Pharmacokinetic-Pharmacodynamic Modelling of Adverse Effects of Nitrendipine I. Locatelli, I. Grabnar, A.Belič, A. Mrhar, R. Karba University of Ljubljana Ljubljana, Slovenia 4 th 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: reversibleirreversible – 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 (CV par )

PK model Two compartment model with lagtime: Two diferential equations:

PK model Two compartment model with lagtime: Overall equation - integrated: Estimated PK parameters: V C /F, k A, k EL, k 12, k 21 and t LAG WinNonLin - software

Compartmental PK models Four linear compartmental models PK modelV C /F [L]k A [h -1 ]k EL [h -1 ]k 12 [h -1 ]k 21 [h -1 ]t LAG [h] one- compartment 2200    0.20 /// one- compartment with t LAG 2360    0.28 // 0.54  0.43 two- compartment 1850      0.24 / two compartment with t LAG 2020       0.50 AIC

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 - EC 50 – concentration at which the probability of response (p) is 50%

PK/PD analysis – 3.STEP (LINK)

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

PK/PD model Additonal parameters estimated: k E0, EC 50, n

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

PK/PD model - case 1

n’k EO [h -1 ]ec 50 [ng/ml] WinNonLin   1.9 EXCEL   2.2 PK/PD parameter estimation

Nonlinear regression (SPSS) 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 t LAG 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 k A, t MAX, C MAX, AUC). subpopulacija skupine z glavobolom ima nižje vrednosti EC 50 (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.