2PHARMACOKINETIC MODELING A Model is a hypothesis using mathematical terms to describe quantitative relationshipsMODELING REQUIRES:Thorough knowledge of anatomy andphysiologyUnderstanding the concepts and limitationsof mathematical models.Assumptions are made for simplicity
3OUTCOMEThe development of equations to describe drug concentrations in the body as a function of timeHOW?By fitting the model to the experimental data known as variables.A PK function relates an independent variable to a dependent variable.
4FATE OF DRUG IN THE BODY ADME Excretion Oral Administration G.I. Tract IntravenousInjectionCirculatorySystemIntramuscularInjectionTissuesMetabolicSitesSubcutaneousInjection
5Complexity of PK model will vary with: 1- Route of administration2- Extent and duration ofdistribution into various bodyfluids and tissues.3- The processes of elimination.4- Intended application of the PKmodel.We Always Choose the SIMPLEST Model
7PHYSILOGIC PK MODELS Models are based on known physiologic and anatomic data.Blood flow is responsible for distributingdrug to various parts of the body.Each tissue volume must be obtained andits drug conc described.Predict realistic tissue drug concApplied only to animal species and humandata can be extrapolated.
8PHYSILOGIC PK MODELS Can study how physiologic factors may change drug distribution from one animal species toanotherNo data fitting is requiredDrug conc in the various tissues are predictedby organ tissue size, blood flow, andexperimentally determined drug tissue-bloodratios.Pathophysiologic conditions can affectdistribution.
9Physiological Model Simulation Perfusion Model Simulation of Lidocaine IV Infusion in ManBloodMetabolismRETMuscleAdiposeLungTimePercent of Dose
10COMPARTMENTAL MODELSThe body is represented by a series of compartments that communicate reversibly with each other.123k12k21
11COMPARTMENTAL MODELS A compartment is not a real physiologic or anatomic region, but it is a tissue or groupof tissues having similar blood flow and drugaffinity.Within each compartment the drug is consideredto be uniformly distributed.Drug move in and out of compartmentsCompartmental models are based on lineardifferential equations.Rate constants are used to describe drug entryinto and out from the compartment.
12COMPARTMENTAL MODELS The model is an open system since drug is eliminated from the system.The amount of drug in the body is the sumof drug present in the compartments.Extrapolation from animal data is notpossible because the volume is not a truevolume but is a mathematical concept.Parameters are kinetically determined fromthe data.
13MAMMILLARY MODELSIs the most common compartmental model used in PK. The model consists of one or more compartments connected to a central compartment213kakelk12k21
14Intravenous and Extravascular Administration IV, IM, SC
15Intravenous and extravascular Route of Administration Difference in plasma conc-time curveTimeCpTimeCpIntravenousAdministrationExtravascularAdministration
16One Compartment Open Model Intravenous Administration
17One Compartment Open Model Intravenous Administration The one compartment model offers the simplest way to describe the process of drug distribution and elimination in the body.Blood(Vd)i.v.InputkelOutputWhen the drug is administered i.v. in a single rapid injection, the process of absorption is bypassed
18One Compartment Open Model Intravenous Administration The one-compartment model does not predict actual drug levels in the tissues, but does imply that changes in the plasma levels of a drug will result in proportional changes in tissue drug levels.
19FIRST-ORDER KINETICS The rate of elimination for most drugs is a first-order process. kel is a first-order rate constant with a unitof inverse time such as hr-1.
21INTEGRATED EQUATIONSThe rate of change of drug plasma conc over time is equal to:This expression shows that the rate of elimination of drug from the body is a first-order process and depends on kel
22INTEGRATED EQUATIONS Cp = Cp0e-kelt ln Cp = ln Cp0 kelt DB = Dose . e-keltln DB = ln Dose kelt
23Elimination Half-Life (t1/2) Is the time taken for the drug conc or the amount in the body to fall by one-half, such as Cp = ½ Cp0 or DB = ½ DB0Therefore,
24ESTIMATION OF half-life from graph A plot of Cp vs. timet1/2 = 3 hr
25Fraction of the Dose Remaining The fraction of the dose remaining in the body (DB /Dose) varies with time.The fraction of the dose lost after a time t can be then calculated from:
26Volume of Distribution (Vd) Is the volume in which the drug is dissolved in the body.Example: 1 gram of drug is dissolved in an unknown volume of water. Upon assay the conc was found to be 1mg/ml. What is the original volume of the solution?V = Amount / Conc = 1/1= 1 literAlso, if the volume and the conc are known, then the original amount dissolved can be calculatedAmount = V X Conc= 1X1= 1 gram
27Apparent VdIt is called apparent because it does not have any physiological meaning. Drugs that are highly lipid soluble, such as digoxin has a very high Vd (600 liters), drugs which are lipid insoluble remain in the blood and have a low Vd.For digoxin, if that were a physiological space and I were all water, that would weigh about 1320 lb (599 kg).
28Apparent VdVd is the ratio between the amount of drug in the body (dose given) and the concentration measured in blood or plasma.Therefore, Vd is calculated from the equation:Vd = DB / CPwhere,DB = amount of drug in the bodyCp = plasma drug concentration
29For One Compartment Model with IV Administration: With rapid IV injection the dose is equal to the amount of drug in the body at zero time (DB).Where Cp is the intercept obtained by plotting Cp vs. time on a semilog paper.
30For One Compartment Model with IV Administration: Cpo
31Calculation of Vd from the AUC Since, dDB/dt = -kelD = -kelVdCpdDB = -kelVdCpdt dDB = -kelVd CpdtSince, Cpdt = AUCThen, AUC = Dose / kelVdModelIndependentMethod
32Significance of Vd Drugs can have Vd equal, smaller or greater than the body massDrugs with small Vd are usually confined to thecentral compartment or highly bound to plasmaproteinsDrugs with large Vd are usually confined in thetissueVd can also be expressed as % of body mass andcompared to true anatomic volumeVd is constant but can change due to pathologicalconditions or with age
33Apparent VdExample: if the Vd is 3500 ml for a subject weighing 70 kg, the Vd expressed as percent of body weight would be:The larger the apparent Vd, the greater the amount of drug in the extravascular tissues. Note that the plasma represents about 4.5% of the body weight and total body water about 60% of body weight.
34CLEARANCE (Cl)Is the volume of blood that is cleared of drug per unit time (i.e. L/hr).Cl is a measure of drug elimination from the body without identifying the mechanism or process.Cl for a first-order elimination process is constant regardless of the drug conc.