Population models characterizing the pharmacodynamic interactions between hypnotics and opioids, such as propofol and remifentanil, can be applied clinically to predict drug behavior in individual patients.1 We previously reported a series of response surface models that characterized the synergistic interaction between predicted remifentanil effect-site concentrations (Ce's) and measured end-tidal (ET) sevoflurane levels in blunting responses to selected verbal and painful stimuli.2 The aim of this study was to evaluate the ability of these models to predict the return of responsiveness (ROR) in patients undergoing elective surgery during emergence from anesthesia and a response to tibial pressure when patients required analgesics in the recovery room. We hypothesized that model predictions would be consistent with observations. One limitation to these models was that measured ET sevoflurane concentrations do not reflect brain concentrations during non-steady-state conditions, such as emergence from anesthesia. We also hypothesized that response surface model predictions would improve if we account for the lag time between brain and ET sevoflurane concentrations.
Section I: Response Surface Model Development
We revised previously reported sevoflurane-remifentanil pharmacodynamic interaction models.2 We modified the models to account for the lag time between changes in ET and brain sevoflurane concentrations during non-steady-state conditions. A physiologic model was used to predict brain concentrations during non-steady-state conditions. In response to a step change in inspired sevoflurane, predicted brain concentrations were slower to change than ET measurements. We also revised the models to account for the effect of altitude (the original model was based on data collected at 5000 feet above sea level).
Two sets of revised response surface models were constructed: one set using predicted remifentanil Ce's and measured ET sevoflurane levels, and a second set using predicted remifentanil Ce's and predicted sevoflurane effect-site levels. Each set consisted of 2 models: a probability of unresponsiveness model (i.e., lack of response to loud verbal and nonpainful tactile stimuli based on the Observer's Assessment of Alertness/Sedation (OAA/S) scale (presented in Table 1)3 and a lack of response to 30 pounds per square inch (PSI) of anterior tibial pressure (pressure algometry) model. Thirty PSI was used in lieu of 50 PSI as in our prior work2 because our recent experience suggests that 30 PSI is a better surrogate for the painful stimuli encountered in the recovery room. In our recent work, we found that 50 PSI was too strong a stimulus, when compared with stimuli typically encountered in the recovery room.1
A pharmacokinetic model for inhaled anesthetics was used to account for the lag between sevoflurane Ce's and ET concentrations.4,5 Model development is presented in the Appendix (see Supplemental Digital Content 1, http://links.lww.com/AA/A13).
The response surface models were constructed using a Greco model structure (Eq. 1).6,7 This structure differs from the Logit model structure we originally used to characterize interactions between remifentanil and sevoflurane.2 The Greco model structure was used to build a revised set of models to be consistent with our prior work with evaluating propofol-remifentanil response surface models in surgical patients.1 Models were built using a naïve pooled technique.8
Emax is the maximal effect (i.e., no response to pressure algometry), C50s (sevoflurane) and C50r (remifentanil) are the concentrations that produce 50% of the maximal effect when administered individually, n is the slope of the pharmacodynamic response curve, and α is the interaction between sevoflurane and remifentanil. Effect ranged from 0 (0% probability of no response) to 1 (100% probability of no response). Model parameters were identified by an iterative process in which the log likelihood between the observations and the model predictions was maximized (Matlab, The MathWorks, Natick, MA). Coefficients of variation were estimated for each parameter using a bootstrap method with 10,000 iterations.9
An assessment of how well the revised models fit observations in our volunteer study was made by calculating the percentage of predictions more than 0.5 (response or no response) that agreed with observations. Responses were compared with model predictions using a Spearman rank correlation (ρ). A two-tailed unpaired t-test was used to determine whether the Spearman ρ was significantly different from 0. The null hypothesis was that the revised models did not correlate with observations.
Section II: Evaluation of Response Surface Models in Patients Undergoing Elective Surgery
After IRB approval at the University of Utah, informed consent was obtained from 20 patients presenting for elective surgery. Twelve male and 8 female subjects participated. Patients with a history of ongoing opioid consumption were excluded. Age, weight, and height were recorded for each patient.
Each patient was instrumented with a pulse oximeter, noninvasive arterial blood pressure cuff set to cycle every 5 min, a 5-lead electrocardiogram, and an oral or nasal temperature probe. Inspired and expired sevoflurane concentrations were continuously monitored (AS/3 Anesthesia Monitor, Datex-Ohmeda, Helsinki, Finland) and stored every 5 s using a computerized data acquisition system (S/5 Collect, Datex-Ohmeda).
Midazolam 12.5 μg/kg was administered IV in the preoperative holding area 10 min before patients were taken to the operating room. Induction consisted of age-adjusted infusions of remifentanil (range 0.1–0.5 μg·kg−1·min−1) and propofol (range 75–300 μg·kg−1·min−1) designed to achieve a loss of response to laryngoscopy within 7 min (Medfusion 2010I or 3010I, Medex, Duluth, GA).1
After loss of responsiveness, patients received either rocuronium (0.6 mg/kg) or succinylcholine (2 mg/kg) followed by tracheal intubation. The propofol infusion was terminated after tracheal intubation. Maintenance of anesthesia consisted of remifentanil and sevoflurane titrated at the anesthesiologist's discretion. Before emergence, anesthesiologists administered fentanyl as per their standard practice to manage postoperative pain.
During emergence, level of responsiveness was assessed using the OAA/S every 20 s by calling the patient's first name and asking, “Can you open your eyes?” If there was no eye opening, the question was repeated. If still unresponsive, the question was asked a third time while shaking the patient's shoulder for 2 s. Assessments began when the remifentanil infusion and the sevoflurane vaporizer were both turned off. They ended when the patient regained responsiveness. ROR was defined as the first of 2 consecutive OAA/S scores >1.
Patients were observed in the recovery room for 30 min. Every 5 min, a study nurse asked the patients to use the visual analog scale (VAS) to give a pain score and a pain score that the patients considered tolerable. Fentanyl was administered in 0.5–2 μg/kg increments when the actual VAS was more than the tolerable VAS, and the recovery room nursing staff considered it appropriate (i.e., lack of excessive sedation or respiratory depression).
Time-stamped data files of drug administration with a resolution of 5 s were used to predict fentanyl10 and remifentanil11 Ce's. Fentanyl Ce's were converted to equivalent remifentanil Ce's using a relative potency of remifentanil to fentanyl = 1:1.2.12,13 Measured ET sevoflurane concentrations were used to predict sevoflurane Ce's. Pharmacokinetic models for propofol14 and midazolam15 were used to estimate residual propofol and midazolam Ce's at the time of ROR.
Evaluation of Response Surface Model Predictions
Model predictions were evaluated at 2 events: ROR after surgery and the first dose of analgesic (fentanyl) administered in the recovery room. For each model (a model based on ET sevoflurane measurements and a model based on estimated effect-site sevoflurane concentrations), a prediction of OAA/S = 1 ranging from 0% to 100% was made every 5 s from once the anesthetic was terminated to 10 min after the time of each patient's ROR. Model predictions were compared with observations with graphical and temporal analyses.
Predictions from each model were compared graphically on 2 plots: a prediction versus time plot and a plot of the remifentanil-sevoflurane concentrations at the time of emergence superimposed on a topographical representation of the response surface model predictions of OAA/S = 1. The topographical plot included the 5%, 50%, and 95% isoboles. Isoboles were defined as the set of remifentanil and sevoflurane concentration pairs that produced the same probability of effect. Mean model predictions recorded at ROR (OAA/S > 1) for the measured ET sevoflurane and estimated sevoflurane effect-site-based models were compared with an unpaired two-tailed t-test.
Empirical Cumulative Distribution
Model predictions from each patient were sorted according to increasing probability.16 A percentage value was assigned to each patient as a percentage of all patients according to increasing probabilities. The patient population percentage was plotted versus the sorted model predictions. A uniform distribution of model predictions across patient percentage values from 0% to 100% was considered a good model fit.
The time from the 50% model prediction for unresponsiveness to the time of the observed ROR was calculated for each patient. A negative, zero, or positive time difference indicated that the observed ROR occurred before, exactly at, or after the 50% probability of unresponsiveness. Time differences were reported as mean ± SD. The time differences between the measured ET sevoflurane and estimated sevoflurane effect-site-based models were compared with an unpaired two-tailed t-test.
Similarly, 2 models of lack of response to 30 PSI of anterior tibia pressure algometry were evaluated at the time patients received their first dose of fentanyl in the recovery room: a model based on ET sevoflurane measurements and a model based on estimated effect-site sevoflurane concentrations. For each model, a prediction of lack of response to 30 PSI of anterior tibial pressure ranging from 0% to 100% was made when patients received analgesic therapy (fentanyl) in the recovery room.
Section I: Response Surface Model Development for Application in Real Time
Sevoflurane-remifentanil interaction model parameters fit to responses previously recorded in volunteers are presented in Table 2.2 Models include the probability of unresponsiveness (OAA/S = 1) and lack of response to 30 PSI of anterior tibial pressure. Two sets of models are presented: one using sevoflurane Ce's and the other using ET sevoflurane concentrations. Coefficients of variation for estimates of remifentanil and sevoflurane C50s, slope, and remifentanil-sevoflurane interaction (α) ranged between 8% and 149%.
Using a probability of 0.5 or higher as a cutoff for model goodness of fit, the percentage of model predictions consistent with observed responses in volunteers was 90% or more for all 4 models (Table 2). The Spearman rank correlation coefficients for all models are presented in Table 2. The two-tailed t-test analysis rejected the null hypothesis that the revised models did not correlate with observations in volunteers.
Section II: Evaluation of Response Surface Models in Patients Undergoing Elective Surgery
All 20 patients completed the study. Their ASA physical status classification ranged from I to III. The height, weight, body mass index, and age were 173 ± 14 cm, 78 ± 18 kg, 26.3 ± 5.1 kg/m2, and 45.4 ± 14.6 yr, respectively. Surgical procedures included open abdominal8 and laparoscopic,3 spine,4 head and neck,2 lower extremity vascular (1), and gynecologic (2) procedures. Estimated blood loss ranged from 0 to 7.5 mL/kg. Thirteen different surgeons and 8 different anesthesiologists participated in the study. The mean estimated Ce's at the time of emergence for the premedication dose of midazolam was 4.3 ± 2.2 ng/mL and for the induction dose of propofol was 0.1 ± 0.1 μg/mL.
Evaluation of Response Surface Model Predictions
Figure 1 shows model predictions of OAA/S = 1 over time during emergence from anesthesia for each patient. The rapid up and down changes in ET-based model predictions in selected patients (i.e., Patient 10, 12, 14, etc.) were attributable to variations in respiratory function during emergence from anesthesia. The ET concentration-based model consistently predicted a high probability of ROR before the observed ROR. The Ce-based model, by contrast, predicted high probabilities of ROR both before and after the observed ROR.
Figure 2 a shows the sevoflurane-remifentanil concentration pairs at the time of emergence superimposed on a topographical representation of the model prediction a OAA/S = 1. Concentrations are nearly equally distributed above and below the 50% isobole (8 below and 12 above) for the sevoflurane effect-site model and predominantly below the 50% isobole (19 below and 1 above) for the ET model. At the time patients responded to voice command or prodding, the mean ET sevoflurane concentration was 0.13 ± 0.13 vol%, predicted sevoflurane Ce was 0.44 ± 0.17 vol%, and remifentanil equivalent Ce was 3.5 ± 1.7 ng/mL. The average predicted probability of no response was 53% ± 37% and 9% ± 19% for the effect-site and ET models, respectively (P < 0.001).
The empirical cumulative distribution plot illustrates the poor distribution of predictions across the patient percentage values for the ET model (Fig. 3a). For example, at the 20th patient percentile, ideally 4 of the model predictions should be between 0% and 20%, and the remainder of the predictions should be above 20%. At the 20th percentile for the ET model, 16 patients were between 0% and 20%. By contrast, the effect-site model had a more uniform distribution of predictions across patient percentage values, but the distribution was weighted at low and high predictions. For example, at the 50th patient percentile, 7 of the model predictions were below 30%, and 10 of the model predictions were above 70%.
The mean time from the termination of the anesthetic until patients emerged from anesthesia was 5.3 ± 6.1 min. Patients emerged from anesthesia 0.9 ± 4.3 min after the effect-site-based model predicted a 50% probability of unresponsiveness and 4.1 ± 4.9 min after the ET-based model predicted a 50% probability of unresponsiveness (P = 0.02, Fig. 4).
Figure 2b shows the 5%, 50%, and 95% probability isoboles for the 2 models and the sevoflurane-remifentanil equivalent concentration pairs when patients received their first dose of fentanyl during the first 30 min after surgery. Seven of the 20 patients did not require fentanyl during this time period. Concentration pairs are distributed predominantly above the 50% isobole for the effect-site-based and ET-based models (3 below and 10 above). At the time of first fentanyl request for the management of postoperative pain, the average ET sevoflurane was 0.00 ± 0.00 vol%, predicted sevoflurane effect site was 0.02 ± 0.01 vol%, and remifentanil equivalent Ce was 1.9 ± 1.3 ng/mL. The mean probabilities of no response to 30 PSI of anterior tibial pressure at the time patients required additional fentanyl were 61% ± 30% and 59% ± 30% for the effect-site and ET models, respectively (P = 0.893).
The empirical cumulative distribution plot illustrates a similar distribution of predictions across patient percentage values for both the ET and effect-site models (Fig. 3b). At the 50th patient percentile, 6 of the model predictions were below 50%, and 7 of the model predictions were above 50% for both models.
Section I: Response Surface Model Development
Revised models using the Greco model structure fit responses from volunteers reasonably well according to the comparison of prediction probabilities to observed responses. The Spearman rank correlation coefficients for the probability of unresponsiveness models had stronger correlations with observations than the lack of response to pressure algometry models. There was no appreciable difference in model fit between the sevoflurane effect-site- and ET-based models. This suggests that the original experiment was conducted at near steady-state conditions because a parameter to adjust for disequilibrium between ET and effect-site sevoflurane concentrations did not appreciably alter the interaction parameters.
In comparison with prior studies, there is large variability between our work and previously published remifentanil C50's for predictions of OAA/S = 1.2,17 One explanation may be that the remifentanil C50 Greco model parameter is estimated from a data set where the majority of observations were made below the remifentanil C50 of 50.9 ng/mL.
Section II: Evaluation of Response Surface Models in Patients Undergoing Elective Surgery
In this study, we conducted a preliminary evaluation of previously developed models of unresponsiveness and lack of response to a moderately painful stimulus (tibial pressure) in patients undergoing elective surgery. One study aim was to evaluate how well these models predicted emergence from anesthesia and the need for additional opioid in the recovery room.
While patients were anesthetized, model predictions indicated a high likelihood that patients would be unresponsive. With the probability of unresponsiveness models, predictions more than 99% were consistent with observations (no patients demonstrated responsiveness). However, after termination of the anesthetic, model predictions of unresponsiveness rapidly decreased (Fig. 1), and individual patients emerged from anesthesia over a wide spectrum of model predictions ranging from 1% to 97%. It is difficult to comment on the ability of these models to discriminate between awake or asleep during time intervals that are of clinical interest and how well the model predictions are calibrated to observations. The statistical tools that would be used to help answer these questions require a study with substantially larger sample sizes.
A second study aim was to evaluate the value of accounting for the lag time between ET and brain sevoflurane concentrations during non-steady-state conditions on model predictions. Model predictions using effect-site sevoflurane concentrations more adequately predicted ROR in patients emerging from anesthesia than model predictions using ET sevoflurane concentrations. As illustrated in Figures 1 and 4, the model predictions of OAA/S = 1 using ET sevoflurane levels typically predicted ROR before emergence. This model misspecification is likely due to the biophase between ET and effect-site sevoflurane concentrations during emergence. This was confirmed by the differences in mean predictions of emergence and mean time intervals between observed and predicted emergence between the 2 models. The improvement was also visualized in the topographical representation of the model predictions of OAA/S = 1 (Fig. 2a). Ideal model predictions would be equally distributed at about the 50% isobole. The concentration pair predictions are more equally distributed around the 50% isobole for the effect-site model but not the end-site model.
The benefit of using Ce's, however, was not as useful in model predictions in the recovery room. The ET and effect-site model predictions of a lack of response to tibial pressure at the time when additional analgesic was required were similar (Fig. 2b). Mean model probabilities were skewed above the 50% isobole (61% and 59%) predicting a lack of response to anterior tibial pressure in a majority of patients. This suggests that using 30 PSI may be a slightly less painful surrogate of pain encountered in the recovery room (an ideal distribution would be at about the 50% isobole). Because sevoflurane levels were negligible, both models collapsed to a single drug (remifentanil equivalents) pharmacodynamic model. This is the most likely explanation for similar predictions between models (i.e., the sevoflurane concentrations are so low that they are nearly irrelevant in the recovery room in terms of analgesia).
These results in the recovery room, although promising, are difficult to interpret given the narrow spectrum of patients evaluated. We did not control for duration, type, or extent of surgery, use of local infiltration into the surgical site, and patient age. These factors and others may play a role in how patients respond to assessments of perceived pain in the recovery room.
Several assumptions were made in implementing the Lerou model to predict sevoflurane Ce's. Cardiac output was normalized to weight but assumed to be constant (Appendix, see Supplemental Digital Content 1, http://links.lww.com/AA/A13) and did not account for changes in cardiac output with induction of anesthesia, blood loss, etc. Cerebral blood flow was also assumed constant (16% of total cardiac output) and did not account for changes in PaCO2. This could be especially important during emergence from anesthesia when changes in cardiac output and PaCO2 with hyperventilation or permissive apnea could potentially change the time to ROR.18 Future work directed at continuously updating model estimates of cerebral blood flow may improve accuracy of sevoflurane effect-site predictions.
In addition, we used the OAA/S score to build a response surface that predicts the probability of unresponsiveness. In the volunteer study, the OAA/S assessments were done in the absence of ongoing pain and without an endotracheal tube in place. We used this model to predict emergence from general anesthesia in patients whose tracheas were intubated after surgeries associated with mild to moderate surgical pain. No volunteer study can fully emulate the complexities of the clinical environment. The differences between the volunteer study on which the models are based and the clinical environment in which the models are applied likely impacts model performance to some degree.
Premedication with midazolam and induction with propofol may have prolonged emergence beyond model predictions, but their contribution was most likely small. For example, midazolam levels were just below the C50 for a Ramsay score of 2 (patient cooperative, oriented, and tranquil—5.7 ng/mL) and well below the C50 for a Ramsay score of 3 (patient sedated but responds to commands—71 ng/mL).8 Propofol levels also were well below the C50 for loss of responsiveness (2.2 μg/mL),1,17 making its contribution to prolonging emergence negligible.
In conclusion, predicted Ce's are frequently used to guide the delivery of IV anesthetics using target-controlled delivery systems.19 Extension of this concept to inhaled anesthetics and to drug-drug interaction models may have value in guiding the delivery of anesthetics in combination by predicting the likelihood of adequate sedation, analgesia, and time to emergence. In fact, clinical pharmacology display systems that apply these concepts and models in real time are currently under development.20,21
Dwayne R. Westenskow is the Section Editor of Technology, Computing, and Simulation for the Journal. This article was handled by Tony Gin, Section Editor of Anesthetic Clinical Pharmacology, and Dr. Westenskow was not involved in any way with the editorial process or decision.
Ken B. Johnson, Noah D. Syroid, Talmage D. Egan, and Dwayne R. Westenskow either hold equity positions and/or receive salary/consulting fees from Applied Medical Visualizations L.L.C., a medical device development company, which has a vested interest in the outcome of this study.
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