Post on 03-Jun-2018
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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
Relation between concentration and
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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Sensitivity of the concentration-effect relation
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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Relation between concentration and
the intensityof an effectDirect effects models
Indirect effects models
Relation between concentration and
probabilityof occurrence of an effect
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
Indirect effects models
Relation between concentration and
probabilityof occurrence of an effect
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
Sensitivity of the concentration-effect relation
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Sensitivity of the concentration-effect relation
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