1 Department of Anaesthesiology, Section of Research, University of Berne, Inselspital, CH-3010 Berne, Switzerland. 2 Automatic Control Laboratory, Swiss Federal Institute of Technology (ETH), CH-8092 Zurich, Switzerland
*Corresponding author. E-mail: peter.schumacher{at}dkf5.unibe.ch
Accepted for publication: February 1, 2004
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Abstract |
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Methods. We studied 16 ASA III patients (mean age 38 (range 2059) yr; weight 67 (5487) kg) during i.v. anaesthesia for elective surgery. After periods of normal ventilation the patients were either hyper- or hypoventilated to assess precision and dynamic behaviour of the control system. These data were compared with a previous group where a fuzzy-logic controller had been used. Responses to different clinical events (invalid carbon dioxide measurement, limb tourniquet release, tube cuff leak, exhaustion of carbon dioxide absorbent, simulation of pulmonary embolism) were also noted.
Results. The model-based controller correctly maintained the setpoint. No significant difference was found for the static performance between the two controllers. The dynamic response of the model-based controller was more rapid (P<0.05). The mean rise time after a setpoint increase of 1 vol% was 313 (SD 90) s and 142 (17) s for fuzzy-logic and model-based control, respectively, and after a 1 vol% decrease was 355 (127) s and 177 (36) s, respectively. The new model-based controller had a consistent response to clinical artefacts.
Conclusion. A model-based FE'CO2 controller can be used in a clinical setting. It reacts appropriately to artefacts, and has a better dynamic response to setpoint changes than a previously described fuzzy-logic controller.
Br J Anaesth 2004; 92: 8007
Keywords: anaesthesia, closed-loop system; models, biological; ventilation, mechanical
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Introduction |
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We designed a new model-based controller for mechanical ventilation, applied it clinically and studied the response to artefacts. We assessed setpoint precision and dynamic behaviour and compared this with a fuzzy-logic controller presented by Schäublin and colleagues.2 We expected the new device to be as stable and have a better dynamic response.
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Methods |
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The patients were given omeprazole 40 mg orally the evening before surgery and premedicated with midazolam 7.5 mg orally 12 h before surgery. Anaesthesia was induced with propofol 2 mg kg1and fentanyl 0.3 µg kg1 i.v. followed by a continuous infusion of propofol and remifentanil according to clinical needs. A dose of mivacurium 0.3 mg kg1 was given using an Asena-GHTM pump and the trachea was intubated. Oesophageal temperature was measured and kept above 35 °C using a forced air warmer blanket. Standard measures during the study included: invasive continuous and non-invasive intermittent systolic, diastolic and mean arterial pressure, continuous ECG, heart rate, FE'CO2, ventilatory frequency (f), tidal volume (VT), minute volume (MV), transcutaneous peripheral oxygen saturation, peak (PPeak) and plateau airway pressure, inspired oxygen fraction, bispectral index and neuromuscular blockade monitoring using electromyography.
The FE'CO2 was measured at the mouthpiece by side-stream infrared spectrometry (Dräger Medical AG, Lübeck, Germany), calibrated according to the manufacturers instructions. This gave an input signal for the automatic ventilation controller. Normoventilation was defined as FE'CO2=4.5% (35 mm Hg), hyperventilation as FE'CO2=3.5% (28 mm Hg) and hypoventilation as FE'CO2=5.5% (42 mm Hg). All patients were initially normoventilated. After reaching the target FE'CO2 and having maintained a stable measurement period of at least 15 min, the setpoint was randomly changed to either hyperventilation or hypoventilation (1 vol% (7 mm Hg) setpoint change respectively). To assess the dynamic performance of the controller, the setpoint was changed by 2 vol% and 1 vol% steps until the end of the operation, maintaining a setpoint for at least 15 min. Manual control of ventilation was re-established for the end of anaesthesia. All monitoring data were digitized every 5 s and stored on a hard disk.
Mathematical model and controller design
The physiological model was derived from Chiari and colleagues.3 They presented a comprehensive model of oxygen and carbon dioxide exchange, transport and storage in the adult human that gave realistic responses under different physiological conditions. The model had three compartments (lung, brain and body tissue) with corresponding mass-balance descriptions including compartment volume, gas exchange and metabolic production. For the controller design, the model was simplified by assuming constant cardiac output and constant oxygen saturation in arterial and venous blood, so that carbon dioxide dissociation curves were not affected by oxygen saturation.4 This gave a model that was considered sufficiently descriptive for closed-loop control purposes. A simplified schematic structure of the controller is shown in Figure 1.
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The desired MV was calculated by the controller every 5 s. Algorithm J was developed to translate this value into appropriate values of f and VT for the ventilation system. An upper constraint on Ppeak and desired settings for ventilatory frequency fD and tidal volume VTD was set by the anaesthetist to account for different patient features. When Ppeak was reached, f was automatically increased, thus VT decreased and Ppeak was reduced.
Observer-based feedback systems are generally less sensitive to variation and therefore the controller could be tuned more aggressively than standard proportional-integral-derivative controllers. By adding an integral action (kI), steady-state errors could be minimized. The controller was set up on a real-time control platform interfaced with a modified Cicero anaesthesia workplace (Dräger Medical AG, Lübeck, Germany).
Performance analysis and statistics
Controller performance was assessed by comparing the measured FE'CO2 values (the controlled variable Cm) and the preset FE'CO2 reference values (Cr) and calculating eFE'CO2 as the difference between the FE'CO2 reference value and the measured FE'CO2 value. To assess the setpoint precision, the variables listed below were calculated for each patient for all setpoint values of the ventilation pattern (normo-, hyper- and hypoventilation) for the period of 10 min before changing to the next setpoint. The first two variables were defined as in the previous group with fuzzy-logic control, whereas variables 37 were calculated for the model-based control group only:
(1) MD, the mean deviation from setpoint (MD=mean eFE'CO2) as an indicator of the bias of the control.
(2) MDS, the standard deviation of eFE'CO2 as an indicator of the stability and range of deviation of the control.
(3) MAD, the mean absolute deviation from setpoint resulting in Equation 1 for subject i as an indicator of inaccuracy of the control, where Cmij and Crij represent the jth measured and reference value for the ith subject, respectively.
Additional measures as proposed by Varvel and colleagues5 for the evaluation of the prediction performance of computer-controlled infusion pumps and also used to assess setpoint precision of feedback systems,6 7 were calculated.
(4) MDAPE, the median absolute performance error, an indicator of precision or inaccuracy of the control in subject i.
where PEij is the performance error calculated as the weighted difference between measured and reference values (Equation 3) and Ni is the number of performance errors in the ith subject.
(5) MDPE, the median performance error, indicator of bias of the control in subject i, including the signs of the errors (Equation 4).
(6) The wobble is the measure of the variability of the performance errors in subject i (Equation 5).
(7) The divergence measures the time-related trend of the measured effects in relation to the targeted values.
As indicators of dynamic performance, we measured rise time (time required to move from 10% to 90% of steady state of the desired change) and overshoot (the absolute maximum value achieved, expressed as absolute value above or below the steady-state value after a step change of the setpoint).2 8 9
Schäublin and colleagues2 studied 20 male and 10 female ASA class IIII patients (mean age 47 (range 1284) yr; weight 67 (4193) kg), during general anaesthesia for elective surgery. Anaesthetic management except ventilation was according to usual practice. They imposed two step changes from a target FE'CO2 of 4.5 to 5.5%, each step lasting at least 20 min. The sequence of the two steps done manually and by the fuzzy-logic controller was chosen randomly. They measured static performance, using indicators 1 and 2 above, for each individual in the last 10 min of each step. Dynamic performance was assessed as above.
The patients in the current clinical trial were compared with this historic control group using Students t-test. P<0.05 was considered significant using a power of 0.8.
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Results |
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Setpoint precision evaluation
In Table 2 the groups are compared in terms of the precision measures and the ventilation values for normo-, hypo- and hyperventilation. No significant difference was found between the groups for these steady-state condition results. Measures of setpoint precision, calculated for the model-based control group only, confirm the stable performance of the model-based controller.
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When the carbon dioxide absorbent was exhausted towards the end of the operation, carbon dioxide accumulated in the breathing system and was re-breathed by the patient. The controller reacted by increasing MV to maintain the target setpoint (Fig. 4).
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The effect of a pulmonary embolism was simulated. The pulmonary shunt of the model was suddenly increased, thereby reducing the pulmonary flow and in consequence alveolar perfusion. The control system reacted by considerably decreasing MV in order to maintain FE'CO2at the preset level.
The potentially harmful consequences of the latter two incidents are discussed below.
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Discussion |
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Patients were satisfactorily ventilated with either control algorithm (model-based or fuzzy-logic) and no difference was found in the setpoint precision. The model-based system responds significantly faster to setpoint changes (P<0.05). The SD of the rise time was less in the model-based group (P<0.05), indicating a more consistent behaviour with step changes. This could be useful when rapid changes in ventilation are needed such as when carbon dioxide partial pressure increases after limb tourniquet release or if ventilation has to be adapted to prevent or treat cerebral oedema.10
Additional measures of setpoint precision and dynamic behaviour were calculated for the model-based group. Because of the very small control bias (MD), the MAD indicator of inaccuracy showed a direct correlation to the SD of eFE'CO2 (MDS), confirming stability of control. However, the measures defined by Varvel and colleagues5 and used by others7 to estimate control quality proved to be quite insensitive to the control deviations. Except for the very small divergence values, all other values were zero. The use of median values reduces sensitivity (e.g. if the controller would maintain an exact setpoint for more than half of the time, the indicators would be zero without showing what happened the rest of the time). In summary all these measures indicated that the controller could regulate FE'CO2 appropriately.
We found that the rise time for the model-based controller was significantly less for an increase than for a decrease for the 1 vol% steps but longer for the 2 vol% steps. This was caused by two different constraints of the controller: (i) MV was allowed to change by only 10% from one control cycle to the next. Increasing FE'CO2 means decreasing MV, in which case the actuator was reacting faster because of the 10% constraint; (ii) for the large increase the minimal MV (2.12.6 litre min1 depending on body weight) was imposed before the 5.5% FE'CO2 was achieved, therefore dominating the rise time.
Bickford11 described the first example of the application of closed-loop systems in anaesthesia in 1950, in animals and in man. Automatic control of FE'CO2 was suggested as early as 1974, and subsequent research showed that this could be done.12 13 Different methods of feedback control have been developed and implemented to improve the control of anaesthesia, relieve physicians from routine activities and increase safety.7 8 1416 Several attempts have been undertaken to automate mechanical ventilation. Laubscher and colleagues17 described a PI-based controller (controller with an output proportional (P) to the difference between input value and setpoint, and to the (I) integration of this difference over a certain time). Special selection algorithms were used to maintain target alveolar ventilation by selecting f and VT as close to physiological needs as possible. This allowed ventilation to be adjusted according to the state of health of the patient. In this case, continuous measurements and analysis of expired carbon dioxide, airway pressure and airway flow were required.
The fuzzy-logic controller described by Schäublin and colleagues2 had a satisfactory steady-state performance. However, its structure, based on 29 interacting linguistic rules, was very complex and hindered optimization and artefact handling. The present model-based controller performed well and also had a straightforward design based on mathematical models, which could facilitate future approval by authorities and/or official bodies. The model-based controller is familiar with the behaviour of the process that it is adjusting; a priori information about the natural process not available to model-independent controller types such as fuzzy-logic can be used to improve dynamic performance. We have shown this was indeed the case. Furthermore, with a sufficiently general model, the controller can handle different ventilation regimens.
However, automatic controllers of mechanical ventilation cannot directly recognize dead-space ventilation, for example in the case of pulmonary embolism. With decreasing FE'CO2 because of increased dead-space ventilation, the controller would react by reducing the ventilation, thereby keeping FE'CO2 as close to setpoint as possible and this would increase arterial carbon dioxide partial pressure. This also occurred during a trial when the tube cuff leaked, which resulted in a reduced effective VT and reduced alveolar ventilation. With pulmonary embolism, the controller would react to the decrease of FE'CO2 with a reduced MV, as was verified in a simulation environment. The detection of increased dead-space ventilation and/or circulatory compromise, leading to decreased carbon dioxide return, is therefore possible when monitoring MV. However, we consider an MV alarm to be less dependable in a clinical setting than an FE'CO2 alarm, because it depends on the size of the patient. To increase safety, we suggest that the controller should detect and alarm if a sudden or unexplained decrease in MV occurs in relation to patient features such as weight, height and sex. In an alarm situation, the controller could be switched to the (calculated) predicted value of FE'CO2, thus maintaining MV according to standard patterns until the anaesthetist resolves the situation and clears the alarm. The controller could also process the continuous carbon dioxide fraction and flow measurement, calculate anatomical dead space and signal changes.
Automated control in anaesthesia is increasingly studied for various input and output measurements. Because our model-based controller can maintain adequate control despite various measurement artefacts, it could serve as an example for development of robust (artefact-tolerant) controllers. Once robust control is routinely established in anaesthesia, the simultaneous use of automatic controllers of different systems (e.g. mean arterial pressure, bispectral index, neuromuscular relaxation, ventilation) could considerably relieve the anaesthetist from routine control work, allow better understanding of the interactions between the various control loops and should improve patient care. This could open new perspectives for both research and clinical use.
Both the fuzzy-logic and the model-based controller can maintain a chosen setpoint with high precision. The dynamic performance of the model-based controller was better. The responses to several artefacts showed that the model-based control is robust. This controller seems to meet the requirements for routine clinical application.
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Acknowledgement |
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References |
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