Pharmacokinetic and Pharmacodynamic Modeling

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The presentation gives you a bird eye's view regarding basics of PK-PD modeling, its applications, types, limitations and various softwares used for the same.

Text of Pharmacokinetic and Pharmacodynamic Modeling

  • 1. PRESENTED BYJaspreet SinghDeepika(M.Pharm I)

2. As defined by F.H. Dost in 1953, Pharmacokinetics is ascience dealing with study of biological fate of drug &/or itsmetabolite(s) during its sojourn within the body of a man oranimal, with the help of mathematical modeling. In simple words it is the study of what body does to the drug. The term Pharmacokinetics was coined by Torston Teorell. It involves the study of ADME. 3. SCHEMATIC REPRESENTATION ADMEDOSEDRUG INTISSUESABSORPTIONDRUG INSYSTEMICCIRCULATIONELIMINATIONEXCRETIONANDMETABOLISMDISTRIBUTION 4. It refers to the relationship between drug concentration at thesite of action and the resulting effect, including the timecourse and intensity of therapeutic and adverse effects. In simple words it is the study of what drug does to the body. IUPAC definition : Branch of pharmacology concerned withpharmacological actions on living systems, includingreactions with and binding to cell constituents, and thebiochemical and physiological consequences of theseactions. 5. RECEPTOR OCCUPANCY MODEL Given by Langley, hill and Clarke. Based on law of Mass Action. Drug effect is related to proportion of receptors occupied.[DRUG] + [RECEPTOR] [DRUG][RECEPTOR]RESPONSEK1K2 6. Any drug that binds to a receptor and stimulates thefunctional activities Has both affinity as well as intrinsic activity. e.g. AchReceptorAcetylcholineSome EffectA Cell 7. It has affinity to receptor but no intrinsic activity. It prevents binding of agonist to receptor. e.g. atropineAtropineDude, yourein my way!Acetylcholine 8. Any drug that binds to a receptor and produces anopposite effect as that of an agonist.ReceptorInverse agonistEffect oppositeto that ofthe true agonistA Cell 9. Produces a sub maximal response. Affinity is there but intrinsic activity is less than agonist.Partial agonistTrue agonistOh!!!, I shouldHave been hereSubmaximaleffect 10. RATE THEORY Pharmacological response is not dependent on drug-receptorcomplex concentration but rather depends upon rate ofassociation of drug and receptor. LOCKAND KEY MODEL Only a drug of specific chemical structure can bind with thereceptor. INDUCED FIT MODEL When the drug binds to the receptor, it produces someconformational change in the receptor which helps in betterfitting of the drug inside active site of receptor. 11. PK/PD modeling is a scientific mathematical tool whichintegrates PK model to that of PD model. PK model - describes the time course of drug concentrationin the plasma or blood. PD model - describes the relationship between drugconcentration at site of action and effect. PK/PD models use data derived from plasma drugconcentration vs. time profile and from the time course ofpharmacological effect to predict the Pharmacodynamics ofthe drug. Result is summation of Pharmacodynamics andpharmacokinetics effect. 12. ADVANCED/NONSTEADY-STATE/TIMEDEPENDENT MODELSSIMPLE DIRECTEFFECT/STEADY-STATE/TIMEINVARIANTMODELS 13. Linear modelLog-linearmodelEmax modelSigmoidal EmaxmodelBiophasedistributionmodelSignaltransductionmodelTolerancemodelMechanismbased indirectresponse modelSimple direct effectmodelsNonsteady-state & time-dependentmodels 14. LinearmodelLog-LinearModelEmax ModelSigmoidalEmax ModelEffect of drug is direct.Fast mechanism of action.Rapid equilibrium existsbetween site of action andthe sampling biofluids.PD parameters are timeinvariant. 15. Drug effect is directly proportional to drug concentration. Pharmacodynamically it is explained as:E C ..(1)E = SC ..(2)where,E = Effect of drugC = Drug concentrationS = Slope obtained from E vs C graph In case of baseline effect (E0), when the drug is absent, modelmay be represented as:E = E0 + S*C ..(3) 16. so,slope = Sintercept= E0EffectE0ConcentrationSE = E0 + S*Cy = c + mx 17. Advantages Model is simple and parameter estimation can be easilyperformed by linear regression.Limitations Applicable at low drug concentrations only excludes the prediction of maximum effectExample Relationship between central activity of diazepam andplasma drug concentration 18. When the effect of drug is measured over a large range, therelationship between concentration and effect is not linearand may be curvilinear and log transformation is needed. The log concentration-Effect is roughly linear inconcentration range of 20-80% of maximum Effect. It is given by:E = E0 + S*log C (4)where,E = effectE0=Baseline effectS = slopeC= concentration 19. ELog C It expands the initial part of the curve where response isslowly making progression before it accelerates It contracts the latter part of the curve where a large changein concentration produces a slight change in response. In middle part relationship is linear. 20. Advantage Unlike linear model it is applicable over large concentrationrange.Limitations Pharmacological effect cannot be estimated when theconcentration is zero because of the logarithmic function. Maximum effect cannot be predicted.Example This model has been successfully used in predicting thepharmacological activities of beta blockers andanticoagulants. 21. This model incorporates the observation known as the lawof diminishing returns. This law shows that an increase in drug concentration nearthe maximum pharmacological response produces adisproportionately smaller increase in the pharmacologicalresponse. This model describes the drug action in the terms of : E max (maximum effect) EC50 ( the drug concentration that produces 50%maximum pharmacological effect).(5)E CmaxEC CE50 22. It mimics the hyperbolic shape of pharmacologic responsevs. drug concentration curve. After maximum response (Emax) has reached, no furtherincrease in pharmacologic response is seen on increase inconcentration of the drug. EC50 is useful for determining drug concentration that lieswithin the therapeutic range.EEC50CEmax 23. ContdIn case, there is a baseline effect i.e. the measuredpharmacologic effect has some value in absence of drug (e.g.blood pressure, heart rate, respiratory rate) then the equationbecomes:.(6)where,E CmaxE Eo EC C 50E0 = Pharmacologic effect (baseline activity) at zerodrug concentration in the bodyIt is a saturable process and resembles the Michaelis-Mentonequation. 24. A double-reciprocal plot of equation is used to linearize therelation, similar to Lineweaver-Burke equation.(7)EC50 1 1E C Emax maxE 1/ Emax-1/ EC50 1/Cslope = EC50 / EmaxContd1/E 25. Advantages Maximum pharmacological response can be found out. EC50 can be calculated (i.e., concentration needed toproduce half maximum response).Limitations In case of highly potent drugs it is not possible to find themaximum effect because test organisms die long before themaximum effect is attained. The method can be time consuming if maximum effect isobtained at a very high concentration.Example Bronchodilator activity of Theophylline is studied by thismodel. 26. Given by Hill. It describes the pharmacologic response versus drugconcentration curve for many drugs that appear to be S-shaped(i.e. Sigmoidal) rather than hyperbolic asdescribed by more simple Emaxmodel. The equation for the sigmoid Emax Model is an extensionof the Emax Model:(8) nnE CmaxEC CE50n is an exponent describing the number of drug moleculesthat combine with each receptor molecule.When n=1, the Sigmoid Emax Model reduces to the Emax Model 27. A value of n>1 influences the slope of the curve and themodel fit. In the Sigmoid Emax Model, the slope is influenced by thenumber of drug molecules bound to the receptor. A very large n value may indicate allosteric or cooperativeeffects in the interaction of the drug molecules with thereceptor. Cooperativity is the case when binding of substrate at onbinding site affects the affinity of other sites to theirsubstrates. 28. EEMAXGraphical representationEC50CONCENTRATIONn > 1n = 1E n < 1CONCENTRATION 29. Biophasedistribution modelMechanism-basedindirect responsemodelSignaltransductionmodelTolerance model 30. Indirect effect of the drug. The effect is not immediate. Distribution of the drug is the rate limiting step. Slow association and dissociation of drug with thereceptors. 31. For some drugs, the pharmacologic response produced bythe drug may be observed before or after the plasma drugconcentration has peaked. Such drugs may produceindirect or delayed response. Drug distribution to the effect site may represent a rate-limitingstep for drugs in exerting their pharmacologicaleffect. To account for this indirect or delayed response, ahypothetical effect compartment has been postulated byHolford and Sheiner. 32. EFFECT COMPARTMENTIt is not part of the pharmacokinetic model but is ahypothetical pharmacodynamic compartment that links to theplasma compartment containing drug.It is because amount of drug entering this compartment isconsidered to be negligible and is therefore not reflected inpharmacokinetics of the drug. 33. k1e keoV C1 Ve Ce Effectk1PlasmaCompartmentEffectCompartmentDrug transfer from plasma to hypothetical effect compartmenttakes place with first order rate constant.Only free drug can diffuse into the effect compartment.The pharmacological response of the drug depends on the rateconstant ke0 and the drug concentration in the effectcompartment. 34. The amount of drug in the effect compartment after i.v. bolusdose may be given by:...(9)dDe k1eD1 ke0Dedtwhere,De = amount of drug in effect compartmentD1 = amount of drug in central compartmentke0 = rate constant for drug transfer out of the effectcompartmentK1e = rate constant for drug transfer from plasma to effectcompartment 35. Integrating the equation we get:(10)D k0 1 kt k tDe e e e ek k( )Dividing by Ve ,(11)( 0)0eD k0 1 kt k tC e e e( )eV k k( )00e eeThe above equation is not very useful as parameters Ve andk1e are both unknown and cannot be obtained from plasmadrug concentrations. Therefore assumptions are made. 36. Even though an effect compartment is present in additionto the plasma co