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Anaesthesia, 2011, 66, pages 1112–1120 doi:10.1111/j.1365-2044.2011.06875.x .....................................................................................................................................................................................................................

ORIGINAL ARTICLE

Clinical evaluation of a simultaneous closed-loop anaesthesia control system for depth of anaesthesia and neuromuscular blockade* M. Janda,1 O. Simanski,2 J. Bajorat,1 B. Pohl,3 G. F. E. Noeldge-Schomburg4 and R. Hofmockel3 1 Consultant, 3 Senior Physician, 4 Head of Department, Department of Anaesthesiology and Intensive Care Medicine, University of Rostock, Rostock, Germany 2 Professor of Automation, Department of Electrical Engineering & Computer Science, University of Applied Sciences – Technology, Business and Design Wismar, Wismar, Germany

Summary

We developed a closed-loop system to control the depth of anaesthesia and neuromuscular blockade using the bispectral index and the electromyogram simultaneously and evaluated the clinical performance of this combined system for general anaesthesia. Twenty-two adult patients were included in this study. Anaesthesia was induced by a continuous infusion of remifentanil at 0.4 lg.kg)1.min)1 (induction dose) and then 0.25 lg.kg)1.min)1 (maintenance dose) and propofol at 2 mg.kg)1 3 min later. The combined automatic control was started 2 min after tracheal intubation. The depth of anaesthesia was recorded using bispectral index monitoring using a target value of 40. The target value of neuromuscular blockade, using mivacurium, was a T1 ⁄ T10 twitch height of 10%. The precision of the system was calculated using internationally defined performance parameters. Twenty patients were included in the data analysis. The mean (SD) duration of simultaneous control was 129 (69) min. No human intervention was necessary during the computer-controlled administration of propofol and mivacurium. All patients assessed the quality of anaesthesia as ‘good’ to ‘very good’; there were no episodes of awareness. The mean (SD) median performance error, median absolute performance error and wobble for the control of depth of anaesthesia and for neuromuscular blockade were )0.31 (1.78), 6.76 (3.45), 6.32 (2.93) and )0.38 (1.68), 3.75 (4.83), 3.63 (4.69), respectively. The simultaneous closed-loop system using propofol and mivacurium was able to maintain the target values with a high level of precision in a clinical setting. . ......................................................................................................

Correspondence to: Dr M. Janda Email: [email protected] *Presented in part at the American Society of Anesthesiologists’ Annual Meeting, Chicago, USA, October 2006. Accepted: 24 July 2011

The anaesthetist’s workload in a complex and dynamic working environment has increased over the last few decades. All anaesthetic decisions are made on the basis of continuous monitoring of all information available (such as clinical status, several monitoring parameters, observation of the operating field etc) as well as the resultant continuous adaptation of one’s own actions. Gaba et al. differentiate between two components when it comes to decision-making in anaesthesia – 1112

typical decisions of routine care and non-routine decisions made during the management of problems or accidents, both of which have to be made simultaneously [1]. Control theory deals with the automation of the typical decisions to minimise the workload via delegation of routine tasks, as well as increasing safety. Feedback control systems in anaesthesia are used for computer-assisted dosing of anaesthetics as the result of data collection and analysis of the parameters 2011 The Authors Anaesthesia 2011 The Association of Anaesthetists of Great Britain and Ireland

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Anaesthesia, 2011, 66, pages 1112–1120 M. Janda et al. Simultaneous closed-loop control of anaesthesia and neuromuscular blockade . ....................................................................................................................................................................................................................

that make up the most important components of anaesthesia (depth of anaesthesia, analgesia, neuromuscular blockade). The resulting advantages, such as the prevention of under- or overdosing via more precise dosing, the faster detection of even small changes in vital parameters via continuous monitoring, as well as the reduction in the anaesthetists’ workload, freeing them for other patient care requirements, can contribute greatly to increased patient safety [2]. At the same time, a reduction in emergence time, which can be achieved via closed-loop techniques [3–5], is an important contribution towards optimising peri-operative workflow. Another advantage associated with the use of control systems in anaesthesia is the possibility of individualised, patient-adjusted dosing of anaesthetics. As the result of co-medications, receptor up- and down-regulations, enyzme deficiencies, organ insufficiencies, age or genetic polymorphisms, patients react differently both pharmacodynamically and pharmacokinetically to the same dose of a medication. Thus, closed-loop systems may have enormous potential as part of future technological innovations in anaesthesia. To promote this vision, we developed a closed-loop system to control depth of hypnosis and neuromuscular blockade using both the bispectral index (BIS) and the electromyogram (EMG) simultaneously. The purpose of this study was to evaluate the clinical performance of this combined system under the conditions of general anaesthesia. Methods

After approval by the institutional review board and written informed consent, 22 adult patients, ages 18– 65 years and of ASA physical status 1–3, who were scheduled for elective intra-abdominal or orthopaedic surgery in the supine position, were included in the study. None of the patients were taking psychiatric medications or medications known to interact with neuromuscular blocking drugs. Exclusion criteria were a history of a neuromuscular or neurological disease, a known contraindication for the use of mivacurium (patients with a genetic deficiency in plasmacholinesterase activity), a difficult or potentially difficult airway caused by an abnormal airway anatomy (such as Mallampati class 3 or 4), as well as kidney or liver disease. All patients received midazolam 7.5 mg orally for premedication. Before the start of study, patients were prepared as usual for anaesthesia (intravenous access, ECG, non-invasive blood pressure monitoring, pulse oximetry). Bispectral index electrodes (BIS 2011 The Authors Anaesthesia 2011 The Association of Anaesthetists of Great Britain and Ireland

QuatroTM Sensor, AspectTM Medical Systems Inc., Newton, MA, USA) were applied to the patient’s forehead in accordance with the manufacturer’s specifications to monitor the bispectral index of the EEG (A-2000 BISTM monitor (V3.30), Aspect Medical Systems Inc.). Neuromuscular transmission was monitored with the EMG by measuring the signal at the first dorsal interosseus muscle following stimulation of the ulnar nerve in compliance with guidelines for good clinical research practice in pharmacodynamic studies of neuromuscular blocking drugs [6]. After careful skin preparation, the recording electrode was placed on an index finger, and stimulating electrodes with an appropriate contact area (10 mm in diameter) were placed 3–6 cm apart over the ulnar nerve in the patient’s forearm. After 3 min of pre-oxygenation, anaesthesia was induced by a continuous infusion of remifentanil at 0.4 lg.kg)1.min)1 and propofol 2 mg.kg)1 was administered 3 min later. After loss of consciousness, the patient’s trachea was intubated without the administration of neuromuscular blocking drugs, and mechanical ventilation with oxygenated air (FIO2 = 0.4) in a pressure-controlled mode was adjusted to maintain an end-tidal carbon dioxide tension between 4.5 and 5.5 kPa. Analgesia was maintained with remifentanil at 0.25 lg.kg)1.min)1. Body temperature and skin temperature at the site of the neuromuscular measurement were checked and maintained at > 35 C for the body cavity and > 32.0 C for the skin, using heating blankets. The combined automatic drug administration of mivacurium and propofol was started 2 min after tracheal intubation. At the end of surgery, the administration of propofol and mivacurium was stopped. Neuromuscular blockade was not reversed, and adequate extubation was assumed once the train-of-four ratio was 0.9 or more. The depth of anaesthesia was recorded by BIS monitoring using a target value of 40. The degree of neuromuscular blockade was recorded electromyographically using single twitch stimulation of the ulnar nerve with a sampling period of 12 s. The target value was a T1 ⁄ T10 twitch height of 10% (90% neuromuscular blockade). Both measuring signals were transmitted via a RS232 connection to the control computer every 5 s. The control algorithm on this computer used a decentralised multi-input-multi-output (MIMO) controller written in MATLAB programming language. For neuromuscular blockade, a generalised predictive controller (GPC) and for depth of anaesthesia, a fuzzy proportional, differential plus integral 1113

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M. Janda et al. Simultaneous closed-loop control of anaesthesia and neuromuscular blockade Anaesthesia, 2011, 66, pages 1112–1120 . ....................................................................................................................................................................................................................

(PD+I) controller were implemented. The infusion rates, calculated from the controller, were transmitted to the infusion pumps via a RS232 connection every 5 and 12 s for propofol and mivacurium administration, respectively. The infusion pumps (Perfusor fm; B.Braun, Melsungen, Germany) were implemented in the closed loop as the actuators. Figure 1 shows the structure of the MIMO system. The quality of both controllers was first calculated for each patient according to the current international criteria and then the mean (SD) was calculated [7, 8]. The following values are the parameters that characterise the performance of controlling systems: the median performance error (MDPE), which is comparable to the bias that describes whether the values measured systematically lie above or below the target parameter; the median absolute performance error (MDAPE), which represents a measure of the system’s precision; and the wobble, a measure of the intra-individual variability in performance error, whereby a lower wobble represents a higher system quality. The commencement of simultaneous closed-loop control drug administration (used as the basis for the calculations of performance parameters) was determined when the target values for BIS and T1 ⁄ T10 were achieved at steady-state. The proportion of time during closedloop control that the BIS and the T1 ⁄ T10 were each within a target corridor of set point ± 10% (defined as excellent) and more than ± 30% outside the target set point (defined as inadequate) was calculated. To limit the influence of artefacts or low signal quality on the calculations for propofol dosaging, we accepted only BIS values with a signal-quality-index (SQI) > 50 for

analysis [3]. The mathematical calculations behind these quality parameters are described in the Appendix. Propofol and mivacurium consumption were recorded. Patient satisfaction with respect to their anaesthesia was assessed by a postoperative questionnaire within 24 h of surgery [9]. Results

Twenty-two patients were enrolled in this investigation; two patients were excluded from data processing because of problems with the EMG signal quality. Patient characteristics and the types of surgery are shown in Tables 1 and 2. The cumulative time of simultaneous closed-loop control administration of mivacurium and propofol for all patients was 43 h 05 min. Patients underwent simultaneous control for a mean (SD) of 129 (69) min and received a mean (SD) propofol dose of 92 (31) lg.kg)1.min)1 and a mean (SD) mivacurium dose of 4.25 (1.25) lg.kg)1.min)1. The maximum and minimum doses in any patient were 288 (44) lg.kg)1.min)1 and 48 (26) lg.kg)1.min)1 for propofol and 6.85 (1.38) lg.kg)1.min)1 and 2.30 (1.30) lg.kg)1.min)1 for mivacurium, respectively. No human intervention was necessary during the computer-controlled administration of propofol and mivacurium, and operating conditions were satisfactory in all patients. All patients assessed the quality of anaesthesia as ‘good’ to ‘very good’; there were no episodes of awareness. The MDPE, MDAPE and wobble of the target BIS control were )0.31 (1.78), 6.76 (3.45) and 6.32 (2.93), respectively. The BIS was maintained within 10% of

Figure 1 The main algorithm of the simultaneous closed-loop anaesthesia control system. Flow chart of the multi-input-multi-

output system for the control of neuromuscular blockade and depth of anaesthesia with prefilter (PF), scaling factors (K1, K2, KI), Int. (integrator), GPC (generalised predictive controller), Fuzzy-PD (P, proportional-, D, differential-part) reference system, Fuzzy-I (I, integral-part) reference system, Ts is the sampling time. 1114

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Table 1 Patients’ characteristics. Values are mean (SD) or

number. Age; years Male: female BMI; kg.m)2 ASA; 1:2:3

47 (10) 12:8 25.8 (4.7) 2:15:3

BMI, body mass index.

(4.69), respectively. We noted excellent control during 87.3% of the time for neuromuscular blockade control and 3.9% of the time was noted as inadequate control. Figure 2 demonstrates a typical sequence of a patient trial with the specification of controlled parameter levels and their corresponding drug infusion rates. The typical best-case performances and worst-case performances are presented for both components of anaesthesia in Figs 3 and 4.

Table 2 Types of surgery performed under closed-loop

anaesthesia. Values are number. Types of surgery Abdominal surgery

General surgery Thyroid surgery Orthopaedic surgery

Discussion n = 20

Pancreatic surgery Hemihepatectomy Colorectal resection Reversal of ileostomy Herniotomy Thyroidectomy Internal fixation of fracture Tibial osteotomy Acetabular reconstruction

6 2 3 1 1 1 4 1 1

the target (excellent control) and more than 30% outside the target (inadequate control) during 65.5% and 5.7% of the automated anaesthesia time, respectively. The proportion of the maintenance period with a valid SQI (> 50) was 99.3 (1.2)%. The MDPE, MDAPE and wobble of the obtained neuromuscular blockade were )0.38 (1.68), 3.75 (4.83) and 3.63

This study evaluated the first use of simultaneous closed-loop control of anaesthesia depth and neuromuscular blockade in a clinical setting. We have demonstrated the high accuracy of the system with respect to the maintenance of the anaesthesia and the degree of neuromuscular blockade with the use of BIS and EMG. For the regulation of anaesthesia depth, Struys et al. reported a MDPE of ) 6.6% and a MDAPE of ) 7.7%, as well as a median wobble of 5.9%, using an adaptive control algorithm with the BIS as a control variable [4]. Absalom et al. used a proportional-integral-differential (PID) controller for the automatic regulation of propofol administration and achieved a MDPE of )0.42% and a MDAPE of 5.63% [10]. With the aid of the proportional-differential controller (PDcontroller), which allowed for the first performance comparison of BIS-controlled automatic anaesthesia

Figure 2 Typical data recording. The upper plots show the T1 (%) muscle response with a set point of 90% neuromuscular

blockade measured with EMG and the corresponding mivacurium infusion rate. The lower plots show the desired BIS-index with a set point of 40 and the propofol infusion rate. 2011 The Authors Anaesthesia 2011 The Association of Anaesthetists of Great Britain and Ireland

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propofol administration with manually controlled propofol infustion, a MDPE of ) 3.32%, a MDAPE of 9.94% and a wobble of 8.10% could be achieved [3]. Our results are slightly better with respect to the percentage time of excellent control (BIS was within 10% of target for 65% of the time vs 55%) and equivalent with respect to the time of inadequate control (BIS > 30% for 6% vs 7%) in comparison with the results reported by Hemmerling and colleagues [5]. However, it is difficult to compare the quality of the control system evaluated in this study with that of the control systems used in other studies. Eleveld and colleagues, for example, reported that 96.1% of recorded twitch values were within target range, defined as one twitch out of four (TOF 1 ⁄ 4) over a total of 39 h using rocuronium [11]. Schumacher et al. achieved a MDPE of 0.1%, MDAPE of 1.4% and wobble of 1.4% when using mivacurium to maintain a 90% blockade [12]. Illman et al. used a closed-loop 1116

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Figure 3 Bispectral index (BIS) values for the best and the worst case. (a) best patient – male patient undergoing tibial osteotomy who received a mean dose of propofol of 78 lg.kg)1.min)1. The BIS values are within ± 10% of the target setpoint for 97% of the time. There was no BIS value outside a ± 30% corridor of the target; (b) worst patient – male patient undergoing reversal of ileostomy surgery who received a mean dose of propofol of 94 lg.kg)1.min)1. The BIS was within 10% of the target for 26% of the time. The percentage of time BIS remained outside ± 30% of the target was 25%.

system to dose rocuronium for the maintenance of a 90% neuromuscular blockade with good success and a rapid return to neuromuscular function at the end of the operation [13]. With respect to the control quality of the single components, the multivariable controller developed by our group is similar to other available single systems. In addition, our combined application represents a further development within the realm of closed-loop systems. Hemmerling et al. recently reported preliminary results of a novel fully automatic anaesthesia delivery system based on closed-loop control of depth of hypnosis, analgesia and neuromuscular blockade named ‘McSleepyTM’ [14]. This is a further, important advance in the implementation of control systems in everyday clinical practice. The accuracy and reproducibility of the physiological signal measured are decisive factors in the effectivity of a closed-loop control system; such signals serve as control variable within the system [15]. Ha¨nzi et al. 2011 The Authors Anaesthesia 2011 The Association of Anaesthetists of Great Britain and Ireland

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(T1 ⁄ T10) ratio for the best and the worst case. (a) best patient – male patient undergoing partial pancreatoduodenectomy (Whipple’s procedure) who received a mean dose of mivacurium of 3.3 lg.kg)1.min)1. The T1 ⁄ T10 ratio was within 10% of the target setpoint for 98% of the time. The percentage of time T1 ⁄ T10 ratio remained outside ± 30% of the target was < 1%; (b) worst patient – male patient undergoing reversal of ileostomy surgery who received a mean dose of mivacurium of 7.5 lg.kg)1.min)1. The T1 ⁄ T10 ratio was within 10% of the target for 78% of the time. The percentage of time T1 ⁄ T10 ratio remained outside ± 30% of the target was 6%.

60 50 40 30 20 10 0 0

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stated that the EMG is more reliable than acceleromyography for use in daily practice, as it is less influenced by external disturbances [16]. We chose the EMG as a sensor, providing a better input signal for closed-loop control of neuromuscular blockade. We have previously shown the validity of an EMG- determined T1value as a control variable within the regulation of the neuromuscular blockade [17]. Though no ‘gold standard’ exists [18], closed-loop systems have mostly used the BIS to regulate the depth of hypnosis with propofol – probably because of market saturation [3–5, 10, 19]. The regulation of the neuromuscular blockade can be divided into two phases. In phase one (the identification phase), the goal should be to reach 90% neuromuscular blockade as quickly as possible as well as identify the patient’s individual reaction to a defined bolus of neuromuscular blocking drug. During phase two, the focus should be on maintaining the target neuromuscular block within a narrow tolerance 2011 The Authors Anaesthesia 2011 The Association of Anaesthetists of Great Britain and Ireland

margin, whereby the controller must continuously adapt to the current state of the patient because of the possibility of intra-individual variability. Therefore, an adaptive generalised predictive controller (aGPC) with an upstream on-off controller was chosen. The controller starts after neuromuscular blockade is administered via a body weight-adjusted bolus of mivacurium and waits for 3 min for the patient’s reaction to the drug. Next, the degree of blockade present is assessed and an additional dose is administered if necessary (phase one). After successful modulation, the system is switched over to the aGPC-driven controller (phase two), which was defined as the starting time for simultaneous control in the present study. The idea to use GPC in anaesthesia therapy was first introduced by Mahfouf [20]. There are several different clinically evaluated assistance systems with different control strategies available for the control of anaesthesia depth [3–5, 7, 10, 19]. Target controlled infusion 1117

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(TCI) systems allow for the automatic application of intravenous anaesthetics based on pharmacokinetic and pharmacodynamic models within predefined target concentrations, and such systems have been implemented in routine clinical practice for over a decade, mostly for the computer-assisted dosing of propofol. However, it seems that closed-loop systems, which implement target parameters (such as anaesthesia depth) as controls in their strategies, are better than open-loop TCI systems. De Smet and colleagues were recently able to show that a target BIS level based on closedloop system-titrated propofol use is much more exact than manual BIS control via a TCI system [19]. For the development of a control system based on expert knowledge without a mathematical model for the automated application of a continuous propofol infusion, the use of a fuzzy controller seemed appropriate as it allows human experience and observation-based knowledge to produce the rules for decision-making. It is useful to implement fuzzy logic when, as in this situation, imprecise mathematical models are used to describe a non-linear phenomenon for the interaction between propofol dosing and BIS and when such mathematical descriptions can be formulated out of linguistically formulated rules via fuzzy logic. For this process the controller was developed on the basis of documented operative courses with the goal of mimicking the reaction of the anaesthetist and his actions. The reported mean mivacurium consumption for continuous administration to maintain neuromuscular blockade at 89–99% twitch suppression without the use of a control system in adults is 6–7 lg.kg)1.min)1 [21]. We found that only 4.25 (1.25) lg.kg)1.min)1 of mivacurium was needed to maintain 90% neuromuscular blockade during the adaptive control phase. In contrast, Kansanaho and Olkkola reported a mean (SD) mivacurium consumption of 7.5 (3.1) lg.kg)1.min)1 [22]. Unlike our study, however, theirs targeted a set value of 95% block. Schumacher et al. reported a mean (SD) consumption of 7.0 (2.2) lg.kg)1.min)1 related to a target value of neuromuscular blockade of 90% [12]. They found large intrapatient variability in mivacurium requirements during surgery – the mean infusion rate differed by a factor of 1.8 between the lowest and highest requirements over a 30-min period in the same patient. Hemmerling et al. reported on a clinically relevant effect of propofol and the length of propofol anaesthesia on mivacurium potency (augmentation after 20 min approximately 1.5-fold) and mentioned the conflicting data on whether or not 1118

propofol directly affects peripheral muscle contractility [23]. Our results suggest a positive interaction, considering the comparatively low mivacurium requirements in this first simultaneous controlling of anaesthesia depth and neuromuscular blockade. The interaction of neuromuscular blockade and BIS monitoring are discussed in the literature and previous work is conflicting. Vivien et al. found that the BIS values in ICU patients receiving neuromuscular blocking drugs are lower than in patients not receiving them [24]. In contrast, Dahaba et al. could not show changes in the BIS-XPTM-index for neuromuscular blockade with a TOF ratio between 0 and 0.68 [25]. The mean (SD) propofol consumption in our study was 92 (31) lg.kg)1.min)1 (or 5.5 (1.8) mg.kg)1.h)1), which is comparable to the results from other working groupsHemmerling et al. 120 (28) lg.kg)1.min)1 [5], Liu et al. 4.40 (1.8) mg.kg)1.h)1 [3], Struys 6.39 (1.13) mg.kg)1.h)1 [4]. In summary, there may be a distinct advantage in using computer-assisted anaesthetic dosing that is adjusted specifically to the individual patient and intra-operative requirements. It may prevent underdosing-related awareness events and insufficient neuromuscular blockade and overdosing. Several experimental control and assistance systems have been successfully implemented. However, they are not widely accepted. The reasons for this include technical problems with respect to signal quality, the need for plausibility checks to rule out artefacts and user-friendliness. The decisive criterion for future implementation of anaesthetic control systems will be the development of user-friendly systems to demonstrate their potential advantages. The simultaneous closed-loop system evaluated in this study allows for a clinically practical, nearly fully automated infusion of propofol and mivacurium during medium-length surgical procedures with acceptable technical requirements and high precision. Therefore, the combined maintenance of anaesthesia depth and neuromuscular blockade with the use of a model-based closed-loop controller at the level desired by the anaesthesiologist is a promising alternative to current practice. Acknowledgement

The authors are grateful to the German Science Foundation (DFG) for financial support. Competing interests

No competing interests declared. 2011 The Authors Anaesthesia 2011 The Association of Anaesthetists of Great Britain and Ireland

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References 1 Gaba DM, Fish KJ, Howard SK. Crisis Management in Anesthesiology. New York: Churchill Livingstone Inc, 1994. 17. 2 Struys MM, Mortier EP, De Smet T. Closed loops in anaesthesia. Best Practice & Research Clinical Anaesthesiology 2006; 20: 211–20. 3 Liu N, Chazot T, Genty A, et al. Titration of propofol for anesthetic induction and maintenance guided by the Bispectral index: closed-loop vs manual control. Anesthesiology 2006; 104: 686–95. 4 Struys MM, De Smet T, Versichelen LF, Van de Velde S, Van den Broecke R, Mortier EP. Comparison of closed-loop controlled administration of propofol using bispectral index as the controlled variable vs ‘standard practice’ controlled administration. Anesthesiology 2001; 95: 6–17. 5 Hemmerling TM, Charabati S, Zaouter C, Minardi C, Mathieu PA. A randomised controlled trial demonstrates that a novel closed-loop propofol system performs better hypnosis control than manual administration. Canadian Journal of Anesthesia 2010; 57: 725–35. 6 Fuchs-Buder T, Claudius C, Skovgaard LT, Eriksson LI, Mirakhur RK, Viby-Mogensen J. Good clinical research practice in pharmacodynamic studies of neuromuscular blocking agents II: the Stockholm revision. Acta Anaesthesiologica Scandinavica 2007; 51: 789–808. 7 Locher S, Stadler KS, Boehlen T, et al. A new closedloop control system for isoflurane using bispectral index outperforms manual control. Anesthesiology 2004; 101: 591–602. 8 Varvel JR, Donoho DL, Shafer SL. Measuring the predictive performance of computer-controlled infusion pumps. Journal of Pharmacokinetics and Biopharmaceutics 1992; 20: 63–94. 9 Bauer M, Bo¨hrer H, Aichele G, Bach A, Martin E. Measuring patient satisfaction with anaesthesia: perioperative questionnaire vs standardised face-to-face interview. Acta Anaesthesiologica Scandinavica 2001; 45: 65–72. 10 Absalom AR, Sutcliffe N, Kenny GN. Closed-loop control of anesthesia using bispectral index. Anesthesiology 2002; 96: 67–73. 11 Eleveld DJ, Proost JH, Wierda JM. Evaluation of a closed loop muscle relaxation control system. Anesthesia and Analgesia 2005; 101: 758–64. 12 Schumacher PM, Stadler KS, Wirz R, Leibundgut D, Pfister CA, Zbinden AM. Model-based control of neuromuscular block using mivacurium: design and clinical verification. European Journal of Anaesthesiology 2006; 23: 691–9. 13 Illman H, Antila H, Olkkola KT. Quantitation of the effect of nitrous oxide on rocuronium infusion


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requirements using closed-loop feedback control. Anesthesiology 2008; 108: 388–91. Hemmerling TM, Charabati S, Mathieu PA. McSleepyTM- a completely automatic anesthesia delivery system. STA Annual Meeting abstracts 2009: 47. Gentilini A, Rossoni-Gerosa M, Frei CW, et al. Modeling and closed-loop control of hypnosis by means of bispectral index (BIS) with isoflurane. IEEE Transactions on Biomedical Engineering 2001; 48: 874–89. Ha¨nzi P, Leibundgut D, Wessendorf R, Lauber R, Zbinden AM. Clinical validation of electromyography and acceleromyography as sensors for muscle relaxation. European Journal of Anaesthesiology 2007; 24: 882–8. Pohl B, Hofmockel R, Simanski O, Wende K, Lampe BP. Feedback control of muscle relaxation with a varying on-off controller using cisatracurium. Anaesthesist 2004; 53: 66–72. American Society of Anesthesiologists Task Force on Intraoperative Awareness. Practice advisory for intraoperative awareness and brain function monitoring: a report by the american society of anesthesiologists task force on intraoperative awareness. Anesthesiology 2006; 104: 847–64. De Smet T, Struys MMRF, Neckebroek MM, van den Hauwe K, Bonte S, Mortier EP. The accuracy and clinical feasibility of a new Bayesian-based closed-loop control system for propofol administration using the bispectral index as a controlled variable. Anesthesia and Analgesia 2008; 107: 1200–10. Mahfouf M. Generalised predictive control (GPC) in the operating theatre. In: Linkens D, ed. Intelligent Control in Biomedicine. London: Taylor & Francis, 1994: 37–77. Apfelbaum JL. Mivacurium chloride administration by infusion. Acta Anaesthesiologica Scandinavica 1995; 39 (Suppl. 106): 55–7. Kansanaho M, Olkkola KT. The effect of halothane on mivacurium infusion requirements in adult surgical patients. Acta Anaesthesiologica Scandinavica 1997; 41: 754–9. Hemmerling TM, Le N, Decarie P, Cousineau J, Bracco D. Total intravenous anesthesia with propofol augments the potency of mivacurium. Canadian Journal of Anesthesia 2008; 55: 351–7. Vivien B, Di Maria S, Ouattara A, Langeron O, Coriat P, Riou B. Overestimation of bispectral index in sedated intensive care unit patients revealed by administration of muscle relaxant. Anesthesiology 2003; 99: 9–17. Dahaba AA, Mattweber M, Fuchs A, et al. The effect of different stages of neuromuscular block on the bispectral index and the bispectral index-XP under remifentanil ⁄ propofol anesthesia. Anesthesia and Analgesia 2004; 99: 781–7.

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Appendix

PEij ¼

ðBIS or T1measured BIS or T1setpoint Þ 100 BIS or T1setpoint

MDPEi ¼ medianfPEij ; j ¼ 1; . . . ; Ni g

BIS – bispectral index i – subject number j – jth measurement of observation period MDAPE – median absolute performance error MDPE – median performance error N – total number of measurements during the observation period PE – performance error T1 – first neuromuscular response following a trainof-four stimulation

MDAPEi ¼ medianfjPEij j; j ¼ 1; . . . ; Ni g

wobblei ¼ medianfjPEij MDPEi j; j ¼ 1; . . . ; Ni g

1120
