Comparison of pharmacokinetic parameters of propofol for modeling Bispectral Index response: With or without consideration of dead-time  

Yoshihito Sawaguchi M.E. ¹, Eiko Furutani Ph.D. ¹, Gotaro Shirakami M.D. ²,
Mituhiko Araki Ph.D. ¹ and Kazuhiko Fukuda M.D. ^2
1 Department of Electrical Engineering, Kyoto University, Kyoto, Japan,
² Department of Anesthesia, Kyoto University Hospital, Kyoto, Japan.

Introduction:

Pharmacokinetic (PK)-pharmacodynamic (PD) model is generally accepted for simulating the changes of the Bispectral Index (BIS) values produced by propofol administration ¹.  PK model parameters can be obtained from measured propofol plasma concentrations, and different researchers have proposed different values ^{for example 2,3}.  However, it is not clear whose values are the best for constructing an appropriate mathematical model of the BIS response.  Furthermore, most of them paid no attention to dead-time, or time delay existing between the time when propofol is administered and the time when BIS response caused by the administration appears. In order to elucidate whose PK parameters are the best for modeling the BIS response with or without the consideration of dead-time, we compared 20 sets of PK parameters proposed by the previous 20 reports using measured BIS data at clinical settings.

Methods:

Adult ambulatory surgical patients (n=146, age 17-77 yr., male 24/ female 122, ASA PS 1-2) were anesthetized with propofol at the dose of 2 mg/kg IV bolus and subsequent continuous infusion according to the “10, 8, 6” (mg/kg/h) scheme to keep BIS value to 40-60.  Propofol concentrations c(t) were calculated using each set of PK parameters.  Parameters of PD model were yielded using the calculated c(t) and measured BIS values without or with taking dead-time L into account, i.e. BIS(t) = E₀ -E_max c(t) ^γ / (c(t) ^γ+c₅₀^γ) or BIS(t+L) = E₀ -E_maxc(t) ^γ / (c(t) ^γ+c₅₀^γ).  The constructed PD models were compared each other to identify the best one in which mean of the squared errors of the output of the model was minimum.

Results:

Kazama’s set⁴ (Gepts’s parameters² and k_e0 = 0.301 min^-1) indicated the minimum mean squared errors (54.2 ± 28.3, mean ± SD) among the dead-time neglected models.  When the dead-time was taken into consideration, the mean errors were reduced significantly (p < 0.01) in 16 PK models.  Marsh’s set³ showed the minimum errors (46.1 ± 26.8) among the dead-time incorporated models.

Conclusion:

The dead-time incorporated PK-PD model using Marsh’s set of parameters is the best for modeling the BIS response.

References:

1) Billard et al. Clin Pharmacol Ther 1997; 61: 45-58. 2) Gepts et al. Anesth Analg 1987; 66: 1256-1263. 3) Marsh et al. Br J Anaesth 1991; 67: 41-48. 4) Kazama et al. Anesthesiology 1999; 90: 1517-1527.