Somatosensory evoked potentials for closed-loop control of

British Journal of Anaesthesia 85 (3): 431±9 (2000)

LABORATORY INVESTIGATIONS Somatosensory evoked potentials for closed-loop control of anaesthetic depth using propofol in the urethane-anaesthetized rat A. Angel1 *, R. H. Arnott1 3, D. A. Linkens2 and C. H. Ting1

2 4

1

Centre for Research into Anaesthetic Mechanisms, Department of Biomedical Science, The University of Shef®eld, Western Bank, Shef®eld S10 2TN, UK. 2Department of Automatic Control and Systems Engineering, Amy Johnson Building, The University of Shef®eld, Mappin Street, Shef®eld S1 3JD, UK *Corresponding author. Present address:3MRC Institute of Hearing Research, University Park, Nottingham NG7 2RD, UK and 487, Hsiding, Taihsi, Yunlin 63608, Taiwan Primary somatosensory cortical mass responses have been shown to exhibit dose-dependent changes in latency when general anaesthetics are administered. Here we describe a system in which the latency of evoked responses was measured automatically in real time in ®ve animals. Latency changes were used to operate a closed-loop control of propofol delivery by intravenous infusion. The system attempted to induce and maintain a 1 ms increase in evoked response latency; this was reversed when infusion was discontinued. Allowing for the rapid and large biological ¯uctuations in the evoked response, this was achieved successfully. The system maintained a mean increase in latency of 1.27 (SD 0.42) ms. The mean statistical dispersion index of data obtained during the controlled period was 1.23 (0.3); in an ideal controllable system it approximates to 1. Such a system may provide a means for the automatic delivery of anaesthetics. Br J Anaesth 2000; 85: 431±9 Keywords: brain, evoked potentials; brain, cortex, cerebral; anaesthetics i.v., propofol Accepted for publication: April 15, 2000

Closed-loop control of the delivery of anaesthetic drugs offers the prospect of anaesthetic administration which is precisely matched to the anaesthetic requirements of the patient on a moment-by-moment basis. Systems of closed-loop control depend upon measuring an index of anaesthetic depth in real time so that alterations in the neurological state of the subject can be matched by appropriate alterations in the rate of delivery of anaesthetic drugs. The purpose of this study was to design and implement a system of closed-loop control based on realtime measurement of evoked potential latency, which is used as an index of anaesthetic depth. 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,2±6 but signal processing and electroencephalographic pattern analysis have proved complex and dif®cult. 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 con®ned 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 proportional±integral (PI) control, the system executes instantaneous adjustments to the rate of delivery of intravenous propofol. Once the operator has de®ned 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

Ó The Board of Management and Trustees of the British Journal of Anaesthesia 2000

Angel et al.

population-average pharmacokinetic data; they are crucially reliant upon modi®cations 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.

Materials and methods Experiments were performed in accordance with Project Licence PPL 40/1965 issued under the United Kingdom Animals (Scienti®c Procedures) Act 1986. 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 ®ve experiments was undertaken because, in experiments examining anaesthetic mechanisms, a sample of this size is usually suf®cient to elucidate neurophysiological effects.

Surgical procedures Five female albino Wistar rats of the Shef®eld strain, in the weight range 190±210 g, were anaesthetized by intraperitoneal injection of 1.25±1.5 g kg±1 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 ®rst cervical vertebra was removed, exposing the dorsal surface of the medulla. An extensive craniotomy was performed and the dura mater was re¯ected 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 paraf®n pool was formed over the surface of the brain. The animal's body temperature was maintained at 37.560.5°C.

Stimulation Somatosensory mass responses were evoked, ®ve times per second, by percutaneous electrical stimulation of the contralateral forepaw using 0±100 V square-wave pulses of 100 ms duration (Mark IV isolated stimulator; Devices Ltd, Welwyn Garden City, UK). Stimuli of suf®cient intensity to activate Group A ®bres 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, ampli®ed and ®ltered with a bandpass of 0.5 Hz±2 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 ml±1 (Diprivan; Zeneca, Maccles®eld, 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 modi®ed 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 ®rst positive in¯ection in the somatosensory evoked potential always exists, regardless of the shape of the onset and the ®rst 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

432

Closed-loop control of anaesthetic depth

two in¯ections. The in¯ection is represented as a regression model with the peak as a seed point for model inference. The peak of the ®rst positive in¯ection was localized with a feature-extraction engine which is a composite of wavelet transforms, geometric analysis, arti®cial intelligence and mathematical analysis. For each subsequent response, the change in latency, compared with that of the template response, was calculated. After an initial control period, the program was instructed to infuse suf®cient propofol to achieve and maintain a 1 ms increase in the latency. The control parameters of the infusion were determined by the results of prior modelling and simulation and the use of data from pilot experiments. The same control parameters were used for all ®ve animals in this study and were unchanged during the course of automatic control. The set-point of the controller was adjusted to re¯ect the desired latency increase. By con-

tinuous comparison of new data for the onset latency of the evoked potential with this new set-point, the controller undertook continuous change in the rate of delivery of propofol using the PI control algorithm. PI control was adopted because of the simplicity of tuning the control parameters on-line, as there were no adequate models for the control of propofol anaesthesia with somatosensory evoked potential as the feedback variable. Thus, at the beginning of the infusion period there was a large discrepancy between the desired latency change and the actual latency change, with the result that propofol was infused at a high rate. This rate was restricted by an infusion rate-limiter incorporated in the controller to prevent overdose. The rate limit was based on experimental values determined in pilot experiments. When values of actual latency change became closer to the desired latency change, the rate of infusion was lowered and was balanced continuously against any small discrepancies which arose during the remainder of the infusion period. Through this process, an elevated onset latency was maintained until the set-point change was returned to its control level and the animal was allowed to recover. Implementation of the control system is described in Fig. 2.

Results Somatosensory mass evoked responses Fig 1 The technique of in¯ection latency estimation. Two successive average evoked responses are shown by dotted lines. Upon these are superimposed solid lines to show the in¯ection models which were mathematically derived from the biological data. Dashed lines show the in¯ection model of the average after being shifted (q, Dy) towards the template. It is the extent of this shift which provides the index for changing latency between averages. Reproduced from Angel et al.,27 with permission.

Electrical stimulation of the contralateral forepaw was followed, with a latency of approximately 4 ms, by a characteristic series of in¯ections in the potential recorded from the surface of the primary somatosensory cortical receiving area. These in¯ections were of large amplitude (approximately 100 mV to the peak of the ®rst in¯ection), were easily measurable, and had a clearly de®ned onset latency.

Fig 2 Block diagram to show the drug delivery control system. All system parameters (i.e. of the PI controller, level limiter and ®lter) are adjustable in real time. The infusion pump is driven by analogue voltage commands and has two ramp modes, mm h±1 and mm min±1, with a resolution of 1 ramp unit. An appropriate ramp mode is selected by the pump driver according to the calculated infusion rate. The drug delivery control system was encapsulated as an additional module to an electrophysiological data acquisition system developed in Shef®eld.28 The overall system was implemented using the C++ language (Visual C++ v2.2, Microsoft, USA) based on the object-oriented programming technique, on personal computers running Windows 95. System operations were performed via a friendly graphic user interface with both hot keys and a mouse. Only the latency change was used as a feedback variable; however, other diagnostic components of the somatosensory evoked potential were also displayed.

433

Angel et al.

Fig 3 Records of the latency changes which were recorded in two of the animals in the study. (A) Data taken from an animal exhibiting a large degree of spontaneous ¯uctuation in its responsiveness. The upper panel shows the raw data obtained by measurement of changing latency (grey dots), upon which is superimposed the smoothed values of latency change which were calculated on-line and which were used by the controller in regulating infusion rate. The rapid onset of the effect of propofol is apparent, as is the period of gradual recovery which followed the cessation of infusion. The period during which the controller was instructed to induce a 1 ms increase in the latency, compared with that measured in the control period, is indicated by the horizontal black bar. The lower panel shows the rate of infusion of propofol 10 mg ml±1 i.v. under closed-loop control. The mean rate of administration, over the whole of the controlled period, was 32 mg kg±1 h±1. (B) Similar data taken from an animal which exhibited less spontaneous ¯uctuation in its responsiveness to the stimulus. The narrower scattering in the grey dots, which represent the raw data, is evident. Again, the superimposed line shows the smoothed values for latency change which were used in regulating the infusion rate. The lower panel shows the rate of infusion of propofol during the experiment, which had a mean rate of 27.6 mg kg±1 h±1 in this animal.

Closed-loop control of propofol infusion In a series of ®ve 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 ¯uctuation 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 ¯uctuations occurred. The extent of this ¯uctuation varied between animals but is characteristic of animals anaesthetized with urethane11 or halothane.12 The onset of infusion of propofol was associated with a rapid rise in the latency of responses measured in each animal. In each animal, the controller soon discontinued

infusion owing to overshoot in the latency change beyond the desired set-point. As the latency of response began to recover, the controller then recommenced infusion so as to catch the latency and maintain it at the set-point. In each animal, the controller then followed a unique pattern of propofol infusion in response to changes in the latency of evoked responses. The pattern was commonly an oscillation in infusion rate in response to ¯uctuation in the biological responses about the desired set-point or, possibly, a result of inadequate tuning of the control parameters. In one of the animals (Fig. 4) the latency change showed an unexpected excursion from the set-point approximately 40 min after the beginning of the infusion period. This unusual example illustrates the fast response of the controller in causing a rapid but short-lived increase in infusion rate, resulting in the return of the latency change to the set-point. Thus, the infusion rate was matched to changes in the latency of the

434


Fig 4 Plots similar to those obtained from the two animals which are represented in Fig. 3. Of interest is the excursion from the latency change set-point which occurred approximately 40 min after the beginning of the infusion period (asterisk). The rapid response of the controller (lower panel) in acting to restore the set-point through an increased rate of infusion is shown.

evoked potential. In each animal, the cessation of infusion was associated with a gradual recovery in the latency of the evoked response until the control level was restored. Figure 5 shows the mean latency changes recorded in our sample. The initial period of recording was associated with a stable baseline from which there was a stepped increase in latency when the administration of propofol commenced. This increase was maintained until the delivery of propofol was deliberately discontinued, after which baseline conditions returned gradually. The cumulative sum (cusum) technique was developed originally to facilitate the analysis of industrial quality control data;13 it facilitates the appreciation of changes in the average level of a set of sequentially obtained data. Assessment of the performance of the controller in closedloop control of the depth of anaesthesia is essentially a problem of quality control. Application of the cusum technique has allowed us to gauge easily the extent to which the controller achieved and maintained desired changes in the latency of the somatosensory evoked response. Horizontal portions of the cusum curve re¯ect periods in which collected data differ little from a predetermined set-point; more rapidly changing portions of the curve correspond to periods during which deviation from the set-point occurs. Figure 5 shows a cusum plot drawn using the mean values obtained from our sample. The comparison level is taken as the mean latency at the start of

Fig 5 Mean values of latency change which were recorded in our animals (n=5) are shown in the upper panel. The black curve represents the smoothed data, as in Figs 3 and 4, which are superimposed upon the raw mean values obtained every 6 s during the experiment (grey dots). The period of infusion of propofol is indicated by the vertical lines and the horizontal black bar. The lower panel shows the cusum plot constructed from these raw mean data. Periods in which measured values differed little from those at the start of the experiment are re¯ected in horizontal portions of the cusum plot. When values differed from this comparison level, these differences were cumulatively summed to yield a portion of the curve which shows an increased gradient. When propofol infusion was discontinued, the animals commenced gradual recovery such that the rate of change in the cumulatively summed differences declined. Thus, as the animals recovered, the gradient of the cusum plot gradually returns to horizontal. The stability of the increased latency that was induced by the controller is re¯ected in the unchanging gradient in the portion of the cusum plot corresponding to the period of propofol infusion. Note that the cusum plot has units of milliseconds, but these are not meaningful in this type of representation.

the recording period. Controlled infusion of propofol was associated with a constant deviation from this level; this is re¯ected in a diverging portion of the curve in which the constant new gradient re¯ects the consistent deviation. Discontinuation of infusion was associated with the gradual recovery (60 min in comparison with 23 min after administration of a bolus of propofol)10 of the animals. Recovery is seen in the gradual return of the gradient of the cusum curve towards the horizontal gradient obtained using data from the control period; thus the gradient of the plot is related to the extent to which mean data deviate from the comparison level. 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 de®ned as

435

Angel et al. Table 1 Performance of the PI control system. Fig. refers to the ®gure illustrating data from individual animals. SP=set-point; sb=standard deviation of the baseline; mc=mean latency in the controlled period; sc=standard deviation in the controlled period; ESS%=statistical steady-state error; sd=statistical dispersion index. For a stable and controllable system, sd should approximate to 1. Responses in the controlled period are strongly governed by the controller if sd is less than 1 Experiment

Fig.

SP (ms)

sb

mc

sc

ESS%

sd

1 2 3 4 5

4 3A ± 3B ±

1.0 1.0 1.0 1.0 1.0

0.6157 0.6205 1.3138 0.2904 0.8257

1.4227 1.0381 1.9046 0.8284 1.1286

0.6913 0.5734 1.5023 0.4979 1.0466

42.27 3.81 90.46 17.16 12.86

1.1228 0.9241 1.1435 1.7145 1.2675

ESS=(mC±SP)/SP

(1)

and a statistical dispersion index sd=sc / sb

brain tissue of our animals acting as a reservoir of propofol after an extended period of its administration.

(2)

where the mean value m de®nes the central tendency of a time series {y(t)} and the standard deviation s de®nes the dispersion of {y(t)}, the subscript `c' representing the controlled period and `b' the baseline period; SP is the setpoint. For a good control session, the mean value m should overlap the set-point at a maximum coincidence with a certain level of variance (s2). For a stable or an asymptotically stable system, the system output should cease oscillation when the system becomes stable. Thus, the dispersion variable s 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 sd describes the dispersion of the controlled responses (governed by proportional control) relative to the baseline. In a stable and controllable system, sd 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 sd is less than 1 and, hence, where it achieves less oscillation than is seen during the uncontrolled period. Results from the ®ve experiments which are reported here are given in Table 1. Although the control system was able to track the set-point, there were signi®cant steady-state errors in each experiment. This occurred because control parameter values were ®xed across the ®ve experiments and hence were not optimized for each individual animal.

Discussion In common with the results of previous experiments in the rat, propofol increased the latency of the somatosensory evoked response. Our automated system of infusion control, using the results of on-line measurement of changes in the latency of response, successfully induced and maintained an increase in response latency under closed-loop control. When propofol administration was discontinued, the latency gradually returned to preinfusion values; we speculate that the slowness of the recovery was a consequence of the non-

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 re¯ect 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 ®elds 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± (0.832)=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 s±1. This value is considerably higher than the maximum conduction velocity of 30 m s±1 which has been observed in `fast pain' A¶ ®bres. Thus, on the basis of the spinal cord location of afferent ®bres, their peripheral receptive ®eld properties and the speed of conduction in the ascending pathway, the cortical evoked responses re¯ect activity in the tactile, rather than the nociceptive or thermal, sensory afferent pathways.

436


Effects of urethane anaesthesia on somatosensory evoked responses

Automatic control of depth of anaesthesia

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.21±23 Previous experiments under the same conditions as those used in the current study have shown bolus administration of propofol 5 mg kg±1 to cause a rapid increase in the latency of the cortical surface mass evoked response.10 This increase in latency became signi®cantly 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 ¯uctuations 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 ¯uctuations.14 These ¯uctuations 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 ®lter which had a time constant of 24 s. Pilot experiments showed that this value was suf®cient to damp short-lived ¯uctuations 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.

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 momentby-moment basis. Such a system would have the clear advantages of minimizing the subject's 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 ®rst 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 signi®cant re®nement 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 re®ned 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 kg±1 h±1, respectively. These values are somewhat higher than the 14 mg kg±1 h±1 reported to be required for laparotomy in unpremedicated rats,24 but are somewhat lower than the 40 mg kg±1 h±1 that Yang et al.25 found was necessary to achieve a plasma concentration of 1.7 mg ml±1, which they associated with loss of the tail-¯ick re¯ex 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

437

Angel et al.

unlikely to have been affected by concurrent anaesthesia with urethane and we were not surprised, therefore, to ®nd 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 anaesthetics.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 ®ltering 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 ¯uctuations 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 system's 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 onequarter 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 4±12 s. It is for this reason that we delivered stimuli at the rate of ®ve 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 subject's 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 dif®culty associated with inappropriate control parameters is clearly re¯ected in Fig. 5, which shows a signi®cant steady-state error during the automatic control period. The problems of ¯uctuating 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 ®nely tuned to the requirements of the individual.

References

438

1 Bickford RG. Automatic electroencephalographic control of general anaesthesia. EEG Clin Neurophysiol 1950; 2: 93±6 2 Schwilden H, Stoeckel H. Closed-loop feedback controlled administration of alfentanil during alfentanil±nitrous oxide anaesthesia. Br J Anaesth 1993; 70: 389±93 3 Vijn PCM, Sneyd JR. I.v. anaesthesia and EEG burst suppression in rats: bolus injections and closed-loop infusions. Br J Anaesth 1998; 81: 415±21 4 Sebel PS, Lang E, Rampil IJ, White PF, Cork R, Jopling M, et al. A multicenter study of bispectral electroencephalogram analysis for monitoring anaesthetic effect. Anesth Analg 1997; 84: 891±9 5 Gajraj RJ, Doi M, Mantzaridis H, Kenny GNC. Comparison of bispectral EEG analysis and auditory evoked potentials for monitoring depth of anaesthesia during propofol anaesthesia. Br J Anaesth 1999; 82: 672±8 6 Sleigh JW, Donovan J. Comparison of bispectral index, 95% spectral edge frequency and approximate entropy of the EEG, with changes in heart rate variability during induction of general anaesthesia. Br J Anaesth 1999; 82: 666±71 7 Nayak A, Roy RJ. Anesthesia control using midlatency auditory evoked potentials. IEEE Trans Biomed Eng 1998; 45: 409±21 8 Huang JW, Lu YY, Nayak A, Roy RJ. Depth of anesthesia estimation and control. IEEE Trans Biomed Eng 1999; 46: 71±81 9 Sebel PS. Somatosensory, visual and motor evoked potentials in anaesthetized patients. BaillieÁre's Clin Anaesthesiol 1989; 3: 587± 602 10 Angel A, LeBeau F. A comparison of the effects of propofol with other agents on the centripetal transmission of sensory information. Gen Pharmacol 1992; 23: 945±63 11 Angel A, Dodd J, Gray, JD. Fluctuating anaesthetic state in the rat anaesthetised with urethane. J Physiol 1976; 259: 11±12P 12 Angel A, Wolstenholme, SC. Steady state halothane anaesthesia oscillates between two states of electrocortical arousal. Br J Anaesth 1998; 81: 633P 13 Woodward RH, Goldsmith PL. Cumulative Sum Techniques: ICI Monograph on Mathematical and Statistical Techniques for Industry, No. 3. Edinburgh: Oliver and Boyd, 1964 14 Angel A. The G. L. Brown lecture: adventures in anaesthesia. Exp Physiol 1991; 76: 1±38 15 Angel A. Central neuronal pathways and the process of anaesthesia. Br J Anaesth 1993; 71: 148±63


16 Angel A, Berridge DA. Pathway for the primary somatosensory evoked response in the rat. J Physiol 1974; 237: 35±6P 17 Banks D. An Analysis of the Functional Organisation of the Rat Forepaw Sensorimotor Cortex. PhD Thesis, University of Shef®eld, 1982 18 Eccles JC. The Physiology of Synapses. Berlin: Springer, 1964 19 De Wildt DJ, Hillen FC, Rauws AG, Sangster B. Etomidateanaesthesia, with and without fentanyl, compared with urethane anaesthesia in the rat. Br J Pharmacol 1983; 79: 461±9 20 Angel A, Gratton DA. The effect of anaesthetic agents on cerebral cortical responses in the rat. Br J Pharmacol 1982; 76: 541±9 21 Buckley PM. Propofol in patients needing long-term sedation in intensive care: an assessment of the development of toleranceÐ a pilot study. Intensive Care Med 1997; 23: 969±74 22 Engbers E. Practical use of Diprifusor systems. Anaesthesia 1998; 53 Suppl. 1: 28±34 23 Glen JB. The development of `Diprifusor': a TCI system for propofol. Anaesthesia 1998; 53 Suppl. 1: 13±21

439

24 Mills CO, Freeman JF, Salt PJ, Elias E. Effect of anaesthetic agents on bile ¯ow and biliary excretion of [131I]cholylglycyltyrosine in the rat. Br J Anaesth 1989; 62: 311±5 25 Yang C-H, Shyr M-H, Kuo TBJ, Tan PPC, Chan SHH. Effects of propofol on nociceptive response and power spectra of electroencephalographic and systemic arterial pressure signals in the rat: correlation with plasma concentration. Pharmacol Exp Ther 1995; 275: 1568±74 26 Drummond JC, Todd MM, Hoi Sang U. The effect of high dose sodium thiopental on brainstem auditory and median nerve somatosensory evoked responses in humans. Anesthesiology 1985; 63: 249±54 27 Angel A, Linkens DA, Ting CH. Estimation of latency changes and relative amplitudes in somatosensory evoked potentials using wavelets and regression. Comput Biomed Res 1999; 32: 209±51 28 Angel A, Linkens DA, Ting CH. A data acquisition and signal processing system for electrophysiology. J Physiol 1997; 499: P46