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Basic Pharmacokinetics Workbook Basic Pharmacokinetics Workbook Document Transcript

  • Making the connections Profession Course Unit Lesson Institution Competency ILO ILO ILO ILO Francis A. Ndemo, PharmD.MRPharmS. Doctor of Pharmacy Program Creighton University Medical Center School of Pharmacy and Health profession
  • A professional may be defined as person with special skills; an expert. He has a unique body of knowledge. Based on this unique knowledge and skills, society as empowered these individuals to make decisions on behalf of their clients. A Pharmacist is such a professional whose social object is the Medicine (drug). The profession of Pharmacy has for a long time focused mainly on the quality and distribution of medicines. However, with the increased awareness of drug use problems the profession responded by introducing clinical Pharmacy as means of promoting the effective and safe use of medicines. In order to put the Pharmacokinetics course in perspective it is important to understand the historical development of Clinical Pharmacy. Traditional systems of healthcare have consisted of a network of individual systems, specifically, Medical service, Nursing service and Pharmaceutical service. All the three have been involved to some degree with drugs, but no particular discipline operating at a clinical level has exercised a broad responsibility for the total drug use process. Typically, the drug prescribing, dispensing and administration functions have occurred independently with no effective coordination. Prior to mid '60s the Pharmacy practitioner sought to isolate himself from the patient and other health practitioners. He was not prepared to accept responsibility for patient outcomes except for drug stability, storage and dispensing. He was said to be product-oriented and not patient- oriented. The end result of this lack of coordinated effort on optimizing drug use was drug misuse, abuse, and serious untoward effects. The situation was compounded by increased number of therapeutic agents, information explosion, heavy advertisement, and increased availability. During the latter part of '60s, a number of healthcare and Pharmacy leaders in United States, concerned about these unresolved issues in drug use, started to press for changes in Pharmacy practice and education. Greater emphasis was placed on the quot;clinical' involvement of the Pharmacists with the intent of making them take more responsibility for the safe and appropriate use of drugs in society. Hence, the birth of Clinical Pharmacy. Since inception of Clinical Pharmacy the mission statement of Pharmacy profession has been redefined to include responsibility for therapeutic outcomes (=patient oriented), a concept enshrined in the Pharmaceutical care model.
  • In order for the Pharmacist to ensure desirable therapeutic outcomes the following 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 use of 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 minimum requirements that a Pharmacist must meet before being allowed to practice legally. 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 drug therapy 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. Therapy consisted of a best guess based on Physician experience. In many cases it was not necessary to be precise as every patient was expected to respond to drugs similarly. Population data was more often used than individualized data. There were no tools either to optimize drug therapy even in cases where precision was found necessary. It soon became apparent that when a standard dose of certain drugs was given to a population of patients they exhibited varying Pharmacological responses. This response ranged from having no therapeutic effect (under-dose) to showing overt toxic effect (over-dose).This led to the thinking that specific patient factors
  • must be responsible for these outcomes since all the patients received the same amount of drug. It also indicated that the amount of drug reaching the respective receptors responsible for the Pharmacologic effect could be varying between patients. The study of these specific patient factors and the use of such knowledge in optimizing drug therapy in individual patients is the basis of Pharmacokinetics discipline. The most important uses of Pharmacokinetic principles in optimizing drug 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 in optimizing 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 a more objective and rational approach. The rationale for the discipline is based on the demonstration that the intensity of the pharmacological action of many drugs correlates better with plasma concentration than with dosage. It should be noted , however, that the application of Pharmacokinetic principles is just one of the tools available for optimizing drug therapy and only applies to certain class of drugs whose concentration-pharmacologic response relationship is well established. By characterizing the pharmacokinetics of a drug in a specific patient one can predict individual dosage requirements. The pharmacokinetic parameters 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 directly without indirect use of concentration. This is done by using the pharmacodynamic response. Good examples are antiarrythmics where heart rate is monitored, antihypertensives where blood pressure is monitored and anticougulants where the bleeding time is monitored.
  • Finally, it is important to note that Pharmacokinetic discipline uses concepts to optimize drug therapy .Since pharmacokinetics is a quantitative science,these concepts are used to develop theories or equations that can be used to predict the dose, dosing interval etc. Pharmacokinetic course is divided into two parts: The Basic Pharmacokinetics (PHA 443) which addresses the development of these concepts (tools) and Clinical Pharmacokinetics(PHA 464) which addresses the application of these concepts. This workbook is intended to be a companion to the electronic text; Basic Pharmacokinetics,Makoid et al , hence the hyperlinks or references imbended throughout 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 to achieve them is through comprehending the concepts through engaged-learning and mastery of 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 for comprehension will be made. The overriding philosophy in this workbook is that all the students expectations are duly spelled out and that the Intended Learning Outcomes(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 principles the pharmacokinetic concepts have been matched with the criteria used to optimize drug therapy in the table below.
  • Criteria for effective & Safe use Pharmacokinetic Principles Selecting the right Chemical Entity T1/2,Ka,tmax Selecting the right dosage form Bioavailability Selecting the right Product Bioequivalence Selecting the right dose(start& MD) Vd, Cl ,MEC,MTC,MIC Selecting the right Frequency Kd,t1/2,tdur,MRT,CL,MIC Selecting the right duration Time to Cpss(t1/2), Abx course, Washout periods(t1/2) Ensure safety& Diagnose Drug Toxicity Plasma Level, PK-PD relationship. Establish Compliance Plasma level
  • A. Study Guide……………………………………………… B. Course outline and syllabus……………………………... C. Course Schedule and topics……………………………… D. Pre-quiz (Pharmacokinetic terminologies)……………… E. Introduction to Pharmacokinetic Concepts…………….... F. Unit objectives. 1. Basic Mathematical Skills…………………………… 2. Pharmacological response…………………………… 3. IV One compartment model ( Plasma, Urine)……….. 4. Oral One Compartment Model………………………. 5. Two Compartment Model…………………………… 6. Biopharmaceutical factors………………………….. 7. Bioavailability……………………………………… 8. Multiple dosing……………………………………. 9. Organ Clearance…………………………………… 10.Multi compartment Models……………………….. 11.Non-Linear Kinetics………………………………. G. Lesson Format………………………………………… H. Pharmacokinetic Model(simulation)…(Hyperlink to Animation& Games) I. Learning experiences …………………………………… J. Practice Problems………………………………………… K. 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- Examination U. Newsletter……………………………………………….. V. Glossary of terminologies………………………………… W. Summary of Pharmacokinetic Equations………………
  • Pharmacokinetics may be defined as the quantitative study of the rate processes of drug absorption, distribution, and elimination (i.e excretion and metabolism),ADME. In order to optimize drug dosage for a specific patient pharmacokinetic parameters must be established. The results are then interpreted according to how the physiological factors and the formulation characteristics of the drug (biopharmaceutics) affect ADME. In this course there will be a focus on the development of the basic tools and their use in designing drug dosage regimens. The factors that affect that the interpretation 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 a knowledge of Algebra, differential and integral calculus, physiology and pharmacology. An overview of math skills is covered in chapter 1 of the recommended text (Basic Pharmacokinetics by Makoid).Printed copies are available. Contact Dr Francis Ndemo. 2. Mastery of the necessary computer skills especially use of the excel spreadsheet. 3. Following the written course objectives as presented under course schedule 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 the deadline 7. The post-quizzes may be repeated as many times as necessary until a desirable mastery of the skills is achieved.
  • 8. Ability to select an appropriate pharmacokinetic theory This workbook is intended to supplement the recommended text. The relevant chapters are provided in the course schedule. The main approach used in this workbook is the linking of the given objectives to the body of text. Explanations of the basic pharmacokinetic concepts are given where found necessary. By following the objectives, learning the concepts, appreciating the worked out problem, solving the pre-quiz and post-quiz problems mastery of pharmacokinetic skills necessary to design optimal dosage regimen would not be difficult. Because the pharmacokinetic theories are based on certain basic concepts. understanding of the latter is therefore paramount. These theories are built on each other. Therefore there should be no rushing through the course material .Attempts have been made to clarify these concepts through everyday models.The approach here is NOT to cram the material but rather use to understand the concepts in the subsequent sections.They have been separated from the body of the text so as to allow for better arrangement of calculations. 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 for discussion in the scheduled lectures.
  • 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 drug therapy, 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: Pharmaceutical Care Course Objective Bloom’s Taxonomy Level (number objectives) (refer to Bloom’s Abilities (Ability Based Outcome) Taxonomy Flip Chart) 3, 8 III 1) Given a patient pharmacokinetic profile, the student shall calculate the pharmacokinetic parameters.
  • 1, 8 IV 2) Given an appropriate patient assessment, the student will calculate the modifications of the pharmacokinetic parameters which result from illness. 2,3,4,8 VI 3) Given the modifications of pharmacokinetic parameters which result from illness, the student shall justify appropriate dosage regimens. 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.
  • GRADING: The School of Pharmacy and Health Professions default grading system will NOT be utilized in this course. The assessment will be as follows: Activity Weight Prequizes (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 of 70% to successfully complete the course. Prequizzes must be completed prior to attempting appropriate section quiz. They are designed to assess if materials 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 student must 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% C 70% 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. 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.”
  • 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, the student 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 the relationship 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. 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, the student 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. 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 sufficient data to compare an oral product with another oral product 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, Tp and 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 assumptions of 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. v. Given a literature article, the student will evaluate (V) it with respect to 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: 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 will devise (V) and justify (VI) dosage regimen recommendations for the compromised patient v. Given a literature article, the student will evaluate (V) it with respect to the tools learned. 30 Final Examity-Based Educational Outcomes for Graduates See http://pharmacy.creighton.edu/programs/goals_obj.asp for more detailed explanations of outcomes. Pharmaceutical Care Abilities 1. 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 patient’s drug therapy 4. 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 harmony with the law. 6. Systems Management - The student shall use and evaluate acquisition, inventory control and distribution systems. General Education Abilities 7. Communication Skills - The student shall read, write, speak, listen and use multimedia to communicate 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 an ethical manner. The student shall identify, analyze, and resolve ethical problems. 10. Social Interaction, Citizenship, Leadership, Professionalism - The student shall demonstrate appropriate interpersonal behaviors. 11. Life-long Learning - The student shall continuously strive to expand his or her knowledge to maintain professional competence. 12. Information Management – The student shall apply technology to pharmacy practice and scienc
  • 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: LEC BASIC TOPIC OBJECTIVE QUIZ NO WEEK PK ENDING CHAPT 01/17 1 Basic Math Skill 1.Calculate slope & intercept None 2 2.Demonstrate proper procedures of math & algebraic manipulations 3 Demonstrate proper calculus 01/17 2 Pharmacological 1. Response Vs Conc. 01 3 Response 2. Response Vs Time 01/24 3 Pharmacological 3. Conc Vs Time 01 3 Response 4. Computing slope of third 4 questions when given two other slopes Due by midnight 2/02/03 01/24 4 IV bolus dosing 1. Describe PK model 02 4 one compartment 2. Relationship between model Model(Plasma) and ADME 3.1 Define & calculate Vd 3.2 Define & calculate K 3.3 Define & calculate t1/2 01/31 5 IV bolus dosing 3.4 Define & calculate AUC 02 4 one compartment 3.5 Define & calculate MRT 11 questions Model(Plasma) 3.6 Define & calculate CL Due by for Parent drug 3.7 Given Patient data midnight and metabolite calculate above PK 2/9/03 parameters 01/31 6 IV bolus dosing 1.Calculate K 04 & 05 4 one compartment 2.Calculate Kr 8 questions in Model(urine) 3.Calculate Km each for parent drug 4.Calculate% metab/excret Due
  • and metabolite midnight 2/16/03 02/07 7 IV Infusion 1.Calculate:Vd,t1/2,Km,Kr,AUC 03 dosing CL,MRT using infusion data 8 questions One Compart. 2.Utilize rate Vs time to Due calculate K and Vd midnight 3. Calculate infusion rate for 2/16/03 desired steady state. 4.Calculate dose for desired Cpss 5. Calculate time to reach steady state 6.Calculate conc. at end of infusion 7. Calculate conc. at any time after discontinuation of infusion. 02/07 8 Oral one 1.Calculate Ka from oral 06 7 compartment data(plasma) 16 questions model 2. Calculate K from oral due data(plasma) midnight 3/06/03 02/14 9 Oral one 3.Calculate Kr from oral 07 7 compartment data(urine) 16 questions model 4.Calculate Km from oral data due midnight 3/13/03 02/21 10 Oral one 5. Calculate Vd from oral data 7 compartment 6.Calculate AUC from oral data model 02/21 11 Oral one 7. Calculate CL from oral data 7 compartment 8. Calculate MRT from oral data model 02/28 12 Bioavailability 1.Define PK parameters used in 8 bioavalability studies 2. Describe PK model that describe profile 3. Estimate absolute bioavailability 02/28 13 Bioavailability 4. Estimate bioavailability using 08, 09, &10 8 bioequivalence 10 questions
  • Due Midnight 3/23/03 Quizes 11- 15 65 Conceptual questions Due Midnight 3/23/03 03/07 14 MID-TERM Exam1 9 EXAM Due between 12:01 A.M. 3/21/03 and 11:59 P.M. 3/23/03 03/10- SPRING 03/14 BREAK 03/21 15 Clearance 1.Define and show relationship 9 to ADME 2.Describe PK model used to describe profile (model- dependent approach to estimating CL) 03/21 16 Clearance 3.State importance of CL to 9 clinical practice 4.Show how creatinine clearance is related to organ clearance 03/28 17 Clearance 5. Estimate total clearance based 9 on dose and AUC 03/28 18 Clearance 6. Estimate clearance of an 9 organ based on dose,AUC,and fraction eliminated by organ 04/04 19 Clearance 7.Determine change in CL due 9 to functional changes in an organ
  • 04/04 20 Clearance 8. Determine change in 9 clearance due to change in rate of blood flow. 04/11 21 clearance 9.Devise and justify dosages for 9 given organ functions 04/11 22 clearance 10 Devise and justify dosages 9 for given organ functions 04/18 * 23 Multiple dosing 1.Introduction to Therapeutic 10 Drug Monitoring(TDM) 2.Detemining Cpmax , 3.Dtermining Cpmin 04/18 * 24 Multiple dosing 3.Determining Cpavg 10 4.Modifying dose using *Good bioavailability and salt factors Friday Sec CC Class TBA 04/25* 25 Multiple dosing 5.Determining the dosing 10 Easter interval Monday *SecCA TBA 05/02 26 Multiple dosing 6.Modifying dose based on 10 altered CL 7.Modifying dose based on altered K 8.Modifying dose based on altered Vd 05/02 27 Multiple dosing 9. Modifying dose based altered 10 protein binding 05/09 28 Multiple dosing 10. Devise and justify dosage 10 regimen for given altered organ function 05/09 29 Multiple dosing 11. Devise and justify dosage 16 10 regimen for given altered Due organ function 5/11/03 05/15 30 FINAL EXAM Final Exam 10,11,12 May Between 12:01 A.M. 5/10/03 until 11:59 P.M. 5/12/03
  • THE BIG PICTURE- DIAGRAM 1 Methods for Factors IV bolus A Absorption Estimating: Rate Affecting IV infusion Level in Rate in Rates Main Interpret Observation: Plasma Drug Plasma Level Level How much? Concentration (Level) Rate in? Rate out? Factors Other: Rate Affecting Renal Hepatic Distribn Dialysis out Rate out Lungs Others: E M D Gut Renal exc Cr Cl Basic PK Clinical PK Tools Factors/interpretation. Plasma PD Level Response Indirect Predict tool Outcome
  • As stated before the rationale for pharmacokinetics is based on the fact that plasma or serum concentrations of certain life-saving drugs can be related to their pharmacologic activity.It is an indirect tool for predicting therapeutic outcomes. Once this relationship has been quantified through pharmacokinetic theories Pharmacists are then able to design dosage regimens that would result in predictable therapeutic outcomes. From the above diagram 1 it should be evident that plasma concentration is basically determined by two rate processes: the rate at which the drug appears in plasma and the rate at which the drug is eliminated from plasma. The rate of appearance in plasma(input) is in turn determined by the rate of absorption for oral products or rate of administration for parenteral (IV) products.On the other hand the rate 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 be due to distribution. The most basic questions Basic pharmacokinetics seeks to answer is:how much drug is required to be given any one time(dose)? and often should this be given.The how much question will be addressed by volume of distribution concept and how often by the rate concepts. Basic Pharmacokinetics, therefore, addresses the basic tools and clinical Pharmacokinetics the applications of these tools in the clinical setting,In addition,Clinical Pharmacokinetics addresses the factors that affect interpretation.These would be factors that affect the rate of drug input and elimination i.e affecting ADME.
  • In order that the pharmacokinetic concepts addressed in the subsequent sections are well understood models that depict these concepts are given below. A water tank that has an inlet and outlet best represents drug input into the blood circulation and subsequent distribution in the body.The body can be seen as the tank and volume into which the drug is 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 rate of water flow will depend on the water level so will the rate of drug elimination depend on the plasma level(concentration).The higher the water level the higher the rate of water flow and vice versa.This is a first-order rate of flow or elimination as the rates depend on the level.A summary of the features of the water tank model and the respective pharmacokinetic 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 Elimination Rate Constant(Kd) Initial Vol. 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 graph appended below it for comparison.
  • DIAGRAM 2 WATER TANK MODEL ILLUSTRATING Vd, Cpss ,Ra and Re Ra Ra Ra Ra Rate of Administration (Ra) Volume of Distribution (Vd) A B C D E F Plasma Conc.(Cp) Rate of Elimination Re (Re) Ra>>Re Ra =Re Ra = Re Ra=0 Elimination Only. Absorption Phase Steady State Elimination phase 90 80 70 60 50 40 30 20 10 0 1 2 3 4 5 6 7 8 9 Observation: Absorption Phase/Steady State/Elimination phase. If one considers a water tank(Diagram 2). As one runs in water at a constant hourly rate depicted by Ra the amount coming out at the drain pipe(Re) keeps increasing as the level keeps rising(pressure).If ABCDEF represents different periods of time then the
  • rate of outflow in B is greater than A because of greater water pressure(higher water level).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 where as dosing continues the drug plasma level continues(accumulates) and corresponding rise in elimination.This state continues until such a time (approximately 5 half-lives) the amount administered per hour(rate) will be equal to the amount of drug the body is eliminating per hour(Ra=Re) i.e steady state. Once absorption is complete, as is in the case of oral dosage forms (with respect to the tank once the inlet pipe is closed) the rate of elimination will decline as the Plasma concentration drops(with respect to the tank as the water level drops the outflow rate of drops too due to decreasing pressure). Note:The time time it takes for the drug to be fully eliminated depends on the half-life of the drug.The shorter the half- life(i.e the bigger the elimination constant) the shorter the the 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 a bigger elimination rate constant(K) i.e a bigger outflow rate. It therefore follows that the increase in elimination rate matches the absorption rate faster in a case of a drug with a big elimination constant if compared to a drug with a smaller elimination constant. Hence a 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 of elimination. 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 the latter the total amount lost is more, however. In terms of mass of drug eliminated the same arguments holds and the fraction of mass eliminated will a constant but the amount eliminated will depend on the initial amount (concentration.). This fraction is defined as the elimination rate constant.
  • DIAGRAM 3 THE MOP MODEL Cleared Vd Volume/hr = CL 5L 10L 10L 5L C A B Initial Theoretical Real situation Plasma conc Conc in uncleared Conc after 1hr 10units/10L volume after 1hr =5units/10L or =1unit/L =5units/5L 0.5unit/L =1unit/L Clearance is defined as the volume of plasma cleared of the drug in unit time.The above model, diagram 3 ,depicts the elimination(clearing process) as a mop.Think of a situation where the drug molecules are mopped from the top of a container but without redistribution (B) of the molecules. Clearance can be thought as the theoretical volume that ‘ 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 units to 5 units , in clearance the volume which contains the eliminated mass is considered were the concentration remained the same. In this case the volume that will contain 5 units of the drug at the concentration of 1 unit /ml. However, in the real situation, the concentration does drop as shown in C.
  • DIAGRAM 4 THE ADSORPTION MODEL Drug Absorption molecules Rate in(Ra) mass 50mg/hr Central Compartment Vd Hypothetical 100L Cleared Clearance Conc Plasma Organs 5mg/L Clearance Vol cleared/hr Rate of Elimination/hr Volume (Re) (Fraction Vd) 10L/hr Mass Cleared of Vol cleared/hr x Plasma Drug/hr Conc= 10L/hr x5mg/L=50mg/hr A more realistic model is the adsorption model ,diagram 4 above.The organs of clearance are depicted as adsorption agents where fluid that contains a drug flows through but returns back in a loop.The a mount of fluid remains the same.The volume cleared of the drug per unit time will depend on the adsorptive capacity (intrinsic clearance of the organ).This volume may be defined as a fraction of volume of distribution(Vd).The fraction cleared(eliminated) as defined before is the elimination rate constant K. Therefore clearance is a product of K and Vd. CL = K*Vd
  • Lecture No: 2& 3 Objectives: Given Patient data construct a graph & Compute a slope of: (Blooms Level IV) 1. Response Vs Concentration 2. Response Vs Time 3. Concentration Vs Time 4. Compute any of the above slopes when given any two data sets (or slopes) Reference: Basic Pharmacokinetics (Makoid), chapter 3 Making the connection: Selecting the right dose. Objective 1:Response Vs Concentration Introduction to objective, What is the clinical Significance of establishing a relationship between Pharmacologic response and drug concentration? If a quantitative relationship is established between these two variables: Response(R), the dependent variable and the concentration(C), the independent variable, we are able to come up with a theory (equation) with which to predict the response. The rate at which the dependent variable varies with the independent variable is determined by the slope . The slope is, therefore, the proportionality constant in the equation Y= m*X + b Linear equation dependent Variable Slope Independent variable Intercept Once you get a valid theory all you need to predict the response is the determination of the slope. Clinically, using the theory we are then able to predict a desired pharmacologic response(therapeutic), diagnose a sub-therapeutic or toxic response provided we know the plasma concentration .Ultimately, if in turn we establish the relationship between dose and
  • concentration (see Volume of distribution objective ) we would be able to calculate the desirable dose that gives us the target concentration. Hence desired therapeutic response. How do we compute the slope of Response Vs Concentration plot? There are three steps involved: 1. Make observations: Response Vs Concentration (raw data) 2. Plotting the response data on the Y axis and Concentration data on the X(linear scale) 3. If a linear plot is obtained, the slope will be Rise (∆Y)/Run (∆X). The following example demonstrates the three steps. Step 1 Making observations Concentration( e.g ng/ml) Response(Max = 1) or 100% 0.0 0.0(0%) 0.8 0.55(55%) 1.6 0.70(70%) 2.4 0.78(78%) 3.2 0.81(81%) 4.0 0.85(85%) Step 2 plotting the data on a linear scale DIAGRAM 1 Response Vs conc. 1.00 0.90 Response( as Fraction) 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.0 1.0 2.0 3.0 4.0 5.0 Conc.
  • Observation: The above graph (diagram 1) is hyperbolic; the intensity appears to vary with concentration until some maxima, the asymptote of the curve. Theory: The occupation theory has been applied to explain this observation. It assumes that as more receptors are occupied by drug molecules, a greater pharmacologic response is obtained until a maximum response is reached.(see diagram 3 below for illustration of theory) The above hyperbolic curve can not be used to develop theories as the slope changes with the 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 proportionality constants that quantify the relationships. The data, therefore, must be further manipulated to 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. (X axis) (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 Response 100% 80% Linear 20% 1 2 3 Ln ( Conc.) (b) Semi-log scale The graph below has a semi-log scale. By plotting the raw concentration data a linear relationship as in (a) is obtained at the middle portion of the sigmoid curve. 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 for determining the slope. See example below (table 1) Response changes with concentration (Log scale) DIAGRAM 3 Response v Concentration Maximal response 1.20 1.00 0.80 0.60 Linear response Response (20-80%) 0.40 0.20 0.00 No response 0.01 0.10 1.00 10.00 100.00 1000.00 10000.00 100000.00 Concentration Receptor Drug Molecule Table 1: Hypothetical Patient data set showing range for linear plot. = or < 80% Concentration(Dose) Response % of Max response. X1 Y1 100 X2 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 values v. Click on insert menu and then chart. vi. Select XY scatter vii. Click on Finish viii. Click on X value ,format axis and select scale, logarithm ix. Click on any point (coordinate) inside the graph x. Right click on it. xi. Select trend line xii. 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) for further details.
  • Making the connections: Selecting the right dosing interval Objective 2: Response Vs Time Introduction What is the clinical significance of establishing the relationship between Pharmacologic Response and time? A number of disease conditions require prolonged drug therapy beyond the first dose. It is important ,therefore, to establish how soon, following a dose, the therapeutic effect wears out(reaching MEC) so that the subsequent dose may be given(Ref: Multiple dosing) .A good example is epilepsy where continued drug therapy is indicated so that the patient remains seizure- free. Hence this relationship is necessary for establishing the dosing interval, a vital parameter used for designing dosages in Therapeutics. How do we compute the slope for Response Vs Time plot? Plot Response data on Y axis and Time on X axis using a regular Cartesian scale. See example below. The slope may be obtained in three ways: 1. Rule of thumb approach Connect two points, the first being the beginning of the straight part of the curve and the second 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 one side then the line is not a straight !Compute the slope ,dR/dt by rise/run method Using data points from the straight line created BUT not from the original data. The method is rarely used. 2. Eyeball approach Connect 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 by using 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 the slope. To obtain a slope dR/dt follow the method described (Response Vs Concentration) above for using excel spread sheet. REMEMBER YOU DO NOT NEED TO FORMAT X AXIS AS TIME IS PLOTTED ON A REGULAR CARTESIAN SCALE
  • Making the connections Selecting the right dosing interval Objective 3: Concentration Vs Time Introduction What is the clinical importance of establishing the relationship between the plasma/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) we are able to predict: (a) The time it takes an initial concentration to drop to some desired concentration (b) A resultant concentration given an initial concentration and the time of drug exposure. A good example when such prediction could be necessary is when a loading dose is desirable in an emergency in a patient who already has been taking the drug. Knowledge of the existing drug level would be necessary for calculating the loading dose. But in the absence of laboratory levels the prediction of what the concentration could be can be made done if the initial concentration and elimination rate constant or half-life is known. Establishing the relationships between plasma concentration and time, therefore, is central to the field of Pharmacokinetics. How do you compute a slope for Concentration Vs Time plot? There are three methods that may be employed: Method 1 Ln Concentration Vs Time on Cartesian (regular) scale The concentration data is converted into natural log and plotted on the Y axis and Time data on the X axis. The best line fit (eyeball method) is drawn. Using rise over run determine the slope.eg LnC K= LnC1-LnC2 t1-t2 t
  • Method 2 Concentration Vs Time on semi-log scale. Plot the raw Concentration data on the Y logarithmic axis and Time on the regular scale X axis. The data points for use in calculating the rise (Y1-Y2), however, must be converted 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-LnC2 t t1-t2 Method 3 Concentration Vs Time in Excel 1. Arrange the data set so that time data goes into the first column ( X axis) and Concentration in the second column. 2. Compute the slope , dLnC/dt, from the formula using the procedure used in objective one or the 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. CAUTION ON SELECTING THE TRENDLINE There are three trend lines you will be using. These are: Y Log Scale Cp B (i) Exponential (A&B) (Y & X regular scale) X regular Scale GENTAMICIN IV BOLUS A y = 7.6135e-0.1394x 12 10 t CONC(MG/L) 8 6 4 2 0 0.00 5.00 10.00 15.00 20.00 25.00 30.00 TIME(HRS) C (ii)Linear (C) (Y& X axis regular scale) LnC Or R t D E 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) Significance Ordinarily the elimination rate constant is determined by using Concentration Vs time data set.(LnCp= Ln Cpo-Kt).This, however, is an invasive method as you have to obtain plasma samples for drug assay. If dR/dt and dR/LnC are already known then the third slope dLnC/ dt or K can be calculated using the relationship shown below .An important pharmacokinetic parameter, K, can therefore be obtained without drawing plasma samples. Note that any of the other slopes may also be obtained from this relationship provided two of the slopes are known. dR = dR * dLnC dt dLnC dt Needless to say, as discussed above all the three parameters: Concentration, Time and Response are interrelated. By rearranging the above equation the elimination rate constant K, can be obtained using the response slopes .By using Ln( dose ) instead of dLnC in the response Vs concentration slope(dR/LnC) the elimination rate constant can be obtained without obtaining biological fluid samples. K= dLnC = dR/dt = dR/dt dt dR/dLnC dR/dLndose The two slopes are first computed from the respective data sets and then the third slope K can obtained using the above equation.
  • Lecture No: Making the Connections 4&5 How much drug? How often do you give? One Compartment Model Objectives: 1. Describe (I) the Pharmacokinetic model used to develop the Pharmacokinetic theories stating all the assumptions of the model. 2. Demonstrate (II) the relationship between the model and ADME processes 3. 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 above Pharmacokinetic parameters from IV data Reference: Basic Pharmacokinetics (Makoid), chapter 4 Objective 1 Describe(1)the Pharmacokinetic model used to develop the Pharmacokinetic theories, stating all the assumptions of the model As described in the introduction to concepts a model is a hypothesis, using mathematical terms concisely describes the quantitative relationships. It is an explanation to what appears to be happening, given a developed theory. Simplified assumptions are normally made to describe a complex biologic system concerning movement of drugs. Various mathematical models can be devised to simulate the rate processes: ADME. In the case of IV bolus when the dose is correlated with the extrapolated plasma concentration (Cpo) it appears as if the drug is dissolved in some fixed volume of plasma. This is the apparent volume of distribution discussed later. Based on this observation the body would appear to be divided into compartments and the IV bolus would, therefore, be presumed to be administered into the central compartment. Another observation made following the IV bolus drug administration is the subsequent decline of the concentration. It appears as if drug is moving out of the central compartment i.e. the compartment is open as the drug can move in and out. This model that is used to describe the drug concentrations in the body as a function of time and where the body appears to be divided into compartments is referred to as the compartment model. The assumptions in this model are as follows:
  • The body is represented as a series, or systems, of compartments that communicate reversibly with each other. A compartment is not a real physiologic or anatomic region but is considered as a tissue or group of tissues that have similar blood flow and drug affinity. Within each compartment, the drug is considered to be uniformly distributed. Mixing of the drug within each compartment is rapid and, homogenous and is considered to be “well stirred”, so that drug concentration represents an average concentration, and each drug molecule has an equal probability of leaving the compartment. Compartment models are based on linear assumptions using linear differential equations. (For further reading :Basic Pharmacokinetics(Makoid) page…) Conceptually, drugs move out dynamically, in and out of compartments. Rate constants represent the overall rate processes of drug entry into and exit from the compartment. At any time ,the amount of drug in the body is simply the sum of drug present in the central compartment plus the drug present in the tissue compartment(peripheral compartment). Remember, the drug administered as bolus has to be accounted for. Matter is neither destroyed nor created! It is important to note that while accounting for the administered drug in human beings we are only able to look at the plasma events i.e. the concentration. Unlike in animals where we could estimate the amount of drug in the liver by taking a liver issue we can not do the same in human beings. So we rely mainly ON THE PLASMA. If were able to do such tissue estimates Physiological models could be more appropriate. Finally, there are two main types of compartment models, i.e. one compartment and two compartment models (see figure below) This course will only be addressing the one compartment model. 1 Model 1 K One-Compartment IV 1 Model 2 Ka K One- compartment Oral-First order Absorption
  • Objective 2: demonstrate the relationship between the Model and the ADME processes. As explained above Models are mathematical explanations to the theories. Provided these concepts give us good predictions there would be no need to know the complex biological processes. However, it is important to note that there are limitations to this model for it does not shade any more light into the drug kinetic processes in the body. For example 1. We know that the drug may not be instantaneously mixed in the “compartment” as the model assumes. The central compartment represents the plasma and the highly perfused tissues 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 being eliminated* (one way arrow)and none is coming in from the peripheral compartment, a case we know not to be true as there is some distribution into the peripheral(tissue) compartment. In one- compartment open model, mathematically ,this distribution is insignificant. (*Elimination is removal of active drug through biotransformation or physical removal through excretion) A patient’s Pharmacokinetic parameters are usually characterized by a single IV Bolus dose a procedure known as pharmacokinetic study.
  • Making the connection. How much? Objective: 3 & 4 define and Calculate the following Pharmacokinetic Parameters. (a) VOLUME OF DISTRIBUTION(Vd) Definition The volume of distribution represents a volume that must be considered in estimating the amount 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 specific concentration, mathematically ,there must be a specific” volume” into which the drug appears to be dissolved. Because the value of the of Vd does not have a physiologic meaning 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 Cpo Known Known Having two parameters known (Dose & Cpo) Vd can be worked from the following equation: Vd = Dose/Cpo What is the clinical significance of Volume of distribution? We learnt from the Pharmacodynamic studies that Response depends on concentration which in turn depends on Volume of distribution. Loading dose Once 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 to estimate loading doses in emergencies e.g. Lidocaine in cardiac arrhythmias. Desired dose = Desired conc. * Vd Note the desired concentration is usually predetermined using the pharmacologic response Vs concentration relationship where therapeutic window is obtained. Dialysis The second use of Vd is in evaluating whether the drug is easily dialyzable. For example A large Vd would mean that the drug is concentrated in the peripheral compartment and hence not readily dialyzed .The drug has to be the central compartment(blood) to be dialyzed. On the other hand highly water soluble drugs like Amino glycosides have a small volume of distribution as they are concentrated in the central) vascular compartment and are easily dialyzed.
  • Calculating Vd How 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= D Cpo Unlike in the laboratory where you can take the sample any time as the concentration remains constant, in the human body drug concentration changes with time hence the sampling time becomes critical. In order to get a concentration corresponding to the IV dose 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 is given some drug would have been lost. Our desired initial plasma concentration at time Zero (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 an intercept on the Y axis as shown below. The intercept on the Y axis will be Cpo..Calculate Vd using equation: Vd= D/Cpo GENTAMICIN IV BOLUS B y = 7.6135e-0.1394x 100 CONC(LOG SCALE) 10 Cpo 1 0.00 10.00 20.00 30.00 0.1 TIME(HRS) (ii) Using Excel spread sheet plot the time on a logarithmic scale Y axis and display the equation as already explained in Concentration Vs Time objective above. The intercept in the equation would be Cpo. Y = I e-Kt is obtained from excel(shown in above graph). Calculate Vd using equation: Vd= D/Cpo (I)
  • (iii) Using excel by getting the exponential equation from an exponential curve as shown below.The intercept 7.713 would be Cpo. GENTAMICIN IV BOLUS A y = 7.6135e-0.1394x 12 10 CONC(MG/L) 8 6 4 2 0 0.00 5.00 10.00 15.00 20.00 25.00 30.00 TIME(HRS)
  • Making the connections How often? Dosing interval (b) ELIMINATION RATE CONSTANT( K) Definition The rate of elimination of most drugs is a first order process .The elimination rate constant,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 elimination processes e.g. metabolism & excretion for a drug that is eliminated by metabolism and excretion only. K=Km + Ke Km = First- order rate constant for metabolic process Ke = First- order rate constant for Excretion process There may be several routes of elimination of a drug by metabolism or excretion. In such a case each of these processes has its own first-order rate constants. From the Equation 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 . LnCp= LnCpo-Kt i.e. K = LnCpo-LnCp t 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 dosing interval. From the above equation ,values can be set for desired peaks and troughs. In this case Cp would be the trough(MEC) and in place of Cpo the peak in the equation. We can then calculate t ,the time between the peak and the trough i.e the dosing interval provided 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 excel the slope K is the integer before x GENTAMICIN IV BOLUS A y = 7.6135e-0.1394x 12 10 CONC(MG/L) 8 6 4 2 0 0.00 5.00 10.00 15.00 20.00 25.00 30.00 TIME(HRS) GENTAMICIN IV BOLUS B y = 7.6135e-0.1394x 100 CONC(LOG SCALE) 10 C 1 C2 1 0.00 10.00 20.00 30.00 t t2 1 0.1 TIME(HRS) K= LnC1-LnC2 t1-t2
  • Making the connection (c) HALF-LIFE(T1/2) How often? (i)Definition Half-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. We know 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 elimination processes :metabolism and excretion. An alteration of any of the two processes would affect the half-life.The alteration can be due to diseases that affect the hepatic or renal functions.(This will be a subject in the clinical Pharmacokinetics). By determining the half-life the appropriate dosing interval can be calculated.(see later dosing in disease states.
  • (ii) How do you calculate Half-life? NAPROXYN IV BOLUS TIME(MIN) MCG/ML 5 45.2 11 29.7 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) A 50 45 y = 57.331e-0.0634x 40 35 Conc(Mcg/ml) K 30 25 20 15 10 5 0 0 10 20 30 40 50 Time(min)
  • Conc (log scale Y axis) Vs Time B 100 -0.0634x y = 57.331e Conc.(Mcg/Ml) 10 t1/2 5 t1/2 1 28 30 38 40 0 10 20 50 Time(min) There are two ways you can calculate half-life: (a) By first obtaining Elimination constant (K) and solving for t1/2. You may obtain K using excel explained earlier. (i) Enter the profile in the spread sheet (ii) Highlight the data set and click on the chart (iii) Click on XY scatter (iv) Click Finish (v) Right Click on any data point on the graph area (vi) Select trend line (vii) Click on exponential trendline. (viii) Click option (ix) Click on display formula(see graph (x) The formula that you will get will represent the first-order rate of reaction equation: Cp = Cpoe-Kt (xi) Solve for t1/2 using the following equation: t1/2= 0.693 K You may also obtain K by getting the slope of linear plot of conc Vs time on a semi-log paper.(Already addressed) (b) By directly reading off from a linear plot of conc. Vs time (See graph B above)
  • Important Note on the above graphs. Note that graph A has an exponential trendline.You can, therefore, not be able to get your half-life directly but through K, an exponent in the displayed formula. In order to read directly the Y scale has to be logarithmic. This method of course will be applicable if you were to use a semi-log paper Graph B was computer-generated for the purpose of illustrating the direct method of obtaining half-life. (d) AREA UNDER THE CURVE.(AUC) Definition This is the area under the plasma level-time curve when considering IV bolus drug injection. What is the clinical significance of AUC? The area under the curve represents the amount of drug in the body and is one of the parameters used to evaluate oral products in bioequivalence studies. The topic is fully covered under bioavailabity section. Why is AUC used as measure of bioavailability? 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 elimination applies. We know that to get the amount eliminated at any given time you need to multiply the rate of elimination with time Let: Rate of elimination= R mg/hr Time=T hr The amount eliminated in T hours = R * T. If the plasma concentration were to represent the rate of elimination then amount eliminated would be: The amount eliminated = Cp * T In 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 not a 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 triangle With reference to segment A: Area of a rectangle= base * height =Concetration,Y axis * Time X axis =(Cpn+1) * dT………1 Area of triangle = ½ base * height = ½*(Cpn-Cpn+1) * dT…..2 Hence the total area (Trapezoid) = 1 + 2 = (Cpn+1) * dT +½*(Cpn-Cpn+1) * dT = (Cpn+Cpn+1)/2 * dT ……3 Conc Vs Time on regular scale(cartesian) A 50 Cpn 45 40 Cpn+1 35 Conc(Mcg/ml) Cp last 30 Cpn+2 25 20 15 A 10 B C 5 D E ∞ F 0 0 10 20 30 40 50 Rectangle Triangle Time(min) The Stepwise procedure is as follows:
  • 1.Identity the time interval (the interval should be ideally as small as possible lest a big interval 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 AUC for a specified period will be the total area of the segments: AUCA +AUC B + AUC C AUC D…etc 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 the following formula. AUC(terminal)= Cplast/K where K the elimination rate constant. The trapezoidal rule written in the full form is: AUC o-∞ = ΣAUC tn-tn+1 + Cpn/ k = Sum of segment areas + terminal area CREATE BOXES YOU CAN HIGHLIGHT. AUC(tn - Time hr ng/ml(Plasma tn+1) AUCo- 0 9586.2 2 7309.4 16895.6 1689 4 4489.2 11798.6 2869 6 3541 8030.2 3672 8.5 2355.9 7371.125 44095 10.5 1812.8 4168.7 48264 12.5 1111.6 2924.4 51188 14.5 902.7 2014.3 53202 17 561.6 1830.375 5503 ∞ Cplast/K 3383.133 58416 K=0.166hr-1
  • 8000 7000 -0.166x y = 9586.2e 6000 5000 Cpo 4000 K 3000 2000 1000 0 0 5 10 15 20 STEPWISE APPROACH TO CALCULATING AUC USING EXCEL 1.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 be zero 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 above 5.Find the value of K using the data set given .When highlighting the data set DO NOT INCLUDE THE ROW THAT CONTAINS TIME ZERO!IF YOU DO YOU WOULD NOT GET YOUR EXPONENTIAL CURVE THAT WILL GIVE K. 6.From the formula also obtain Cpo .Enter the value in the respective cell next to time zero as shon in the example above. 7.In the third column(AUCtn-tn+1) in the second cell (see example above) enter the following formula: ( Cpn + Cpn+1)/2 * (tn-tn+1)……. The first area woulb be time zero and the first recorded time.In this example.Zero time ant 2 hours 8.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 the following formula COPY 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 last column. 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 a statistical distribution curve. After an intravenous bolus drug dose (Do) ,the drug molecules distribute throughout the body. These molecules will stay (reside) in the body for various time periods.Some molecules may leave the body immediately whereas other molecules 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 be considered also as the mean transit time. Normal distribution curve What is the significance of MRT? From the foregoing section all the Pharmacokinetic parameters were calculated on the assumptiom thet the body behaved as if it is made of compartments where the drug moves freely between the compartments.Such Pharmacokinetic models help explain theories.In addition to the compartment models ,Physiologic Pharmacokinetic models have been developed.The latter model is the closest in terms of explaining the physiological processes,ADME if compared to the compartment model. Noncompartmental approach in pharmacokinetics There are times it is difficult to assign a model .This leads to use of model independent methods in calculating pharmacokinetic parameters.These noncompartmental Pharmacokinetic parameters are based on statistics. The principle of noncompartmental analysis is based on application of the statistical theory called the moments of a random variable.In theory a set of plasma-concentration data may be considered a statistical distribution.
  • The AUC may be viewed as a distribution curve for plasma concentration(random variable).This parameter is considered to be under the Zero moment and MRT under the first moment.( For further reading on Statistical Moment Theory refer Pharmacokinetics by Mehdi Boroujrdi page331…but it is not required) In Statistical Moments, the elimination rate of a drug may be estimated by MRT or Clearance. MRT in this case is analogous to half-life. MRT represents the time when 63% 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 molecules We know that AUC represents the amount of drug leaving the body following an IV bolus dose.It is the sum of many little areas(Cp*dt).This areas represent the rate of elimination at any time t .The resident time for a molecule leaving at time t will be t hours.If the AUC were to represent the total number of molecules then the total Residence time will be: AUC* t = Cp*t *. Hence MRT= total residence time for all drug molecules = ∫Cp dt*t =AUMC (FIRST MOMENT) Cp dt AUC (ZERO MOMENT) Total number of drug molecules AUC and MRT are described as the zero and first moment of the drug concentration time curve respectively.If you examine the numerator of the above equation the total residence time is an area ,a product of AUC (zero moment) ,and time t.This second area is referred to 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 sure of the model use this method. 2.USING ONE COMPARTMENT MODEL rate constant. In the case of one compartment model after intravenous administration, the MRT is equal the reciprocal of the elimination constant. MRTiv =1/kd = 1.44t1/2 3.USING A DERIVED RATE CONSTANT K( 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 the volume of distribution at steady state. using noncompartmental method:statistical momentl=Div/AUC Note that MRT depends on how the drug is administered.MRT for noninstanteneous administration (e.g oral) will always be greater than MRT for I.V bolus administration. Assignment Quiz 2 Question 7,8,9
  • (f)Clearance Definition. Clearance may be defined as the volume of plasma that is cleared of the drug per unit time.It is one of the parameters used to describe the rate of drug elimination.The other parameters being half-life and elimination rate constant.Although all these parameters describe the same process they give different level of insight and application in pharmacokinetics.The topic is fully covered under Clearance. (Clearance may further defined as the fraction of the volume of distribution that is cleared of the drug.Note that the fraction is K .This same fraction can also be applied to the mass eliminated 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 the Pharmacokinetics of a drug. It is a measure of elimination from the body without identifying the mechanism or the process.Total body clearance(Cl) considers the whole body as a drug-eliminating system from which many eliminating processes may occur.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 Assignment Quiz 2 Question 11
  • C Making the Connections Lecture 2 How much drug? Activity 4 How often do you give? 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