https://orcid.org/0000-0002-9184-4190
Abstract
Target controlled infusion (TCI) systems use population-based pharmacokinetic (PK) models that do not take into account inter-individual residual variation. This study compares the bias and inaccuracy of a population-based vs a personalized TCI propofol titration using Bayesian adaptation. Haemodynamic and hypnotic stability, and the prediction probability of alternative PK models, was studied.
. A double-blinded, prospective randomized controlled trial of 120 subjects undergoing cardiac surgery was conducted. Blood samples were obtained at 10, 35, 50, 65, 75 and 120 min and analysed using a point-of-care propofol blood analyser. Bayesian adaptation of the PK model was applied at 60 min in the intervention group. Median (Absolute) Performance Error (Md(A)PE) was used to evaluate the difference between bias and inaccuracy of the models. Haemodynamic (mean arterial pressure [MAP], heart rate) and hypnotic (bispectral index [BIS]) stability was studied. The predictive performance of four alternative propofol PK models was studied.
. MdPE and MdAPE did not differ between groups during the pre-adjustment period (control group: 6.3% and 16%; intervention group: 5.4% and 18%). MdPE differed in the post-adjustment period (12% vs. −0.3%), but MdAPE did not (18% vs. 15%). No difference in heart rate, MAP or BIS was found. Compared with the other models, the Eleveld propofol PK model (patients) showed the best prediction performance.
. When an accurate population-based PK model was used for propofol TCI, Bayesian adaption of the model improved bias but not precision.
Dutch Trial Registry NTR4518.
Editor’s key points
Target-controlled infusion (TCI) systems rely on population-based pharmacokinetic models that do not adjust for individual variation.
Point-of-care measurement of blood propofol concentrations was used to compare population-based vs individualized propofol titration in a prospective clinical study of cardiac surgery patients.
Personalized propofol titration did not improve accuracy of propofol TCI in this population.
All current TCI systems use population-typical values for drug distribution and clearance as the basis for further estimation in the individual patient. While this approach of using population estimates to steer drug infusions in an individual can achieve clinically acceptable anaesthetic conditions, it does retain a source of error because it does not adjust for inter-individual variability. Individuals do not exactly match calculated population typical individuals because of non-modelled residual biological variability, even if covariates such as age, sex, weight and height are included in the typical values for drug distribution and clearance.1,10,11 Sources of intra-individual variability, such as chronopharmacokinetics, are not included in current propofol PK models.12
A fully patient-specific pharmacokinetic model has the potential to achieve a more precisely controlled time course of plasma concentration, but this approach suffers from practical drawbacks, mostly the lack of sufficient samples in a wide range of plasma concentrations for the individual. Bayesian forecasting provides a compromise by tailoring the starting (population) model to a more patient-individualized model on the basis of measured blood samples.13 Individualizing pharmacokinetic models using intermittent or continuous drug concentration measurements in a Bayesian approach has been demonstrated successfully in an off-line setting.14,15 This approach has seldom been applied in clinical practice for propofol administration because a method of fast, bedside measurement of propofol concentration has not been available. Recently, point-of-care analysis of propofol has become available (Pelorus 1500, Sphere Medical, Cambridge, UK) enabling the clinician to obtain accurate propofol blood concentration information at the bedside in less than five min.16
The question remains if individualization of the propofol model during TCI results in a significantly better prediction of subsequent propofol plasma concentrations. In this study, our primary aim was to compare the bias and precision of classical population-based TCI propofol vs personalized TCI propofol administration. We used a Bayesian approach for adjustment and individualization of the propofol pharmacokinetic model using bedside measured propofol concentrations. Secondly, we compared hypnotic and haemodynamic stability before and after the adaptation as measured by processed electroencephalography and other vital signs registered during routine clinical monitoring. Additionally, we investigated the accuracy of the applied propofol pharmacokinetic model published by Eleveld and colleagues vs previously published models.7
Methods
Study management and registration
This trial was conducted at the Department of Anaesthesiology at the University Medical Center Groningen, University of Groningen, The Netherlands, in accordance with the Declaration of Helsinki, and in compliance with Good Clinical Practice and applicable regulatory requirements. Ethics committee approval was obtained (UMCG Ethics’ Committee, Groningen, The Netherlands, METc 2013/374) and the study was registered in a public registry (Dutch Trial Register, NTR4518) before the start of the study. All patients provided written informed consent before participation.
Subjects
Patients between 18 and 75 yrs of age, with a BMI between 18 and 35 kg m−2, ASA Physical Status Classification of I-III, undergoing elective off-pump coronary artery bypass surgery and receiving propofol per standard clinical practice were eligible for this study. Subjects were excluded in case of neurological disease (dementia, cerebral stroke, seizures), psychiatric diseases, regular intake of benzodiazepines, antidepressants, antipsychotics or anticonvulsants, regular intake of opioids, hepatic disease (Child B or higher), pregnancy or currently nursing, overt signs of alcohol abuse, contra-indications or allergies to the drugs used in the study or expected blood loss during surgery of > 2000 ml.
Study execution
This study was designed as a double-blinded, prospective, randomized controlled trial. As a result of the specific screen design of the computer software used, the anaesthetist responsible for the clinical care of the patient could be blinded to the arm in which the subject was enrolled during the whole operation. Subjects were randomized to one of the two study groups using the sealed envelope technique (60 intervention vs 60 control group).
All subjects in both groups received standard clinical anaesthesia care and monitoring. On arrival in the operating room, a peripheral i.v. line was inserted in the subject’s non-dominant hand or forearm to deliver the required drugs and fluids. Routine vital signs monitors consisting of 5-lead electrocardiography (ECG), pulse oximetry, non-invasive blood pressure (IntelliVue MX800, Philips, Eindhoven, The Netherlands) and frontal bispectral index (BIS, Covidien, Dublin, Ireland) were connected. Before induction of anaesthesia, a catheter was placed under topical anaesthesia in the radial artery of the non-dominant hand and connected to a pressure transducer to measure continuous arterial blood pressure and to draw blood samples.
Anaesthesia was induced with a bolus dose of sufentanil and propofol TCI as part of routine clinical care. The initial plasma target concentration was set by clinician discretion and TCI was started. At loss of consciousness, rocuronium was administered to facilitate tracheal intubation. Anaesthesia was maintained with sufentanil and propofol TCI. Specific propofol target concentrations were selected to ensure haemodynamic stability and hypnosis (BIS values between 40 and 60). Additional drugs and therapy to ensure homeostasis during anaesthesia were allowed as part of routine anaesthetic practice. All subjects received a central venous catheter for additional fluid and drug administration and for measuring central venous pressure.
Sufentanil was also used during maintenance of anaesthesia. Propofol was administered via a validated PC-based TCI system (RUGLOOP II, Demed, Temse, Belgium) connected to an infusion pump (Carefusion GH, Basingstoke, UK). In order to calculate the time course of propofol infusion to reach and maintain a target plasma concentration, the pharmacokinetic model published by Eleveld and colleagues7 was used. We applied the patient model, not the volunteer model. For sufentanil, the model of Gepts and colleagues17 was used.
Propofol blood concentrations were obtained from arterial blood samples drawn at baseline before the start of drug administration and at 10, 35 and 50 min after the start of propofol infusion. These measured propofol blood concentrations were entered into a computer program and for the intervention group a Bayesian adjustment algorithm to individualise the predicted volumes of distribution and clearances in the propofol pharmacokinetic model for the individual being studied. After 60 min of propofol infusion, the individualized pharmacokinetic model was used for further propofol concentration predictions and TCI infusion rate calculations. Details of the algorithm can be found in the technical Supplementary Appendix. In the control group, no model adjustment was performed and the population typical parameters were used for TCI throughout the procedure. We hypothesized that the error between predicted and measured propofol concentrations would be smaller after model adjustment in the intervention group compared with the error in the control group. To evaluate this, propofol blood concentration was determined from arterial blood samples drawn at five and 15 min after adjustment of the pharmacokinetic model parameters, followed by an additional sample every 60 min until the end of the infusion in both groups. One last sample was obtained at the end of infusion. In the control group, blood samples were measured at identical times, and were also entered into the computer programme, similarly to the intervention group, but without execution of the Bayesian adjustment algorithm. As a result, subjects in the control group received propofol during the entire case using an unadjusted TCI pharmacokinetic model. We refer to the first h of drug infusion before the moment of adaptation as the “pre-adjustment period” and the remaining part of the case after adaptation as the “post-adjustment period”. For clarity, during comparisons between groups we also refer to the time period after 60 min of drug infusion in the control group as “post-adjustment period” even though no adjustment of the propofol pharmacokinetic parameters was done in this group.
Blood samples were handled by an investigator not involved in the clinical management of the subject. The results of propofol concentration measurements were not made available to the clinician responsible for clinical care and were only known by the independent investigator operating the computer system. In contrast, the predicted plasma concentrations were available to the clinician (on the Rugloop II software screen) at all times in both groups. As clinicians were blinded to group allocation they did not know if subjects’ pharmacokinetics were adjusted or not. In order to maintain blinding in the post-adaption situation, the clinician only had access to the propofol concentrations estimated by the population model, whereas the researcher was aware of the new Cp values. After adaptation the clinician could ask the researcher for an incremental change in the target Cp (e.g. “increase Cp by 0.5” or “decrease Cp by 0.2” etc). The researcher applied the changes to the target Cp without informing the clinician of the calculated Cp of the adapted model.
The propofol concentration in all samples was measured on site using the Pelorus 1500 analyser (Sphere Medical, Cambridge, UK). This small tabletop device is capable of analysing propofol blood concentrations within five min (linearity up to 12 μg ml−1 (R2=0,9993), lower limit of 0.25 μg ml−1. Device imprecision in control solutions: 0.11 μg ml−1 at 5.32 μg ml−1 and 0.17 μg ml−1 at 10.3 μg ml−1; within run precision 0.04 μg ml−1 at 2.84 μg ml−1 and 0.08 μg ml−1 at 6.68 μg ml−1; overall bias 0.15 μg ml−1 (95% conference interval −0.11–0.51 μg ml−1)) using visible absorption spectrometry, as described.16,18
Sample size calculation
The required sample size was determined by Monte-Carlo simulations of the experimental design. Post hoc estimated “true” individual pharmacokinetic models were taken from previously published propofol population pharmacokinetics.7 It was assumed that the studied population of cardiac patients had a 15% lower clearance because of reduced cardiac output and liver blood flow. We simulated 10000 experiment replicates and found that with a sample size of 50 subjects per group 82.5% of replicates were successful (P<0.05) in detecting improved predictive performance (lower MdAPE, defined in the next section) in the intervention group in the post-adjustment phase compared with the control group. Taking into account the possibility for blood sample and technical problems and a risk of shorter than expected surgical procedures, we included 60 subjects in each group.
Data analysis and applied statistics
Recorded heart rate and mean arterial pressure (MAP) were filtered with a combination of manual (four samples from one individual) and automatic artefact detection (>30% change within one min treated as missing). To study inter-group differences in time-course of predicted propofol plasma concentrations, BIS, heart rate, and MAP, the difference between the mean values is plotted vs time, as published previously.19 The closer the differences between means are to zero, the less difference exists between groups at that specific time. Significance is reached between groups at that specific time when zero is not included in the 95% confidence interval area. Between groups, continuous data were analysed using the independent samples Student’s t-test or Mann-Whitney U-test, where appropriate. Significance was set as P<0.05 unless otherwise stated.
For these measures, the median values are reported, being the MdPE which indicates bias and the median APE (MdAPE) which indicates precision. These measures were compared between the control and intervention groups using a Mann-Whitney U-test (two-sided). Results were considered significant for P<0.01.
For comparison of predictive performance of models from the literature we also evaluated Divergence and Wobble.20 For Divergence we calculated the linear regression slope of APE with time for all individuals and report the population median value in %/h. For Wobble we calculated the median absolute deviation of PE from MdPE in the individual and we report the population median.
Post-hoc simulations of the predictive performance of other pharmacokinetic models
Infused amounts of propofol were continuously recorded and logged by the RUGLOOPII system. This enables a post-hoc simulation to test the predictive performance of other models from the literature vs the observed concentrations. We considered the pharmacokinetic models published by Marsh and colleagues,4 Schnider and colleagues,5,6 and Cortinez and colleagues21 in addition to the applied model for patients and volunteers published by Eleveld and colleagues.7
Each model was applied to the entire dataset with no Bayesian adjustment to generate the predicted propofol plasma concentrations to compare with observed concentrations.
Results
A total of 120 subjects were included in the data analysis as required to obtain sufficient power (Fig. 1). The ethics’ committee agreed that excluded patients could be replaced by adding individuals to the randomization list.
CONSORT flowchart of screened, considered, included and excluded patients. CNS, Central Nervous Systems; HLM, Heart Lung Machine.
The distribution of subject characteristics was similar between groups (Table 1). In total, 870 propofol plasma concentration observations were obtained from 120 individuals. Figure 2 shows the targeted, predicted and measured propofol plasma concentrations in the control and intervention groups. The absolute mean difference plots that the time course of these concentrations was similar between groups for both targeted and actual predicted propofol plasma concentrations in the pre-adjustment period. As expected, a drift in the absolute mean difference in target and predicted propofol plasma concentration was observed at the end of the case between groups.
Subject characteristics from data analyzed. Data are presented as median (standard deviation, sd) and ranges as [min, max]
| Group | N= | Age (yr) | Weight (kg) | Height (cm) | BMI | Sex (male/female) |
|---|---|---|---|---|---|---|
| Control | 60 | 62.0 (7.4) | 91.5 (13.8) | 178 (9) | 27.6 (3.1) | 54/6 |
| [44, 75] | [46, 114] | [152,197] | [19.9,35.0] | |||
| Intervention | 60 | 62.5 (7.5) | 81.5 (12.7) | 178 (8) | 26.3 (3.1) | 56/4 |
| [44, 75] | [57,111] | [156,192] | [20.7,34.0] | |||
| Mann-Whitney U-test P-value | 0.827 | 0.184 | 0.721 | 0.157 | 0.490 |
| Group | N= | Age (yr) | Weight (kg) | Height (cm) | BMI | Sex (male/female) |
|---|---|---|---|---|---|---|
| Control | 60 | 62.0 (7.4) | 91.5 (13.8) | 178 (9) | 27.6 (3.1) | 54/6 |
| [44, 75] | [46, 114] | [152,197] | [19.9,35.0] | |||
| Intervention | 60 | 62.5 (7.5) | 81.5 (12.7) | 178 (8) | 26.3 (3.1) | 56/4 |
| [44, 75] | [57,111] | [156,192] | [20.7,34.0] | |||
| Mann-Whitney U-test P-value | 0.827 | 0.184 | 0.721 | 0.157 | 0.490 |
Subject characteristics from data analyzed. Data are presented as median (standard deviation, sd) and ranges as [min, max]
| Group | N= | Age (yr) | Weight (kg) | Height (cm) | BMI | Sex (male/female) |
|---|---|---|---|---|---|---|
| Control | 60 | 62.0 (7.4) | 91.5 (13.8) | 178 (9) | 27.6 (3.1) | 54/6 |
| [44, 75] | [46, 114] | [152,197] | [19.9,35.0] | |||
| Intervention | 60 | 62.5 (7.5) | 81.5 (12.7) | 178 (8) | 26.3 (3.1) | 56/4 |
| [44, 75] | [57,111] | [156,192] | [20.7,34.0] | |||
| Mann-Whitney U-test P-value | 0.827 | 0.184 | 0.721 | 0.157 | 0.490 |
| Group | N= | Age (yr) | Weight (kg) | Height (cm) | BMI | Sex (male/female) |
|---|---|---|---|---|---|---|
| Control | 60 | 62.0 (7.4) | 91.5 (13.8) | 178 (9) | 27.6 (3.1) | 54/6 |
| [44, 75] | [46, 114] | [152,197] | [19.9,35.0] | |||
| Intervention | 60 | 62.5 (7.5) | 81.5 (12.7) | 178 (8) | 26.3 (3.1) | 56/4 |
| [44, 75] | [57,111] | [156,192] | [20.7,34.0] | |||
| Mann-Whitney U-test P-value | 0.827 | 0.184 | 0.721 | 0.157 | 0.490 |
Targeted, predicted and measured propofol concentrations (Cp=Plasma concentration) for the control (A, B, and C) and intervention (D, E, and F) groups. Red lines denote the pre-adjustment phase and blue lines the post-adjustment phase. Vertical grey lines indicate the moment of PK model adjustment (intervention group). Panel G and H shows the difference between the mean values (and confidence intervals) between groups vs time for targeted and predicted propofol concentrations, respectively. Abs. Mn diff. Cp target, Absolute Mean different plasma concentration target.
Figure 3 depicts the individualization of the individual pharmacokinetic parameters (volumes of distribution and clearances) pre- and post-adaptation in the intervention group. In general, model parameters Q3 and V1 showed the greatest differences between the pre- and post-adaptation phases. This is likely as a result of limitations of the pre-adaptation sampling schedule (it cannot be too long) and that Q3 was unconstrained for adaptation.
Changes in the individual volumes of distribution (V) and clearances (Cl) pre- and postadaption in the intervention group.
The ratio of measured to predicted propofol concentrations and the predictive performance of the TCI systems for the control and intervention groups are plotted in Figure 4. The groups do not differ significantly in the pre-adjustment phase (MdPE of 6.3% vs 5.4% and MdAPE of 16% vs 18% for the control and intervention groups, respectively), but bias (MdPE) in the post-adjustment phase was lower in the intervention group compared with the control group (-0.3% vs 12%) and overall (1.4% vs 11%). Thus, the intervention group is better balanced with respect to over- or under-prediction than the control group. Accuracy (MdAPE) did not differ between control and intervention groups, and thus neither group was better with respect to how closely the target was achieved.
The ratio of measured to predicted propofol concentration for the control and intervention groups. Vertical grey lines indicate the moment of PK model adjustment (intervention group) or observations later than 60 min (Control group). Red lines denote the pre-adjustment phase and blue lines the post-adjustment phase. The * defines P<0,05. MdPE, Mean different Prediction Error; MdAPE, Mean different Absolute Prediction Error.
No differences were found in depth of anaesthesia level as measured by BIS (except for a short-lasting difference at the induction) or haemodynamic stability (heart rate and MAP) between groups (Fig. 5).
Time course of heart rate and mean arterial blood pressure (INV MAP) and BIS for the control (A, B and C) and intervention (D, E and F) groups. Red lines denote the pre-adjustment phase and blue lines the post-adjustment phase. Vertical grey lines indicate the moment of PK model adjustment (intervention group). Panels G, H and I shows the difference between the mean values (and confidence intervals) between groups. Beats min−1, beat per min; INV MAP, Invasive Mean Arterial Pressure in mm Hg (obtained from an arterial line); Abs. Mn. Diff. Heart Rate/INV MAP/Bispectral Index, Absolute Mean different Heart Rate/Invasive Mean Arterial Pressure/Bispectral Index.
Table 2 depicts the predictive performance of other published propofol pharmacokinetic models when simulating the predicted plasma concentrations using recorded drug infusion rates and comparing these with measured propofol plasma concentrations for each subject. Compared with the Eleveld model for patients, worse performance was observed for the Eleveld model derived from volunteers and the Schnider model, and very poor performance was found for the Marsh and Cortinez models.
Predictive performance of propofol pharmacokinetic models from the literature. Maximum and minimum values are represented as [min, max]. MdPE, Median Prediction Error; MdAPE, Median Absolute Prediction Error
| MdPE (%) | MdAPE (%) | Divergence (%/h) | Wobble (%) | |
|---|---|---|---|---|
| Eleveld (patients)7 | 9.0[−74.8,255] | 17.3[0.0,255] | 0.8[−36.1, 43.2] | 9.8[2.8, 31.7] |
| Eleveld (volunteers)7 | 44.1[−68.6, 363] | 44.6[0.15, 363] | 2.9[−36.5, 59.6] | 13.8[1.9, 40.4] |
| Marsh4 | 85.0[−55.2, 523] | 85.0[0.4, 523] | −0.2[−84.9, 61.9] | 17.6[4.2, 54.4] |
| Schnider5 | 27.9[−73.5, 299] | 30.5[0.1, 299] | 4.6[−33.0, 60.9] | 12.0[1.7, 39.9] |
| Cortinez8 | 46.7[−68.0, 360] | 47.9[0.0, 360] | 6.2[−36.8, 70.0] | 13.8[0.5, 47.4] |
| MdPE (%) | MdAPE (%) | Divergence (%/h) | Wobble (%) | |
|---|---|---|---|---|
| Eleveld (patients)7 | 9.0[−74.8,255] | 17.3[0.0,255] | 0.8[−36.1, 43.2] | 9.8[2.8, 31.7] |
| Eleveld (volunteers)7 | 44.1[−68.6, 363] | 44.6[0.15, 363] | 2.9[−36.5, 59.6] | 13.8[1.9, 40.4] |
| Marsh4 | 85.0[−55.2, 523] | 85.0[0.4, 523] | −0.2[−84.9, 61.9] | 17.6[4.2, 54.4] |
| Schnider5 | 27.9[−73.5, 299] | 30.5[0.1, 299] | 4.6[−33.0, 60.9] | 12.0[1.7, 39.9] |
| Cortinez8 | 46.7[−68.0, 360] | 47.9[0.0, 360] | 6.2[−36.8, 70.0] | 13.8[0.5, 47.4] |
Predictive performance of propofol pharmacokinetic models from the literature. Maximum and minimum values are represented as [min, max]. MdPE, Median Prediction Error; MdAPE, Median Absolute Prediction Error
| MdPE (%) | MdAPE (%) | Divergence (%/h) | Wobble (%) | |
|---|---|---|---|---|
| Eleveld (patients)7 | 9.0[−74.8,255] | 17.3[0.0,255] | 0.8[−36.1, 43.2] | 9.8[2.8, 31.7] |
| Eleveld (volunteers)7 | 44.1[−68.6, 363] | 44.6[0.15, 363] | 2.9[−36.5, 59.6] | 13.8[1.9, 40.4] |
| Marsh4 | 85.0[−55.2, 523] | 85.0[0.4, 523] | −0.2[−84.9, 61.9] | 17.6[4.2, 54.4] |
| Schnider5 | 27.9[−73.5, 299] | 30.5[0.1, 299] | 4.6[−33.0, 60.9] | 12.0[1.7, 39.9] |
| Cortinez8 | 46.7[−68.0, 360] | 47.9[0.0, 360] | 6.2[−36.8, 70.0] | 13.8[0.5, 47.4] |
| MdPE (%) | MdAPE (%) | Divergence (%/h) | Wobble (%) | |
|---|---|---|---|---|
| Eleveld (patients)7 | 9.0[−74.8,255] | 17.3[0.0,255] | 0.8[−36.1, 43.2] | 9.8[2.8, 31.7] |
| Eleveld (volunteers)7 | 44.1[−68.6, 363] | 44.6[0.15, 363] | 2.9[−36.5, 59.6] | 13.8[1.9, 40.4] |
| Marsh4 | 85.0[−55.2, 523] | 85.0[0.4, 523] | −0.2[−84.9, 61.9] | 17.6[4.2, 54.4] |
| Schnider5 | 27.9[−73.5, 299] | 30.5[0.1, 299] | 4.6[−33.0, 60.9] | 12.0[1.7, 39.9] |
| Cortinez8 | 46.7[−68.0, 360] | 47.9[0.0, 360] | 6.2[−36.8, 70.0] | 13.8[0.5, 47.4] |
Discussion
TCI is traditionally applied using population pharmacokinetic models to predict drug concentrations and to calculate required infusion profiles. This approach focuses on a population typical individual and the drug administration profile necessary to achieve and maintain the desired target drug concentrations. However, TCI systems are applied to specific individuals and the predictions will not be perfect because individuals will not exactly match the typical population individual.10 While clever covariate correction methods (corrections for weight, age, etc.) can reduce this variability to some degree, some residual variability is unavoidable. The irreducible variability is expressed as unexplained population variability in the pharmacokinetic model parameters. The origin of this variability is the biological variability not captured by the simplistic (compared with biology at least) structure of the models, its’ variability over time, and limitations of currently available data.22 Much of this variability is not understood by current pharmacological science and consequently cannot be captured properly in current models. While we might not be able to shed light on the unexplained biological variability, we can, to a degree, measure its influence in an individual. This can be achieved by making observations of drug concentrations and effects and comparing these to values predicted by the model. This information can be used to refine the model for a specific individual. If these actions can be performed within a clinical time frame it might enable on-line individualization of a pharmacokinetic model during the time course of a clinical procedure. Such an individualized model might be expected to achieve less biased and inaccurate predictions for that individual compared with the unadjusted population model, and consequently might be more useful for guiding ongoing drug dosing. The value of an on-line method to minimize bias and inaccuracy of individual propofol plasma-concentration predictions during TCI is not to be underestimated for clinical practice. It provides future possibilities to optimize propofol titration in pharmacologically challenging populations that already receive propofol without model adjustment.
Our primary aim was to compare the bias and precision of TCI propofol administration based on a classical population-based model, with that of TCI propofol administration based on an individualized model. We applied a Bayesian adjustment algorithm to individualize propofol pharmacokinetic (PK) model parameters of distribution and clearance, using bedside measured propofol concentrations. As shown in Figure 2, propofol titration was performed similarly in both groups. In the pre-adjustment period, we logically observed similar propofol PK model bias and inaccuracy, as described by MdPE and MdAPE, respectively, in both groups. In the post-adjustment period, a significant reduction in bias was found, both intra-individually and between groups (Fig. 4), when using Bayesian adaptation to adjust propofol PK model parameters to individuals. This means that the individual reduction in bias resulted in less overall prediction bias. It should be noted that MdPE is a signed value and represents the direction of the over- or under-prediction rather than the size of the possible bias, which is better represented by MdAPE.23 The beneficial results of MdAPE did not result in a significant reduction of inaccuracy of the propofol PK model as described by MdAPE. Even though MdAPE does not reveal information on the direction of the possible bias, it quantifies its amplitude.
It has been shown that for most clinically applicable and acceptable PK models, MdAPE lies between 20 and 30%. To have a better understanding of the values of MdPE and MdAPE in our specific cardiac population, we compared the predictive performance of the Eleveld model (patients) to other published propofol PK models, such as the Marsh, Schnider and Cortinez models. Both the Marsh and the Schnider model are clinically available in various commercialized TCI pumps. With an MdAPE of less than 20%, predictive performance of the Eleveld PK model for patients is better than that of other PK models in the literature and better than the Eleveld model derived from data from volunteers who received propofol without opioids. This analysis of performance error when using the patient version of the Eleveld model proves that this model is already accurately predicting the time course of propofol plasma concentration in the individual patient in our study, even without applying Bayesian adjustments. This might have contributed to the lack of improvement in accuracy with Bayesian adaptation. It might be more difficult to improve an already well performing model compared with a poorly performing one, even if one only considers performance within a dosing occasion. Another obstacle is that adaptation cannot correct for structural model misspecification, an unavoidable source of error in models of biological processes. Although our results were obtained in a specific population with probable altered pharmacokinetics, our results might not necessarily reflect other patient groups, such as children,24 underweight patients,25 or patients with neuropathology.26 In more pharmacologically challenging populations, the unadjusted Eleveld PK model may perform more poorly, and Bayesian adaptation might be more beneficial.
A Bayesian-based adjustment algorithm is influenced by the specific values of the applied PK model variances. For example, the variances in the applied Eleveld model7 are larger than the rather small variances described in the model published by Schnider and colleagues.5,6 leading to a larger degree of adjustment. There are also complex performance tradeoffs with sampling and adaptation times. A longer pre-adaptation period with a greater number of samples might have enabled greater precision in estimating the individual effects. However, this might not be clinically beneficial because the improved estimates only become available closer to the end of the procedure. Bayesian individualization across occasions has been shown to not be beneficial for flumazenil.27 This would imply that there is only limited value for increasing the number of samples. However, this is a more difficult problem than we attempt here, individualization within a single occasion. The possibility of erroneous observations leading to mal-adaptation of the PK model should also be considered as these can occur because of process or device errors or sample mishandling. Detecting and correcting these errors is not a straightforward process, but would be important for broader clinical use of PK adaptation schemes. In addition, on-line adaptation techniques require correct functioning of the complex devices needed to estimate propofol concentrations intraoperatively. Periodic device failure was a reason for dropouts in this investigation and this is a drawback of the technique. Reliability of the complete system will always be poorer than the least reliable essential component.
A similar range of propofol plasma concentrations was targeted in both groups. No differences were found in both hypnotic and haemodynamic conditions between groups. As such, application of the model adjustment did not result in altered anaesthetic conditions. This might be because of the fact that the anaesthetist was able to alter targeted propofol concentrations to maintain a specific hypnotic drug effect. Nevertheless, when comparing the target plasma concentrations in the post-adjustment period between the control and intervention group, a time-related drift towards significant differences in target concentration can be observed from the difference between the means and confidence intervals. This indicates the effect of adjustment in the PK model in the required target concentration to maintain a specific hypnotic effect.
We conclude that when an accurate population-based PK model was used for propofol TCI, Bayesian adaption of the model improved bias but not precision.
Authors’ contributions
Study design/planning: J.P.v.d.B, D.J.E., T.D.S., B.J.L., T.W.L.S., A.R.A., M.M.R.F.S.
Study conduct: J.P.v.d.B, A.V.M.v.d.H., B.J.L., T.W.L.S.
Data analysis: J.P.v.d.B, T.D.S., D.J.E., K.v.A., A.V.M.v.d.H, M.M.R.F.S.
Writing paper: J.P.v.d.B., D.J.E., T.D.S., A.R.A., M.M.R.F.S.
Revising paper: all authors
Supplementary material
Supplementary material is available at British Journal of Anaesthesia online.
Acknowledgements
The authors thank the following members of the Department of Anaesthesiology, University of Groningen, University Medical Center Groningen, Groningen, The Netherlands, for their assistance and support: H.E.M. Vereecke, MD, PhD; R. Bergman, MD; J.S. Brommundt, MD, PhD; V. Cernak, MD, PhD; E.M.E. Craenen, MD; A.J. De Vries, MD, PhD; J.S. Jainandunsing, MD; M. Modestini, MD; M.N. Morei, MD; H.E. Mungroop, MD; G.W. Rietman, MD, PhD; J.M.A.A. van der Maaten, MD; E. van Hooren; N. Feenstra and K. Dubero. We also acknowledge the support of the members of the Department of Thoracic Surgery (University Medical Center Groningen, The Netherlands).
Declaration of interest
J.P.v.d.B., D.J.E., K.V.A., A.V.M.v.d.H., B.J.L.: no conflicts of interest reported, For departmental conflicts of interests (see MMRFS).
T.D.S.: received a consultancy fee from Sphere Medical, Cambridge, UK.
T.W.L.S.: received honoraria from Edwards Lifesciences and Masimo Inc. (Irvine, CA, USA) for consulting. Received honoraria from Pulsion Medical Systems SE for lecturing. For departmental conflicts of interest, see M.M.R.F.S.
A.R.A.: his research group/department received grants and funding from The Medicines Company (Parsippany, NJ, USA), Masimo (Irvine, CA, USA), Fresenius (Bad Homburg, Germany), Acacia Design (Maastricht, The Netherlands), Medtronic (Dublin, Ireland); and he has received honoraria from The Medicines Company (Parsippany, NJ, USA), and Janssen Pharmaceutica NV (Beerse, Belgium). A.R.A. is an Editor of the BJA but was not involved in the editorial process of this work.
M.M.R.F.S.: his research group/department received grants and funding from The Medicines Company (Parsippany, NJ, USA), Masimo (Irvine, CA, USA), Fresenius (Bad Homburg, Germany), Acacia Design (Maastricht, The Netherlands), Medtronic (Dublin, Ireland), Sphere Medical (Cambridge, UK) and honoraria from The Medicines Company (Parsippany, NJ, USA), Masimo (Irvine, CA, USA), Fresenius (Bad Homburg, Germany), Baxter (Deerfield, IL, USA), Medtronic (Dublin, Ireland), Demed Medical (Temse, Belgium). M.M.R.F.S. is a member of the Editorial Board of the BJA but was not involved in the editorial process of this work.
Funding
This study was supported by departmental funding and partially supported by a grant (equipment and funding) from Sphere Medical, Cambridge, UK. Sphere Medical was not involved in the data analyses and writing of the manuscript.
References
Author notes
Handling editor: Hugh C Hemmings Jr
