Journal of Clinical Monitoring and Computing 16: 583^592, 2000. ß 2001 KluwerAcademic Publishers. Printed in the Netherlands.
Jiann-Shing Shieh,
1Shou-Zen Fan,
2Liang-Wey
Chang,
3and Chien-Chiang Liu
4From the1Department of Mechanical Engineering, Yuan Ze Univer-sity,2Department of Anesthesiology, College of Medicine,3Institute of Biomedical Engineering,4Department of Anesthesiology, College of Medicine, National Taiwan University,Taiwan.
Address correspondence to Dr Jiann-Shing Shieh, Department of Mechanical Engineering, Yuan Ze University, 135 Yuan-Tung Rd., Chung-Li,Taoyuan, 320,Taiwan.
E-mail: [email protected]
ABSTRACT. Objective. The important task for anaesthetists is to provide an adequate degree of neuromuscular block during surgical operations, so that it should not be di¤cult to antagonize at the end of surgery. Therefore, this study exam-ined the application of a simple technique (i.e., fuzzy logic) to an almost ideal muscle relaxant (i.e., rocuronium) at general anaesthesia in order to control the system more easily, e¤-ciently, intelligently and safely during an operation. Meth-ods. The characteristics of neuromuscular blockade induced by rocuronium were studied in 10 ASA I or II adult patients anaesthetized with inhalational (i.e., iso£urane) anaesthesia. A Datex Relaxograph was used to monitor neuromuscular block. And, ulnar nerve was stimulated supramaximally with repeated train-of-four via surface electrodes at the wrist. Initially a notebook personal computer was linked to a Datex Relaxograph to monitor electromyogram (EMG) signals which had been pruned by a three-level hierarchical structure of ¢lters in order to design a controller for administering muscle relaxants. Furthermore, a four-level hierarchical fuzzy logic controller using the fuzzy logic and rule of thumb concept has been incorporated into the system. The Student's t test was used to compare the variance between the groups. p < 0.05 was considered signi¢cant. Results. The system achieved stable control of muscle relaxation with a mean T1% error of 0.19 (SD 0.66) % accommodating a range in mean infusion rate (MIR) of 0.21^0.49 mg kg 1 h 1. When these
results were compared with our previous ones using the same hierarchical structure applied to mivacurium, less variation in the T1% error (p < 0.05) but the same variation in infusion rate were observed. The controller activity of these two drugs showed no signi¢cant di¡erence (p > 0.5). However, the consistent medium coe¤cient variance (CV) of the MIR of both rocuronium (i.e., 36.13 (SD 9.35) %) and mivacurium (i.e., 34.03 (SD 10.76) %) indicated a good controller activity. Conclusions. The results showed that a hierarchical rule-based monitoring and fuzzy logic control architecture can provide stable control of neuromuscular block despite the considerable individual variation in neuromuscular block required among patients. Also, there was less variation in T1% error compared with that of previous study on mivacu-rium. Meanwhile, the consistent medium CV of the MIR of both rocuronium and mivacurium indicated a good control-ler activity which is able to withstand noise, diathermy e¡ect, artifacts and surgical disturbances.
KEY WORDS. Fuzzy logic control, electromyography, hierarch-ical structure, neuromuscular monitoring.
INTRODUCTION
The advent of newer muscle relaxants approaching to an almost ideal neuromuscular blocking agent has grown rapidly in recent years. Rocuronium [1, 2] is a non-depolarizing neuromuscular blocking drug having
an intermediate duration of action similar to that of vecuronium but with much faster onset of e¡ect, thus o¡ering good to excellent intubation conditions like succynlcholine. In addition, extensive clinical trials showed that rocuronium has rapid recovery character-istics coupled with cardiovascular stability and virtually no histamine release or other side e¡ects. These charac-teristics make rocuronium an ideal neuromuscular blocking drug. However, the duration and recovery of this drug are found to be longer than those of mivacu-rium [3, 4]. Therefore, it is not suitable for use in short operation.
Closed-loop drug therapy o¡ers considerable bene¢ts to patient care. It provides the ability to maintain stable neuromuscular block while allowing for variation in individual response to the drug. Also, this bene¢ts the patient because the minimum quantity of drug is ad-ministered and clinical workload is reduced, allowing more time for direct patient care. The reliability of neuromuscular block monitored by electromyography enables a closed-loop control strategy to be imple-mented. However, one problem with feedback control in biomedicine is that there are enormous patient-to-patient variations in dynamic model parameters. This is compounded by large time-varying parameters for an individual patient during the course of an operation, making it di¤cult to design a ¢xed-parameter PID controller which will be suitable in all cases. This arose the need to investigate self-adaptive control strategies, and later organizing controllers. Although the self-tuning trials have been successful, they involve con-siderable work in selecting the design parameters and
mathematical models of the patient. Hence, various controllers developed from the classical control theory have been proposed in the past ten years, from simple on-o¡ type to complex model-based controllers [5^17]. Intelligent control (e.g., fuzzy logic) has recently been implemented into this system via computer simulation and clinical use with atracurium [18^21]. Table 1 shows the comparison of published human clinical results obtained by di¡erent atracurium control strategies with EMG monitor. Fuzzy logic control, therefore, is still a simple and e¡ective technique for controlling non-linear and uncertain processes [22, 23]. The e¡ect of neuromuscular blockers is non-linear, and fuzzy logic provides a simple way to create a non-linear controller. Fuzzy logic not only accommodates uncertainty by dealing with imprecise, qualitative terms such as low, medium and high, but also provides control rules which are easy to understand and modify when discussing with experts. In recent years, there has been a move away from sporadic interest in arti¢cial intelligence concepts by a small number of systems engineers to a worldwide passion for intelligent control, utilizing all the tools that have been developed in the ¢eld of arti¢cial intelligence. Fuzzy logic is one of the many methodologies of intelligent control, which has been widely studied, both in industry and academia. In-telligence means the ability to understand or reason (logically) and to learn or adapt. The derivation of fuzzy rules is a common bottleneck in the application of fuzzy logic controllers. Conventionally, these fuzzy rules are derived from emulating the control actions of an expert (i.e., anaesthetist). There is a recent report on the clinical
Table 1. Comparison of published human clinical results obtained with di¡erent atracurium control strategies using an EMG monitoring technique
Performance measures (mean SD), %)
Atracurium controller Type Mean error SD RMSD
Webster and Cohen, 1987 [10] PD ^1.1 (0.47) ^ ^
Wait et al., 1987 [9] On/o¡ ^ ^ ^
MacLeod et al., 1989 [13] PI ^1.3 (1.3) 1.47 (0.69) 2.21 (1.01) Denai et al., 1990 [14] Adaptive PD 0.98 (4.3) 3.9 (2.3) ^
O'Hara et al., 1991 [15] PID ^ ^ ^
Schwilden and Olkkola, 1991 [16] Model-based 0.04 (0.46) ^ 1.9 (0.6) Mahfouf et al., 1992 [17] Model-based ^0.16 (0.37) 3.12 (1.68) 3.41 (1.69) Mason et al., 1996 [18]
10% (phase I) 1.1 (1.4) 2.4 (0.68) 3.0 (0.62)
20% (phase II) Fuzzy PD+I ^0.43 (1.2) 1.5 (0.29) 1.9 (0.36)
10% (phase III) 0.28 (0.94) 3.4 (0.88) 3.5 (0.85)
Shieh et al., 1996 [24] Fuzzy PD+I 0.62 (1.08) 1.75 (0.86) 2.12 (0.86) Ross et al., 1997 [19] Self-learning fuzzy logic control ^0.52 (0.55) 2.30 (0.62) 2.39 (0.66)
application of fuzzy logic control to muscle relaxation regulation using atracurium [18, 24]. However, with new neuromuscular blocks, no such experience is readily available to draw on for derivation of the fuzzy rule-base. This situation was the main driving force behind the introduction of self-organizing or self-learning fuzzy logic controllers [19, 20].
Almost all of these previous studies were made using atracurium and none of them employed newer agents such as mivacurium and rocuronium. However, we have successfully applied the hierarchical monitoring and fuzzy logic control of neuromuscular block with atracurium and mivacurium via clinical trials [24, 25]. This result has encouraged us to apply this technology using rocuronium. Therefore, this study aimed to inves-tigate the hierarchical rule-based monitoring and fuzzy logic control for neuromuscular block with this almost ideal muscle relaxant (i.e., rocuronium). Also, the ¢lter and control performances of this drug have been inves-tigated in this paper via a comparison with previous clinical trials employing mivacurium [25].
METHODS
Patients
This study was approved by the Ethics Committee of the National Taiwan University Hospital. Ten ASA I or II patients, aged 18^70 yr and weighed 51^90 kg, under-going surgery anticipated to last at least 30 min were enrolled as subjects and gave written informed consent. Patients with hepatic, renal or neuromuscular disease or those taking medications known or suspected to inter-fere with neuromuscular transmission were excluded. On arrival in the operating room, blood pressure was measured either noninvasively with a cu¡ attached to the arm or invasively with an arterial line injected into the artery not involved in neuromuscular monitoring. Pulse oximetry and electrocardiography were moni-tored continuously.
Anaesthesia
Preoperative anaesthetic visit and evaluation were per-formed in all patients the previous day with patients' consent. Anaesthetic agents were given by sta¡ mem-bers, residents or nurse anaesthetist with at least one year of experience in anaesthesia. An attending anaes-thetist involved in the study was always present and responsible for monitoring of the patient. Also, the investigator who designed this monitoring system was
always present and responsible for handling any device or computer dysfunction. After the standard monitors were set up (i.e., ECG, blood pressure, pulse oximeter, and capnography monitor), all patients received a stand-ardized anaesthetic regime. After premedication with atropine, anaesthesia was given with pentothal and fentanyl during the induction stage. An inhalational gas of iso£urane was given after induction and controlled by the anaesthetist or the nurse anaesthetist responsible for anaesthesia. The patient's lungs were then ventilated manually with nitrous oxide in oxygen. The loading dose of rocuronium was 0.6 mg kg 1during induction for intubation. After intubation, neuromuscular block was controlled by the closed-loop using a hierarchical rule-based and fuzzy controller of rocuronium throughout the operation.
Neuromuscular monitoring
Stimulating electrodes for a Datex Relaxograph were placed over the ulnar nerve of the non-infused hand, while the sensing electrodes were placed over the hy-pothenar area. The ulnar nerve was stimulated supra-maximally with repeated train-of-four (TOF) via sur-face electrodes at intervals of 0.5 sec (2 Hz). The TOF stimulus was repeated every 10 sec that produced the expected degree of neuromuscular block more than every 20 sec [26]. The system comprised an IBM com-patible notebook interfaced with a Datex Relaxograph for monitoring neuromuscular block and an Ohmeda 9000 medical infusion pump for administration of ro-curonium. The notebook computer was programmed in the language ``Borland C++'' for using the developed hierarchical rule-based monitoring, the fuzzy logic con-trol structure and co-ordinate communication with the two devices via serial links. The initial default value of EMG (i.e., T1% value) set points was 10% of the base-line, and 10 mg ml 1 concentration of rocuronium was allowed to enter so that the computer could convert the controller output from mass rate (mg h 1) to volume £ow rate (ml h 1). In addition, the patient's weight was entered for calculation of the loading dose of muscle relaxants.
A four-level hierarchical fuzzy logic controller
According to anaesthetists, there are many levels for controlling a patient's muscle relaxation from EMG output. To take this problem manageable, the concept of hierarchical structure is employed. The most impor-tant level is administered ¢rst. If this level does not
work, the second more important level will be used and so on. Therefore, a four-level hierarchical fuzzy logic controller (Appendix) using the fuzzy logic and rule of thumb concept has been incorporated into the system in order to control the system more easily, e¤ciently, intelligently and safely during an operation. The ¢rst level uses the fuzzy set theory to build a look-up table to control the EMG signals around the set point. How-ever, if this level is not suitable for controlling the patient, the self-tuning system in the second level is ¢red to ¢ne-tuning this look-up table. Also, if the T1% error (which means the set point minus the T1% value) and T1% error changed caused by some surgical distur-bances are beyond the range in the look-up table in the ¢rst level, a coarse table in the third level derived from the anaesthetist is applied in order to control the EMG signals returning quickly to set point. Finally, if some unexpected conditions happen and EMG signals are beyond the range of the safety of the clinical operation, an emergency table in the fourth level derived from the anaesthetist needs to be applied in order to bring the patient under control.
The initial T1% set point was entered as 10% of the baseline. However, if the surgeons complain of insu¤-cient muscle relaxation, the set point can be changed to 5% of the baseline. During all operations, the infusion rate was set at an upper limit of 0.4 mg h 1and a lower limit of 0.2 mg kg 1 h 1for the look-up table in the ¢rst level. The self-tuning system in the second level was active since the mean infusion rate (MIR) was above the upper limit or below the lower limit. Also, the coarse table in the third level was active since the T1% value was larger than 3% or less than 3% of the T1% set point. In addition, if the T1% was above the 10% of the T1% set point when neuromuscular block started to recover, the computer was programmed to give an additional 0.05 mg kg 1 bolus over 1 min, repeating necessary until the T1% was less than 10% of the T1% set point level. The infusion rate was tempora-rily stopped if the T1% value is more than 3% below the T1% set point.
A three-level hierarchical ¢lter
There are two types of noises for the Relaxograph to be recognized during the operation. First, when the sur-geon uses a high frequency instrument to stop bleeding in the patient (which is called a diathermy e¡ect), the EMG output signal will be disturbed and often the signals reduce to zero in that situation. Second, a noise may occur due to the movement of the patient that causes sudden change in the EMG output. Hence, a
three-level hierarchical ¢lter (Appendix), which in-cludes a built-in hardware ¢lter inside the instrument, a pharmacological ¢lter, and a digital median ¢lter, was designed for e¤cient pruning of the EMG signals. The EMG signals measured from a Datex Relaxograph were ¢rst passed through an inside built-in hardware ¢lter, followed by a pharmacological ¢lter according to the fade pattern in the evoked response to train-of-four nerve stimulation after injection of a non-depolarizing or depolarizing neuromuscular blocking agent acting as a second stage ¢lter. If the signals were not matched to the fade pattern, these signals were identi¢ed as either noises or diathermy disturbances, and were ignored when entering the next stage ¢lter. Finally, the signals were passed through the median ¢lters that have proved to be suitable for medical signal processing [27]. The length of the ¢ltering window for this system was three samples, corresponding to 30 sec in real time, and producing a real time average delay of 15 sec.
Analysis of data
As we were mainly interested in studying the behaviour of the system during the period of steady neuromuscu-lar block, we needed an operational de¢nition of the ``stable period.'' The start of this period can be de¢ned in two ways, depending on whether or not there is an overshoot above the target after starting automatic con-trol. If there is, the beginning of the stable period is the time at which T1% returns to 10% after the overshoot. If there is no overshoot, the stable period begins when T1% ¢rst starts to decline after the controller has been started. The stable period ends when muscle relaxants stops and surgery is completed. Also, the beginning of the ``controller in operation'' is de¢ned by the time at which the maintenance starts after ¢nishing the intuba-tion. The controller in operation ends the same as the stable period. To assess the performance of the ¢lters for each group, the following parameters were measured: the mean T1% value, the standard deviation (SD) of T1% value and the coe¤cient variance (CV) of each patient. To compare the performance of the controller, the following parameters were measured: the mean of T1% error and the SD of T1% error. To compare the controller activity, the following parameters were also measured: the mean infusion rate (MIR), the SD of MIR, and the CV of MIR. The results obtained from this study and a previous study on mivacurium [25] were compared using the Student's t test.
RESULTS
We studied 10 patients, mean age 48 (range 18^69) yr and mean weight 63 (51^90) kg. The mean total stable period of control was 118 (28^270) min. Satisfactory muscle relaxation was maintained throughout the sur-gical procedure in all cases. Table 2 shows the controller performance analysis of 10 patients. The mean T1% error from set point was 0.18% (SD 0.64%; range
1.12 to +0.66%) without ¢lter, and 0.19% (SD
0.66%; range 1.24 to +0.63%) with ¢lter. Mean SD values were 1.82% (SD 0.64%; range 0.99 to 3.03%) without ¢lter, and 1.47% (SD 0.35%; range 0.96 to 1.93%) with ¢lter, con¢rming that the mean error was close to zero. Table 3 shows the controller activity analy-sis of 10 patients. The mean infusion rate of rocuronium was 0.32 (SD 0.09; range 0.21 to 0.49 mg kg 1 h 1) for the total stable period of control. Also, the mean SD rocuronium infusion rate was 0.11 (SD 0.04; range 0.066 to 0.191 mg kg 1 h 1). As we know, the SD of the infusion rates of rocuronium delivered over the period of control indicates the variation in infusion rate for that period in each patient. Also, it is noted that coe¤cient variance (CV) is the ratio of standard devia-tion to the sample mean and is often expressed as a percentage. And, it is valuable in describing the varia-bility of the sample. Therefore, using CV to interpret
the controller activity for rocuronium is thought to be suitable. The high CV of the mean infusion rate (MIR) indicates high controller activity. On the other hand, £uctuating infusion rates show the impact of noise, diathermy e¡ect, artifacts and surgical disturbances. Also, the low CV of the MIR means that the controller is not sensitive enough to cope with the disturbances. In this study, the CV of MIR was 36.13 (SD 9.35) % in rocuronium as shown in Table 3. Figure 1 shows sample clinical records from one patient to demonstrate the controller performance: (a) representative EMG signals with ¢lters and set points, (b) representative MIR and the variation of the self-tuning parameter, and (c) rep-resentative controller output of infusion rate during an operation.
Table 4 shows the ¢lter performance analysis of each patient. It can be noted that after passing through the ¢lters, some CV values were reduced largely but some
Table 2. Controller performance analysis for rocuronium in 10 patients Parameter Mean error (%) SD (%) Range(%) Mean of T1% error ^0.18 0.64 ^1.12^0.66 SD of T1% error 1.82 0.64 0.99^3.03 Mean of T1% (F) error ^0.19 0.66 ^1.24^0.63 SD of T1% (F) error 1.47 0.35 0.96^1.93
T1% error: set point ^ relaxograph reading of T1%; T1% (F) error: set point ^ relaxograph reading of T1% with ¢lters; SD: the standard deviation of T1% error value.
Table 3. The controller activity analysis for rocuronium in 10 patients Parameter MIR
(mgkg 1h 1) SD(mgkg 1h 1) Range(mgkg 1h 1)
Mean of MIR 0.32 0.09 0.21^0.49 SD of MIR 0.11 0.04 0.066^0.191 CV of MIR 36.13 9.35 25.40^53.30
MIR: the mean infusion rate (mgkg 1h 1); SD: the standard devia-tion of the MIR; CV: the coe¤cient of the variance of the MIR.
Fig. 1. The results of a clinical record from a patient to demonstrate the controller performance: (a) representative EMG (T1%) with ¢lters and 10% set point, (b) representative MIR and the variation of the STP, and (c) representative a controller output of infusion rate. Notation in the horizontal axis of ¢gures: Sec.10: 10 seconds
for one unit of time scale. In the vertical axes of ¢gures: T1% (F), EMG reading with ¢lters (%); MIR: mean infusion rate (-mgkg 1h 1; STP: self-tuning parameter (mgkg 1h 1); IR:
were not. It strongly depends on the type of the surgery because of diathermy e¡ect. However, the overall ¢lter performance of the CV of the T1% value as shown in Table 5 was 17.75 (SD 5.81) % without ¢lter and 14.43 (SD 3.58) % with ¢lter (p > 0.05). Although there is no signi¢cant di¡erence after ¢ltering, the SD of the EMG signals was slightly reduced after passing through the ¢lters. It means that the EMG signals become smooth and can be used to design a controller. Figure 2 shows clinical records from another patient to demonstrate the ¢lter performance: (a) representative raw EMG signals without ¢lters and 10% set point, and (b) representative EMG signals with ¢lters and 10% set point.
DISCUSSION
Several di¡erent computer systems for feedback control of neuromuscular blocking agents have been reported [5^21]. However, no previous study has applied
com-puter systems to feedback control of rocuronium infu-sions. In this paper, the hierarchical rule-based monitor-ing and fuzzy logic control architecture have been successfully employed to control rocuronium infusions. We have used a fuzzy logic controller in the ¢rst level to provide a simple and e¤cient way to communicate
Table 4. Filter performance for rocuronium in individual patient
Patient no. T1% SD CV T1% SD (F) CV (F) 1 9.45 1.66 17.6 9.44 1.65 17.5 2 9.83 0.99 10.1 9.86 0.96 9.74 3 10.64 1.76 16.5 10.73 1.38 12.9 4 10.96 2.26 20.6 10.94 1.74 15.9 5 10.55 3.03 28.7 10.47 1.28 12.2 6 10.39 1.16 11.2 10.38 1.13 10.9 7 9.59 1.90 19.8 9.58 1.82 19.0 8 9.34 1.88 20.1 9.37 1.74 18.6 9 11.12 2.44 21.9 11.24 1.93 17.2 10 9.91 1.09 11.0 9.9 1.03 10.4
T1%: relaxograph reading of T1%; T1% (F): ralaxograph reading of T1% with ¢lters; SD: the standard deviation of the T1% value; CV: the coe¤cient of the variance of the T1% value.
Table 5. The overall ¢lter performance analysis for rocuronium in 10 patients Parameter Mean error (%) SD (%) Range Mean of T1% 10.18 0.64 9.34^11.12 SD of T1% 1.82 0.64 0.99^3.03 CV of T1% 17.75 5.81 11.0^28.7 Mean of T1% (F) 10.19 0.66 9.37^11.24 SD of T1% (F) 1.47 0.35 0.96^1.93 CV of T1% (F) 14.43 3.58 9.74^19.0
T1%: relaxograph reading of T1%; T1% (F): relaxograph reading of T1% with ¢lters; SD: the standard deviation of the T1% value; CV: the coe¤cient of the variance of the T1% value.
Fig. 2. The results of a clinical record from a patient to demonstrate the ¢lter performance: (a) representative raw EMG (T1%) signals without ¢lters and 10% set point, (b) representative EMG signals with ¢lters and 10% set point. Notation in the horizontal axis of ¢gures: Sec.10, 10 seconds for one unit of time scale.
with the anaesthetist in order to control the muscle relaxation more easily and e¤ciently during operation. The second level of this hierarchical structure is a self-tuning fuzzy logic algorithm that can control the muscle relaxation more intelligently. A coarse table in the third level and an emergency table in the fourth level derived from the anaesthetist ensure that the muscle relaxation can be controlled more safely. Hence, we develop a hierarchical structure of a portable closed-loop control system for rocuronium-induced muscle relaxation in order to control the system more easily, e¤ciently, inteligently and safely during operation.
As shown in Table 1, the control performance of mean T1% error with rocuronium in this study has become better than that of previous studies with atracu-rium. Meanwhile, it has also achieved better control performance in comparison with that of our previous study with mivacurium using the similar architecture. The mean of T1% error with ¢lters of 0.19 (SD 0.66) % in rocuronium is signi¢cantly less than 1.67 (SD 0.97) % in mivacurium (p < 0.05). It means that the controller performance in the intermediate duration of action in neuromuscular blocking agents is better than in the short duration of action under this hierarchical structure. Regarding the controller activity of rocuro-nium and mivacurium in 10 patients, the CV of the mean infusion rate was 36.13 (SD 9.35) % in rocuro-nium as compared to 34.03 (SD 10.76) % in mivacu-rium (p > 0.5). The consistent medium CV of the MIR either in rocuronium or mivacurium indicates a good controller activity. Also, we have used a three-level hierarchical ¢lter which includes a built-in hardware ¢lter, a pharmacological ¢lter and a median digital ¢lter, in contrast with Mahfouf [28] who used the three-point non-recursive averaging ¢lter, and with Mason et al. [18] who employed a three-term median ¢lter, and our recent work [25] which adopted a similar ¢lter structure in mivacurium. However, in mivacu-rium, the CV of the T1% value was 33.15 (SD 10.10) % without ¢lter and 24.03 (SD 5.14) % with ¢lter (p < 0.05). But, in rocuronium, the CV of the T1% value was 17.75 (SD 5.81) % without ¢lter and 14.46 (SD 3.56) % with ¢lter (p > 0.05). Hence, the SD of the EMG signals are either signi¢cantly reduced in mivacu-rium or slightly reduced in rocuronium. It means that the EMG signals become smooth and can be used to design a controller, after passing through the ¢lters. However, a three-level hierarchical ¢lter in this study may be not a signi¢cant improvement over previous research using an instrument and median ¢lter [18, 25] because no comparison was made in this paper. How-ever, we did know that it is more logical to prune a clinical vital sign via a pharmacological ¢lter that has
been proved by pharmacokinetics and pharmacodynam-ics. From the viewpoint of electrical engineering, the sensitivity of instrument detection may not be enough. Another independent pharmacological ¢lter can pro-vide a double check on the signals.
The reduction in CV values after passing through the ¢lters depends strongly on the type of the surgery. For example, the patient in Figure 2 (i.e., patient no. 5 in Table 4) had a colon cancer operation which used the electrosu rgical u nits (ESU) a lot of times. The heating e¡ect of the cutting currents and sparks in the ESU electrode has a cauterizing e¡ect on the tissue that inhibits bleeding. Therefore, the ESU can reduce blood loss and minimize the surgery time. However, the basic ESU consists of a radio-frequency oscillator operating between 300 kHz and 3 MHz. It has been reported as a big disturbance to many instruments causing diathermy e¡ect. Fortunately, a three-level hierarchical ¢lter de-signed in this study had been proved to be able to eliminate the diathermy e¡ect even when the surgical operation uses the ESU very often.
Both mivacurium and rocuronium are non-depola-rizing neuromuscular blocking drugs. While mivacu-rium has a short duration of action, rocuronium has an intermediate duration of action. Both have potential in£uence on iso£urane or des£urane anaesthesia. Miva-curium is more di¤cult to control than rocuronium if steady-state anaesthesia with iso£urane or des£urane has not been established. In our previous and current studies, the mean of the T1% error in 10 patients for mivacu-rium was 1.67 (SD 0.96) % with ¢lters. And, the mean of the T1% error in 10 patients for rocuronium was 0.19 (SD 0.66) % with ¢lters. Hence, the neuromus-cular agent with an intermediate duration of action is easier to control than that with a short duration of action.
Clinically, the controller does not take too much e¡ort (i.e., it changes the drug infusion rate too often) controlling the drug administration manually. How-ever, the closed-loop drug therapy and the advance of modern computer technology have changed this situa-tion dramatically. From the closed-loop control theory, the controller is expected to adjust the drug as quickly as possible. Hence, the train-of-four (TOF) was re-peated every 10 sec, that is the fastest interval provided by the Datex Relaxograph. And, the controlling inter-val was set every 10 sec to control the drug administra-tion automatically. However, over-activity of the con-troller may be caused by either high system noise or too big scaling factor of the output in fuzzy logic control-ler. Fortunately, the consistent medium CV of the MIR either in mivacurium (i.e., 34.03 (SD 10.76) %) or in rocuronium (i.e., 36.13 (SD 9.35) %) indicates a good
controller activity compared with Mason et al. [18] who obtained consistent high CV valu es (i.e., 57.50 (SD 12.50) %, 57.89 (SD 12.78) % and 64.70 (SD 20.58) % for phase I, II and III, respectively). In this study, a hierarchical ¢lter has been designed and introduced to reduce the system noise and a self-tuning system in the controller can tune automatically the response of each patient to the muscle relaxant in order to administer the suitable infusion rate.
APPENDIX
A four-level hierarchical fuzzy logic controller
The E (T1%), EC (T1%), RR, IR, MIR, STP and SP used for analysis were de¢ned as follows:
E (T1%): T1% error (i.e. the di¡erence between the set point and the T1% value)
EC (T1%): T1% error change (i.e. the di¡erence between the present error and the previous error)
RR: control output of change in rocuronium amount
IR: infusion rate (ml h 1)
MIR: mean infusion rate (mg kg 1 h 1) STP: self-tuning parameter (mg kg 1 h 1) SP: the set point of T1% value
Therefore, a four-level hierarchical fuzzy logic control-ler was designed as follows:
(i) First level (i.e. a fuzzy logic controller):
There are three steps (membership functions, rules, and defuzzi¢cation) which determine fuzzy logic control. The membership functions are shown in Figure A.1 and the rules are listed in Table A.1. Also, the defuzzi¢cation procedure uses the center of area and the equation can be written as follows. I Xn 1 Mn Un Xn 1 Mn
Where M is the membership function; U is the universe of discourse; n is the number of rules; and I is the control input.
Then, combining these three steps produces a lookup table as shown in Table A.2.
(ii) Second level (i.e. a self-tuning level):
Rule-base for rocuronium infusion rate in a self-tuning level:
IF (MIR (0.4 + STP)) THEN STP = 1.1 (MIR 0.4) mg kg 1 h 1
IF (MIR (0.2 + STP)) THEN STP = 1.1 (MIR 0.2) mg kg 1 h 1
Table A.1. The anaesthetist's rule-base for controlling a rocuronium neuromuscular blocking agent
E (T1%) EC (T1%) NB NS ZO PS PB NB IB IB IS IS ZO NS IB IS IS ZO ZO ZO IS IS ZO DS DB PS IS ZO DS DS DB PB ZO ZO DB DB DB
NB: negative big; NS: negative small; ZO: zero; PS: positive small; PB: positive big; DB: decreasing big; DS: decreasing small; IB: increasing big; IS: increasing small.
Fig. A.1. The membership function of two inputs and one output. Notation in the ¢gure: NB: negative big; NS: negative small; ZO: zero; PS: positive small; PB: positive big; IB: increasing big; IS: increasing small; DS: decreasing small; DB: decreasing big.
Where MIR is calculated every 10 min and the STP is updated every 5 min.
(iii) Third level (i.e. a coarse level):
Rule-base for rocuronium infusion rate in a coarse table:
IF E (T1%) (SP+3) % THEN Infusion Rate = 0.6 mg kg 1 h 1
IF E (T1% (SP+5) % THEN Infusion Rate = 1.0 mg kg 1 h 1
IF E (TI% (SP+7) % THEN Infusion Rate = 1.5 mg kg 1 h 1
IF E (TI%) (SP 3) % THEN Infusion Rate = 0.0 mg kg 1 h 1
(iv) Fourth level (i.e. an emergency level):
Rule-base for rocuronium infusion rate in an emer-gency table:
IF E (T1%) (SP+10) % THEN
Give an additional 0.05 mg kg 1bolus over 1 min and repeat as necessary until E (T1%) < (SP+10) %
A three-level hierarchical ¢lter
The T1, T2, T3 T4, T1% and TR% used for analysis were de¢ned as follows:
T1, T2, T3, T4: ¢rst, second, third and fourth twitches of the Datex Relaxograph
T1%: (¢rst twitch/reference response) 100% TR%: (fourth twitch/¢rst twitch) 100%
Hence, a three-level hierarchical ¢lter was designed as follows:
(i) First level (i.e. an instrument ¢lter):
The computer output of the Datex Relaxograph from the RS232 serial I/O connector has some built-in
func-tions for detecting background noises and high fre-quency disturbances (i.e. diathermia).
Rule-base for ¢lter of T1% value in an instrument ¢lter:
IF (NOISE > 40) THEN Filter ou t this T1% and u se the previous T1% value
IF (High frequency disturbance value = 1) THEN Filter out this T1% and use the previous T1% value
Where NOISE is sent from the instrument and the value is between 0^100; the high frequency disturbance value is also sent from the instrument and the value is either 0 or 1.
(ii) Second level (i.e. a pharmacological ¢lter):
According to the pharmacology of injecting a non-depolarizing neuromuscular blocking agent (e.g. ro-curonium), the evoked response to train-of-four nerve stimulation from T1 to T4 is gradually decreased for each stimulus. Therefore, if it is not matched with this trend, these signals are identi¢ed as artifacts.
Rule-base for ¢lter of T1% value in a pharmacolog-ical ¢lter:
IF (TR% > 110%) THEN Filter out this T1% and use the previous T1% value
IF (T2 > (T1 5)) THEN Filter ou t this T1% and use the previous T1% value
IF (T3 > (T2 5)) THEN Filter out this T1% and use the previous T1% value
IF (T4 > (T3 5)) THEN Filter out this T1% and use the previous T1% value
(iii) Third level (i.e. a median ¢lter):
The median ¢lter algorithm is a simple operation of choosing the median value of the sample inside a mov-ing average window of ¢xed length. It incorporates a non-linear ¢ltering technique known for preserving sharp changes in signal and for being particularly e¡ec-tive in removing impulsive noise. Let SN be a set of N samples {x1, x2, ² , xN}, where N 2k 1. The median is de¢ned by:
Y N MEDfxijxi 2 SNg
Where the medianY is both the (k + 1)th largest and the (k + 1)th smallest element in SN. In our system, the length of the ¢ltering windows was three samples (i.e. N = 3).
Table A.2. A lookup table for E (T1%) and EC (T1%) E (T1%) EC (T1%) ^2 ^1 0 1 2 ^2 1.57 1.28 1.0 0.78 0.57 ^1 1.2 0.95 0.7 0.35 0 0 0.67 0.35 0 ^0.39 ^0.78 1 0 ^0.35 ^0.7 ^1.12 ^1.55 2 ^0.33 ^0.71 ^1.14 ^1.42 ^1.7
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