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 irreversible– direct (rapid,slow) - chemotherapy– indirect: - 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

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

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)

PAROBS NWRSSlnNAIC 2)(

)()( OBSPAROBS NlnNWRSSlnNSC

Nobs

i

PREDi

OBSii CCWWRSS

1

2)(

PK model

Two compartment model with lagtime:

Two diferential equations:

)()( 2112 tUkUkUktUkdt

dUSCCELGITA

C

SCS UkUk

dt

dU 2112

C

CC V

UC

PK model

Two compartment model with lagtime:

Overall equation - integrated:

)(21)(21)(21

))(())(())((LAGALAGLAG ttk

AA

Att

A

tt

AC

AC e

kk

kke

k

ke

k

k

V

kDFC

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] k12 [h-1] k21 [h

-1] tLAG [h]

one-compartment

22001940

1.11.4 0.500.20 / / /

one-compartment

with tLAG

23601940

6.26.7 0.480.28 / / 0.540.43

two-compartment

18501490

1.12 .7 0.480.16 0.170.23 0.100.24 /

two compartment

with tLAG

20201790

4.75.6 0.480.23 0.350.46 0.330.50 0.550.50

AIC

36.7

17.5

39.0

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%

n50

n

n

ECC

C1Yp

)(

PK/PD analysis – 3.STEP (LINK)

PK/PD analysis – 3.STEP (LINK)

Time [h]

0 4 8 12 16 20 24

Pro

bab

ility

of

hea

dach

e

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Nitr

end

ipin

e c

on

cent

ratio

n [n

g/m

l]

0

5

10

15

20

PK/PD analysis – 3.STEP (LINK)

Indirect link model (hysteresis): – Direct response model– Soft link PK/PD model– Time independent link model

Simplifications:

)(0 CeCkdt

dCeCE CekCk

dt

dCe0ECE1

PK/PD model

CENTRAL COMPARTMENT

kA 120 mg

nitrendi-pine V

D/F

kEL

PERIPHERAL COMPARTMENT

k12

k21

tLAG

EFFECT COMPARTMENT

t

lnCP

kEO

kEOC

E(t)

ec50

p

CE

headache

1

t

ABSORPTION

ELIMINATION

2

Additonal parameters estimated:kE0, EC50, n

PK/PD model

Two-compartment PK model with lagtime Fixed effect PD model Indirect link model (to minimaze the hysteresis) Model equation:

))()((

)(

))()((

)(

0

)(21

0

)(210

EA

tt

AEAA

ttkA

C

EA

kk

ek

kkkk

ekk

V

kkDFCe

LAGLAGA

))()((

)(

))()((

)(

000

)(021

0

)(21

0

EAEE

ttkE

EA

tt

kkkk

ekk

kk

ek LAGELAG

PK/PD model - case 1

RTA1

02468

101214161820

0 4 8 12 16 20 24t [h]

kon

c. [

ng

/ml]

0

0.2

0.4

0.6

0.8

1

verj

etn

ost

Cp Ce FK eksp. podatki

p-Excel p- WinNonLin FD eksp. podatki

  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

PK/PD parameter estimation

250ECLN

4n

))(var('

0

0.2

0.4

0.6

0.8

1

0.1 1 10 100Ce

p

Nonlinear regression (SPSS)

0

0.2

0.4

0.6

0.8

1

0.1 1 10 100 1000

concentration in the effect compartment [ng/ml]

p

EC50 = 6.62 ± 0.22 ng/ml (glavobol je prisoten)EC50 = 39.8 ± 2.5 ng/ml (glavobol ni prisoten)

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.