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ANESTHETIC PHARMACOLOGY

Maximizing Prediction Probability P_K as an Alternative Semiparametric Approach to Estimate the Plasma Effect-Site Equilibration Rate Constant k_e0

Richard K. Ellerkmann, MD, DESA^*, Joergen Bruhn, MD, Martin Soehle, MD, DESA^*, Michael Kehrer, Cand. Med.^*, Andreas Hoeft, MD^*, and Sascha Kreuer, MD

From the *Department of Anesthesiology and Intensive Care Medicine, University of Bonn, Bonn, Germany; Department of Anesthesia, Radboud University Nijmegen Medical Centre, Nijmegen, The Netherlands; and Department of Anesthesiology and Intensive Care Medicine, University of Saarland, Homburg/Saar, Saarland, Germany.

Address correspondence and reprint requests to Richard K. Ellerkmann, MD, DESA, Klinik für Anästhesiologie und Operative Intensivmedizin, Universitätsklinikum Bonn, Sigmund-Freud-Str. 25, Bonn D-53105, Germany. Address e-mail to richard.ellerkmann{at}ukb.uni-bonn.de.

BACKGROUND: The k_e0 value is the first order rate constant determining the equilibration of drugs between plasma or end-tidal concentration and effect-site (e.g., brain) concentration. Parametric and semiparametric approaches have been used for estimating individual k_e0 values and describing the drug-response curve. In this study, we introduce a new semiparametric approach calculating k_e0 values for isoflurane, sevoflurane, and desflurane by maximizing the prediction probability P_K.

METHODS: Data from 45 patients scheduled for a radical prostatectomy were analyzed. After lumbar epidural catheterization, patients received remifentanil and propofol solely for induction of anesthesia. Thereafter, epidural analgesia was initiated, and isoflurane, sevoflurane, or desflurane (15 patients each) was added to maintain unconsciousness. At least 45 min later, end-tidal concentrations were varied between 0.5 and 2 minimum alveolar anesthetic concentration. We estimated an individual k_e0 value for each patient by optimizing the prediction probability P_K (P_K-based k_e0) or by minimizing the area within the hysteresis loop (area-based k_e0). Data are mean ± sd.

RESULTS: Both semiparametric approaches led to comparable k_e0 values with 0.18 ± 0.06 min^–1 (P_K based) and 0.15 ± 0.04 min^–1 (area based) for isoflurane and 0.17 ± 0.08 min^–1 (P_K based) and 0.16 ± 0.11 min^–1 (area based) for sevoflurane. k_e0 values for desflurane (P_K based: 0.30 ± 0.17min^–1; area based: 0.32 ± 0.25 min^–1) were significantly higher than for isoflurane and sevoflurane.

CONCLUSION: Maximizing the prediction probability P_K for estimating k_e0 seems to be a promising method that researchers could use on an exploratory basis.