Absorption A IV bolusIV infusion

Plasma Drug

Concentration (Level)

Renal

E

Hepatic

M

Distribn

D

Other:Dialysis

LungsGut

Ratein

Rate

out

Level

MainObservation:Plasma LevelHow much?Rate in?Rate out?

Others:Renal excCr Cl

Methods forEstimating:LevelRates

FactoAffecRate i

Interp

FactoAffec

Rate o

Basic PK

Tools

Clinical PK

Factors/interpretation.

PlasmaLevelIndirect

tool

PDResponsePredict

Outcome


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As stated before the rationale for pharmacokinetics is based on the fact that plasma orserum concentrations of certain life-saving drugs can be related to their pharmacologic

activity.It is an indirect tool for predicting therapeutic outcomes. Once this relationshiphas been quantified through pharmacokinetic theories Pharmacists are then able to designdosage regimens that would result in predictable therapeutic outcomes.

From the above diagram 1 it should be evident that plasma concentration is basicallydetermined by two rate processes: the rate at which the drug appears in plasma and therate at which the drug is eliminatedfrom plasma.

The rate of appearance in plasma(input) is in turn determined by the rate of absorption fororal products or rate of administration for parenteral (IV) products.On the other hand therate of elimination from plasma is determined by the rate of metabolism and or excretion.

For drugs with significant distribution the initial decline in plasma concentration may bedue to distribution.The most basic questions Basic pharmacokinetics seeks to answer is:how much drug isrequired to be given any one time(dose)? and often should this be given.The how muchquestion will be addressed by volume of distribution concept and how often by the rateconcepts.Basic Pharmacokinetics, therefore, addresses the basic tools and clinicalPharmacokinetics the applications of these tools in the clinical setting,In addition,ClinicalPharmacokinetics addresses the factors that affect interpretation.These would be factorsthat affect the rate of drug input and elimination i.e affecting ADME.


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In order that the pharmacokinetic concepts addressed in the subsequent sections are wellunderstood models that depict these concepts are given below. A water tank that has aninlet and outlet best represents drug input into the blood circulation and subsequentdistribution in the body.The body can be seen as the tank and volume into which the drugis distributed(Vd) can be seen as the volume of the tank.The drug plasma concentration can be likened to the water level(pressure).Just as the rateof water flow will depend on the water level so will the rate of drug elimination dependon the plasma level(concentration).The higher the water level the higher the rate of waterflow and vice versa.This is a first-order rate of flow or elimination as the rates depend onthe level.A summary of the features of the water tank model and the respectivepharmacokinetic concepts to which they relate is given below in table 1.

Table 1

Model features Equivalent PK Concept

Volume of tank(V) Volume of Distribution(Vd)Water Level(pressure) Plasma Level(concentration Cp)Rate of water flow Rate of Elimination of drug.(Xmg/hr)Fraction:Vol water eliminated/h = Constant

Initial Vol.Elimination Rate Constant(Kd)

Time to reach stable level Time to reach steady state (Cpss)

Time to drain all the water Time for the drug to be eliminated(wash out period)-No of t1/2

A pictorial illustration of the model is shown in diagram 2 with a plasma Vs time graphappended below it for comparison.


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DIAGRAM 2 WATER TANK MODEL ILLUSTRATING Vd, Cpss ,Ra and Re

Ra>>Re Ra =Re Ra = Re Ra=0 Elimination Only.

0

10

20

30

40

50

60

70

80

90

Observation:Absorption Phase/Steady State/Elimination phase.

Ra Ra Ra

A B C D E F

Absorption Phase Steady State Elimination phase

Ra Rate ofAdministration

Volume ofDistribution (

Rate ofElimination (

Plasma Conc


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If one considers a water tank(Diagram 2). As one runs in water at a constanthourly rate depicted by Ra the amount coming out at the drain pipe(Re) keeps increasingas the level keeps rising(pressure).If ABCDEF represents different periods of time thenthe rate of outflow in B is greater than A because of greater water pressure(higher waterlevel).The outflow rate keeps increasing until such a time it is equal to the inflow

rate.This will be a steady state.This model depicts what goes on in chronic oral dosing or continuous IV dosing whereas dosing continues the drug plasma level continues(accumulates) and corresponding risein elimination.This state continues until such a time (approximately 5 half-lives) theamount administered per hour(rate) will be equal to the amount of drug the body iseliminating per hour(Ra=Re) i.e steady state.

Once absorption is complete, as is in the case of oral dosage forms (with respect to thetank once the inlet pipe is closed) the rate of elimination will decline as the Plasmaconcentration drops(with respect to the tank as the water level drops the outflow rate ofdrops too due to decreasing pressure).

Note:The time time it takes for the drug to be fully eliminated depends on the half-life ofthe drug.The shorter the half- life(i.e the bigger the elimination constant) the shorter thethe time to be completely eliminated from the body.The time to reach a steady state also depends on half-life. A shorter half-life means abigger elimination rate constant(K) i.e a bigger outflow rate. It therefore follows that theincrease in elimination rate matches the absorption rate faster in a case of a drug with abig elimination constant if compared to a drug with a smaller elimination constant. Hencea steady state is reached faster in this case.The reverse is true for a drug with a long half-life in which a longer time is required to reach a steady state.Elimination rate constant K

Note: The Fraction of water eliminated per hour is a constant despite the changing rate ofelimination. For example if water is run at 100L/hour and 10L is drained in the first hour,the fraction drained will 10L/100L=0.1h-1 which is the same as 20L/200L=0.1h-1.In thelatter the total amount lost is more, however.In terms of mass of drug eliminated the same arguments holds and the fraction of masseliminated will a constant but the amounteliminated will depend on the initial amount(concentration.).This fraction is defined as the elimination rate constant.


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DIAGRAM 3 THE MOP MODEL

Clearance is defined as the volume of plasma cleared of the drug in unit time.The abovemodel, diagram 3 ,depicts the elimination(clearing process) as a mop.Think of a situationwhere the drug molecules are mopped from the top of a container but withoutredistribution (B) of the molecules. Clearance can be thought as the theoretical volumethat appears to be cleared, being a fraction of the volume of distribution.

Rather looking at the elimination process as a loss in mass; in this case a drop of 10 unitsto 5 units , in clearance the volume which contains the eliminated mass is considered

10L

A

5L

5L

B

10L

C

VdClearedVolume/hr= CL

TheoreticalConc in unclearedvolume after 1hr=5units/5L=1unit/L

Real situationConc after 1hr=5units/10L or

0.5unit/L

InitialPlasma conc10units/10L=1unit/L


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were the concentration remained the same. In this case the volume that will contain 5units of the drug at the concentration of 1 unit /ml. However, in the real situation, theconcentration does drop as shown in C.

DIAGRAM 4THE ADSORPTION MODEL

Absorption

CentralCompartment

ClearanceOrgans

Volume(Fraction Vd)Cleared ofDrug/hr

A more realistic model is the adsorption model ,diagram 4 above.The organs of clearanceare depicted as adsorption agents where fluid that contains a drug flows through butreturns back in a loop.The a mount of fluid remains the same.The volume cleared of thedrug per unit time will depend on the adsorptive capacity (intrinsic clearance of theorgan).This volume may be defined as a fraction of volume of distribution(Vd).Thefraction cleared(eliminated) as defined before is the elimination rate constant K.Therefore clearance is a product of K and Vd.

CL = K*Vd

10L/hr

ClearedPlasma

Rate in(Ra)mass

50mg/hr

VdHypothetic

100LConc5mg/L

ClearanceVol cleared/hr

Rate of Eliminati(Re)MassVol cleared/hr x PlaConc=10L/hr x5mg/L=50m

Drugmolecules


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Objectives:Given Patient data construct a graph & Compute a slope of: (Blooms Level IV)

1. Response Vs Concentration2. Response Vs Time3. Concentration Vs Time4. Compute any of the above slopes when given any two data sets (or slopes)

Reference: Basic Pharmacokinetics (Makoid), chapter 3

Objective 1:Response Vs ConcentrationIntroduction to objective,

What is the clinical Significance of establishing a relationship between Pharmacologicresponse and drug concentration?

If a quantitative relationship is established between these two variables: Response(R), thedependentvariable and the concentration(C), the independentvariable, we are able tocome up with a theory (equation) with which topredict the response. The rate at whichthe dependent variable varies with the independent variable is determined by theslope .The slope is, therefore, the proportionality constantin the equation

Y= m*X+ b Linear equation

dependent Variable Slope Independent variable Intercept

Lecture No: 2&

3

Making the connection:

Selecting the right dose.


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Response Vs conc.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.800.90

1.00

0.0 1.0 2.0 3.0 4.0

Conc.

Response(asFraction

)

Observation: The above graph (diagram 1) is hyperbolic; the intensity appears to varywith concentration until some maxima, the asymptote of the curve.Theory: The occupation theory has been applied to explain this observation. It assumesthat as more receptors are occupied by drug molecules, a greater pharmacologic responseis obtained until a maximum response is reached.(see diagram 3 below for illustration oftheory)The above hyperbolic curve can not be used to develop theories as the slope changes withthe concentration. If we are using a graph paper we would require a linear relationship to

determine the slope upon which the theories are based. These slopes are proportionalityconstants that quantify the relationships. The data, therefore, must be further manipulatedto give a linear relationship.

There are three ways the data can be handled to give a linear relationship:(a) Use a linear Scale (Cartesian) graph: Response(Y axis) & Ln Conc. (X axis)(b) Use a Semi-log scale where abscissa is the log scale: Response(Y axis) & Conc. (Xaxis)(c)Using a computer program: Excel

(a) Linear scale graph :

By converting the raw data for concentration into natural log (or common log). a sigmoid(shape S)curve will be obtained as depicted below.

DIAGRAM 2


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(b) Semi-log scaleThe graph below has a semi-log scale. By plotting the raw concentration data alinear relationship as in (a) is obtained at the middle portion of the sigmoidcurve. This linear portion has been estimated to be 20-80% of the response.Only data between 20% or above and 80% or below are considered fordetermining the slope. See example below (table 1)

100%

80%

Linear

20%

1 2 3 Ln ( Conc.)


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Table 1: Hypothetical Patient data set showing range for linear plot.

= or < 80%Concentration(Dose) Response % of Max response.

X1 Y1 100X2 Y2 79(Y2/Y1)X3 Y3 68(Y3/Y1)X4 Y4 57(Y4/Y1)X5 Y5 29(Y5/Y1)X6 Y6 19(Y6/Y1) = or > 20 %

(c) Using Excel (see spreadsheet )

i. Enter X axis data (Conc. or dose) on the first column(left)ii. 2, Enter Y axis data (Response Fraction or %) on second

column(right)iii. Highlight on data more than 20% and less than 80%iv. 4.Click edit, paste special and valuesv. Click on insert menu and then chart.vi. Select XY scatter vii. Click on Finishviii. Click on X value ,format axis and select scale, logarithmix. Click on any point (coordinate) inside the graph

x. Right click on it.xi. Select trend linexii. Select option and display formula.xiii. Obtain the slope from the formula using the general linear

equation(Y= mX + b )Connection: Basic Pharmacokinetics PHA443 (web) Video clip the Movies (Makoid) forfurther details.


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See example below.The slope may be obtained in three ways:1. Rule of thumb approachConnect two points, the first being the beginning of the straight part of the curve and thesecond being the end of the straight portion. see diagram)

If all data fall on the line then it is a perfect fit(very rare) and if all the points fall on oneside then the line is not a straight !Compute the slope ,dR/dt by rise/run methodUsing data points from the straight line created BUT not from the original data. Themethod is rarely used.2. Eyeball approachConnect the first and the last data point on the straight portion of curve ensuring that

they are as many points above the line as they are below. compute the slope,dR/dt byusing rise of run method.3. Linear regression approach

In this approach the least- square method is used to obtain the line of best fit(regression line).The use of computer programs e.g excel obviates the need to carry

laborious calculations. The Response data between 20 and 80% is used in computing theslope.To obtain a slope dR/dt follow the method described (Response Vs Concentration) abovefor using excel spread sheet. REMEMBER YOU DO NOT NEED TO FORMAT XAXIS AS TIME IS PLOTTED ON A REGULAR CARTESIAN SCALE

Objective 3: Concentration Vs TimeIntroductionWhat is the clinical importance of establishing the relationship between theplasma/serum concentration and time?

From Objective 2 above, it was established that response declines with time.This is because of a corresponding decline in concentration of the active drug.By determining the rate of decline of concentration i.e. the rate of elimination (slope) weare able to predict:

(a) The time it takes an initial concentration to drop to some desiredconcentration

(b) A resultant concentration given an initial concentration and the time ofdrug exposure. A good example when such prediction could be necessary iswhen a loading dose is desirable in an emergency in a patient who already has beentaking the drug. Knowledge of the existing drug level would be necessary for calculatingthe loading dose. But in the absence of laboratory levels the prediction of what theconcentration could be can be made done if the initial concentration and elimination rateconstant or half-life is known.

Making the connectionsSelecting the right dosinginterval


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Establishing the relationships between plasma concentration and time, therefore, iscentral to the field ofPharmacokinetics.

How do you compute a slope for Concentration Vs Time plot?There are three methods that may be employed:

Method 1Ln Concentration Vs Time on Cartesian (regular) scaleThe concentration data is converted into natural log and plotted on the Y axis and Timedata on the X axis. The best line fit (eyeball method) is drawn. Using rise over rundetermine the slope.eg

LnC

K= LnC1-LnC2t1-t2

t

Method 2Concentration Vs Time on semi-log scale.Plot the raw Concentration data on the Y logarithmic axis and Time on the regular scaleX axis. The data points for use in calculating the rise (Y1-Y2), however, must beconverted into natural logs (LnY1-LnY2) as shown in the example that follows.

C

Y axis (log)(a)Slope= C1-C2

t1-t2 (b) Converting into Ln, K= LnC1-LnC2t t1-t2

Method 3Concentration Vs Time in Excel1. Arrange the data set so that time data goes into the first column ( X axis) andConcentration in the second column.2. Compute the slope , dLnC/dt, from the formula using the procedure used in objectiveone orthe movies. Use the exponential trend line.Note that you can obtain the slope from the exponential equation Cp = Cpoe-Kt

There will be no need to format any axis.


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CAUTION ON SELECTING THE TRENDLINEThere are three trend lines you will be using. These are: Y Log Scale(i) Exponential (A&B) (Y & X regular scale) X regular Scale

GENTAMICIN IV BOLU

y = 7.6135e-0.1394x

0

2

4

6

8

10

12

0 .00 5 .00 10.00 15.00 20.00 25.00 30.0

CONC(MG/L)

A

(ii)Linear (C) (Y& X axis regular scale) LnCOr R

t

Y regular(iii)Logarithmic (D&E) (Regular Scale) R R X Log R

(Semi log)

LnC C

Objective 4. Computing Elimination rate constant K (slope dLnC/dt)when given two pharmacological response data sets( or slopes dR/dt,

dR/LnC)SignificanceOrdinarily the elimination rate constant is determined by using Concentration Vs timedata set.(LnCp= Ln Cpo-Kt).This, however, is an invasive method as you have to obtainplasma samples for drug assay. If dR/dt and dR/LnC are already known then the thirdslope dLnC/dt or K can be calculated using the relationship shown below .An importantpharmacokinetic parameter, K, can therefore be obtained without drawing plasmasamples. Note that any of the other slopes may also be obtained from this relationshipprovided two of the slopes are known.

dR = dR * dLnCdt dLnC dt

Needless to say, as discussed above all the three parameters: Concentration, Time andResponse are interrelated.

C

Cp B

t

D E


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By rearranging the above equation the elimination rate constant K, can be obtained usingthe response slopes .By using Ln( dose ) instead of dLnC in the response Vsconcentration slope(dR/LnC) the elimination rate constant can be obtained withoutobtaining biological fluid samples.

K= dLnC = dR/dt = dR/dtdt dR/dLnC dR/dLndoseThe two slopes are first computed from the respective data sets and then the third slope Kcan obtained using the above equation.

One Compartment ModelObjectives:1. Describe (I) the Pharmacokinetic model used to develop the Pharmacokinetic theoriesstating all the assumptions of the model.2. Demonstrate (II) the relationship between the model and ADME processes3. Define (I) all the following Pharmacokinetic Parameters

Volume of Distribution Vd Elimination rate constant K Half life t1/2 Area Under the Curve AUC Mean Resident Time MRT Clearance CL

4. Given patient drug concentration and /or amount Vs time profiles calculate (IV) the abovePharmacokinetic parameters from IV data

Lecture No:4 & 5

Making the ConnectionsHow much drug?How often do you give?


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Finally, there are two main types of compartment models, i.e. one compartment and twocompartment models (see figure below) This course will only be addressing the onecompartment model.

Model 1K

One-Compartment IV

Model 2 Ka K

One- compartment

Oral-First orderAbsorption

Objective 2: demonstrate the relationship between the Model and theADME processes.

As explained above Models are mathematical explanations to the theories. Provided theseconcepts give us good predictions there would be no need to know the complexbiological processes. However, it is important to note that there are limitations to thismodel for it does not shade any more light into the drug kinetic processes in the body.For example1. We know that the drug may not be instantaneously mixed in the compartment as themodel assumes. The central compartment represents the plasma and the highly perfusedtissues that rapidly equilibrate with the drug. Instantaneous and homogenous mixing is

not possible.

2.We know that in one compartment model we assume the drug is only beingeliminated* (one way arrow)and none is coming in from the peripheral compartment, acase we know not to be true as there is some distribution into the peripheral(tissue)compartment. In one-compartment open model, mathematically ,this distribution isinsignificant.

1

1


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(*Elimination is removal of active drug through biotransformation or physical removalthrough excretion)

A patients Pharmacokinetic parameters are usually characterized by a single IVBolus dose a procedure known as pharmacokinetic study.

Objective: 3 & 4 define and Calculate the following Pharmacokinetic

Parameters.

(a) VOLUME OF DISTRIBUTION(Vd)DefinitionThe volume of distribution represents a volume that must be considered in estimating theamount of drug in the body from the concentration of drug found in the sampling

compartment. What this means is that for a given dose of a drug resulting in a specificconcentration, mathematically ,there must be a specific volume into which the drugappears to be dissolved. Because the value of the of Vd does not have a physiologicmeaning in terms of anatomic space, the term apparent volume of distribution is used.The following example illustrates the apparent Volume of distribution.

Dose Vd Unknown Known

Making the connection.How much?

Cpo

Known


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Having two parameters known (Dose & Cpo) Vd can be worked from the followingequation: Vd = Dose/Cpo

What is the clinical significance of Volume of distribution?We learnt from the Pharmacodynamic studies that Response depends on concentrationwhich in turn depends on Volume of distribution.Loading doseOnce we calculate the volume of distribution we are able to estimate the amount of drug(dose) required to give a desired concentration. Population averages for Vd are used toestimate loading doses in emergencies e.g. Lidocaine in cardiac arrhythmias.

Desired dose = Desired conc. * Vd

Note the desired concentration is usually predetermined using the pharmacologicresponse Vs concentration relationship where therapeutic window is obtained.DialysisThe second use of Vd is in evaluating whether the drug is easily dialyzable. For exampleA large Vd would mean that the drug is concentrated in the peripheral compartment andhence not readily dialyzed .The drug has to be the central compartment(blood) to bedialyzed.On the other hand highly water soluble drugs like Amino glycosides have a small volumeof distribution as they are concentrated in the central) vascular compartment and areeasily dialyzed.

Calculating VdHow do you calculate Volume of distribution(Vd) using IV bolus data ?

Volume of distribution = Amount of drug in the body(IV bolus dose)Plasma drug concentration

Vd= DCpo

Unlike in the laboratory where you can take the sample any time as the concentrationremains constant, in the human body drug concentration changes with time hence thesampling time becomes critical. In order to get a concentration corresponding to the IVdose given we have to get plasma sample when no drug has been lost due to elimination.This would be zero time. Practically it is not possible. By the time all the bolus dose isgiven some drug would have been lost. Our desired initial plasma concentration at timeZero (Cpo) can be obtained in two ways.

(i)Using the line of best fit in Ln Conc. Vs time graph(or semi-log), extrapolate to get anintercept on the Y axis as shown below. The intercept on the Y axis will beCpo..Calculate Vd using equation: Vd= D/Cpo


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GENTAMICIN IV BOLU

y = 7.6135e-0.1394

0.1

1

10

100

0.00 10.00 20.00 30.00CONC(LOG

SCALE)

B

Cpo

(ii) Using Excel spread sheet plot the time on a logarithmic scale Y axis and displaythe equation as already explained in Concentration Vs Time objective above. Theintercept in the equation would be Cpo. Y = I e-Kt is obtained from excel(shownin above graph).Calculate Vd using equation:

Vd= D/Cpo (I)

(iii) Using excel by getting the exponential equation from an exponential curve as shownbelow.The intercept 7.713 would be Cpo.

GENTAMICIN IV BOLU

y = 7.6135e-0.1394x

0

2

46

8

10

12

0.00 5.00 10.00 15.00 20.00 25.00 30.0

CONC(MG/L)

A


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(b) ELIMINATION RATE CONSTANT( K)DefinitionThe rate of elimination of most drugs is a first order process .The elimination rateconstant,K,is a first-order elimination rate constant with units of time -1(e.g. hr-1)The elimination rate constant represents the sum(all ways) of each eliminationprocesses e.g. metabolism & excretion for a drug that is eliminated by metabolismand excretion only.

K=Km + Ke Km = First- order rate constant for metabolic processKe = First- order rate constant for Excretion process

There may be several routes of elimination of a drug by metabolism or excretion. Insuch a case each of these processes has its own first-order rate constants. From theEquation below the elimination constant may be defined as the fraction of the drug

removed per hour. It is the slope of LnCp Vs t graph

Making the connectionsHow often?Dosing interval


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.

LnCp= LnCpo-Kt i.e. K = LnCpo-LnCpt

What is the clinical significance of K?

The elimination rate constant represents the rate of removal of drug from the body.Having the value of K for a specific drug and patient allows prediction on the dosinginterval.From the above equation ,values can be set for desired peaks and troughs. In this caseCp would be the trough(MEC) and in place of Cpo thepeakin the equation. We canthen calculate t ,the time between the peak and the trough i.e the dosing intervalprovided we know the value of K. The bigger the K the shorter the dosing interval.

How do you calculate K from IV bolus data?(i) From the graph LnC Vs t calculate rise/run(ii) From the exponential equation obtained using excelthe slope K is the integer before x


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(i)DefinitionHalf-life is the time it takes a concentration of a drug to drop by half (50%).For a first- order process the half-life is a constant while in zero-order it is not. Weknow the fraction removed per unit time is a constant (K).From the equation below:If Cp is half Cpo then an important equation relating K results. Since K is a constant

t1/2 also becomes a constant.Ln(Cp/Cpo) = -Kt = -Kt1/2 Ln(0.5)=-Kt1/ 2 t1/2=0.693/K

What is the clinical significance of t1/2?Just like the elimination rate constant the half-life is a measure of the eliminationprocesses :metabolism and excretion. An alteration of any of the two processes wouldaffect the half-life.The alteration can be due to diseases that affect the hepatic or renalfunctions.(This will be a subject in the clinical Pharmacokinetics).By determining the half-life the appropriate dosing interval can be calculated.(seelater dosing in disease states.

(ii) How do you calculate Half-life?NAPROXYN IV BOLUS

TIME(MIN) MCG/ML

5 45.2

11 29.7


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16 17.8

22 13.5

27 11.3

32 7.1

38 5.4

43 3.8

Conc Vs Time on regular scale(cartesian)

y = 57.331e-0.0634x

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40

Time(min)

Conc(Mcg/ml)

K

A

Conc (log scale Y axis) Vs Time

y = 57.331e-0.0634x

1

10

100

0 10 20 30 40

Time(min)

Conc.(

Mcg/Ml)

5

28 38

t1/2

t1/2

B

There are two ways you can calculate half-life:(a) Byfirst obtaining Elimination constant (K) and solving for t1/2.

You may obtain K using excelexplained earlier.(i) Enter the profile in the spread sheet


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The best way of understanding this is to consider the plasma drug concentration(mass)as a measure of rate of entry or elimination. In the case of IV bolus only eliminationapplies.We know that to get the amount eliminated at any given time you need to multiply therate of elimination with time

Let:Rate of elimination= R mg/hrTime=T hr

The amount eliminated in T hours = R * T.If the plasma concentration were to represent the rate of elimination then amounteliminated would be:The amount eliminated = Cp * TIn the plasma-time curve Cp* T becomes the AUC.(see simulation.. below)Note,however,the rate of elimination is ever changing with time such that the AUC is nota perfect rectangle but a trapezoid.There are two ways you can get AUC.The first one is through intergration of

infestisimally small Cp*T areas.(refer)The second approach would to calculate the area of a trapezoid.

Rectangle Trapezoid.

The trapezoidal method is given below.The basis foe the Trapezoid equation is as follows:Area of a trapezoid = Area of a rectangle + Area of triangleWith reference to segment A:Area of a rectangle= base * height =Concetration,Y axis * Time X axis

=(Cpn+1) * dT1Area of triangle = base * height = *(Cpn-Cpn+1) * dT..2Hence the total area (Trapezoid) = 1 + 2 = (Cpn+1) * dT +*(Cpn-Cpn+1) * dT

= (Cpn+Cpn+1)/2 * dT 3


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The Stepwise procedure is as follows:1.Identity the time interval (the interval should be ideally as small as possible lest a biginterval will cause a big curve that will introduce an error in estimating the area of the

triangle.The hypotunse will be curved instead of being straight.2. Use Equation 3 above to estimate AUC for each segment, A,B,C ETC..The total AUCfor a specified period will be the total area of the segments:AUCA +AUC B + AUC C AUC Detc

Estimating the TERMINAL area(Area between the last observation(Cplast) and infinity.At time this are may be required to be included .It is done by extrapolation using thefollowing formula.

AUC(terminal)= Cplast/K where K the elimination rate constant.

The trapezoidal rule written in the full form is:AUC o- = AUC tn-tn+1 + Cpn/ k

= Sum of segment areas + terminal areaCREATE BOXES YOU CAN HIGHLIGHT.

Conc Vs Time on regular scale(cartesian)

0

5

10

15

20

25

30

35

40

45

50

Time(min)

C

onc(Mcg/ml)

A

Cp l

Cpn

Cpn+1

Cpn+2

Triangle Rectangle

AB

CD E F


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Time hr ng/ml(PlasmaAUC(tn -tn+1)

0 9586.2

2 7309.4 16895.6

4 4489.2 11798.6

6 3541 8030.2

8.5 2355.9 7371.125

10.5 1812.8 4168.7

12.5 1111.6 2924.4

14.5 902.7 2014.3

17 561.6 1830.375

Cplast/K 3383.133K=0.166hr-1

y = 9586.2e-0.166x

1000

2000

3000

4000

5000

6000

7000

8000

CpoK

STEPWISE APPROACH TO CALCULATING AUC USING EXCEL1.Copy the Conentration- time data set from the spreadsheet provided.2.Enter zero in the cell above the cell containing the first time recorded.(This will bezero time for Cpo)3.Enter infinity symbol (obtained from insert menu) in the last cell of the time column.4.Label all the columns(four)as shown above5.Find the value of K using the data set given .When highlighting the data set DO NOTINCLUDE THE ROW THAT CONTAINS TIME ZERO!IF YOU DO YOU WOULDNOT GET YOUR EXPONENTIAL CURVE THAT WILL GIVE K.6.From the formula also obtain Cpo .Enter the value in the respective cell next to timezero as shon in the example above.


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7.In the third column(AUCtn-tn+1) in the second cell (see example above) enter thefollowing formula: ( Cpn + Cpn+1)/2 * (tn-tn+1).The first area woulb be time zero and the first recorded time.In this example.Zero timeant 2 hours8.Copy this formula and apply to all other remaining cells in the column.

9.The area for all the segments will be done.10.The last column will contain the cumulative area. You need ,therefore,write thefollowing formulaCOPY THE FIRST AREA and then write the formula.The formula will

=copied area+the second area in the adjacent column the enter.11.Calculate the terminal area and enter it in the last column.12.Copy the formula for calculating cumulative area and apply to all cells in the lastcolumn.13.The last value in the column will you total AUC.Common errors!FORGETTING TO ACCOUNT FOR THE FIRST AREA THAT INCLUDES ZERO

TIME AND TERMINAL AREA.

signment:Quiz 2 Question 6

(e)MEAN RESIDENT TIME(MRT)Definition.The time course of concentration of a drug in plasma can often be regarded as astatistical distribution curve. After an intravenous bolus drug dose (Do) ,the drugmolecules distribute throughout the body. These molecules will stay (reside) in the bodyfor various time periods.Some molecules may leave the body immediately whereas othermolecules will leave the body at later periods.The term mean resident time (MRT)describes the average time for all the drug molecules to reside in the body.MRT may beconsidered also as the mean transit time.Normal distribution curve


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What is the significance of MRT?From the foregoing section all the Pharmacokinetic parameters were calculated on theassumptiom thet the body behaved as if it is made of compartments where the drugmoves freely between the compartments.Such Pharmacokinetic models help explaintheories.In addition to the compartment models ,Physiologic Pharmacokinetic models

have been developed.The latter model is the closest in terms of explaining thephysiological processes,ADME if compared to the compartment model.Noncompartmental approach in pharmacokineticsThere are times it is difficult to assign a model .This leads to use ofmodel independentmethods in calculating pharmacokinetic parameters.These noncompartmentalPharmacokinetic parameters are based on statistics.The principle of noncompartmental analysis is based on application of the statisticaltheory called the moments of a random variable.In theory a set of plasma-concentrationdata may be considered a statistical distribution.The AUC may be viewed as a distribution curve for plasma concentration(randomvariable).This parameter is considered to be under the Zero moment and MRT under the

first moment.( For further reading on Statistical Moment Theory refer Pharmacokineticsby Mehdi Boroujrdi page331but it is not required)

In Statistical Moments, the elimination rate of a drug may be estimated by MRT orClearance. MRT in this case is analogous to half-life. MRT represents the time when63% of administered drug is eliminated..

How do you calculate MRT?

There are three methods:i.Area under the curve method.MRT= total residence time for all drug molecules

Total number of drug moleculesWe know that AUC represents the amount of drug leaving the body following an IVbolus dose.It is the sum of many little areas(Cp*dt).This areas represent the rate ofelimination at any time t .The resident time for a molecule leaving at time t will be thours.If the AUC were to represent the total number of molecules then the totalResidence time will be:

AUC* t = Cp*t *.

HenceMRT= total residence time for all drug molecules = Cp dt*t =AUMC (FIRST MOMENT) Total number of drug molecules Cp dt AUC (ZERO MOMENT)

AUC and MRT are described as the zero and first moment of the drug concentration timecurve respectively.If you examine the numerator of the above equation the total residence


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time is an area ,a product of AUC (zero moment) ,and time t.This second area is referredto as the area under the first moment curve,AUMC.For Calculation of AUC refer to AUC objective.The AUMC may also calculated using the Trapezoidal rule.Equation

This method is universal as it is applied irrespective of the model When you are not sureof the model use this method.2.USING ONE COMPARTMENT MODEL rate constant.

In the case of one compartment model after intravenous administration, the MRT isequal the reciprocal of the elimination constant.MRTiv =1/kd

= 1.44t1/23.USING A DERIVED RATE CONSTANTK(NON COMPARTMENTALLY).

If clearance is Known and Volume of distribution K may be calculated

K= Cl/Vdss where Cl is the Total Body clearance and Vdss is thevolume of distribution at steady state.using noncompartmental method:statistical momentl=Div/AUC

Note that MRT depends on how the drug is administered.MRT for noninstanteneousadministration (e.g oral) will always be greater than MRT for I.V bolus administration.

AssignmentQuiz 2 Question 7,8,9


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(f)Clearance

Definition.Clearance may be defined as the volume of plasma that is cleared of the drug per unittime.It is one of the parameters used to describe the rate of drug elimination.The otherparameters being half-life and elimination rate constant.Although all these parametersdescribe the same process they give different level of insight and application inpharmacokinetics.The topic is fully covered underClearance.(Clearance may further defined as the fraction of the volume of distribution that is clearedof the drug.Note that the fraction is K .This same fraction can also be applied to the masseliminated per unit time i.e Volume cleared/hr ,Cl =K * Vd,Mass eliminated/hr =K* Xmg

What is the clinical significance of Clearance?Clearance is viewed as the single-most important parameter describing thePharmacokinetics of a drug. It is a measure of elimination from the body withoutidentifyingthe mechanism or the process.Total body clearance(Cl) considers the wholebody as a drug-eliminating system from which many eliminating processes mayoccur.Clearance is used for calculating maintenance dose.

How do you calculate clearance?

There are two methods that may be used:1. Cl =K*Vd Where K is sum of elimination constants all ways(Km+Kr+..etc)2. Cl = Div/AUC

AssignmentQuiz 2 Question 11


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One Compartment Model

Objectives

Given parent drug urine data:

1.Calculate apparent first-order elimination rate constant K

2.Calculate apparent first- order rate constant for urinary(renal)excretion of unchanged drug.(ku)

3.Calculate apparent first- order rate constant for metabolism of

CLecture 2

Activity 4

Making the ConnectionsHow much drug?How often do you give?


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Documents

BasicPKworkbook1