Pharmacodynamic (PD) models relate drug effect to some measure of drug exposure, typically either drug dose or drug concentration. PD models can be studied during steady-state conditions or during non–steady-state conditions using a pharmacokinetic (PK)/PD modeling approach.1,2 One advantage of a PK/PD approach is that it can predict the time-course drug effect. PK/PD modeling has made an enormous contribution to IV anesthesia, and provided insight into the factors affecting the onset and offset of drug effect.3 For inhaled anesthetics, PK/PD modeling can be performed through the application of an effect compartment model, linking the measured end-tidal concentration (CET) to the measured hypnotic drug effect.4 – 6
Obesity is associated with important physiologic changes that can potentially affect the PK/PD profile of anesthetic gases.7 Ventilatory changes such as reductions in functional residual capacity, expiratory reserve volume, and total lung capacity are frequently seen in obese subjects.8,9 General anesthesia in this population can further alter gas exchange and right-to-left shunt fraction.8,10
The onset and offset of inhaled anesthetic drug effect might be modified by ventilatory and gas exchange alterations in obese patients. Using an electrical analog model to simulate uneven pulmonary distribution of blood and gas on induction with anesthetic gases, right-to-left shunt has been shown to produce an increase in the anesthetic tension gradient between end-tidal gas and arterial blood. This increased gradient results in a delay of induction, particularly with less-soluble anesthetics.11 Sevoflurane is a modern anesthetic frequently used in obese patients.12 Sevoflurane is poorly soluble in blood (blood/gas partition coefficient of 0.6).13 Nonetheless, the physiology of obesity suggests that induction and recovery times could be longer in obese patients receiving sevoflurane than in lean subjects.11
The aim of this study was to create a PK/PD model of sevoflurane to assess the influence of obesity and positive end-expiratory pressure (PEEP) on the onset and offset of sevoflurane hypnotic effect as measured by the bispectral index (BIS). We hypothesized that the onset and offset of sevoflurane effect expressed as the effect-site elimination rate constant (k e0) was slower in obese patients than in lean subjects. In addition, because the use of PEEP has been shown to improve functional residual capacity and arterial oxygen tension,8,14 we postulated that an improvement in ventilatory function with PEEP might result in faster equilibration between CET and effect-site sevoflurane concentration.
After receiving IRB approval (School of Medicine, Pontificia Universidad Católica, Santiago, Chile), and obtaining written informed consent, 15 obese patients (body mass index [BMI] >35) and 15 normal-weight patients (BMI = 20–25) scheduled to undergo general anesthesia for elective laparoscopic surgery (bariatric surgery or cholecystectomy) were prospectively studied. Patients were ASA physical status I or II, between 20 and 50 years old, and received no premedication. Exclusion criteria were any known cerebrovascular disease, long- or short-term (within the previous 24 hours) intake of any drug acting in the central nervous system, and history of adverse reaction to the study drugs.
In the operating room, standard monitoring was placed. The QUATRO sensors of the BIS monitor (Aspect A-2000 BIS® monitor, version XP; Aspect Medical Systems, Newton, MA) were attached according to the manufacturer's recommendations. The smoothing time period of BIS was set at 15 seconds. A 1-minute baseline period of BIS measurements was recorded before anesthesia induction. During this period, the patient was undisturbed and the operating room was kept silent. Anesthesia was then induced with propofol 1 to 2 mg · kg−1, fentanyl 1 to 3 μg · kg−1 and rocuronium 0.6 mg · kg−1. The trachea was intubated with an endotracheal tube and the patient's lungs were mechanically ventilated with a Draeger Fabius® GS anesthesia machine (Draeger Medical, Inc., Telford, PA), attached to a disposable anesthesia adult circle breathing circuit. Tidal volumes, ventilatory rate, and PEEP were adjusted by the anesthesiologist. Carbon dioxide was eliminated by washout with fresh gas flow (2 L · min−1) and by soda lime absorption.
In our institution, PEEP and alveolar recruitment maneuvers are frequently used in obese patients 1 or 2 times during surgery. In patients enrolled in our study, alveolar recruitment maneuvers were performed by increasing airway pressure to 40 cm H2O for 10 seconds. This was followed by ventilation with PEEP set at 8 cm H2O.
Anesthesia was maintained with sevoflurane in oxygen to maintain BIS values between 40 and 60. Additional fentanyl boluses were given as necessary to maintain mean arterial blood pressure and heart rate between 20% of baseline values. Although mean arterial blood pressure and heart rate were the primary end points to administer fentanyl, if the patient presented signs of inadequate anesthesia (e.g., lacrimation or movement), the anesthesiologist was allowed to administer additional fentanyl boluses. Additional rocuronium boluses were allowed at the discretion of the anesthesiologist.
To avoid interference with BIS measurements by surgical stimulation, study measurements were performed after the surgery was finished. After the end of surgery, fresh oxygen flow was set at 5 L · min−1 and sevoflurane concentrations were gradually decreased to obtain stable BIS values of 60 to 65. Tidal volumes were adjusted to keep peak airway pressures <35 mm Hg. The ventilatory rate was adjusted to obtain an end-tidal carbon dioxide between 35 and 40 mm Hg. After 5 minutes of stable BIS and end-tidal carbon dioxide values, sevoflurane inspired concentrations were increased to 5 vol% for a maximum of 5 minutes or until BIS decreased to <40. The vaporizer was then turned off until BIS increased to >60. Thereafter, the study was finished and patients were allowed to recover from anesthesia. Sevoflurane transitions were performed once in normal-weight subjects (without PEEP) and twice in obese patients (once without PEEP and once with a PEEP of 8 cm H2O). The order of these 2 consecutive transitions was randomly assigned. During the study period, no surgical or tactile stimulation was allowed. BIS values and expiratory sevoflurane concentrations, measured by a Datex Capnomac monitor (Datex, Helsinki, Finland), were automatically recorded every 10 seconds.
In every patient, we recorded the following sevoflurane anesthesia and ventilation measurements during the study period: sevoflurane concentration before transition, maximum inspired sevoflurane concentration, maximum sevoflurane CET, administration time, oxygen saturation during the study period, and end-tidal CO2 during the study period. In every patient, we also recorded the following descriptors of sevoflurane PDs: baseline BIS, the BIS before transition, the minimum BIS during the transition, the time to reach half-maximal effect, the time to reach maximal effect, and the time to 75% recovery.
Observed levels of BIS were related to the predicted concentrations of sevoflurane in the effect compartment (Ce) using Equation (1):
E0 is the BIS value immediately before sevoflurane transitions (not the awake BIS value), Emax is the BIS at the maximal drug effect, Ce50 is the effect-site concentration eliciting half of Emax, and γ is the steepness of the concentration-response curve.
Equation (2) 1 was used to calculate Ce, the concentration of sevoflurane in the effect site, as a function of the observed sevoflurane CET.
dCe/dt represents the rate of change of Ce, and k e0 represents the elimination rate constant out of the effect site. In the current context, because we used sevoflurane CET instead of plasma concentrations, sevoflurane transfer between the alveoli gas and the arterial blood is included in k e0.
The parameters of the above models were estimated with a population approach using the NONMEM system, version VI, with the First Order Conditional Estimation (FOCE) method and the INTERACTION option.15 Model selection was based on the inspection of goodness-of-fit plots and minimum value of the objective function (−2 · log-likelihood [−2LL]) provided by NONMEM. For 2 nested models, a decrease in −2LL of 3.84, or 6.63 points for an added parameter, is considered significant at the 0.05 or 0.01 level, respectively. Two models are nested if one model can be reduced to the other model by setting the additional parameter(s) to either 0 (for additive parameters) or 1 (for multiplicative parameters).
Results from the population models are presented as parameter estimates, together with the corresponding 95% confidence intervals (CIs). CIs were based on the likelihood profile method implemented in PLT Tools version 3.4 (a graphical interface for the NONMEM system, developed by Dennis M. Fisher and Steven L. Shafer, available at www.PLTsoft.com).
Intersubject variability (ω2 in NONMEM parlance) was estimated by NONMEM on all parameters, and is reported as the intersubject coefficient of variation, CV(%). The model for intersubject variability was additive for the parameter E0 and Emax, as these parameters model BIS measurements expected to be normally distributed in the range of data gathered in this study. Intersubject CV was calculated for E0 and Emax as
Parameter. Exponential intersubject variability was applied to C50, γ, and k e0, reflecting the expected logarithmic distribution of these parameters. For these parameters, intersubject CV was calculated as
The model parameters were estimated simultaneously using NONMEM. A model without covariates was developed first (base population model). Then, the covariate effects of BMI and PEEP on every estimated parameter were explored. Significant covariates (if any) were incorporated, starting with the covariate that led to the largest decrease in −2LL, one at a time until the full covariate model was obtained (forward inclusion). Although the study planned called for both forward inclusion and backward inclusion, because no significant covariate effects were identified in this first step, there was no requirement for additional covariate analysis (see supplemental data, Supplemental Digital Content 1, http://links.lww.com/AA/A285, and 2, http://links.lww.com/AA/A286).
Performance error was calculated to evaluate the final model performance as described elsewhere.16 The median performance error and median absolute performance error (MDAPE) were calculated as indicators of bias and inaccuracy, respectively. These were calculated for the population and for every individual based on the individual post hoc model predictions. The best, median, and worst individuals according to the MDAPE were selected for graphical display.
A descriptive analysis of sevoflurane inspired and expired concentrations, BIS values, and time to reach different BIS end points was used to compare the PK/PD characteristics between obese (with and without PEEP) and lean subjects. Administration time was defined as the time measured from the start of the transition (vaporizer set to 5%) until the moment when the vaporizer was turned off. Time to reach half of maximal effect was defined as the time measured from the start of the transition until the moment when 50% of the observed maximal effect (minimum BIS) was reached. Time to recovery 75% was measured from the time of maximal effect until 75% of recovery target (BIS = 60) was reached.
As described, the effect of covariates (weight, PEEP) on model parameters was assessed using the difference in log likelihood. CIs were calculated using the log-likelihood profile. A value of P < 0.05 was considered significant.
All patients completed the study (15 obese patients and 15 normal-weight patients). Demographics and anesthetic data are shown in Table 1.
PD Modeling of BIS Data
A total of 2954 BIS versus time observations were used in the analysis (98 ± 29 data points per subject). Observed BIS-versus-time profiles during the transition periods are shown in Figure 1. A typical individual sevoflurane transition is shown in Figure 2.
The model represented by Equations (1) and (2) provided an adequate description of the data and was selected as the base population model. During model selection, it was found that the use of the effect-site concentration, Ce, resulted in a far superior fit than the use of observed sevoflurane CET (improvement in −2LL = 4860.163 points, P ≪ 0.001). This confirmed the presence of hysteresis and the need of an effect-site model to characterize the concentration-effect relationship. Figure 3 shows the relationship between BIS and CET (left panel) or Ce (right panel) in which the hysteresis loop was collapsed.
The speed of equilibration between CET and effect-site sevoflurane concentration, modeled using the effect-site elimination rate constant (k e0), was not influenced by BMI or PEEP (Fig. 4). None of the covariates tested (BMI and PEEP) showed significant effects on any of the parameters of the model (P > 0.05), and therefore the base population model was the final population model describing the BIS data. Table 2 lists the population parameter model estimates. Figure 5 shows the measured and the corresponding individual model predictions for the best, median, and worst prediction according to the values of MDAPE. The population median performance error was −0.05% and the median MDAPE was 3.7%.
Likelihood profiles of individual parameters estimated and the corresponding 95% and 99% CIs are shown in Figure 6.
The sevoflurane anesthetic, ventilatory, and PD measurements in Tables 3 and 4 do not suggest any effect of obesity or PEEP on the recorded observations.
Although we assessed the dynamic relationship between CET and BIS at relatively deep hypnotic states (BIS values between 30 to 65), our results do not suggest prolonged induction or recovery times in obese patients when sevoflurane, a poorly soluble anesthetic drug,13 is used for anesthetics lasting from 90 to 120 minutes. In addition, we did not find any effect of PEEP on the PD of sevoflurane.
A PK study by Lemmens et al.17 determined that the effect of obesity on the delivered/alveolar and inspired/alveolar ratios of volatile anesthetics was only modest, with a more apparent effect for the more soluble drugs. This observation was explained on the basis of an increased uptake of the more soluble drugs by the blood, lean, and fat tissues in obese patients. We focused our analysis on the effects of obesity on k e0, defined in this study as the equilibration rate between the CETsevo and Cesevo. With this approach, a potential influence of obesity in the anesthetic tension gradient between end-tidal gas and arterial blood should result in different k e0 values in obese and non-obese subjects. The similar PK/PD parameters found in our study between obese and lean patients in conjunction with the results of previous studies6,17 – 20 confirm the PK and PD predictability of modern inhaled anesthetics in this population. It should be noted that because we did not include obese patients with BMI >50, our results cannot be extrapolated to that population.
The absence of clinically relevant respiratory gas exchange alterations during the study period in our obese patients should be considered in the current results. Normal oximetry (SpO2) and end-tidal CO2 values were observed in all patients, before and during sevoflurane transitions (Table 3). Per protocol, we did not instruct the anesthesiologists how to manage ventilation during surgery. In obese patients, PEEP and recruitment maneuvers were routinely used to prevent atelectasis during surgery (before the study period).9 This might have prevented us from finding relevant gas exchange alterations that would have potentially affected the dynamic profile of sevoflurane effect.11
Oxygen consumption and CO2 production are increased in obese subjects as a result of increased metabolic activity.8 The similar end-tidal CO2 values maintained during the study period in obese and lean subjects may have been the result of relatively higher minute ventilation in obese patients compared with lean patients. This relatively increased minute ventilation in conjunction with the higher cardiac outputs normally seen in obese subjects8 might have offset the expected decrease in anesthetic uptake of sevoflurane caused by right-to-left shunting.
Finally, increased central sensitivity to inhaled anesthetics in obese patients has also been suggested as an additional contributor to possible delayed recovery times in this population.7 This is not supported by our results. We found similar C50 values for the effect of sevoflurane on BIS in obese and normal-weight patients (Table 2). It should be noted that, in our model, the maximal effect represents a decrease in BIS values of approximately 30 points, from BIS values of 60 to 30, and that the C50 represents the sevoflurane concentration that produces 50% of this maximal effect (Table 4). The C50 value is useful to assess a possible influence of obesity in the sensibility to sevoflurane effect.
Because BIS before transition might be influenced by the residual effect of fentanyl, possible differences in fentanyl concentration between groups was not accounted for in our model. However, no differences in fentanyl doses were found between groups during surgery. This is further supported by the similar sevoflurane CET and BIS values reported before transitions in both groups (Tables 3 and 4). In addition, no difference in the E0 was found between groups in our model analysis.
Although we assessed the dynamic relationship between CET and BIS at relatively deep hypnotic states (BIS values between 30 to 60), our results do not support prolonged induction or recovery times in obese patients when sevoflurane, a poorly soluble anesthetic, is used for anesthetics lasting from 90 to 120 minutes. Similarly, the use of PEEP showed no effect on the rate of onset or offset of sevoflurane hypnotic effect.
1. Sheiner LB, Stanski DR, Vozeh S, Miller RD, Ham J. Simultaneous modeling of pharmacokinetics and pharmacodynamics: application to d-tubocurarine. Clin Pharmacol Ther 1979;25:358–71
2. Struys MM, Coppens M, De Neve N, Mortier E, Doufas A, Van Bocxlaer J, Shafer S. Influence of administration rate on propofol plasma-effect site equilibration. Anesthesiology 2007;107:367–8
3. Minto CF, Schnider TW. Contributions of PK/PD modeling to intravenous anesthesia. Clin Pharmacol Ther 2008;84:27–38
4. Olofsen E, Dahan A. The dynamic relationship between end-tidal sevoflurane and isoflurane concentrations and bispectral index and spectral edge frequency of the electroencephalogram. Anesthesiology 1999;90:1345–53
5. Rehberg B, Bouillon T, Zinserling J, Hoeft A. Comparative pharmacodynamic modeling of the electroencephalography-slowing effect of isoflurane, sevoflurane, and desflurane. Anesthesiology 1999;91:397–405
6. Cortinez LI, Troconiz IF, Fuentes R, Gambus P, Hsu YW, Altermatt F, Munoz HR. The influence of age on the dynamic relationship between end-tidal sevoflurane concentrations and bispectral index. Anesth Analg 2008;107:1566–72
7. Casati A, Putzu M. Anesthesia in the obese patient: pharmacokinetic considerations. J Clin Anesth 2005;17:134–45
8. Adams JP, Murphy PG. Obesity in anaesthesia and intensive care. Br J Anaesth 2000;85:91–108
9. Whalen FX, Gajic O, Thompson GB, Kendrick ML, Que FL, Williams BA, Joyner MJ, Hubmayr RD, Warner DO, Sprung J. The effects of the alveolar recruitment maneuver and positive end-expiratory pressure on arterial oxygenation during laparoscopic bariatric surgery. Anesth Analg 2006;102:298–305
10. Bellami M, Stuys M. Anaesthesia for the Overweight and Obese Patient. New York: Oxford University Press, 2007:45–54
11. Eger EI II, Severinghaus JW. Effect of uneven pulmonary distribution of blood and gas on induction with inhalation anesthetics. Anesthesiology 1964;25:620–6
12. De Baerdemaeker L, Mortier E, Struys M. Pharmacokinetics in obese patients. Contin Educ Anaesth Crit Care Pain 2004;4:152–5
13. Eger EI II. New inhaled anesthetics. Anesthesiology 1994;80:906–22
14. Santesson J. Oxygen transport and venous admixture in the extremely obese: influence of anaesthesia and artificial ventilation with and without positive end-expiratory pressure. Acta Anaesthesiol Scand 1976;20:387–94
15. Beal SL, Sheiner LB. NONMEM Users Guide. Parts I and II. San Francisco: University of California, 1980
16. Varvel JR, Donoho DL, Shafer SL. Measuring the predictive performance of computer-controlled infusion pumps. J Pharmacokinet Biopharm 1992;20:63–94
17. Lemmens HJ, Saidman LJ, Eger EI II, Laster MJ. Obesity modestly affects inhaled anesthetic kinetics in humans. Anesth Analg 2008;107:1864–70
18. La Colla G, La Colla L, Turi S, Poli D, Albertin A, Pasculli N, Bergonzi PC, Gonfalini M, Ruggieri F. Effect of morbid obesity on kinetic of desflurane: wash-in wash-out curves and recovery times. Minerva Anestesiol 2007;73:275–9
19. La Colla L, Albertin A, La Colla G, Mangano A. Faster wash-out and recovery for desflurane vs sevoflurane in morbidly obese patients when no premedication is used. Br J Anaesth 2007;99:353–8
© 2011 International Anesthesia Research Society
20. Casati A, Marchetti C, Spreafico E, Mamo D. Effects of obesity on wash-in and wash-out kinetics of sevoflurane. Eur J Anaesthesiol 2004;21:243–5