1Centre for Research into Anaesthetic Mechanisms, Department of Biomedical Science, The University of Sheffield, Western Bank, Sheffield S10 2TN, UK. 2Department of Automatic Control and Systems Engineering, Amy Johnson Building, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK 3MRC Institute of Hearing Research, University Park, Nottingham NG7 2RD, UK and 487, Hsiding, Taihsi, Yunlin 63608, Taiwan
Accepted for publication: April 15, 2000
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Abstract |
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Br J Anaesth 2000; 85: 4319
Keywords: brain, evoked potentials; brain, cortex, cerebral; anaesthetics i.v., propofol
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Introduction |
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Various strategies have been employed in attempts to develop systems of feedback control in anaesthesia. Some studies have investigated the use of the electroencephalogram1 or its derivatives,26 but signal processing and electroencephalographic pattern analysis have proved complex and difficult. An alternative approach has been the use of auditory evoked potentials for anaesthetic monitoring and control.7 8 Likewise, somatosensory evoked potentials show progressive changes with alterations in the depth of anaesthesia.9 10 The absence of appropriate techniques for estimating rapidly and reliably the diagnostic components of evoked responses has, however, led to their use being confined to off-line anaesthesia analysis and to neurological diagnostic tests; they are never used in the control of anaesthesia in real time.
We have developed a system which obtains reliably an estimate of moment-by-moment changes in the latency of the somatosensory evoked response. Using a process of proportionalintegral (PI) control, the system executes instantaneous adjustments to the rate of delivery of intravenous propofol. Once the operator has defined a desirable anaesthetic end-point, in terms of altered evoked response latency, the system is able, through closed-loop feedback, to maintain this end-point reliably until instructed otherwise. This technique contrasts both with semi-automated methods of control, such as target-controlled infusion (TCI), and with the step-down manual approach to propofol administration. These latter techniques are open-loop methods derived from population-average pharmacokinetic data; they are crucially reliant upon modifications made by the anaesthetist in each individual case. In our closed-loop system, the anaesthetic state is monitored continuously and the rate of delivery of drugs is matched to the precise requirements of the subject. In addition, the burden of repetitious manual evaluation of the depth of anaesthesia is much reduced, and a continuously updated graphical display of changing evoked response indices provides an easily appreciable measure of the depth of anaesthesia of the subject.
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Materials and methods |
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Experiments were conducted consecutively after the control system had been properly validated and any programming problems had been eliminated. Initial pilot trials included calibration of the infusion pump and tuning of the PI control parameters (see below). Subsequently, a series of five experiments was undertaken because, in experiments examining anaesthetic mechanisms, a sample of this size is usually sufficient to elucidate neurophysiological effects.
Surgical procedures
Five female albino Wistar rats of the Sheffield strain, in the weight range 190210 g, were anaesthetized by intraperitoneal injection of 1.251.5 g kg1 of urethane 25% (ethyl carbamate; Sigma-Aldrich, Poole, UK) in saline 0.9% without premedication. Tracheotomy was performed and the left external jugular vein was cannulated with PP30 polythene tubing (Portex, Hythe, UK) containing 0.9% saline. The foramen magnum was opened and the arch of the first cervical vertebra was removed, exposing the dorsal surface of the medulla. An extensive craniotomy was performed and the dura mater was reflected to expose the surface of the left cerebral hemisphere. No signs of cortical surface damage or of cerebral oedema were observed in any animal. The animal was suspended in a stereotaxic frame and a liquid paraffin pool was formed over the surface of the brain. The animals body temperature was maintained at 37.5±0.5°C.
Stimulation
Somatosensory mass responses were evoked, five times per second, by percutaneous electrical stimulation of the contralateral forepaw using 0100 V square-wave pulses of 100 µs duration (Mark IV isolated stimulator; Devices Ltd, Welwyn Garden City, UK). Stimuli of sufficient intensity to activate Group A fibres supramaximally were delivered.
Recording
Cortical mass responses were recorded via a pair of silver wire electrodes which were fused at their tips to form small balls of approximately 0.5 mm diameter. One electrode was placed gently in contact with the surface of the primary somatosensory receiving area, the other in contact with the surface of the occipital cortex. Mass responses, amplified and filtered with a bandpass of 0.5 Hz2 kHz, were visualized on a cathode ray oscilloscope and were digitized at 25 kHz. On-line averaging and analysis were performed using a microcomputer running locally written software, which is described below. A common timing pulse was used to trigger the stimulator, oscilloscope and microcomputer. Average evoked responses of 30 individual responses were calculated, thus providing a sampling period of 6 s for signal processing and control.
Administration of drugs
Anaesthesia was induced and maintained by administration of a single dose of urethane. Neurophysiological recording did not commence until at least 1 h after the completion of surgery. Before neurophysiological recording commenced, the majority of the saline in the intravenous cannula was displaced with propofol emulsion 10 mg ml1 (Diprivan; Zeneca, Macclesfield, UK). Care was taken to ensure that propofol was not administered inadvertently to the animal at this stage of the experiment. The propofol-containing syringe was mounted in a Harvard variable-speed infusion pump (Harvard Apparatus, Edenbridge, UK), which was modified to allow control of the infusion rate by a microcomputer.
After a 50 min period of recording under urethane anaesthesia alone, the closed-loop control system was instructed to administer propofol so as to achieve and maintain a 1 ms increase in the latency of the somatosensory evoked potentials. After an 80 min period, during which this latency increase was maintained, propofol administration was discontinued and recording continued for a further period of 110 min to allow complete recovery to the baseline. In no experiment did the animal receive a total volume of propofol of more than 0.9 ml.
Automatic measurement of somatosensory evoked potentials and infusion of propofol
In each experiment, the analysis program obtained an initial average response, which it used as a template against which all subsequent average responses were compared. The first positive inflection in the somatosensory evoked potential always exists, regardless of the shape of the onset and the first positive peak. As illustrated in Fig. 1, the time difference, or latency change, between two averages was measured by shifting the estimation average towards the template average, to arrive at a maximum match along the two inflections. The inflection is represented as a regression model with the peak as a seed point for model inference. The peak of the first positive inflection was localized with a feature-extraction engine which is a composite of wavelet transforms, geometric analysis, artificial intelligence and mathematical analysis. For each subsequent response, the change in latency, compared with that of the template response, was calculated.
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Results |
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Closed-loop control of propofol infusion
In a series of five experiments, the desired prolonged increase in latency, followed by recovery to baseline values, was attained. Figure 3 shows records obtained in two of the animals in our sample. These two examples were chosen because they illustrate the difference in the extent of spontaneous fluctuation in the latency of response that occurs between animals. The pattern of controlled infusion of propofol under each set of conditions is also shown. In each case, the initial period under urethane anaesthesia alone was associated with a constant mean latency change about which small fluctuations occurred. The extent of this fluctuation varied between animals but is characteristic of animals anaesthetized with urethane11 or halothane.12
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The success of the system may be evaluated using statistical methods. The performance of the control system is indicated using a statistical steady-state error defined as
ESS=(µCSP)/SP(1)
and a statistical dispersion index
d=
c /
b(2)
where the mean value µ defines the central tendency of a time series {y(t)} and the standard deviation defines the dispersion of {y(t)}, the subscript c representing the controlled period and b the baseline period; SP is the set-point. For a good control session, the mean value µ should overlap the set-point at a maximum coincidence with a certain level of variance (
2). For a stable or an asymptotically stable system, the system output should cease oscillation when the system becomes stable. Thus, the dispersion variable
can be used as an index in measuring how stable and controllable the system is.
The variable ESS% was used as an index of how well integral control performed, while d describes the dispersion of the controlled responses (governed by proportional control) relative to the baseline. In a stable and controllable system,
d approximates to 1, meaning that the controlled period oscillates at an intensity similar to the baseline period. A controller is said to have good performance when
d is less than 1 and, hence, where it achieves less oscillation than is seen during the uncontrolled period.
Results from the five experiments which are reported here are given in Table 1. Although the control system was able to track the set-point, there were significant steady-state errors in each experiment. This occurred because control parameter values were fixed across the five experiments and hence were not optimized for each individual animal.
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Discussion |
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Use of somatosensory mass evoked responses
Mass responses recorded from the cortical surface following electrical stimulation of the contralateral forepaw have been suggested to result from the transmission of information in the dorsal column medial lemniscal pathway. The size of the responses has been suggested to reflect the magnitude of the thalamocortical afferent volley and the activation of cortical neurons (reviewed by Angel14). The administration of all general anaesthetics which have been tested has been found to cause a dose-dependent increase in the onset latency of the evoked potential.15 Likewise, the imposition of noxious stimuli or the administration of stimulant drugs is associated with a reduction in the latency. Changes in the onset latency thus provide an index of the action of anaesthesia on the transfer of information in the dorsal column pathway and, by implication, of the depth of anaesthesia.
The cortical responses which we measured have been shown in previous studies to result from the transmission of touch/pressure-type proprioceptive information rather than from the transmission of information related to pain: cortical evoked responses disappear after lesion of the dorsal columns of the spinal cord.16 The vast majority of cells which are activated by electrical stimulation have small, spot-like peripheral receptive fields on the contralateral forepaw and are activated by touch, pressure and claw and hair movement.17 The latency of the evoked response in the unanaesthetized rat is 3.5 ms,14 which, assuming a synaptic delay of 0.8 ms,18 leaves 3.5(0.8x2)=1.9 ms for conduction from the wrist to the cortex. The total length of this path was approximately 140 mm in our animals, suggesting a conduction velocity of approximately 74 m s1. This value is considerably higher than the maximum conduction velocity of 30 m s1 which has been observed in fast pain A fibres. Thus, on the basis of the spinal cord location of afferent fibres, their peripheral receptive field properties and the speed of conduction in the ascending pathway, the cortical evoked responses reflect activity in the tactile, rather than the nociceptive or thermal, sensory afferent pathways.
Effects of urethane anaesthesia on somatosensory evoked responses
Urethane anaesthesia was used in this study because it provides good surgical anaesthesia, has an extremely long half-life and has little cardiovascular or respiratory effect.19 It has been found to provide a stable baseline upon which to test the neuronal effects of other general anaesthetic drugs.14 Previous experiments in this laboratory have demonstrated the precise agreement, in terms of the direction and magnitude of anaesthetic-induced perturbation in somatosensory evoked responses, between results obtained in studies in urethane-anaesthetized animals and those from experiments in chronically implanted, initially conscious animals.20 The effects of propofol that were observed in this study are likely, therefore, to mirror those which would be obtained in an initially conscious animal.
Choice of propofol for this study
Several studies have demonstrated recently the advantages of anaesthesia in which the anaesthetic state is maintained by intravenous infusion of propofol.2123 Previous experiments under the same conditions as those used in the current study have shown bolus administration of propofol 5 mg kg1 to cause a rapid increase in the latency of the cortical surface mass evoked response.10 This increase in latency became significantly different from the control value for latency within 50 s of the bolus and lasted 15 min after the administration of propofol. Propofol was thus clearly indicated as an agent with which to attempt computer-controlled regulation of the depth of anaesthesia in the rat.
Spontaneous fluctuations in depth of anaesthesia
Intentional changes in anaesthetic dosage, or in stimulation of the animal, cause well-characterized alterations in the latency of the evoked response, which have been described elsewhere.14 In addition, however, for reasons which remain obscure, indices of the depth of anaesthesia, including evoked responses (both somatosensory and auditory), the electrocorticogram, respiration, heart rate and blood pressure, exhibit apparently spontaneous fluctuations.14 These fluctuations are short-lived and vary about a relatively constant mean value. In order to avoid unnecessarily frequent changes in the control signals delivered to the infusion pump, data for latency change were smoothed using a low-pass digital filter which had a time constant of 24 s. Pilot experiments showed that this value was sufficient to damp short-lived fluctuations in the latency record without introducing a lag in controller responsiveness so great as to render the controller unable to compensate adequately for changes in the mean onset latency.
Automatic control of depth of anaesthesia
The results of this series of experiments show that it is possible to measure components of the somatosensory average evoked response in real time and to use this data as an index for the closed-loop control of delivery of an anaesthetic drug. Furthermore, the data suggest that it may be possible to regulate changes in the average evoked response, and thus in the depth of anaesthesia, on a moment-by-moment basis. Such a system would have the clear advantages of minimizing the subjects exposure to anaesthetic drugs, thus improving safety and cost-effectiveness while ensuring the delivery of appropriate quantities of these agents. The applicability of this system to the induction and maintenance of anaesthesia in initially conscious subjects could be demonstrated, subject to the necessary legal authority, by two series of fairly straightforward experiments. In the first series, animals could be anaesthetized and undergo surgery, as described above, using halothane (or some other readily reversible agent). With the control system activated, the halothane could be gradually withdrawn and, while concurrently monitoring physiological indices of arousal such as heart rate, blood pressure and electroencephalogram, the ability of the controller to maintain an appropriate depth of anaesthesia could be determined. In a second series of possible experiments, animals could be implanted chronically with intravenous cannulae and cortical surface electrodes (as described by Angel and Gratton).20 After a period of postoperative recovery, the animals could be connected to the controller, which would be instructed to induce and maintain anaesthesia. We have undertaken significant refinement of our system of closed-loop control, which is described below. We suggest that tests of closed-loop control using somatosensory evoked potentials in conscious animals should be delayed until these refined systems of automation have been validated.
The mean rate of administration of propofol that was determined by the controller fell within the middle of the range of values which are reported in the literature for intravenous administration in rats. In the two animals shown in Fig. 3, the controller delivered a mean infusion rate of 32 and 27.6 mg kg1 h1, respectively. These values are somewhat higher than the 14 mg kg1 h1 reported to be required for laparotomy in unpremedicated rats,24 but are somewhat lower than the 40 mg kg1 h1 that Yang et al.25 found was necessary to achieve a plasma concentration of 1.7 µg ml1, which they associated with loss of the tail-flick reflex and profound electroencephalographic changes. The reason for this wide variation is unclear, but may result from such factors as differences in animal susceptibility, differences in handling and differences in stimulation paradigms. It is likely that it was necessary for propofol to reach a minimum brain concentration in our animals in order to cause changes in the latency of the evoked response. This concentration, and its dependence on the infusion rate, is unlikely to have been affected by concurrent anaesthesia with urethane and we were not surprised, therefore, to find that values for mean infusion rate fell within the mid-range of values reported in the literature.
Although this system was developed using experimental animals, we argue that the technique has relevance for the development of schemes for the control of anaesthesia in humans. Human somatosensory evoked potentials have been shown, like those in our animals, to undergo an increase in latency and a decrease in amplitude with progressively increasing concentrations of most anaes thetics.9 26 The signal-to-noise ratio in human evoked response data is almost an order of magnitude poorer than that in animal studies. This problem may be overcome, however, using an appropriate, selective filtering scheme, such as that already incorporated in the latency change estimator.27 It is thus conceivable that human somatosensory evoked potentials could be analysed in real time for use in a system of closed-loop control of drug delivery.
The system which we have described has the important limitation that it responds to changes in the latency of the evoked response. Thus, there is an inevitable time lag in response to changes in the biological signal which we have taken as an index of neurological arousal. The problem of lag is further compounded by the need, which we have described, to smooth the data so as to reduce the effect of biologically unavoidable spontaneous fluctuations in the evoked response. The effect of smoothing, which is essentially an autoregressive process, is thus to add further delay between the time of occurrence of a biological change and the onset of the systems response. The simplest means by which to minimize performance deterioration owing to time lag is to choose a short sampling period. A rule of thumb in choosing an adequate sampling period is to select a period with one-twelfth to one-quarter of the rise time of the response. In rats, the rise time of the response to propofol administration is approximately 50 s;10 this indicates a range of sampling periods of 412 s. It is for this reason that we delivered stimuli at the rate of five per second, and hence achieved a sampling period of 6 s, so as to reduce, as far as possible, the time taken to acquire each measure of the average latency of response. A further stratagem for addressing this problem is to choose a set-point which is somewhat higher than that which is desired. This ensures that, at all times, the index of responsiveness remains safely above the set-point. This solution is less elegant, however, as it undermines one of the principal advantages of the closed-loop control system: that of minimizing the subjects exposure to anaesthetic.
The integral action of PI control is to eliminate steady-state error if the control parameters are selected appropriately. Selection of appropriate parameter values requires detailed model analysis and is only practicable in systems with consistent dynamics. It is unlikely, therefore, to be of use in living systems which have inherently varying dynamics. The difficulty associated with inappropriate control parameters is clearly reflected in Fig. 5, which shows a significant steady-state error during the automatic control period.
The problems of fluctuating response and steady-state error, which are caused by time lag and inappropriate parameter selection, has led us to combine the system of PI control, which we describe here, with a system of adaptive predictive control. We are currently working on such a system in which the controller learns the susceptibility and the responsiveness of each animal to propofol. The controller can thus make changes to the infusion rate in anticipation of the resulting biological changes. Thus, the problem of lag in controller responsiveness will be addressed and the delivery of propofol will be even more finely tuned to the requirements of the individual.
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Footnotes |
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References |
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