Response-surface modeling of drug interactions on
cardiorespiratory control

E. Olofsen, E.Y. Sarton, A. Dahan.

Departments of Anesthesiology and Physiology, Leiden University Medical Center, POBox 9600, 2300 RC Leiden, The Netherlands.      E-mail: E.Olofsen@lumc.nl

Causes for perioperative respiratory complications include anesthetic- and opioid-induced reduced ventilatory drive.¹ Previous studies predominantly described the influence of single agents on the performance of the ventilatory controller. Since in clinical practice an anesthetic is complemented by an opioid, we designed a study to quantify the interaction of an inhalational anesthetic, sevoflurane (S), and an opioid, alfentanil (A), on ventilation and heart rate during normoxia and acute isocapnic hypoxia.

Methods: Nine healthy male volunteers participated after approval of the protocol by the local Human Ethics Committee. The effect of S and A, given separately and in combination was assessed on resting normoxic ventilation and the changes in ventilation due to acute isocapnic hypoxia (duration of hypoxia = 3 min, P_ETO₂Hg). The end-tidal concentrations of S (C_S) tested were 0, 0.1, 0.2 and 0.3%; the target alfentanil plasma concentrations (C_A) tested were 0, 10, 20, 30, 40 and 50 ng/ml. The nature of the A-S interaction was assessed for the following parameters: ventilation (V_i), tidal volume (V_T), respiratory rate (f), heart rate (HR), DV_i/DS_pO₂, DV_T/DS_pO₂, Df/DS_pO₂ and DHR/DS_pO₂.
The function defined as Z(C_A,C_S), where Z is any experimentally recorded parameter, can be visualized in three-dimensional space as a ``response surface''. It was modeled (cf. ref. 2) as

Z(C_A,C_S) = Z_max ·(1- [(U_A+U_S)]^g ·I(Q)/2)

where U_A = C_A / EC_50,A, U_S = C_S / EC_50,S, g a nonlinearity parameter and I(Q), a spline function describing interaction with, following Minto et al.³, Q = U_A/(U_A+U_S). EC_50,S and EC_50,A are the sevoflurane and alfentanil concentration causing a 50% decrease of a parameter). The spline function parameters I_max and Q_max denote the maximum value of the interaction and the value of Q at which I(Q_max)=I_max, respectively. The population model parameters and their interindividual variability were estimated using NONMEM.⁴ The likelihood-ratio test was used to determine statistical significance of nonlinearity (g ¹ 1) and synergism (I_max > 1).

Results: Pure additive interactions were found for V_T, DV_i/DS_pO₂, DV_T/DS_pO₂, Df/DS_pO₂ and DHR/DS_pO₂. Depression of DV_i/DS_pO₂ by 50% occurred at an alfentanil concentration of 31.3 ± 2.8 ng/ml and a sevoflurane concentration of 0.27 ± 0.05 ET%. Synergistic interactions were found for normoxic V_i and normoxic HR. Depression of V_i by 25% occurred at an alfentanil concentration of 37.7 ± 11 ng/ml and a sevoflurane concentration of 0.73 ± 0.44 ET% with interaction parameters I_max = 1.92 ± 0.28 at Q_max = 0.68 ±0.11. Nonlinearities were never present.

Discussion: Response surface modeling seems a promising technique to analyze interactions between two (or more) drugs on respiration. We observed synergistic interactions of an inhalational anesthetic and an opioid on V_i and HR, while all other parameters tested showed additive interactions. These additive interactions may be related to similar sites of action of S and A on neuronal systems in the CNS (e.g., A and S compete for the same receptor with ultimately saturation in effect). The synergy may be due to an effect of both agents on separate pathways/receptors in the CNS (e.g., saturation in effect in one pathway has no effect on the ultimate effect of both agents). Our data indicate that, over the dose range tested, the hypoxic response is more sensitive to the effects of anesthetics and opioids relative to resting ventilation. This is true when these agents are given separately and when combined and hence is independent on the nature of the interaction.

1. Br J Anaesth 1999; 83: 199-201. 2. J Exp Botany 1959; 10: 290-300, 3. CF Minto, personal communication. 4. NONMEM Users's Guide 1999, UCSF.