Obesity is defined as an excess of fat tissue compared with normal values for an individual of the same age and sex. The international WHO classification of obesity is based upon the BMI, calculated as total body weight (TBW) divided by the square of the height in metres. Obesity is defined as a BMI of at least 30 kg m−2, and morbid (or class III) obesity as a BMI of at least 40 kg m−2. Obesity affects almost every system , resulting in important changes in drug disposition. These include increases in total blood volume that are less than those observed in nonobese individuals on a volume/weight basis . Cardiac output is also increased , whereas hepatic  and renal  clearances are usually unaffected or increased. Combined, these changes may markedly influence required dosages of drugs used in anaesthesia.
Propofol is a short-acting intravenous anaesthetic with an excellent recovery profile  as well as pharmacokinetic characteristics that are particularly suitable for continuous infusion. In addition, the introduction of target-controlled infusion (TCI)  has improved the accuracy by which a desired level of anaesthesia may be achieved and maintained. The ‘Marsh’  pharmacokinetic parameter set has been incorporated in TCI systems, but was developed from and evaluated in nonobese individuals. Even though the central volume of distribution of the ‘Marsh’ kinetic set is proportional to weight , there is a degree of uncertainty with regard to an appropriate weight input when using propofol TCI. For example, during a constant infusion, plasma propofol concentration may depend on TBW . However, it has been shown that anaesthetic induction doses are proportional to lean body mass (LBM) rather than to TBW . The difference between TBW and LBM increases as TBW increases , causing concern that, when propofol dosage to obese patients is based on TBW, excessively deep anaesthesia and deleterious cardiovascular effects may result. Certain authors [11,12] have recommended an adjustment to the dosing weight according to the formula presented in (Equation 1) (see Methods).
In a previous report , we tested the predictive performance of TCI when the weight input to the ‘Marsh’ model was adjusted according to (Equation 1) and noted that there was general overprediction of the blood concentrations by the TCI system. However, predictive performance of TCI in morbidly obese patients without weight adjustment has not been evaluated. The purpose of this prospective, randomized, double-blind study was to determine the predictive performance of propofol TCI to morbidly obese patients when no weight adjustment was used vs. a weight adjustment. We hypothesized that TCI without a weight adjustment would result in a marked (at least 50%) reduction in median performance errors (MDPE).
After acquiring ethics committee approval for this prospective, randomized, double-blind study, written informed consent was obtained from 24 patients (ASA physical status II or III, aged 25–62 years) undergoing elective biliointestinal bypass surgery. Patients with ASA physical status greater than III, aged less than 20 or more than 65 years, or with a history of alcohol or drug abuse, were excluded a priori.
Randomization was performed using a computer-generated sequence of numbers (Microsoft Excel 2007). Provided they satisfied the inclusion criteria, patients were recruited during the usual preanaesthesia evaluation visits and assigned to a particular group by the same anaesthesiologist who would later set the infusion pump. The anaesthesiologist who administered anaesthesia and recorded patients' data for subsequent analysis was not aware of each patient's group.
Patients were randomly allocated to receive either a propofol TCI based on the weight adjustment formula (group adjusted) or a propofol TCI with no weight adjustment (group TBW).
Patients fasted for 8 h before surgery and received no premedication. After arrival in the operating room, two 18-gauge intravenous cannulas were placed into the forearm and Ringer's lactate solution 6 ml kg−1 was infused. A radial artery catheter was inserted for arterial blood sampling and invasive arterial blood pressure monitoring. Standard monitoring was used throughout the study, including electrocardiography, heart rate (lead II) and pulse oximetry. In all patients, the electroencephalogram (EEG) was monitored using the bispectral index (BIS; BIS XP monitor A 2000; Aspect Medical Systems Inc., Natick, Massachusetts, USA). All patients were intubated awake by means of a flexible fibreoptic bronchoscopic technique facilitated by a target-controlled effect-site concentration of remifentanil set at 2.5 ng ml−1 that was maintained until the first surgical stimulus. Thereafter, the target concentration was adjusted in order to ensure haemodynamic stability, by maintaining patients' heart rates and mean blood pressures between ±10% of the basal values (values recorded at patients' arrival in the operating theatre).
After awake fibreoptic endotracheal intubation, general anaesthesia was induced by propofol TCI, targeting plasma concentration initially at 6 μg ml−1 in both groups. After 2 min, the target was reduced and adapted to the needs of each patient to maintain stable BIS values ranging between 40 and 50. Patients' lungs were mechanically ventilated using a 50% oxygen in air mixture and controlled using a Cato-Dräger (Dräger, Lubeck, Germany) anaesthesia workstation set to maintain an end-tidal partial pressure of carbon dioxide ranging between 32 and 35 mmHg. Cisatracurium was used for neuromuscular blockade.
The propofol TCI system consisted of an Acer TravelMate 518TX computer connected to a Graseby 3500 infusion pump (Sims Graseby Limited, Waterford, Herts, UK) using the Rugloop software (designed by Tom De Smet and Michel Struys, Department of Anaesthesia, University Hospital, Ghent, Belgium, v. 1.3). The pharmacokinetic parameters used in the computer-assisted continuous infusion for administration of propofol were based on the model described by Marsh et al. .
Propofol was administered differently in the two groups. In the group adjusted, the central volume of distribution was calculated as being proportional to body weight according to (Equation 1) (originally proposed by Gepts  and De Baerdemaeker et al. ), where CBW stands for corrected body weight, and in which ideal body weight (IBW) was estimated according to the formula suggested by Lemmens et al. (Equation 2). This formula has been used to administer manually adjusted infusions to obese patients by Servin et al.
In the group TBW, TBW was used to calculate the central volume of distribution of propofol. Remifentanil was administered using a commercially available TCI system (Base-Primea, Fresenius, Italy – Minto model) in which the input weight was adjusted according to the formula suggested by Lemmens et al. (Equation 2).
Arterial blood samples for the determination of blood propofol concentrations were collected before the start of the infusion and then every 15 min thereafter, until the end of the procedure.
Propofol (2,6-diisopropylphenol) was provided by AstraZeneca (Mereside, UK). Thymol, used as an internal standard, was obtained from Riedel-deHaen (Sigma-Aldrich, Seelze, Germany). Cyclohexane, 2-propanol, trifluoroacetic acid (TFA) and tetramethylammonium hydroxide were supplied from Fluka (Buchs, Switzerland). HPLC-grade acetonitrile and methanol were supplied by VWR (Darmstadt, Germany).
An HPLC system Gold (Beckman, Palo Alto, California, USA) was equipped with a Shimadzu fluorescence detector RF-551 (λec=276 nm, λem = 310 nm). A Hypersil ODS column (100 × 4.0 mm; 3 μm) protected by guard column Hypersil ODS (4 × 4.0 mm; 5 μm; Agilent Technologies, Santa Clara, USA) was used. The mobile phase, as reported by Plummer , was a mixture of acetonitrile/bidistilled water/TFA (6: 4:0.01 = v:v:v). Flow rate was 0.4 ml min−1 and the total run lasted 8 min. Propofol and thymol solutions were prepared immediately prior to running. The drugs were diluted in methanol to appropriate working concentrations of 0.83 and 0.02 mg ml−1 for propofol and internal standard, respectively. Blood samples were collected in BD Vacutainer FX 5 mg /4 mg tubes and stored at 4°C until the analysis . Blood standards were prepared by spiking 1 ml of sample blood with 100 μl of internal standard solution and with 50 μl of each standard solution (0–8.2 μg/ml). A liquid extraction procedure was carried out according to Plummer . Linearity was assessed by adding known amounts of propofol to the blood samples in the final concentration ranges of 0–8.2 μg ml−1. Linear regression analysis was performed by plotting the area ratio of propofol/internal standard against the known concentration of the anaesthetic yielded: Y = 0.0977 (±0.0979) + 0.414 (±0.023) × (±SE), r = 0.995. Analytical recovery, tested in the same concentration ranges for linearity, was 97.2%.
The lowest level of detection of propofol in blood found with a S/N ratio of 3 was 25 ng ml−1. Within-day and between-day variations were determined by performing replicate (n = 3) analyses on blood samples spiked with propofol in concentrations used for the calibration curve. Coefficient of variation (%) values ranged from 0.9 to 6.8% and from 1.3 to 9.8% for within-day and between-day, respectively.
The predictive performance of TCI of propofol was evaluated by calculating the performance errors for each blood sample according to the methods described by Varvel et al.. Intrapatient bias (i.e. direction and size of deviation from predicted concentration) and inaccuracy (i.e. size of the typical miss) were assessed by determination of median performance error (MDPEi) and median absolute performance error (MDAPEi). Divergence, a measure of the expected systematic time-related changes in performance (that is, the tendency towards the narrowing or the widening over time of the gap between measured and calculated concentrations in a given patient) was calculated as the slope obtained from linear regression of that individual's |PE|ijs against time. Wobble, a measure of the total intraindividual variability in performance errors, which is directly related to the ability to achieve stable drug concentrations, was calculated as the median value of the absolute differences between the individual performance errors at each sampling time and the MDPE for that patient.
Based on our previous data (published and unpublished) and simulations in obese patients receiving propofol TCI with a weight adjustment, we considered a 50% reduction in the previously obtained MDPE of 33 ± 13% to be clinically important, so that a sample size of 12 patients per group was calculated to be adequate to detect a difference with an α error of 0.05 and a power of 0.8.
Statistical analysis was performed using SPSS (SPSS, Chicago, Illinois, USA) and Excel (Microsoft, Redmond, Washington, USA). Normality of distribution was assessed by means of the Kolmogorov–Smirnov test. A two-way analysis of variance for repeated measures extended by Sheffe's post-hoc test was used to analyse changes over time. Student's t-test was used to test the inequality of means between the two groups. Ordinal data were analysed using Fisher's exact test. A value of P less than 0.05 was considered significant.
Results are presented as means ± SD or percentage or median (25–75th percentile).
Seven men and 17 women aged 25–62 years were included in this study, 12 in each group. The groups were similar with regard to their characteristics as well as the sampling periods (Table 1). A total of 614 samples, 292 for the group adjusted and 322 for the group TBW, were analysed. Blood propofol concentrations ranged from 0.94 to 6.80 μg ml−1. The course of propofol plasma concentrations over time in each group is depicted in Fig. 1. Measured blood propofol concentrations were generally lower than those predicted in both groups. Regression analysis of predicted (Cp) vs. measured (Cm) blood concentration of propofol yielded the following results: Cm = 0.63Cp + 0.5, R2 = 0.24 for group adjusted and Cm = 0.56Cp + 0.8, R2 = 0.16 for group TBW.
For the group adjusted, performance errors were distributed within a range of −69.5 to 21.8% with a median value of –30.0%. For the group TBW, performance errors were distributed within a range of –64.6 to 175.0%, with a median value of −17.2% (Fig. 2). In Fig. 3, the performance errors are plotted against time. There were no significant differences between the groups with regard to MDPE, MDAPE, divergence and wobble of individual patients (Table 2). MDPE, a measure of the intrapatient bias (i.e. direction and size of deviation from the targeted concentration), ranged from −46.8 to −8.6% in the group adjusted, with a median value of −31.8% and an interquartile range of −35.9 to −19.4%, the negative values suggesting a significant overprediction (see also Fig. 1). In the group TBW, MDPE ranged from −54.6 to 10.5%, with a median value of −16.3% and an interquartile range of −26.3 to 2.2%. In Fig. 4, the patients with the best agreement between measured and predicted concentrations (i.e. lowest MDPE) and the patients with the worst agreement between measured and predicted concentrations (i.e. greatest MDPE) are depicted for both groups. MDAPEs, a measure of inaccuracy (i.e. size of the typical miss), were similar in the two groups. Group adjusted MDAPEs ranged from 15.0 to 46.8%, with a median value of 31.7% and an interquartile range of 20.2 to 35.9%; in group TBW, MDAPEs ranged from 3.3 to 54.6%, with a median value of 20.6% and an interquartile range of 14.8 to 26.9% (Table 2). Wobble (a measure of total intraindividual variability in performance errors) was similar in both groups, as well. In the group adjusted, wobble ranged from 2.5 to 10.3%, with a median value of 7.4% and an interquartile range of 3.8 to 8.4%; in the group TBW, wobble ranged from 3.3 to 13.2%, with a median value of 8.2% and an interquartile range of 7.0 to 9.6% (Table 2). Wobble can also be inferred from Fig. 5, in which the difference between performance errors and MDPEs for every patient of each group is plotted against time. Divergence values (i.e. time-related changes in performance errors) were also similar in both groups. In group adjusted, divergence ranged from −27.0 to 4.2% h−1, with a median value of −4.6% h−1 and an interquartile range of −8.0 to 0.0% h−1; in group TBW, divergence ranged from −39.6 to 18.0% h−1, with a median value of −4.5% h−1 and an interquartile range of −9.5 to 2.8% h−1. These values suggest that the overprediction decreased slightly with time for most patients in each group.
Over recent years, different pharmacokinetic models for propofol have been introduced and validated with regard to their ability to predict plasma drug concentrations. In particular, the predictive performance of the ‘Marsh’ pharmacokinetic parameter set  (which has been programmed into commercially available TCI systems) has been evaluated in different clinical settings [18–20]. However, its performance has not been adequately assessed in morbidly obese patients. As a result, even though the Marsh model includes a weight proportional parameter, applying a model derived from a sample of nonobese individuals to obese patients could lead to errors or inaccuracies . On the other hand, using a weight adjustment may lead to errors in the estimates of the central volume of distribution. Nevertheless, many authors suggest that there should be a weight adjustment [11,12]. In addition, even though, during a fixed infusion rate, plasma propofol concentration correlates well with TBW , it has been suggested that the induction dose should be calculated according to LBM rather than TBW in nonobese female patients . Bouillon and Shafer  showed that the difference between TBW and LBM increases as TBW increases. The same authors suggest that when uncertainty exists about the true relationship between anthropometric parameters and pharmacokinetics, especially with regard to obese patients, a reasonable approach would be to scale dose to IBW and some fraction of the difference between TBW and IBW in a nonlinear fashion. This approach resembles the weight adjustment formula presented in (Equation 1). We decided to test the effect of weight adjustment vs. no adjustment on predictive performance.
In the group adjusted, results are in agreement with our previous study , namely that significantly higher target plasma concentrations seem to be required to maintain adequate hypnosis than those required in nonobese patients. This is probably not due to different pharmacodynamics in morbidly obese patients, considering the fact that obese and nonobese patients have similar awakening plasma propofol concentrations [15,22]. On the contrary, the differences between predicted and measured concentrations required to obtain hypnosis are most likely due to the marked overprediction of the infusion algorithm (Fig. 1), whose MDPEs of −31.74 and −16.33% for the adjusted and TBW groups, respectively, did not differ statistically if a value of 0.05 for the α error was assumed in the analysis.
Median MDAPE values in the two groups did not differ significantly and these findings are in agreement with our previous study  as well as with the values obtained from nonobese individuals [18,20]. The inaccuracy observed when no weight adjustment is used (20.58%) is slightly lower than the inaccuracy observed in nonobese patients (29%) . Divergence values were not significantly different in our groups and were similar to those obtained by Swinhoe et al.. The negative divergence in the two groups suggests a progressive diminishing of the difference between predicted and measured concentrations over time. The more negative value obtained by Swinhoe et al. (−7.6%)  suggests that convergence of the measured and the predicted values is more pronounced for normal patients than for obese ones. Finally, the median wobble values for the two groups were similar, but much lower than those obtained by Swinhoe et al. (21.9%) , because propofol was titrated according to bispectral index. Wobble can also be inferred from Fig. 5, in which the difference between performance errors and MDPEs for each patient is plotted against time.
It has been suggested that the performance of a TCI system is clinically acceptable if the bias (MDPE) is no greater than 20%  and the inaccuracy (MDAPE) falls between 20 and 30% [23,24]. Considering these limits, the performance of propofol TCI using the weight adjustment formula for the ‘Marsh’ pharmacokinetic model is not acceptable and, therefore, no weight adjustment formula should be used to correct the input weight in TCI systems. This problem appears to be partially corrected when no weight adjustment is used. Even though in this case the difference is not statistically significant (but the P value is near its limit of significance), the predictive performance is acceptable according to Schuttler et al.. However, even though inaccuracies were found, adequate anaesthesia was obtained because BIS-guided administration of propofol was used. In this manner, it was possible to maintain a stable level of hypnosis regardless of the actual plasma propofol concentration.
The inability of the weight adjustment to improve errors is not surprising because in 1993 it had already been concluded that initial volume of distribution was not modified in obese patients, whereas total body clearance and the volume of distribution at steady state were correlated with TBW .
The choice to combine an opioid with propofol, although appropriate from a clinical point of view, could be considered a drawback of our study, as Mertens et al.  suggested an interdependence between the kinetics of alfentanil and propofol. This interrelationship is possibly due to the haemodynamic changes associated with the use of both drugs. The vasodilator and possible negative inotropic effects of propofol, in particular, could have a major influence on systemic arterial blood pressure, heart rate and thus cardiac output. These changes, in turn, could affect the delivery and redistribution of drugs to tissues. In this study, careful titration of remifentanil target concentrations to match patients' requirements and to maintain systemic arterial blood pressures within ±10% of baseline values may have prevented the shifts in cardiac output that are possibly the basis of the interdependence between the kinetics of alfentanil and propofol observed by Mertens et al. .
In conclusion, we compared the effect of a weight adjustment with no adjustment as weight input to the ‘Marsh’ pharmacokinetic parameter set for propofol TCI in morbidly obese patients and we showed that weight adjustment causes a clinically unacceptable bias with regard to performance errors. We cannot recommend a weight adjustment when using the ‘Marsh’ model for propofol. The poor performance is only partially corrected when TBW is used, but anaesthesiologists should be aware that generally an overestimation of real plasma concentration results in morbidly obese patients, and therefore, in our opinion, it is advisable to titrate predicted plasma propofol concentrations using an EEG monitor.
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