Pharmacokinetic analysis of mathematical data - Pharmacokinetic models

Introduction of compartment model. Method for analysis of pharmacokinetic data. Application of Pharmacokinetic model. Types of pharmacokinetic models. One compartment open model. Multicompartment model. Application of compartment modelling approach.

1. PHARMACOKINETIC ANALYSIS OF MATHEMATICAL DATA:- PHARMACOKINETIC MODELS PRESENTED BY- JYOTSNA BHATT M.PHARM (PHARMACEUTICS)

2. CONTENT- Introduction Method of analysis of pharmacokinetic data Pharmacokinetic model approach Types of pharmacokinetic models Compartment models Mammillary model Catenary model Application of compartment model Limitation of compartment model 19.4.17 PHARMACOKINETIC MODELS 2

3. INTRODUCTION Drug movement within the body is a complex process. The major objective is therefore to develop a generalized and simple approach to describe, analyse and interpret the data obtained during in vivo drug disposition studies. T he two major approaches in the quantitative study of various kinetic process of drug disposition in the body are- Model approach Model independent approach 19.4.17 PHARMACOKINETIC MODELS 3

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5. PHARMACOKINETIC MODEL APPROACH MODEL- A Model is a hypothesis that employ mathematical terms to concisely describe quantitative relationship. PHARMACOKINETIC MODEL- I t provide concise means of expressing mathematically or quantitatively, the time course of drug(s) throughout the body and compute meaningful pharmacokinetic parameters. 19.4.17 PHARMACOKINETIC MODELS 5

6. APPLICATIONS OF PHARMACOKINETIC MODEL Pharmacokinetic model are useful in- Characterizing the behaviour of drugs in patients. Predicting the conc. of drug in various body fluids with any dosage regimen. Predicting the multiple dose concentration curves from single dose experiment. Calculating the optimum dosage regimen for individual patients . Correlating plasma drug concentration with pharmacological response. Determination of altered ADME level in specific disease condition. Predicting the possibility of drug interaction. 19.4.17 PHARMACOKINETIC MODELS 6

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8. COMPARTMENT MODELS It is a hypothetical model and this model simply interpolate the experimental data and helps to estimate the kinetic of a particular drug by using simple formula. S ince it is hypothetical approach it is based on certain assumption:- The body is represented as a series of compartment arranged either in series or parallel to each other, which communicate reversibly with each other. 19.4.17 PHARMACOKINETIC MODELS 8

9. CONT.. Each compartment is not a real physiological or anatomical region but of a fictitious or virtual one and considered as a tissue or group of tissue that have a similar drug distribution characteristics. Within each compartment the drug is considered to be rapidly and uniformly distributed. The rate of drug movement between two compartment is described by first order kinetics. Rate constants are used to represent rate of entry and exit from the compartment. 19.4.17 PHARMACOKINETIC MODELS 9

10. TYPES OF COMPARTMENT MODELS MAMMILARY MODEL:- compartment arranged in parallel to central compartment. CATENARY MODEL:- compartment arranged in series with central compartment 19.4.17 PHARMACOKINETIC MODELS 10

11. MAMMILARY MODEL This is the most common compartment used in pharmacokinetics. The model consists of one or more peripheral compartments connected to a central compartment. The central compartment consists of plasma and highly perfused tissues in which drug distributes rapidly. The peripheral compartments or tissues compartments (denoted by numbers 2,3,etc.) are those with low vascularity and poor perfusion. The no. of rate constant which will appear in a particular compartment model is given by R. for intravenous admin. R = 2n-1 for extravascular admin. R = 2n where n is no. of compartments. 19.4.17 PHARMACOKINETIC MODELS 11

12. MAMMILARY COMPARTMENT MODEL ONE COMPARTMENT OPEN MODEL:- The one compartment open model offers simplest way to describe the process of drug distribution and elimination in the body. one compartment open model is divided into four category- Intravenous bolus administration Intravenous infusion administration Extravascular zero order administration Extravascular first order administration. 19.4.17 PHARMACOKINETIC MODELS 12

13. ONE COMPARTMENT OPEN MODEL i.v. bolus administration i.v. infusion administration e.v. zero order administration e.v. first order administration 19.4.17 PHARMACOKINETIC MODELS 13

14. ONE COMPARTMENT OPEN MODEL It is based on the following assumption- The body is considered as a single, kinetically homogenous unit. Drugs move dynamically, in (absorption) and out (elimination) of this compartment. Final distribution eqb. between drug in plasma and other body fluid is attained instantaneously. Elimination is a first order (monoexponential) process . Rate of input (absorption) > rate of output (elimination). 19.4.17 PHARMACOKINETIC MODELS 14

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16. MULTI COMPARTMENT MODEL A multi compartment model is a type of mathematical model used for describing the way material or energies are transmitted among the compartments of a system. These are used in many fields including pharmacokinetics, epidemiology, biomedicine, systems theory etc. 19.4.17 PHARMACOKINETIC MODELS 16

17. Multi compartment models are based on the following assumption:- Blood/plasma and the highly perfused tissues such as brain, liver, lung etc. constitute the central compartment. Other tissues with similar distribution characteristics are pooled together to constitute the peripheral compartment. Intravenously administered medications are introduced directly into central compartment. Irreversible drug elimination, either by hepatic biotransformation or renal excretion takes place only from the central compartment. Reversible distribution occurs between central and peripheral compartments. After drum equilibration between central and peripheral compartment, elimination of drug follows first compartment kinetics. 19.4.17 PHARMACOKINETIC MODELS 17

18. TWO COMPARTMENT MODEL The commonest of all multi compartment models is a two compartment model. In such a model, the body tissues are broadly classified in two categories- Central compartment Peripheral compartment 19.4.17 PHARMACOKINETIC MODELS 18

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20. TYPES OF TWO COMPARTMENT MODEL Depending upon the compartment from which a drug is eliminated, the two compartment model can be categorized into 3 types:- Two compartment model with elimination from central compartment. Two compartment model with elimination from peripheral compartment. Two compartment model with elimination from both the central and peripheral compartments. 19.4.17 PHARMACOKINETIC MODELS 20

21. CATENARY MODEL In this model, the compartment are joined to one another in a series like compartments of a train. This is however not observable physiologically/anatomically as the various organs are directly linked to the blood compartment. Rarely used. 19.4.17 PHARMACOKINETIC MODELS 21

22. APPLICATIONS OF COMPARTMENT MODELLING APPROACH I t is a simple and flexible approach and thus widely used. It give a visual representation of various rate processes involved in drug disposition and also give data. It enables monitoring of drug concentration change with time with a limited amount of data. It is useful in predicting drug concentration time profile in both normal physiological and in pathological condition. It is useful in the development of dosage regimens. Its allow the easy tabulation of parameters such as volume of distribution, half life etc. 19.4.17 PHARMACOKINETIC MODELS 22

23. DISADVANTAGE OF COMPARTMENT MODELLING The compartments and parameters bear no relationship with the physiological functions or anatomical structure of species. Extensive efforts are required in the development of exact model that predict or describe the ADME of a certain drug. The model is based on curve fitting of plasma conc. with complex multi exponential mathematical equations. The approach can be applied only to a specific drug under study. Owing to its simplicity, compartment models are often misunderstood. 19.4.17 PHARMACOKINETIC MODELS 23

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