Pharmacodynamic Models Final Bis

8/12/2019 Pharmacodynamic Models Final Bis

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Pharmacodynamic models


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Interactions

PharmacologicalTargets

ABSORPTION

PHARMACODYNAMICS

Dose response relation : PK and PD stages

ELIMINATION

DISTRIBUTION

FunctionaTherapeutResponse

PHARMACOKINETICS

Biophase

Concentrations

BacteriaInsects

Parasites

Plasma

Concentrations

CellularAction

Administereddrug


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Population Dose-Response : Variability

Mild Extreme

Many

Few

Numbe

rofIndividuals

Response to SAME dose

Sensitive

Individuals

Maximal

Effect

Resistant

Individuals

Minimal

Effect

Majority of

Individuals

Average Effect


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Digoxin in Human: Therapeutic and adverse effects

Variability of pharmacodynamic origin


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Pharmacokinetics / Pharmacodynamics

Quantification of drugs effects To link intensity of the effect with drug concentration

Objective: to determine the range of drug concentrations (drugexposure) associated with a desired effect

Quantification of drug disposition processes To link the quantity of administered drug with plasma and tissula

concentrations

Objective: to determine the external (administered) doses that

produce a given exposure


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Effect Endpoints

Graded

Quantal

Continuous scale (doseeffect)

Measured in a single biologic unit

Relates dose to intensity of effect

All-or-none pharmacologic effect

Population studiesRelates dose to frequency of effect


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Relation between concentration and

the intensityof an effect

Direct effects models

Indirect effects models


probabilityof occurrence of an effect

Fixed-effect model


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Direct effect models

Models describing relations between intensity of an effect

and drug concentrations at the site of actionCan be used in in v ivoPK/PD modelling when it exists a

direct and immediate link between plasma concentrations

and effect

Emax model

Simplifications of the Emax model :

Linear model

Log-linear model

A useful extension of the Emax model :

Sigmod-Emax model


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concentration

Effect /response


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concentration

Effect /response


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concentration

Effect /response

Emax

Emax / 2

EC50

POTENCY

EFFICACY

E =Emax. C

EC50+ C


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Emax model

Relation described by two parameters Emax: intrinsic activity, EFFICACY

EC50: conc. Associated with half-maximal effect

POTENCY

Empirical justifications The most simple mathematical description of the occurrence o

maximum

Theoretical justifications Ligand-receptor interaction

E =Emax. C

EC50+ C


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Drug-Receptor Interactions

k1k2

Drug

Receptor

Effect

Drug-ReceptorComplex

(KD= k2/k1)

Ligand-binding

domain

Effector domain

DrugK DrugReceptorComplex Dmax


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Consequences of amplification phenomenon

Log[conc.]

Binding to the recept

100 %

50 %

KDEC50

EC50< KD

Effect


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Log[conc.]

Range of therapeutic concentrations :

100 %

50 %

KDEC50

-No enzyme saturation

-Linear kinetics

Consequences of amplification phenomenon

Binding to enzymeEffect


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Graphical representations

Emax model


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Theoretical basis

[L] + [R] [RL] Effect

relations KD/ EC50

Graphical representation

conc. in arithmetic scale : hyperbola

conc. in logarithmic scale : sigmod

Comparison of drugs in term of efficacy a

potency

Emax model


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Less potent, more efficacious

More potent, less efficacious

A

B

EC50,A EC50,B Log (concentrations

Efficacy and potency

Effect

Emax,A

Emax,B

Emax model


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Inhibition of an effect :

Emax-inhibition

Fractional Emax-inhibition

E = E0- Imax. C

IC50

+ C

Emax-inhibition

E = E0.(1 -C

IC50

+ C)


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Simplifications of the Emax model

Linear model

Log-linear model


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Linear model

E = S.C + E0 Effect is linearly related to concentrations

Parameters of the model (S, E0) are estimated by linea

regression


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conc

Effect /response

Emax

Emax / 2

EC50

Linear model


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E = S.C + E0 Examples : in vivoplasma concentrations of

digoxin and systolic function

quinidine and duration of Q-T interval

verapamil and duration of P-R interval

pilocarpine and salivary flow

Linear model


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Log-linear model

E = S.logC + b Developed with in vitropharmacology

Graphical characteristic of log transformation

Wide concentration ranges : zoom on the sm

concentrations

Linearization of the portion of the curve from 20

to 80% of maximal effect : linear regression to estima

the slope Problem : maximal effect is not estimated


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Log conc

Effect /response

Emax

Emax / 2

EC50

Log-linear model


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E = S.logC + E0

Examples : in vivoplasma concentrations of

propranolol and reduction of

exercise-induced tachycardia

Log-linear model


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Extension of Emax model

Sigmod Emax model


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Sensitivity of the concentration-effect relation

E =E

max. C n

EC50

n+ C n

Sigmod Emax model

Log[conc.]

Effect

E80

E20


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Empirical model

when conc.-effect relation cannot be not fitted with Emax

the third parameter provides flexibility around t

hyperbola

Influence of n the shape of the relation

n = 1: classical Emax

n < 1: upper before EC50, lower after EC50

n > 1: lower before EC50, upper after EC50

E =E

max

. C n

EC50

n+ C n

Sigmod Emax model


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Empirical model

Introduced by Archibald Hill to describe the cooperative bind

of oxygen to haemoglobin : Hill coefficient

Theoretical basis : receptor occupancy

Examples :in vivoplasmaconcentrations

n < 1 : Conc.-effect relation very flat propranolol

n > 5 : all-or-none response tocaidine /NSAID

n = SENSITIVITY of the conc-effet. relation

Sigmod Emax model


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Sensitivity : influence of the pharmacodynamic endpoint

Log[conc.]

Effect

COX inhibition

Quantification of lameness (for

plate)

E80

Surrogate endpoint

versusClinical endpoint

Sigmod Emax model

NSAID

S iti it f th t ti ff t l ti


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Impact on selectivity and safety

Therapeutic indexTD50

ED50

TD1

ED99Safety factor


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Extension of Emax model

Sigmod Emax model

Sigmod Emax inhibition


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0

10

20

30

40

50

60

70

80

90

100

1 10 100 10001000

Melatonine (ng/mL)

Observed

Predicted

Sigmoid Emax-inhibition

B

C

X

DADY

1

nn

n

XEC

XEEY

50

max0


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the intensityof an effectDirect effects models




Fixed-effect model


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Response

(R)

Kin Kout

= Kin - Kout*R

dR

dt

Decrease of the response

Increase

of the response

+-

-+

Indirect effect models


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Relation between concentration and the

intensityof an effectDirect effects models




Fixed-effect model

Fi d ff t d l


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Fixed-effect model

The link between a concentration and the probabilityof occurrence of a defined effect

Concept of threshold concentration

The threshold concentration is different from a subjec

to another one : it is a random variable, characterized

by a distribution in the population

We can association concentrations with a probabilit

of occurrence of the effect

Example : adverse effects of digoxin

Fixed effect model


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Histogram

20

40

60

80

100

120

20 %

40 %

60 %

80 %

100 %

C10% C50%

Fixed-effect model

Variability of pharmacodynamic origin

Determination of the therapeutic window



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Impact on selectivity and safety

Sensitivity of the relation=

variability of the response in the population

Fixed-effect model : the logistic regressio


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Transformation of the probability of the response

Logite

P

1

1

;-P1

PLnPLogit 1;0P

Fixed-effect model : the logistic regressio

Assumption: the Logit is linearly linked to the explicative variable

.XPLogit 21

Reciprocal of the Logit equation :

.X 21e11P

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Pharmacodynamic Models Final Bis