Resection of brain tumours or epileptogenic areas close to language regions is often performed during awake craniotomy in order to minimise postoperative impairment.1–4 There are different anaesthetic methods used, one of which is the ‘asleep-awake-asleep’ technique with propofol. This renders the patient unconscious at the beginning and end of the procedure but ensures an awake and co-operative patient for neurological testing during surgery.5,6
Usually, propofol is delivered continuously using an infusion pump. However, due to the redistribution of propofol, a constant infusion rate results in neither a constant plasma concentration (Cpl) nor constant effect-site concentration (Ce). Therefore, anaesthetic depth, which is thought to be determined by propofol Ce is not constant but varies over time. As a consequence, target-controlled infusion (TCI) pumps have been developed, wherein the desired Cpl or Ce is targeted and the infusion rate adjusted accordingly by a computer. TCI pumps calculate the required infusion rate to maintain (or reach) the desired target propofol concentration based on a pharmacokinetic/pharmacodynamic (PK/PD) model of propofol.7 At least six PK/PD models have been published for propofol use in adults.8–13 In the first commercially available TCI-pump, the Diprifusor, users were restricted to a preset PK/PD model, but more recently, users have been able to choose between different models in most available TCI pumps. Of those PK/PD models, the two published by Marsh et al.14 and Schnider et al.9 seem to be the most commonly used by anaesthesiologists. However, it remains unclear which of the two is more accurate and appropriate for the special situation of awake craniotomy, where an insufficient anaesthetic depth might cause unintended awareness during the initial (craniotomy) and final periods of surgery. In contrast, inappropriately deep anaesthesia might impede spontaneous breathing and delay both intraoperative awakening and performance of neurological tests.
In order to precisely manage the various stages of anaesthesia during awake craniotomy, an accurate PK/PD model of propofol is required. Therefore, we performed a study to investigate the following two questions. First, which of the two (Marsh or Schnider) PK/PD models predicts the propofol plasma concentration more precisely and with less bias? Second, which of the models predicts the electroencephalographic effect of propofol with the higher probability?
Patients and procedure
Ethical approval for this study (Ethical Committee No. 226/08) was provided by the Ethical Committee of the Bonn University Hospital, Bonn, Germany (Chairperson: Prof. K. Racké) on 23 December 2008. After obtaining written informed consent from the study participants, patients undergoing awake craniotomy were investigated in this prospective observational study. Pregnancy or age less than 18 years were exclusion criteria. All patients were anaesthetised using the ‘asleep-awake-asleep’ technique.15
On arrival in the induction room, standard monitoring was applied and a peripheral venous cannula and radial artery catheter were inserted. The electroencephalographic effect of propofol was quantified using the bispectral index (BIS). The BIS-electrode (XP-sensor, Covidien plc, Dublin, Ireland) was attached to the right forehead and connected to an A-2000 BIS monitor (Version XP, BIS version 4.0, Covidien plc). The propofol infusion was started at a rate of 2000 mg h−1 until the BIS decreased to the desired range between 40 and 60. Thereafter, the infusion rate was reduced stepwise in order to keep the patient in the recommended BIS range. A tracheal tube was inserted through the nose, with the tip above the vocal cords and the glottis. Therefore, the patients’ ability to speak intra-operatively was not impeded but the trachea could be intubated by advancing the tube under fibreoptic guidance if necessary. Oxygen (4l min−1) was delivered via the nasal tube and spontaneous breathing was maintained throughout surgery.
The patient was transferred to the operation room, where a scalp block was performed.16 In addition, the skin was infiltrated with local anaesthetic at the site of the Mayfield pins and skin incision. The neurosurgeons fixed the patient's head in a Mayfield holder and performed the craniotomy. After opening of the dura, the propofol infusion was discontinued to allow the patient to wake up for neurological testing. After completion of the tests, the propofol infusion was resumed and tailored to keep the BIS between 40 and 60. After skin suturing had been completed, the propofol infusion was stopped again and, after emergence from anaesthesia, the nasal tube was removed while still in the operating room. Subsequently, patients were transferred to the neurosurgical ICU.
Patients received remifentanil during the painful periods of Mayfield fixation, skin incision and skin suture using a TCI system. To do so, the PK/PD model described by Minto et al.17 was used and a low target effect-site concentration of 0.8 ng ml−1 was set, which permitted spontaneous breathing. The tube was advanced into the trachea and the lungs were ventilated mechanically only if the arterial PCO2 rose above 6 kPa subsequent to the awake period. Otherwise, spontaneous breathing was maintained.
Throughout the operation, BIS values and the propofol infusion rates were recorded and stored on a laptop computer every 5 s using Win Log software (version 1.0, Aspect Medical Systems, Newton, Massachusetts, USA) and TCI Bonn (written by JL Griffoul and H Schwilden, University of Bonn, Bonn, Germany), an in-house built software, respectively. The actual pharmacokinetic and pharmacodynamic analyses were performed offline.
The plasma concentration (Cpl) of propofol was measured by high-performance liquid chromatography in a certified laboratory (C3P analysis, Pharmacy Department, Plymouth Hospitals NHS Trust, UK) on arterial blood samples drawn intraoperatively. The plasma was separated and stored at −20 °C until analysis.
In addition, Cpl was simulated in 5-s intervals based on the PK/PD models of Marsh et al.14 or Schnider et al.9 To do so, an Excel spreadsheet (Microsoft Corporation, Redmond, Washington, USA) was used, which calculated Cpl using the recorded propofol infusion rate as input as well as patient-specific data such as sex, age, height and weight.18 This Excel spreadsheet called ‘excelsior.xls’ was developed by Bruhn and Bouillon19 and validated in comparison with the Tivatrainer software (version 9.1, GuttaBV, Aerdenhout, The Netherlands, downloadable at http://www.eurosiva.eu/tivatrainer/TTweb/TTdownload.html).
Subsequently, the measured and simulated plasma propofol concentrations were compared using the parameters prediction error (PE), bias and inaccuracy:
For each plasma sample, PE was calculated20:
For each patient, the bias or median prediction error (MDPE) and its standard deviation σPE were determined20:
where i denotes the i-th patient, in whom ni samples were drawn. Accordingly, the inaccuracy or median absolute prediction error (MDAPE) and its standard deviation σAPE are calculated using the absolute value of PE20:
Pharmacodynamic analysis requires knowledge of the propofol concentration at the site of its action, that is, the brain. As this effect-site concentration Ce cannot be measured directly but is calculated, for example, by simultaneous PK/PD modelling as described in detail elsewhere.21 The plasma (Cpl) and the effect-site concentration (Ce) are related to each other by the equilibration constant keo and the following differential equation:
Hence, keo determines the rate at which propofol is distributed between the plasma and the effect compartment. In this study, three different approaches of how to choose appropriate keo values were applied. First, predefined (published) keo values of 0.26 and 0.456 min−1 were used for the Marsh and the Schnider models,22 respectively. Second, keo values which were fitted to the individual patient were implemented. Third, a fixed ‘time-to-peak’ approach was applied as described in detail by Minto et al.23 Here, keo was calculated so that the maximum propofol effect will occur at a predefined time-to-peak (tpeak) of 1.6 min.
Subsequently, we analysed the concentration-effect curve of propofol in individual patients. To do so, the propofol effect E was defined as depth of anaesthesia and quantified by means of the BIS. A sigmoid relationship between the propofol (effect-site) concentration and its effect E (BIS) was assumed according to Hill.24 Application of different pharmacokinetic models (Marsh or Schnider) and different keo values (predefined, individually fitted or to obtain a fixed tpeak) result in different predicted propofol effect-site concentrations (Ce). To quantify how well these concentrations translated into depth of anaesthesia, we calculated a parameter called prediction probability (PK) as described by Smith et al.25 PK can assume any value between 0 and 1, and we applied the Excel spreadsheet PKMACRO25 to calculate it.
During PK/PD analysis, we obtained one value of MDPE, MDAPE, σPE, σAPE, keo and PK for each patient and for each pharmacokinetic model. These were finally averaged within the patient population to obtain results for the different pharmacokinetic models.
The number of patients required was planned according to a power analysis, based on the MDAPE results published by Ihmsen et al.26 We calculated that 13 patients would be required to achieve a power of 0.8 at an alpha of 0.05.
SigmaPlot for Windows version 12.3 (Systat Software Inc., Erkrath, Germany) was used for the statistical analysis. In case of normal distribution, the parameter sets were compared using a paired Student's t-test, otherwise a Wilcoxon rank sum test was performed. Statistical significance was assumed when P ≤ 0.05. All data are displayed as mean ± SD unless stated otherwise.
Thirteen patients were included, but blood samples were unavailable in one patient, leaving 12 patients for final analysis. They consisted of seven women and five men, with a mean ± SD age of 45 ± 14 years, a height of 173 ± 6 cm and a weight of 74 ± 10 kg. Three patients underwent surgery because of epilepsy resistant to pharmacological treatment, whereas the remaining nine patients suffered from a brain tumour.
Between 16 and 28 arterial blood samples (mean 20 ± 3) were drawn from each patient, yielding a total of 244 samples. In the range of high propofol concentrations (>5 μg ml−1), the Marsh model underestimated the measured plasma concentration (Fig. 1). The bias using the Marsh model (MDPE −11.7 ± 14.3%) tended to be higher (P = 0.09) compared with the Schnider model (MDPE −5.4 ± 20.7%). In addition, the inaccuracy was significantly larger (P = 0.05) when applying the Marsh model (MDAPE 28.9 ± 12.0%) in comparison with the Schnider model (MDAPE 21.5 ± 7.7%, Fig. 2).
The mean standard deviation σ of both MDPE and MDAPE was significantly smaller with the Schnider model than with the Marsh model (σPESchnider 21.9 ± 6.7%, σPEMarsh 40.8 ± 11.0%, P < 0.001; σAPESchnider 16.0 ± 4.9%, σAPEMarsh 25.8 ± 9.3%, P = 0.007, Fig. 3). MDPE was outside the accepted limits (± 20%) in three or four (of 12) patients when applying the Marsh (MDPE −28.2, −31.7, −34.6%) or the Schnider model (MDPE 33.9, −26.2; −27.6, −34.6%), respectively. MDAPE exceeded the accepted threshold of 30% in six and two patients using the Marsh (MDAPE 31.7, 32.6, 37.2, 38.0, 42.7, 49.7%) or the Schnider model (MDAPE 33.9, 34.6%), respectively.
Individual pharmacodynamic fitting resulted in different keo values (Marsh, keo 0.404 ± 0.143; Schnider, keo 0.150 ± 0.042) compared with the original parameter sets described by Marsh et al.14 (keo 0.26) and Schnider et al.9 (keo 0.456, Table 1). For the Schnider model with a fixed tpeak of 1.6 min, keo values ranging between 0.337 and 0.459 (mean keo 0.384 ± 0.043 min−1) were obtained.
The prediction probability PK was above 0.78 for both the Marsh and the Schnider models (Table 1). PK was significantly improved by individual fitting (PK 0.807 ± 0.056) based on the Schnider dataset in comparison with the original (PK 0.787 ± 0.055, P < 0.001) and the tpeak-optimised (PK 0.794 ± 0.048, P = 0.017) dataset.
The main purpose of a target-controlled propofol infusion is to achieve the plasma concentration which has been set. However, the actual plasma concentration will differ from the predicted one, which is quantified by the two parameters bias (MDPE) and inaccuracy (MDAPE). According to Schuttler et al.27 and Glass et al.,28 accepted limits for the performance of a TCI should be within −20 and +20% for bias (MDPE) and below 30% for inaccuracy (MDAPE). In our study, both the Marsh and the Schnider models fulfilled these criteria, making them both reliable models for calculating plasma propofol concentrations. Nevertheless, the model of Schnider et al.9 achieved a significantly higher precision (that is a lower inaccuracy in MDAPE) and showed a trend towards a lower bias (MDPE). Therefore, we recommend use of the Schnider model for propofol TCI during awake craniotomy. The higher precision associated with the Schnider model could be explained by the higher number of variables incorporated; whereas Marsh et al.14 only use the body weight for their calculation, Schnider et al.9 also take age, height and lean body weight into account.
Despite the widespread use of propofol TCI, the comparative performance of the Marsh and the Schnider PK/PD models has been investigated in; only a few studies (Table 2). These included no neurosurgical procedures, except for the study of Glen et al.29 which contained a few neurosurgical patients. Glen et al.,29,30 Ihmsen et al.26 and Masui et al.31 reported – similar to our study – that both the Marsh and the Schnider models achieved sufficient bias and precision. Only the Marsh model was associated with an insufficiently high inaccuracy (MDAPE 34.8%, Table 2) according to the analysis by Masui et al.31 based on the data obtained from Doufas et al.32 Poor performance of both the Marsh and the Schnider models was described by Wietasch et al.33 (Table 2), who observed a systematic underestimation of plasma propofol concentration by both models. We found such an underestimation only for the Marsh model and only for propofol plasma concentrations above 5 μg ml−1. However, below 4 μg ml−1, the Marsh model tended to overestimate the plasma propofol concentration, resulting in a negative bias. This is in agreement with Ihmsen et al.26 and Masui et al.,31 who also reported a negative bias (that is an overestimation of plasma concentration).
We observed a great interindividual variability in the sizes of prediction error, MDPE and MDAPE. Although both models fit exceptionally well in some patients, they failed to achieve satisfactory results in others. Both PK/PDMarsh and PK/PDSchnider reached a MDAPE of more than 30% in six and two of the 12 patients, respectively. This means that in these patients, the models did not predict plasma propofol concentration with sufficient accuracy. Therefore, we recommend monitoring depth of anaesthesia during awake craniotomy.
TCI pumps do not only allow to target a certain plasma concentration, but a given effect-site concentration instead. Both concentrations are related to each other by the equilibration constant keo, which determines the rate at which propofol is distributed between the plasma and the effect-site compartment. Therefore, the performance of a TCI in effect-site mode depends on the choice of an adequate keo which in turn depends on the pharmacokinetic model from which keo was obtained. For example, the clinical observation of a maximum propofol effect 1.6 min after bolus injection (time-to-peak)34 can be explained by different PK/PD models; a high central volume (V1 15.9 l, resulting in a low Cpl) in combination with a high keo of 1.2 min−1 (Marsh model in a patient with 70 kg body weight) or a low central volume (V1 4,3 l, resulting in a high Cpl) in conjunction with a low keo of 0.456 min−1 (Schnider model). Therefore keo values cannot be exchanged readily between different pharmacokinetic models.
There is ongoing uncertainty about the most appropriate keo value to use with the Marsh pharmacokinetic model, with reported keo values ranging from 0.2 to 1.2 min−1.35 The Diprifusor incorporated a keo of 0.26 min−1,36 based on data which have never been published in the peer-reviewed literature,34 but resembles the keo of 0.20 min−1 proposed by Billard et al.37 Significantly higher keo values were obtained in our study (keo 0.40 ± 0.14 min−1) as well as by Thomson et al.35 (keo 0.61 min−1). Struys et al. reported an even higher keo of 1.20 min−1, which has been implemented in the Base Primea TCI system (Fresenius Kabi, Bad Homburg, Germany).
With regard to the Schnider pharmacokinetic model, there is also considerable but somewhat less variability reported. Schnider et al.22 themselves recommended applying a keo of 0.456 min−1, whereas we obtained a much lower keo of 0.15 ± 0.04 min−1. This difference might be explained by the EEG processing time which is presumably less for the semi-linear canonical correlation used by Schnider et al. than the BIS algorithm used in our study.
Another approach to choosing keo is based on the time delay between a propofol bolus injection and the maximum hypnotic effect of propofol, which is referred to as ‘time-to-peak’.23 This time-to-peak is considered independent of the propofol bolus size and equals 100 s (1.6 min) according to clinical observation.22 We calculated keo for a given tpeak of 1.6 min as described by Minto et al.,23 which resulted in keo values ranging from 0.337 to 0.459 min−1. This algorithm based on the Schnider model and a fixed tpeak of 1.6 min has been implemented in the Alaris PK TCI System (Carefusion Corp., San Diego, California, USA).
We quantified the predictive pharmacodynamic performance of the Marsh and Schnider models by applying the prediction probability PK. This technique has been proposed by Smith et al.25 to compare the performance of different anaesthetic depth indicators. PK has a value of 0.5 if the anaesthetic depth indicator predicts observed anaesthetic depth no better than by 50 : 50 chance, and a value of 1.0 if the indicator predicts observed anaesthetic depth perfectly.25 As we used the same anaesthetic depth indicator (BIS) in all patients, any observed difference in PK between the models must be due to their different pharmacodynamic performances. With both the original Marsh and the original Schnider models, satisfactory results with a PK of approximately 0.79 were achieved. Thus, when anaesthetic depth – as determined by the effect-site propofol concentration – is changed 100 times, the BIS monitor will indicate this change correctly in 79 cases (and incorrectly in the remaining 21 cases). A notable (and, in case of the Schnider model, significant) increase in PK was achieved after individual pharmacodynamic fitting, which is not surprising because individual fitting corrects for inter-individual pharmacodynamic variability. The PK values for Schnider tpeak were between those of the original models and those of the individualised fitted models. The tpeak model is slightly more individual than the original Schnider model because one variable (keo) is fitted to each patient, which could explain the higher PK values obtained using the tpeak model compared with the original model. However, the tpeak model is not as individual as the fitted Marsh and Schnider models because the latter uses more pharmacodynamic variables. Unfortunately, such an adaptation of an established PK/PD model to the individual patient is usually performed retrospectively because many pairs of variates (Ce/BIS) are necessary to individually adjust the model. Alternatively, these pairs of variates could either be gained during previous anaesthesia in the same patient, or during the induction phase. However, this approach is not feasible in clinical practice.
Other authors have investigated the Marsh or Schnider models in the context of awake craniotomy with different techniques, but similar results. Hans et al.38 reported that BIS correlated better with patients’ responsiveness than did the predicted effect-site concentration of propofol as calculated using the Marsh model. In contrast, Lobo and Beiras39 observed a close and significant correlation (r2 = 0.547) between BIS and Ce when applying the Schnider model.
This study has a number of limitations. Although there has been a recent increase in the number of awake craniotomies being performed, it is still a relatively rare operation.40 Therefore, the number of patients included in this trial was rather small.
The co-administration of remifentanil might have influenced our analysis, although remifentanil does not alter propofol pharmacokinetics in the clinical range between 0 and 4 ng ml−1.41 Moreover, pharmacokinetic simulation yielded that 33 out of 244 samples (13.5%) theoretically contained remifentanil, whereas the remaining 211 samples did not. Finally, any potential effect of remifentanil on propofol PK/PD would have affected both the Marsh and the Schnider models in our study.
Our results were obtained in a neurosurgical population using a specific anaesthetic regimen. They might not readily be extrapolated to other patients or other procedures. First, we used quite a low opioid dosage (to maintain spontaneous breathing) and, therefore, had to administer a higher propofol dose. Consequently, the plasma propofol concentrations of up to 9 μg ml−1 measured in our study are somewhat higher than in other patients, where concentrations in the range between 2.5 and 5 μg ml−1 are typically targeted.42 Second, our patients suffered from neurological disorders and took antiepileptic drugs, which are both conditions that might affect the EEG and thus the pharmacodynamic effect of propofol.43
When propofol PK/PD models are used for patients undergoing awake craniotomy, we advocate using the model proposed by Schnider et al.9 because it predicts plasma propofol concentrations with higher accuracy. Due to the considerable interindividual variability of PK/PD parameters, PK/PD models may predict inaccurate propofol concentrations in some patients. It is not practical in clinical routine to adjust PK/PD models to the individual patient, and it seems advisable to monitor depth of anaesthesia by means of EEG-derived parameters in addition to simply relying on calculated effect-site concentrations.
Acknowledgements relating to this article
Assistance with the study: none.
Financial support and sponsorship: this study was funded by departmental sources. Covidien plc supplied complimentary electroencephalographic electrodes for study purposes.
Conflicts of interest: MS and RKE have received honoraria for lectures from Covidien Germany (Neustadt/Donau, Germany).
Presentation: preliminary data from this study were presented as a poster presentation (3AP2–8) at the European Society of Anaesthesiology (ESA) Euroanaesthesia congress, 1–4 June 2013, Barcelona. Data presented here are part of the doctoral thesis of CFW.
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