Pharmacokinetic models

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2. OVERVIEW Basic considerations in pharmacokinetics Compartment models One compartment model Assumptions Intravenous bolus administration Intravenous infusion Extravascular administration (zero order and first order absorptionmodel) Multi-compartment model 3. BASIC CONSIDERATIONS INPHARMACOKINETICS Pharmacokinetic parameters Pharmacodynamic parameters Zero, first order & mixed order kinetic Rates and orders of kinetics Plasma drug conc. Time profiles Compartmental models physiological model Applications of pharmacokinetics Non compartment model 4. Common units in Pharmacokinetic parameter Abbreviation Fundamental units Units example1. Area under the curve AUC Concentration x time g x hr/mL2. Total body clearance ClT Volume x time Litres/time3. Renal clearance ClR Volume x time Litres/time4. Hepatic clearance ClH Volume x time Litres/time5. Apparent volume of distribution VD Volume Litres6. Vol. of distribution at steady state VSS Volume Litres7. Peak plasma drug concentration CMAX Concentration mg/L8. Plasma drug concentration CP Concentration mg/L9. Steady-state drug concentration Css Concentration mg/L10. Time for peak drug concentration TMAX Time Hr11. Dose DO Mass mg12. Loading dose DL Mass mg13. Maintenance dose DM Mass mg14. Amount of drug in the body DB Mass Mg15. Rate of drug infusion R Mass/time mg/hr16. First order rate constant for drug absorption Ka 1/time 1/hr17. Zero order rate constant for drug absorption KO Mass/time mg/hr18. First order rate constant for drug elimination K 1/time 1/hr19. Elimination half-life t Time hr 5. Mixed Order Kinetics Kinetics of a pharmacokinetic process changes from First order to Zero orderwith increasing dose or chronic medication. Deviations from original Linear kinetic profile Non Linear kinetics. Dose dependent kinetics Seen when Pkinetic process Carriers / SubstratesCapacity Limited get saturated atHigher drug Conc.Michaelis MentenKinetics Describes velocity of Capacity limited, enzyme reactions and nonlinear pharmacokinetics 6. Some examples;Absorption (Vitamin C), Distribution (Naproxen), and EliminationMICHAELIS MENTON EQUATION-DC/DT = VMAX . C / KM + CKM = Michaelis constantVMAX = Theoretical maximumRate of process(Riboflavin) 7. PLASMA DRUG CONCENTRATION TIMEPROFILEEffectiveness of DosageRegimenConcentration of Drug in the BodyConc. at Site ofactionConc. in whole Blood (Plasma,Serum), Saliva, Urine, CSFPK Parameters determine drugConc. 8. A TYPICAL PLASMA DRUG CONC. AND TIME CURVEOBTAINED AFTER A SINGLE ORAL DOSE OF ADRUG, SHOWING VARIOUS P'KINETIC ANDPDYNAMIC PARAMETERS DEPICTED IN BELOWFIG8 9. PHARMACOKINETIC PARAMETERSThree important parameters useful in assessing the bioavailability of a drugfrom its formulation are:1. Peak plasma concentration ( cmax )the point at which, maximum concentration of drug in plasma.Units : g/ml Peak conc. Related to the intensity of pharmacological response, itshould be above MEC but less than MSC. The peak level depends on administered dose and rate of absorptionand elimination. 10. 2. Time of peak concentration (tmax )the time for the drug to reach peak concentration in plasma(after extra vascular administration).Units : hrs Useful in estimating onset of action and rate of absorption. Important in assessing the efficacy of single dose drugs used to treat acuteconditions (pain, insomnia ). 11. 3. Area under curve (AUC)It represents the total integrated area under the plasma level-time profile andexpresses the total amount of the drug that comes into systemic circulation afterits administration.Units : g/ml x hrs Represents extent of absorption evaluating the bioavailability of drug from itsdosage form. Important for drugs administered repetitively for treatment of chronic conditions(asthma or epilepsy). 12. PHARMACODYNAMIC PARAMETERS1. Minimum effective concentration (MEC)Minimum concentration of drug in plasma/receptor site required to producetherapeutic effect. Concentration below MEC sub therapeutic level Antibiotics - MEC2. Maximum safe concentration (MSC)Concentration in plasma above which adverse or unwanted effects areprecipitated. Concentration above MSC toxic level 13. 3. Onset timeTime required to start producing pharmacological response.Time for plasma concentration to reach mec after administrating drug4. Onset of actionThe beginning of pharmacologic response.It occurs when plasma drug concentration just exceeds the required mec.5. Duration of actionThe time period for which the plasma concentration of drug remains above MEClevel.6. Intensity of actionIt is the minimum pharmacologic response produced by the peak plasma conc. Ofdrug.7. Therapeutic range the drug conc. Between MEC and MSC 14. CONCEPT OF HALF LIFE Life = how much time it takes for blood levels of drug to decrease to halfof what it was at equilibrium There are really two kinds of life Distribution life = when plasma levels fall to half what they wereat equilibrium due to distribution to/storage in bodys tissue reservoirs. Elimination life = when plasma levels fall to half what they wereat equilibrium due to drug being metabolized and eliminated. It is usually the elimination life that is used to determine dosingschedules, to decide when it is safe to put patients on a new drug. 15. PHARMACOKINETIC MODELS ANDCOMPARTMENTS 16. PharmacokineticModellingCompartment ModelsNon-CompartmentModelsPhysiologicModelsCaternaryModelOne comptMamillaryModelMulti compt Two compti vbolusSingle oralDosei vinfusionIntermittent i v infusionMultipledosesi v bolusOraldrugAUC, MRT, MAT, Cl,VSS 17. PHARMACOKINETIC MODELSMeans of expressing mathematically or quantitatively, time course of drugthrough out the body and compute meaningful pharmacokinetic parameters.Useful in : Characterize the behavior of drug in patient. Predicting conc. Of drug in various body fluids with dosage regimen. Calculating optimum dosage regimen for individual patient. Evaluating bioequivalence between different formulation. Explaining drug interaction.Pharmacokinetic models are hypothetical structures that are used to describe thefate of a drug in a biological system following its administration.Model Mathematical representation of the data. It is just hypothetical 18. WHY MODEL THE DATA ?There are three main reasons due to which the data is subjected to modelling.1. Descriptive: to describe the drug kinetics in a simple way.2. Predictive: to predict the time course of the drug after multiple dosing basedon single dose data, to predict the absorption profile of the drug from the ivdata.3. Explanatory: to explain unclear observations. 19. PHARMACOKINETIC MODELING IS USEFULIN :- Prediction of drug concentration in plasma/ tissue/ urine at any point of time. Determination of optimum dosage regimen for each patient. Estimation of the possible accumulation of drugs/ metabolites. Quantitative assessment of the effect of disease on drugs adme. Correlation of drug concentration with pharmacological activity. Evaluation of bioequivalence. Understanding of d/i. 20. COMPARTMENTAL MODELS A compartment is not a real physiological or anatomic regionbut an imaginary or hypothetical one consisting of tissue/ groupof tissues with similar blood flow & affinity. Our body is considered as composed of several compartmentsconnected reversibly with each other. 21. ADVANTAGES Gives visual representation of various rate processes involved in drugdisposition. Possible to derive equations describing drug concentration changes in eachcompartment. One can estimate the amount of drug in any compartment of the system afterdrug is introduced into a given compartment.DISADVANTAGES Drug given by IV route may behave according to single compartment modelbut the same drug given by oral route may show 2 compartment behaviour. The type of compartment behaviour i.E. Type of compartment model maychange with the route of administration. 22. TYPES OF COMPARTMENT1. Central compartmentBlood & highly perfused tissues such as heart, kidney, lungs, liver, etc.2. Peripheral compartmentPoorly per fused tissues such as fat, bone, etc.MODELS:OPEN and CLOSED models: The term open itself mean that, the administered drug dose is removed frombody by an excretory mechanism ( for most drugs, organs of excretion of drug iskidney) If the drug is not removed from the body then model refers as closed model. 23. LOADING DOSE A drug dose does not show therapeutic activity unless it reaches the desired steadystate. It takes about 4-5 half lives to attain it and therefore time taken will be too long ifthe drug has a long half-life. Plateau can be reached immediately by administering a dose that gives the desiredsteady state instantaneously before the commencement of maintenance dose x0. Such an initial or first dose intended to be therapeutic is called as priming dose orloading dose x0,l. 24. CALCULATION OF LOADINGDOSE After e.V. Administration, cmax is always smaller than that achieved after i.V.And hence loading dose is proportionally smaller. For the drugs having a low therapeutic indices, the loading dose may bedivided into smaller doses to be given at a various intervals before the firstmaintenance dose. A simple equation for calculating loading dose is :xo,l = css,av vdF 25. CALCULATION., When vd is not known, loading dose may be calculated by the followingequation :xo,l = 1___________Xo (1 e-ket) (1 e-kat) Given equation applies when ka >> ke and drug is distributed rapidly. When drug is given i.V. Or when absorption is extremely rapid, theabsorption phase is neglected and the above equation reduces toaccumulation index: 26. ASSUMPTIONS1. One compartment The drug in the blood is in rapid equilibrium with drug in the extra-vasculartissues. This is not an exact representation however it is useful for a numberof drugs t


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