Diapositiva 1

Pharmacokinetic /PharmacodynamicmodellingBy Ikksheta Sharma Supriya Verma M Pharm 1st sem PharmaceuticsCONTENTSBasic concepts of PK/PD modellingTypes of PK/PD models - Simple / time invariant - Advanced / time dependantBiomarkersHysteresis of pharmacodynamic responsePK/PD modelling techniquesApplications

Basic concepts of PK/PD modelling

What is Pharmacokinetics ? As defined by F.H. Dost in 1953, Pharmacokinetics is a science dealing with study of biological fate of drug &/or its metabolite(s) during its journey within the body of a man or animal, with the help of mathematical modelling.

Schematic diagram to represent ADMEDRUGADMINISTEREDDRUG IN TISSUESDRUG IN SYSTEMIC CIRCULATIONEXCRETION AND METABOLISMAbsorptionDistributionEliminationWhat is Pharmacodynamics ?Pharmacodynamics describes the time course and the magnitude of pharmacological response of drugs.

Based on the classic receptor-occupancy theory, after drug molecules reach the target , it binds to the receptors to form the drugreceptor complex to exert pharmacological response.

[DRUG] + [RECEPTOR] [DRUG][RECEPTOR] RESPONSESchematic diagram showing drug receptor binding+What is a Model ?It is a hypothesis based on sound and rational assumptions to describe the fate of drug inside the human body.

These are of 2 types: - EMPIRICAL - EXPLICATIVE

What is PK/PD modelling ?

Pharmacokinetic/pharmacodynamic modeling relates the dose or concentration (exposure) of a drug provided by the kinetic model to its observed pharmacological effects (response) by establishing an exposureresponse relationship.By combining pharmacokinetic and pharmacodynamic expressions, we can examine the relevant relationship between drug effect and time.Components of a PK/PD model -Pharmacokinetic model: They show time course of drug concentration in the plasma or blood.Pharmacodynamic model: Describe relationship between drug concentration and effect.Link model: Accounts for observed delay between effect and plasma concentration.

PK Compart-mentResponsemodel Drug InputDrug EliminationPHARMACOKINETICSPHARMACODYNAMICSSchematic diagram of PK/PD modellingResponsePharmacological effects can be of two types - DIRECT EFFECTSObserved when there exists a direct correlation between the plasma drug concentrations and pharmacological effects.The intermediary processes are fast and they do not influence the correlation.Modeling is simple and requires only a proportionality constant to relate conc. to the effect. INDIRECT EFFECTSObserved when the plasma drug concentration is not related to pharmacological effects observed.May occur due to: Indirect biochemical effects , Finite onset/offset rates, Tissue distribution , etc.Indirect effects results in a hysteresis loop between concentration and the effect.

Types of PK / PD models - Direct or time independent modelLinear ModelLog- LinearModelEmax ModelSigmoidEmax Model

The bases of direct effect models are-

Effect of the drug is direct.

Rapid equilibrium exists between site of action and sampling biofluids.

Fast mechanism of action.LINEAR MODEL - Simplest model

It is described as below : E = S*C (1)If there is a baseline effect (E0) when the drug is absent, model may be represented as: E = E0 + S*C (2)where, E = effect E0 = baseline effect in the absence of drug S= slope C= concentration

ConcentrationEEoS E = E0 + S*Cy = c + mx Graphical representation -LOG LINEAR MODEL -If the concentration-effect relationship does not conform to a simple linear function, a logarithmic transformation of data is needed. It is given by: E = E0 + S*log C (3)

where, E = effect E0=Baseline effect S = slope C= concentration

Graphical representationEConcentrationThere is a linear relationship between drug concentrations producing effects of between 20% to 80% of the maximum pharmacologic effect.LIMITATION: Pharmacological effect cannot be estimated when the concentration is zero because of the logarithmic function.

MAXIMUM EFFECT ( Emax ) MODEL -This is based on the law of diminishing returns.Acc. to this law, increase in the drug concentration near the maximum pharmacological response produces a disproportionately smaller increase in the pharmacological response.This model describes drug action in terms of:Maximum effect (Emax) and EC50, the drug concentration that produces 50% response of the maximum effect.

The relation between effect and concentration is given as: (4)

where, E= effect( pharmacological response) Emax = maximum effect due to the drug C= drug concentration EC50= concentration required to achieve 50% of the maximum effect

The equation shows that it is a saturable process and resembles the Michaelis-Menton equation. Important features of this model:EmaxEC50 E Conc.As plasma drug concentration increases, the pharmacologic response approaches Emax asymptotically.After maximum response (Emax) has reached, no further increase in pharmacologic response is seen on increase in concentration of the drug.

A double-reciprocal plot of equation is used to linearize the relation, similar to Lineweaver-Burke equation.

1/Eslope = EC50 / Emax 1/ Emax -1/ EC50 1/C (6)SIGMOIDAL Emax MODEL - It describes the pharmacologic response versus drug concentration curve for many drugs that appear to be S-shaped (i.e. sigmoidal) rather than hyperbolic as described by Emax model. The equation for the sigmoid Emax Model is an extension of the Emax Model: (7)

where, n is an exponent describing the number of drug molecules that combine with each receptor molecule. When n=1, the Sigmoid Emax Model reduces to the Emax Model.

EConc.n < 1n = 1n > 1 Conc. EMAXEC50EIn the Sigmoid Emax Model, the slope is influenced by the number of drug molecules bound to the receptor.A very large n value may indicate allosteric or cooperative effects in the interaction of the drug molecules with the receptor.Effect of the value of n -Biophase Distribution Model

Mechanism- Based Indirect Response Model

Tolerance Model

Signal-Transduction Model Indirect or time dependent models

The basis of indirect effect models are :- Indirect effect of the drug.

Distribution of the drug is the rate-limiting step.

Slow association and dissociation of drug withthe receptors.

BIOPHASE DISTRIBUTION MODEL - For some drugs, the pharmacologic response produced by the drug may be observed before or after the plasma drug concentration has peaked. Such drugs may produce indirect or delayed response. Drug distribution to the effect site may represent a rate-limiting step for drugs in exerting their pharmacological effect. To account for this indirect or delayed response, a hypothetical effect compartment has been postulated by Holford and Sheiner.

Effect compartment -It is not part of the pharmacokinetic model but is a hypothetical pharmacodynamic compartment that links to the plasma compartment containing drug.

It is because amount of drug entering this compartment is considered to be negligible and is therefore not reflected in pharmacokinetics of the drug.

Effect k1ekeoPlasma Compartment (D1)Effect Compartment (De )Drug transfer from plasma to hypothetical effect compartment takes place with first order rate constant.

Only free drug can diffuse into the effect compartment.

The pharmacological response of the drug depends on the rate constant ke0 and the drug concentration in the effect compartment.

The amount of drug in the effect compartment after i.v. bolus dose may be given by: where, De = amount of drug in effect compartmentD1 = amount of drug in central compartmentke0 = rate constant for drug transfer out of the effect compartment K1e = rate constant for drug transfer from plasma to effect compartment

Effect k1ekeoPlasma Compartment (D1)Effect Compartment (De )At steady-state, input = outputk1eD1 = keoDe (9)Rearranging, D1 = keoDe (10) k1eDividing by VD yields the steady state plasma drug concentration C1C1 = keoDe (11) k1e VD De = D0k1e (e-kt e-keot ) .(12) (ke0 k)Substituting for De into eqn 11. (13)

C1 is the steady state concentration and has been used to relate the pharmacokinetic effect of many drugs.Advantages of biophase distribution model -

Dynamic flexibility and adaptability of the model account for drug distribution and pharmacologic response.

The model accommodates the aggregate effects of drug elimination, binding, partitioning and distribution.

Model represent in vivo pharmacologic event relating to plasma drug concentration that clinician can monitor and adjust.

This model has been used to characterise the PK/PD of several drugs (e.g.midazolam,pancuronium,alprazolam, etc.) whose plasma concentrations could not be correlated with the effect being produced. MECHANISM BASED INDIRECT MODEL -The indirect response model is based on the premise that the drug response is indirectly mediated by either inhibition or stimulation of the factors controlling either the production (Kin) or the dissipation of response (Kout).

EXAMPLES:Indirect response modeling was first introduced by Nagashima et al. for the anticoagulant effect of warfarin.These models may be appropriate for various classes of drugs, including histamine H2-receptor antagonists (such as cimetidine) and oral hypoglycemic agents (such as tolbutamide).

Schematic representation of the model -Response [DRUG][DRUG]KinKoutStimulation OrInhibition Stimulation OrInhibition

Mathematical representation -In the absence of drug, the rate of change in response over time (dR/dt) can be described by a differential equation as follows: (14)

where, R = response kin = zero-order rate constant for the production of response kout = first order rate constant for the dissipation of response

Depending on whether kin or kout is either inhibited or stimulated by the drug, the following four basic models have been developed in which the drug effect is mediated by an Emax-like model:Stimulation of Kin -

Inhibition of Kin -

Stimulation of Kout -

Inhibition of Kout -

S(t), I(t) Stimulation and inhibition functionsSIGNAL TRANSDUCTION MODEL - The pharmacological effects of drugs may be mediated by a time-dependent signal transduction process, in which the response measured clinically involves multiple steps removed from the initial biochemical effect of the drug. RESPONSEDRUG INPUT represents a transduction of the response that may depend on several factors like trafficking of endogenous substrates or other mediators of drug effect. The time course of the effect therefore lags behind the time course of the concentration.

There may appear to be no direct association between the concentration of the drug in blood or plasma and the pharmacological response.

This model has been used to characterize the parasympathomimetic activity of scopolamine and atropine in rats.

TOLERANCE MODEL -Tolerance is characterised by a reduction in pharmacological response after repeated or continuous drug exposure.

For some drugs, pharmacodynamic parameters like Emax and EC50 may appear to vary over time, resulting in changes in pharmacological response despite the presence of constant concentrations at the effect site.

The complex mechanism of tolerance may involve:receptor pool depletiondecrease in receptor affinity

The development of tolerance can have a significant impact on the exposure-response relationship and, if not recognized, can contribute to poor clinical outcome.

Pharmacokinetic/pharmacodynamic modelling can be a very useful tool to characterize the time course and magnitude of tolerance development.

DEVELOPMENT OF TOLERANCEPOOR CLINICAL OUTCOME

BIOMARKERSNIH (National Institute of Health) defines biomarkers as,anindicatorof a biological state. It is a characteristic that is measured and evaluated as an indicator of normal biological processes , pathogenicprocesses, orpharmacologicresponses to atherapeutic intervention. CLASSIFICATION OF BIOMARKERS-APPLICATIONS OF BIOMARKERS : Use in early-phase clinical trials to establish proof of concept. Diagnostic tools for identifying patients with a specific disease. As tools for characterizing or staging disease processes. As an indicator of disease progress. For predicting and monitoring the clinical response to therapeutic intervention.

Biochemical markers such as leukotrienes, chemokines & cytokines. Clinical markers such as Pulmonary function tests for asthma & COPD.Electrocardiograms, BP, heart rate measures for hypertension Clinical endpoints such as life or death, cure or failure. Plasma drug concentration for drugs that need to be delivered to their site of action via the vascular space are biomarkers for bioequivalence evaluation in our current regulating paradigm.

Pharmacodynamic measures for PK/PD modeling -

HYSTERESIS OF PHARMACOLOGICAL RESPONSE

Many pharmacological responses are complex and do not show a direct relationship between pharmacologic effect and plasma drug concentration.

Some drugs have a plasma drug concentration and response that resembles hysteresis loop.

Identical drug concentration can result in different pharmacological response, depending on whether the plasma drug concentration is on ascending or descending phase of the loop.

Hysteresis loopClockwise CounterClockwise CLOCKWISE HYSTERESIS - A clockwise hysteresis loop is the one in which the pharmacologic response decreases with time. If we take a concentration say (C), it can be clearly seen that the response at this concentration decreases from E1 to E2 with passage of time. Reason:Decrease in number of receptors.Translocation of receptors. e.g. fentanyl, alfentanil, cocaine

E1

E2CEC

COUNTER CLOCKWISE HYSTERESIS A counterclockwise hysteresis loop is the one in which the pharmacologic response increases with time. If we take a concentration say (C), it can be clearly seen that the response at this concentration increases from E1 to E2 with passage of time . Reason:Slow initial diffusion of the drug into effect compartment.The drug being highly bound to the plasma protein (1-acid glycoprotein) e.g. ajmaline, warfarin

E2

E1CCE

PK/PD MODELLING TECHNIQUES

STEP 1 Data are collected and exploratory graphic analyses of the raw data are usually carried out to:detect outliersexplore distribution of variablesassess correlation between variables for hidden structure and/or relationshipsSTEP 2 - Data are fitted to a selected mathematical model by optimizing an objective function that quantifies the variation between data and model.

Pharmacokinetic/pharmacodynamic modelling is a complex, iterative process involving multiple steps:

STEP 3 - Once the parameter estimates associated with an optimal objective function are achieved, diagnostic assessments have to be performed to ensure that the estimates are reasonable.

STEP 4 - Questionable diagnostic results may call for reevaluation of model assumptions, and/or investigation of alternative models.

STEP 5 - At last, model evaluation on the final model is performed to assess its goodness-of-fit, reliability, stability, and/or predictive performance.

METHODS USED IN PK/PD MODELLINGTWO STAGE APPROACH -The standard two-stage approach can be used to estimate population model parameters:

Simplicity of the approach

Requirement of extensive sampling for each individual in order to estimate individual parameters.

Modifications: global 2-stage approach iterative approach bayesian approachNAVE POOLED APPROACH -It was proposed by Sheiner and Beal.

Method involves pooling all the data from all individuals as if they were from a single individual to obtain population parameter estimates.

Generally, the nave pooled approach performs well in estimating population pharmacokinetic parameters from balanced pharmacokinetic data with small inter-subject variations.

But this approach has some limitatons

Tends to confound individual differences.

Performs poorly in case of imbalanced data.

Produces a distorted picture of the exposureresponse relationship and thereby could have safety implications when applied to the treatment of individual patients.

HIERARCHICAL NON-LINEAR MIXED-EFFECTS MODELLING

Most commonly used program for population analyses.

Can handle both sparse & intensive sampled data.

Powerful tool to study PK/PD in special populations; neonates, elderly,AIDS patients.

Analyzes the data of all individuals at once, estimating individual and population parameters, as well as the interindividual, intraindividual residual, and interoccasion variabilities. It also allows the evaluation and quantification of potential sources of variability in pharmacokinetics and pharmacodynamics in the target population. Influence of patient demographics (e.g., weight, gender, age, etc.) and pathophysiological factors (e.g., hepatic function, renal function, disease status, etc.) on drug PK and PD disposition may be assessed.Advantages of this approach are -

APPLICATIONS OF PK/PD MODELLINGUse of PK/PD studies in -PK/PD STUDIES IN DRUG DEVELOPMENTPreclinical phase PK/PD assist in the identification of potential surrogates or biomarkers. PK/PD assists in identification of the appropriate animal model. Development of mechanism-based PK/PD models are preferred over the development of empirical models. Unlike empirical models, mechanism-based PK/PD models take into account the physiological processes behind the observed pharmacological response, likely making it more predictive for future study outcome.

Allows a better understanding of the mechanism and intrinsic potency of drug candidates

Provides an opportunity for candidate selection in a quantitative manner e.g. In the anticancer area, a typical way of selecting the most potent candidate within a series of anticancer drug candidates is to measure tumor volumes from in-vivo evaluation of the antitumor effect.

Helps in assessing and predicting drugdrug interaction potential as well as formulation development.

2. Clinical phase3. NDA reviewPK/PD modeling plays an important role during the NDA submission and review phase by integrating information from the preclinical and development phases.

Existence of a well defined PK/PD model furthermore enables the reviewer to perform PK/PD simulations for various scenarios.This ability helps the reviewer gain a deeper understanding of the compound and provides a quantitative basis for dose selection.

Thus, PK/PD modeling can facilitate the NDA review process and help resolve regulatory issues.

4. Post marketing studiesPost-marketing strategy involving PK/PD studies can provide the clinician with relevant information regarding the product by:

Characterizing the variability seen on its extensive use by various populations.

Identifying subpopulations with special needs which might not have been included in the clinical trial.PK/PD STUDIES IN DOSAGE REGIMEN OPTIMISATIONPK/PD modeling is a scientific tool to help developers select a rational dosage regimen for confirmatory clinical testing.

Can also be applied to individual dose optimization.

Can account for the time course and variability in the drug action. in the effect versus time relationship can be predicted for different dosage-regimen scenarios.

PK/PD MODELING IN INTERSPECIES EXTRAPOLATIONPrimary source of inter-species variability is often attributable to variability that is mainly of PK origin.Drug plasma concentration required to elicit a given response is rather similar between species, whereas the corresponding dose for eliciting the same effect can differ widely.This can be easily predicted by PK/PD studies and interspecies dose extrapolation can be carried out .

EXTRAPOLATION FROM in vitro to in vivoIf an efficacious concentration is obtained on the basis of an in vitro assay, then a dose can be proposed by incorporating the in vitro effective concentration ( EC ) directly into equation: ED 50 = Cl x EC 50/Bioavailability

As in vitro concentrations are generally equivalent to free drug concentrations, corrections for drug binding to plasma protein are needed to estimate the corresponding in-vivo plasma EC or IC.

PK/PD METHODS TO STUDY DRUG INTERACTIONS Drug interactions study protocols incorporatepharmacodynamic endpoints to allow estimating the clinicalconsequences of drug interactions along with the usualpharmacokinetic outcome measures.This protocol can be effectively followed by the use of PK/PDmodeling study techniques.

SOFTWARES FOR PK/PD MODELING -NONMEM (L. Sheiner and S. Beal, UCSF 1979 to date)USC*PACK (R. Jelliffe, USC/LAPK et al., 1993-to date)Monolix (INSERM, 2005 - to date) Adapt/S-Adapt (USC/BMSR, D. DArgenio, R. Bauer, 1989-to date) PHOENIX (Pharsight, 2009 to date) BUGS, WinBUGS (1999 to date)WinNonLin(*LAPK Laboratory of Applied Pharmacokinetics)(*BMSR Biomedical Simulations Research)