Transcript Pharmacokinetic-Pharmacodynamic Modelling of Side Effects

Pharmacokinetic-Pharmacodynamic Modelling of Adverse Effects of
Nitrendipine
I. Locatelli, I. Grabnar, A.Belič,
A. Mrhar, R. Karba
University of Ljubljana
Ljubljana, Slovenia
4th MATHMOD, Vienna, 2003
PK-PD Modelling

Pharmacokinetics:
–
–
time courses of drug concentration in body fluids
(mainly blood plasma) resulting from a drug dose,
drug (metabolites) concentration determination,
problems with biological matix, LOQ, accuracy
–
–
whole body influence,
steady state or nonsteady state.
PK-PD Modelling

Pharmacodynamics:
–

effects resulting from a certain drug concentration
Types of drug effects:
reversible
– direct (rapid,slow)
– indirect:
irreversible
- chemotherapy
- enzyme inactivation
transduction processes,
enzyme induction

Effect measurements should be:
sensitive, reproducible, objective and meaningful.
PK-PD Modelling

Goals of modellig:
–
–
–
–



optimization of drug therapy,
improvement of drug efficacy and safety,
estimating inaccessible system variables,
predicting system response under new conditions.
PK models (one-, two- compartment, ...)
PD models (Hill function and its derivatives)
Link models (direct vs. indirect link, direct vs. indirect
response... )
Aims

Safety aspect of an antihypertensive drug nitrendipine

Exploration of the relationship between its plasma
concentration and occurrence of adverse effects

Criteria for the design of optimal drug dosage regimen
and for selecting individuals with high probability for
adverse drug reactions
Nitrendipine




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Potent calcium channels blocker
Vasodilatation and decrease in peripheral vascular
resistance, subsequent reduction of blood pressure
Highly variable PK due to extensive first-pass metabolism
(F = 16%) and high plasma protein binding (98 %)
PK is linear, no plasma accumulation after once daily
regimen
Mild, but frequent adverse effects:
–
–
Headache (vasodilatation in the brain)
Flushing, palpitations, ankle oedema, dizziness (peripheral
vasodilatation and increased baroreflex feedback control)
Database



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Replicated 2 x 2 cross over bioequivalence study, 40 male
volunteers (18-30 yrs.), single dose 20 mg
16 blood samples in each period up to 48 hrs. after drug
administration
During the period of 48 hrs. volunteers were observed for
eventual occurrence of adverse effects – recording of onset
time and duration
Adverse effects occurred in 26 out of 160 drug applications:
–
–
–
Headache: 24 (average duration 3.3 ± 2.7 hrs.)
Flush: 4
Vertigo: 1
PK/PD analysis – 1. STEP (PK)
Exploration of nitrendipine pharmacokinetics:
compartmental analysis of individual concentration-time
profiles (160 cases):
-
-
One/two compartment model with first order absorption and
elimination, with or without lagtime
Model evaluation: Akaike Criterion (AIC), Schwartz Criterion
(SC), parameters’ coeficient of variation (CVpar)
AIC  NOBS  ln(WRSS)  2  N PAR
SC  NOBS  ln(WRSS)  N PAR  ln( NOBS )
WRSS 
Nobs
W  (C
i 1
i
OBS
i
 CiPRED ) 2
PK model
Two compartment model with lagtime:
Two diferential equations:

dU C
 k A  U GIT (t )  k EL  U C  k12  U C  k 21  U S (t )
dt
dU S
 k12  U C  k 21  U S
dt
CC 
UC
VC
PK model
Two compartment model with lagtime:
Overall equation - integrated:

CC 
F  D  kA
VC

k21  
k21  
k21  k A
 ( t t LAG )
  ( t t LAG )
 k A ( t t LAG ) 
e



e


e


(k A   )(   )
(  k A )(  k A )
 (k A   )(   )

Estimated PK parameters:
VC/F, kA, kEL, k12, k21 and tLAG
WinNonLin - software
Compartmental PK models
Four linear compartmental models
PK model
VC/F [L]
kA [h-1]
kEL [h-1]
onecompartment
22001940
1.11.4
0.500.20
23601940
6.26.7
0.480.28
18501490
1.12 .7
20201790
4.75.6
onecompartment
with tLAG
twocompartment
two
compartment
with tLAG
k12 [h-1]
k21 [h-1]
tLAG [h]
/
/
/
/
/
0.480.16
0.170.23
0.100.24
0.480.23
0.350.46
0.330.50
AIC
36.7
0.540.43
17.5
/
39.0
0.550.50
13.1
PK/PD analysis – 2. STEP (PD)
Exploration of Pharmacodynamics:
 Adverse

effect-time courses (24 cases only)
Fixed effect (or logistic) pharmacodynamic model:
-
p – probability that adverse effect will happen
EC50 – concentration at which the probability of response
(p) is 50%
Cn
p(Y  1)  n
C  EC50n
PK/PD analysis – 3.STEP (LINK)
PK/PD analysis – 3.STEP (LINK)
1.2
1.0
15
0.8
10
0.6
0.4
5
0.2
0
0.0
0
4
8
12
Time [h]
16
20
24
Probability of headache
Nitrendipine concentration [ng/ml]
20
PK/PD analysis – 3.STEP (LINK)
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Indirect link model (hysteresis):
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–
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Direct response model
Soft link PK/PD model
Time independent link model
Simplifications:
dCe
 k1 E  CC  k E 0  Ce
dt
dCe
 k E 0  (CC  Ce)
dt
PK/PD model
2
ABSORPTION
PERIPHERAL
COMPARTMENT
k21
k12
20 mg kA 1
CENTRAL
nitrendi- t
COMPARTMENT
LAG
lnCP
pine
VD/F
kEL
t
kEO
kEO
CE(t) EFFECT
COMPARTMENT
N
E
L
I
M
I
N
A
T
I
O
N
ec 50
headache
p
1
CE
t
Additonal parameters
estimated:
kE0, EC50, n
PK/PD model
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
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Two-compartment PK model with lagtime
Fixed effect PD model
Indirect link model (to minimaze the hysteresis)
Model equation:
F  D  k A  kE 0
Ce 
VC
 (k21  k A )  e  k A (t t LAG )
(k21   )  e  (t t LAG )



 (  k A )(  k A )(k E 0  k A ) (k A   )(   )(k E 0   )
(k 21  k E 0 )  e  kE 0 ( t tLAG ) 
(k 21   )  e   ( t tLAG )


(k A   )(   )(k E 0   ) (  k E 0 )(  k E 0 )(k A  k E 0 ) 
PK/PD model - case 1
1
20
18
16
14
12
10
8
6
4
2
0
0.8
0.6
0.4
verjetnost
konc. [ng/ml]
RTA1
0.2
0
0
4
8
12
t [h]
16
20
24
Cp
Ce
FK eksp. podatki
p-Excel
p- WinNonLin
FD eksp. podatki
PK/PD parameter estimation
n’
kEO [h-1]
ec50 [ng/ml]
WinNonLin
2.2
0.15  0.12
2.6  1.9
EXCEL
2.0
0.21  0.19
2.9  2.2
n' 
4
var(LN ( EC50))  2
1
p
0.8
0.6
0.4
0.2
0
0.1
1
Ce
10
100
Nonlinear regression (SPSS)
p
1
0.8
0.6
0.4
0.2
0
0.1
1
10
100
concentration in the effect compartment [ng/ml]
EC50 = 6.62 ± 0.22 ng/ml (glavobol je prisoten)
EC50 = 39.8 ± 2.5 ng/ml (glavobol ni prisoten)
1000
Zaključek
• Na podanih eksperimentalnih podatkih dvoprostorni model s tLAG
najbolje opisuje potek plazemskih koncentracij nitrendipina.
• Aplikacije s stranskim učinkom imajo višjo hitrost in večji obseg
absorpcije kot tiste brez stranskega učinka (primerjava povprečnih
vrednosti za kA, tMAX, CMAX, AUC).
• subpopulacija skupine z glavobolom ima nižje vrednosti EC50 (večja
občutljivost) kot celotna populacija
• Tako FK parametri (povečana koncentracija nitrendipina) kot FD
parametri (povečana občutljivost na nitrendipin) vplivajo na pojav
glavobola pri nitrendipinu
Conclusions
• An increased exposure as well as an increased sensitivity
to nitrendipine at the site of action were found to expand
the probability for side effects.
• The developed methodology could supply useful criteria
for the design of optimal drug dosage regimen, moreover
it offers possibility for selecting individuals with high
probability for adverse drug reactions.