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WHAT IS ALREADY KNOWN ABOUT THIS SUBJECT• Remifentanil, an intravenous ultra short-acting opioid, depresses central nervous system activity with an increase in the delta band power, and causes beta activation after discontinuation, resulting in a rebound of the processed electroencephalographic parameters, including 95% spectral edge frequency, the canonical univariate parameter and electroencephalographic approximate entropy.• A sigmoid Emax model, in which the highest predicted values of processed electroencephalographic parameters are restricted to the baseline value, cannot describe a rebound of these parameters.• Electroencephalographic approximate entropy correlated well with the remifentanil blood concentration and demonstrated high baseline stability. WHAT THIS STUDY ADDS• A combined effect and tolerance model effectively characterized the time course of the remifentanil effect on the central nervous system, including the rebound which occurred during recovery from the remifentanil effect.• Temporal linear mode complexity was comparable with approximate entropy as a univariate electroencephalographic descriptor of the effect of remifentanil on the central nervous system. AIMSPreviously, electroencephalographic approximate entropy (ApEn) effectively described both depression of central nervous system (CNS) activity and rebound during and after remifentanil infusion. ApEn is heavily dependent on the record length. Linear mode complexity, which is algorithmatically independent of the record length, was investigated to characterize the effect of remifentanil on the CNS using the combined effect and tolerance, feedback and sigmoid Emax models. METHODSThe remifentanil blood concentrations and electroencephalographic data obtained in our previous study were used. With the recording of the electroencephalogram, remifentanil was infused at a rate of 1, 2, 3, 4, 5, 6, 7 or 8 mg kg -1 min -1 for 15-20 min. The areas below (AUCeffect) or above (AACrebound) the effect vs. time curve of temporal linear mode complexity (TLMC) and ApEn were calculated to quantitate the decrease of the CNS activity and rebound. The coefficients of variation (CV) of median baseline (E0), maximal (Emax), and individual median E0 minus Emax values of TLMC were compared with those of ApEn. The concentration-TLMC relationship was characterized by population analysis using non-linear mixed effects modelling. RESULTSMedian AUCeffect and AACrebound were 1016 and 5.3 (TLMC), 787 and 4.5 (ApEn). The CVs of individual median E0 minus Emax were 35.6, 32.5% (TLMC, ApEn). The combined effect and tolerance model demonstrated the lowest Akaike information criteria value and the highest positive predictive value of rebound in tolerance. CONCLUSIONSThe combined effect and tolerance model effectively characterized the time course of TLMC as a surrogate measure of the effect of remifentanil on the CNS.