Compared with the administration of inhalational drugs, achieving the desired effect site concentration with intravenous drugs is more difficult. Sophisticated vaporizers allow inhalational drugs to be administered in precise concentrations. The partial pressure of inhalational drugs in the exhaled air can be measured easily and noninvasively, thereby enabling the anesthesiologist to examine the effect of changes in flow rate or administered drug concentration on the end-tidal partial pressure. In contrast, intravenous drugs are generally delivered on a dose per kilogram of body weight basis by manually controlled infusion pumps, and online measurement of blood drug concentrations of intravenous drugs is not possible. In recent years, computercontrolled infusion devices have been developed to increase the controllability of intravenous drug administration. These devices enable the clinician to continuously control the drug concentration in the blood, and to administer intravenous anesthetics according to their pharmacokinetic profile without performing the mental gymnastics required to calculate the compartmental drug concentrations on the basis of polyexponential functions. Instead of measuring the blood drug concentration, the computer-controlled infusion device predicts the blood-drug concentration, thereby allowing the anesthesiologist to dose intravenous drugs to a target blood drug concentration instead of on the basis of dose per kilogram of body weight.
Computer-controlled infusion pumps can only be used optimally when three elements have been carefully worked out. First, the model that controls the pump has to work accurately. This can be tested as described recently . Second, the pharmacokinetic parameter set provided to the computer model should match the pharmacokinetics of the patient. If this requirement is met, then the predicted blood-drug concentration will approximate the concentration that is actually achieved in the blood of the patient. Third, the pharmacodynamics of the administered drug should be well defined to enable the clinician to attain the blood concentration needed for the required effect.
With respect to the second issue, the pharmacokinetic parameter set from the literature that corresponds closest to the pharmacokinetics of the drug in the patient can be determined in several ways. First, a pharmacokinetic parameter set can be used that has been determined in a population with patient characteristics that are comparable to those of the patient who is to receive the drug. Second, a population-based pharmacokinetic parameter set can be used that allows adjustment of the pharmacokinetic data to the characteristics of individual patients. Although a population-based pharmacokinetic parameter set has been described for alfentanil , this type of parameter set is not available for other commonly used intravenous anesthetics. Third, a pharmacokinetic parameter set can be determined on the basis of computer simulations. Predicted (simulated) concentrations on the basis of various pharmacokinetic parameter sets then can be compared with the actually measured blood drug concentrations. Subsequently, one then can define the pharmacokinetic parameter set that enables the computer-controlled infusion device to predict the blood drug concentration most precisely in the patients involved.
In this study, we retrospectively examined the performance of a computer-controlled infusion device when provided with five different pharmacokinetic parameter sets of propofol.
The measured and predicted blood propofol concentrations of 19 patients who had received a computercontrolled infusion of propofol during two previous studies of the pharmacodynamics of propofol were used to evaluate the predictive accuracy of the computer-controlled infusion of propofol.
Nine ASA physical status I female patients, aged 20-50 yr, had participated in a study on the pharmacodynamics of propofol during the induction of anesthesia  (Group A), the other 10 ASA physical status I female patients, aged 20-50 yr, had participated in a study on the intraoperative pharmacodynamics of propofol  (Group B). Patients from Groups A and B had received a computer-controlled infusion of propofol using an Atari Portfolio pocket computer that was provided with three-compartment pharmacokinetic data of propofol reported previously by Gepts et al.  and that controlled an Ohmeda 9000 infusion pump. (Ohmeda, Madison, WI). Blood samples were collected at regular intervals (see below) from a radial artery. The infusion schemes and the measured blood propofol concentrations of the patients of Groups A and B were used in computer simulations to define the most appropriate pharmacokinetic parameter set of propofol for the infusion of this drug in this patient population.
The patients from Group A received a stepwise increasing target propofol concentration . The initial target blood propofol concentration was 1 micro gram/mL. The target propofol concentration was increased every 12 min by 1 micro gram/mL until patients lost consciousness. Every 3 min an arterial blood sample was taken to determine the whole blood propofol concentration. In this way, a total of 12-16 blood samples were collected from each patient over a period of 36-48 min. When patients lost consciousness, the trachea was intubated and the study terminated. Throughout the study these patients were breathing 30% oxygen in air via a face mask. The electrocardiogram, arterial blood pressure, heart rate, end-tidal CO2 concentration, and oxyhemoglobin saturation (SpO2; Nellcor N-200; Nellcor Inc., Hayward, CA) were monitored continuously.
The patients from Group B received a constant target blood propofol concentration during lower abdominal surgery , in addition to a variable computer-controlled infusion of alfentanil based on three-compartment population pharmacokinetic parameters from Maitre et al. . Anesthesia was induced in these patients by computer-controlled infusion of propofol and alfentanil with target concentrations of 3 micro gram/mL of propofol and 100 ng/mL of alfentanil, respectively. During the procedure the lungs of the patients were ventilated with 30% oxygen in air to an end-tidal CO2 concentration of 4-5 vol%. Pancuronium was given for muscle relaxation. The target alfentanil concentration was varied intraoperatively according to the presence or absence of responses to intraoperative surgical stimulation, whereas the target propofol concentration was maintained constant at 3 micro gram/mL. Every 20 min an arterial blood sample was taken for determination of whole blood propofol concentrations. In this way, a total of 8-14 arterial blood samples were collected from each patient over a period of 101-344 min. The infusion of propofol and alfentanil and collection of blood samples were discontinued approximately 10 min before skin closure. In both groups, the computer model checked and adjusted the infusion rate every 5 s. Every minute the infusion rate versus time data were stored onto a 128 kB computer disk, except when the infusion rate was rapidly changing during an increase or decrease in the target concentration when data were stored every 5 s. The infusion rate versus time data of each patient were entered off-line into a computer simulation program that recalculated the predicted propofol concentrations when provided with one of four other pharmacokinetic parameter sets of propofol [6-9]. For each measured blood propofol concentration, five predicted propofol concentrations corresponding to five different pharmacokinetic parameter sets were thus obtained, and the performance of each parameter set was then determined.
Arterial blood samples, for determining the blood propofol concentration in the patients, were collected in syringes and immediately transferred into test tubes containing potassium oxalate. Blood propofol concentrations were determined by reversed-phase highperformance liquid chromatography . The coefficient of variation of the high-performance liquid chromatography method did not exceed 7% in the concentration range encountered in this study.
The patient characteristics were compared between the two groups using a two-sample t-test. In accordance with Varvel et al. , the performance of the computer-controlled infusion system implemented with the five different pharmacokinetic parameter sets was characterized on the basis of four parameters; the bias, the inaccuracy, the divergence, and the wobble. First, for each blood sample, the performance error (PE) was calculated as: Equation 1 where Cm and Cp are the measured and predicted blood propofol concentrations. Subsequently, with a pooled data approach for Groups A and B separately, the bias and inaccuracy associated with each pharmacokinetic parameter set were assessed by determining the median PE (MDPE), and the median absolute PE, and the corresponding 95% confidence intervals. When the 95% confidence interval of the MDPE included zero, it was concluded that there was no significant bias. The MDPE and median absolute PE associated with the five propofol pharmacokinetic parameter sets were compared with a multisample median test, followed by a Tukey-type multiple sample comparison test . Furthermore, for each of the five different pharmacokinetic parameter sets, the stability of the performance over time was characterized by the divergence (the change in the absolute PE per 60 min of computer-controlled infusion) and the variability in the PE by the wobble (the median absolute deviation of the performance error from the median performance error), both for Groups A and B separately.
Data are presented as mean +/- SD, median and range, or percentage, unless stated otherwise. P < 0.05 was considered as the minimum level of statistical significance.
The mean age and weight of the patients were similar in Group A (36 +/- 8 yr; 63 +/- 10 kg) and Group B (39 +/- 7 yr; 65 +/- 9 kg). The mean duration of the infusion in the patients from Group A (43 +/- 5 min) was significantly shorter (P < 0.05) compared with that in the patients of Group B (182 +/- 83 min).
(Table 1) presents the central compartment and the intercompartmental rate constants from the pharmacokinetic parameter sets that were studied. Figure 1 shows the blood propofol concentrations measured in a representative patient from Group A, as well as the propofol concentrations predicted by the computer simulation program on the basis of the five different pharmacokinetic parameter sets. In this patient, the pharmacokinetic parameter sets of Shafer et al. , Cockshott et al. , and Tackley et al.  resulted in an equally moderate underprediction of the measured blood propofol concentrations compared to the initially used set by Gepts et al. , whereas the pharmacokinetic parameter set by Kirkpatrick et al.  resulted in a significantly greater underprediction. The measured propofol concentrations exceeded the predicted not only in this particular patient but in all patients in Group A, with all five pharmacokinetic parameter sets Figure 2, Table 2. The bias and inaccuracy associated with the pharmacokinetic parameter set described by Kirkpatrick et al.  were greater than those associated with all other parameter sets (P < 0.001, Table 2). The bias and inaccuracy associated with the pharmacokinetic parameter set described by Shafer et al. , Cockshott et al. , and Tackley et al.  were not different from those with the initially used pharmacokinetic parameter set by Gepts et al. . The bias, inaccuracy, and the wobble in the patients in Group A were similar to those of the patients in Group B for the corresponding pharmacokinetic parameter sets Figure 3, Table 2. For all five pharmacokinetic parameter sets, however, the divergence (median and range) was significantly greater in the patients in Group A (42%; range, 31%-59%), who received a stepwise increasing target concentration, compared to those in the patients in Group B (1%; range, -18%-4%), P < 0.05), who received a single constant target concentration. From this we conclude that the measured-predicted concentration difference does not increase with time but with increasing propofol concentration. Figure 4 shows the relation between the measured blood propofol concentration and the PE as simulated on the basis of three of the five pharmacokinetic parameter sets in the patients of Group A.
Computer-controlled infusion devices are increasingly used in anesthetic practice to optimize the efficacy of intravenous drug administration. The accuracy of the prediction of the blood drug concentration by the computer partially determines the applicability of these systems in clinical practice.
With respect to the accuracy of the prediction of the blood drug concentration by computer-controlled infusion devices, two issues arise. First, the computer might show a continuous absolute over- or underprediction of the actual blood drug concentration in a population as a whole (e.g., ASA physical status I female patients). This mismatch between the selected pharmacokinetic parameter set provided to the computer and the actual pharmacokinetics of the drug in the patients might be caused by differences in the age, weight, and/or gender of the patients, all factors that have been shown to affect the pharmacokinetics of propofol [7,8,12,13]. Second, within a specific patient population, there may be considerable interpatient differences in the accuracy of the prediction by the computer, due to the interindividual variability in pharmacokinetics. Pharmacogenetic determinants of drug metabolism might be partially responsible for this distinct, interindividual variability in pharmacokinetics . For alfentanil, a population-based pharmacokinetic parameter set  is available by which, for each patient, the pharmacokinetic parameter set can be adjusted to the individual's age, weight, and gender. However, when this parameter set was applied in a computer-controlled infusion technique, the accuracy of the prediction by the computer did not improve compared to when a previously described alfentanil pharmacokinetic parameter set was used . For propofol, a population-based pharmacokinetic parameter set has not yet been described.
To enable us to administer propofol by computercontrolled infusion with an acceptable bias and inaccuracy, we selected and tested the most appropriate of the available pharmacokinetic parameter sets for application in computer-controlled infusion devices in a specific patient population.
The computer simulations revealed that the performance of the computer-controlled infusion device was similar when provided with the pharmacokinetic parameter sets described by Gepts et al. , Shafer et al. , Cockshott et al. , and Tackley et al. . The pharmacokinetic parameter set that resulted in the worst prediction of the measured blood propofol concentrations was that of Kirkpatrick et al. . Although this parameter set was determined in a patient population not very dissimilar to the patients participating in our study, and although data were obtained up to 24 h, this pharmacokinetic parameter set was derived from patients who had received a bolus dose of propofol (2.5 mg/kg), in contrast to a short infusion as in the other studies Table 3. It is conceivable that the pharmacokinetics of drugs that affect the cardiovascular system may differ if these are given as a large bolus injection instead of by infusion. Indeed, an intravenous bolus dose of propofol of 2.5 mg/kg, affects the hemodynamic function considerably. The negative inotropic effects of propofol and the reduction in peripheral vascular resistance [16-21] may seriously change the distribution and elimination of propofol in and from the body.
Initially, we implemented the pharmacokinetic parameter set of Gepts et al. , because this parameter set was determined in patients with ages and weights comparable to those of the patients we studied, and because the pharmacokinetic parameters were determined on the basis of an infusion regimen of propofol and of arterial blood samples, just as we did. Despite the similarities between the patients in our study, and those in which the pharmacokinetic parameter set of Gepts et al.  was determined, the measured blood propofol concentrations in our patients exceeded the concentrations predicted, indicating that the pharmacokinetics in our patients differed from those studied by Gepts et al. . This discrepancy might be explained by the fact that, in contrast to our patients, the majority of patients studied by Gepts et al.  underwent surgery during spinal anesthesia Table 3. Spinal anesthesia reduces peripheral vascular resistance and might therefore result in an overestimation of the volume of the central compartment. Using such a pharmacokinetic parameter set for the computercontrolled infusion of propofol in patients in the absence of spinal anesthesia might thus result in unexpected high blood propofol concentrations.
The computer simulations revealed that on the basis of the three other pharmacokinetic parameter sets [Shafer et al. , Cockshott et al. , and Tackley et al. ] the measured propofol concentrations exceeded the predicted concentrations by approximately 25%. Apart from the pharmacokinetic parameter set by Gepts et al. , the other pharmacokinetic parameter sets were determined on the basis of venous blood propofol concentrations. During and shortly after the administration of propofol the measured arterial propofol concentrations have been shown to exceed the venous propofol concentrations considerably . Due to this phenomenon, the measured arterial propofol concentrations will exceed the predicted concentrations in patients who receive a computer-controlled infusion of propofol that has been provided with a pharmacokinetic parameter set based on venous blood samples, even when the pharmacokinetics of these patients perfectly match the pharmacokinetics provided to the computercontrolled infusion pump. The arterial-venous concentration difference decreases rapidly after termination of the infusion. The PE will therefore probably decrease correspondingly after termination of the infusion.
Finally, this study showed that the bias and inaccuracy remained fairly constant with time with the four pharmacokinetic parameter sets [5,6,8,9] that resulted in a clinically acceptable bias, when the target concentration was maintained constant (median divergence of 1% per 60 min in the patients in Group B), whereas the bias and inaccuracy increased considerably when the target concentration was increased (median divergence of 42% per 60 min in the patients of Group A). Crankshaw et al.  recently observed a similar increase in the measured-predicted propofol concentration difference with increasing target propofol concentration. The decrease in performance of the computer-controlled infusion of propofol with increasing target propofol concentration might be explained by two factors. During the analysis of the distribution and elimination of propofol in and from the body, one generally assumes that propofol mixes instantaneously in the blood compartment, and that the distribution and elimination of propofol behaves linear over a wide concentration range. However, this may not be the case. The fact that there is a considerable difference between arterial and venous concentrations during propofol administration  indicates that instantaneous mixing does not occur. Furthermore, the higher the infusion rate of propofol, the more the concentration of propofol will differ between different sites within the blood compartment. Therefore, it might well be that at higher target propofol concentrations, accomplished with higher infusion rates, propofol is not mixed entirely, resulting in unexpectedly high propofol concentrations at the arterial sampling site. In addition to this, increasing propofol concentrations increasingly affect the hemodynamic function of the patient. Propofol has been shown to reduce cardiac output and hepatic blood flow. For a drug with a high hepatic extraction ratio, as propofol, this might result in a decreased clearance at higher concentrations. This also may contribute to the observed increase in the measured-predicted concentration difference with increasing target propofol concentration. Consequently, during the clinical application of computer-controlled infusion of propofol, with higher propofol concentrations, the magnitude of proportional changes in the target concentration should be reduced to avoid unexpected high blood propofol concentrations that may lead to hemodynamic instability.
In conclusion, we determined the performance of a computer-controlled infusion device when provided with five different pharmacokinetic parameter sets. The pharmacokinetic parameter sets by Gepts et al. , Shafer et al. , Cockshott et al. , and Tackley et al.  result in an equally clinically acceptable, although not optimal, performance, whereas the pharmacokinetic parameter set by Kirkpatrick et al.  is less suitable for application in computer-controlled infusion techniques. With all pharmacokinetic parameter sets, the measured propofol concentrations exceed the predicted concentrations. This measuredpredicted propofol concentration difference increases with increasing target propofol concentration.
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