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Multitasked Closed-Loop Control in Anesthesia Automatic Controllers Capable of Regulating Multiple Patient Outputs for Higher-Quality Anesthesia Treatment
TETH is developing a multitask autonohe Automatic Control Laboratory at
Andrea Gentilini1, Christian W. Frei1, Adolf H. Glattfedler1, Manfred Morari1, Thomas J. Sieber2, Rolf Wymann2, Thomas W. Schnider2, Alex M. Zbinden2 1
Automatic Control Laboratory, ETH Zentrum, Zurich 2 Department of Anaesthesiology, University Hospital, Bern
January/February 2001
mous anesthesia system in collaboration with the University Hospital in Bern. Closed-loop controllers that regulate inspired and expired anesthetic gas, O2 and CO2 concentrations have already been used in clinical studies on humans. In this article, two additional complex controllers are discussed: control of mean arterial pressure (MAP) and control of hypnosis through bispectral index (BIS). Both controllers use Isoflurane as input, a hypnotic drug that induces hypotension. The modeling effort and the control design, which accommodates input and output constraints as well as model uncertainty, are discussed for both controllers. Moreover, supervisory functions are outlined that are necessary for application in the operating room (OR). In particular, artifact-tolerant control schemes are presented. The experimental setup and the results of the application of automatic control during clinical studies are also discussed, together with an outline for future research.
Overview: Controlling Anesthesia Problem Formulation Adequate anesthesia can be defined as a reversible pharmacological state in which the patient’s muscle relaxation, analgesia, and hypnosis are guaranteed. Anesthesiologists administer drugs and adjust several medical devices to achieve such goals and to compensate for the effect of surgical manipulation, while maintaining the vital functions of the patient. Figure 1 depicts the input/output (I/O) representation of the anesthesia state. The components of adequate anesthesia are labeled “unmeasurable” because they must be assessed by correlating them to available physiological measurements, as depicted in Fig. 1. IEEE ENGINEERING IN MEDICINE AND BIOLOGY
Muscle relaxation is induced to facilitate access to internal organs and to depress movement responses to surgical stimulation. The degree of relaxation can be estimated by measuring the force of thumb adduction induced by stimulation of the Ulnar nerve [51] or by single twitch force depression (STFD) [3]. Analgesia is associated with pain relief but, at present, there are no specific measures to quantify it, as it is even debatable to speak about pain perception when the patient is unconscious [42]. Another source of complexity results from the fact that clinical signs such as tearing, pupil reactivity, eye movement, and grimacing [7] are partially suppressed by muscle relaxants, vasodilators, and vasopressors. Hypnosis is a general term indicating unconsciousness and absence of postoperative recall of events that occurred during surgery [24]. Some authors believe there is a sharp distinction between conscious and unconscious states [42]. In this respect, it would be improper to speak about depth of anesthesia. However, the patterns of the electroencephalogram (EEG), which is the only noninvasive measure of central nervous system activity while the patient is unconscious, show gradual modifications as the drug concentrations increase in the body. Nowadays, the EEG is considered as the major source of information to assess the level of hypnosis. Better accepted measures exist for the vital functions. Heart rate (HR) and MAP are considered the principal indicators for hemodynamic stability, while oxygen (O2 ) tissue saturation or end tidal carbon dioxide (CO2 ) concentrations provide useful feedback to anesthesiologists about the adequacy of the artificial ventilation. To achieve adequate anesthesia, anesthesiologists regularly adjust the settings of several drug infusion devices as well as the parameters of the breathing system to mod0739-5175/01/$10.00©2001IEEE
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ify the manipulated variables listed in Fig. 1. These adjustments are done based on some patient-specific target values and the monitor readings. Thus, anesthesiologists adopt the role of a feedback controller, and it is natural to ask whether automatic controllers are capable of taking over and/or improving parts of such a complex decision process.
The Benefits of Feedback Controllers in Anesthesia Several authors have recognized the advantages associated with the use of automatic controllers in anesthesia [48, 6, 40]. First, if the routine tasks are taken over by automatic controllers, anesthesiologists
Manipulated Variables
are able to concentrate on critical issues that may threaten the patient’s safety. Secondly, by exploiting both accurate infusion devices and newly developed monitoring techniques, automatic controllers would be able to provide drug administration profiles that, among other advantages, would avoid overdosing. Moreover, controllers may take advantage of the drug synergies, for which a proper modeling framework has now been developed [38]. The ultimate advantage would be a reduction in costs due to the reduced drug consumption and the shorter time spent by the patient in the postanesthesia care unit (PACU).
I.V. Anesthetics
Hypnosis
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Relaxation
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EEG Pattern Heart Rate CO2Conc.
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1. Input/output (I/O) representation of the anesthesia problem.
I.V. Pump
Electronic Gas Dosing
Touchscreen Monitor Computer Manual Gas Dosing BIS Monitor
Emergency Shut-Down
Breathing System
2. The real-time platform for clinical studies. 40
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Further, if tuned properly, automatic controllers should be able to suppress interindividual variability and to tailor the drug administration profile to the particular stimulation intensity of each surgical procedure [35]. Ultimately, automatic controllers could be used for research as a “reference” anesthesiologist in clinical studies.
The Challenges of the Operating Room Several complexities were faced in designing the real-time platform to test closed-loop controllers in the OR. The issues and the solutions adopted are summarized below. n Sensors and actuators: To provide adequate monitoring of the patient’s vital functions and easy access to drug infusion devices, several sensors and actuators had to be assembled on the mobile real-time platform depicted in Fig. 2. n Safety critical system: All the implemented closed-loop controllers use physiological signals that are potentially corrupted by artifacts. Corrupted signals may result either from routine manipulation or calibration of the measuring devices and may cause, if not considered in the control schemes, considerable damage to the patient. To address this problem, supervisory system and fault-tolerant controllers were embedded in the real-time platform to detect sensor failures and/or other abnormal operations. A more detailed description of these safety features of the platform will be given below. n Model uncertainty: A major source of difficulty results from the extreme uncertainty associated with the published models for drug distribution and effect. Nevertheless, anesthesiologists are able to compensate for interindividual variability by tailoring drug administration to the individual patient’s needs, therefore guaranteeing adequate performance across the population. In order to reproduce this feature, feedback controllers must be designed with robust and/or adaptive techniques. Robust techniques lead to controllers for the “worst case” situation, which tends to make them sluggish. Adaptive schemes rely on the excitability by the input signal, which is often limited by ethical constraints. Our approach was to use both data collected from patients under ordinary patients during anesthesia and data acquired January/February 2001
from young healthy volunteers for the design and the validation of the proposed control strategies. n Clinical validation: Improvements for clinical practice and patient care that are envisioned from the use of automatic controllers in anesthesia cannot be quantified unless extensive clinical validation is performed. Therefore the ETH project has been put on solid foundations by establishing a close cooperation between a clinic (University Hospital of Bern) and an anesthesia workstation manufacturer (Dräger Medizintechnik. Lübeck, Germany). Among other advantages, the partnership with the hospital enabled us to acquire data directly from young healthy volunteers for model identification. The support from the industrial partners provided us with the latest available technology on the market. Up to now, six different control strategies have been tested by the ETH-University Hospital team on more than 150 patients during general anesthesia. These controllers regulate O2 , CO2 , inspired and expired anesthetic gas concentrations in the breathing system, as well as MAP and depth of hypnosis derived from the EEG [8, 15, 54, 19, 10, 14].
Closed-Loop Control of Anesthetic Effect Among the several controllers discussed above, two single-input, single-output systems (SISO) extracted from the multiple-input, multiple-output (MIMO) control problem depicted in Fig. 1 will be described extensively in this article: MAP and bispectral index (BIS) control. Both feedback systems use the volatile anesthetic Isoflurane as input and aim at controlling the anesthetic effect. Several reasons motivate MAP control during surgery. MAP decreases with increasing Isoflurane concentrations in the internal organs. As such, MAP is often viewed as an indirect measure of the anesthetic effect. Beyond that, hypotension is also induced to minimize blood losses and increase surgical visibility [17]. Moreover, maintaining MAP within an acceptable physiological range guarantees adequate perfusion of internal organs. Finally, suppressing MAP reactions to surgical stimuli enhances the patient’s safety. MAP is measured invasively by a catheter placed in the radial artery. The signal is transferred to January/February 2001
the monitors by a transducer and sampled at a frequency of 128 Hz. Every repositioning of the patient, as well as calibration of the transducer and flushing of the catheter to prevent blood clogging, leads to an artifact in the measured signal. Artifacts are suppressed with a scheme discussed below. Hypnosis can be assessed with the bispectral index (BIS Index, Aspect Medical System. Newton, Massachusetts). This index is derived from the EEG by combining the higher-order spectra of the signal with other univariate indicators such as spectral edge frequency (SEF) and median frequency (MF) [47, 49, 53]. This combination of indicators is necessary since, for instance, SEF and MF can provide an estimate of the hypnotic state at deep levels but are likely to fail in the region of light sedation [20, 29]. BIS can reveal, unlike simple Fourier analysis, the synchrony of cortical brain signals, which characterizes unconsciousness [43]. BIS values lie in the range 0-100, where 100 is associated with the EEG of an awake subject and 0 denotes an isoelectric EEG signal. BIS predicts accurately return of consciousness [11, 21, 28, 50], and it is the only clinical monitor for hypnosis that, to date, has received US FDA clearance. BIS has been developed and validated based on EEG recordings of 5000 subjects. More than 450 peer-reviewed articles and abstracts provide a clinical evaluation of BIS.
Modeling The model required for control has to account for two qualitatively different systems: the medical devices (actuators
and sensors) and the physiology involving drug distribution, metabolism, and effects in the human body.
The Respiratory System A schematic drawing of the respiratory system depicted at the bottom of Fig. 2 is given in Fig. 3. A pump forces the air into the patient’s lungs while unidirectional valves impose a fixed orientation (one way) for circulation of the gases. The fresh gas stream enters on one branch and excessive air leaves on the other. This gas flow through the system leads to a constant flush. If a high fresh gas flow is used (Q0 > 4 l/min), the dynamics introduced by the respiratory system may be neglected, since a change in the fresh gas composition is effective for the patient almost immediately. During minimal flow anesthesia (Q0 < 1 1 min), fresh gas flow only compensates for gas taken up by the patient and the eliminated CO2, through the absorber. At such low flows, the system is economically more efficient and safer for the patient. In fact, due to recirculation, the patient breathes a gas mixture at almost constant humidity and temperature. The expired gases are now recirculated, which introduces considerable dynamics. A first principles model of the minimal-flow breathing system was derived to capture the behaviors of the system in detail [10]. A simplified description giving the same prediction accuracy can be obtained by considering the respiratory system to be a wellstirred tank. Inspired concentrations depend on the vaporizer fresh anesthetic gas concentrations, C 0 , and the patient’s breathing parameters through the following equation: Fresh Flow Q0, C0
Y-Piece
Unidirectional Valves Pressure-Relief Valve
Absorber
Breathing Bag
3. Schematic representation of the closed-circuit breathing system. Typical ranges for the parameters of the respiratory system [see Eq. (1) for a detailed description] are : Q0 = 1-10 l/min, f R = 4-25 l/min, V T = 0.3-1.2 l, V = 4-6 l, ∆Q = 0.1-0.5 l/min, C 0 = 0-5%, expressed as Isoflurane volume percent in the breathing mixture. IEEE ENGINEERING IN MEDICINE AND BIOLOGY
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V
dC insp dt
= Q0C 0 − ( Q0 − ∆Q )C insp
(
− fR ( VT − ∆ ) C insp − C 1
)
(1) where V [l] is the volume of the respiratory system; C 1 [%] is the alveolar concentration or endtidal concentration, measured as volume percent of the breathing mixture; fR [1/min] is the respiratory frequency; VT [l] is the tidal volume; and ∆ [l] is the physiological dead space. ∆Q [l/min] represents the losses of the breathing circuit through the pressure-relief valves. Q0 and C 0 [%] are the fresh gas flow and its anesthetic concentration entering the respiratory circuit, respectively. C 0 is the manipulated variable in our control system. We will refer to C 0 as the “vaporizer setting” in the below sections.
Modeling the Effect of Anesthetic Drugs The physiological mechanisms regulating drug distribution and effects are only partially known. Therefore, first principles modeling is almost impossible. Thus, one has to select from approximate first principles physiological models [2], black-box identification schemes [26], and knowledge-based modeling. All these approaches exhibit certain drawbacks. In
physiological models, parameters are highly uncertain and collected from different sources where experiments may have been performed under very different conditions. Black-box models and knowledge-based models suffer from poor extrapolation properties. For the design of both BIS and MAP controllers, we used physiology-based models consisting of a pharmacokinetic (PK) part describing the drug distribution into the internal organs, and a pharmacodynamic (PD) part describing the drug effect on the physiological variables of interest. The structure of the PK part is common to both controllers, since both use Isoflurane as input. The PD part differs in the two models and will be discussed below. Any PK model consists of differential equations resulting from mass balances for the drug within different compartments [27]. For the generic ith compartment, we may write [62]: Vi
dC i = Qi (C)(C a − C i , o ) − ki (C)C i dt (2) C i , o = C i / Ri
(3)
where Qi is the blood flow bathing the organ, Vi is the distribution volume of the drug, ki is the elimination rate, and Ri is
20 18
Modeling for Control of MAP
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4. MAP deviations (o) from values before stimulation are plotted versus time after a tetanus stimulus for one subject at 0.5% end tidal concentration of Isoflurane. The neuronal (first peak) and humoral (second peak) components of the MAP reaction are distinguishable from the plot. 42
the apparent partition coefficient that macroscopically describes drug absorption and metabolism as a ratio between inte rn a l (C i ) a n d out f l ow (C i , o ) concentration [2]. C is the vector of drug concentrations in the different compartments, andC a is the drug concentration in the arterial pool. Since the pharmacological properties of Isoflurane have been extensively documented [13, 57, 61, 60], some of the parameters in Eqs. (2) and (3) were derived from the literature. The other parameters were estimated from the data collected during general anesthesia with Isoflurane. For further details on the identification procedure, the reader is referred to the literature [14]. Inspired and end tidal concentrations of the anesthetic agent (Isoflurane) are measured on-line and provide a reliable indication of the patient’s drug uptake. An inhalation anesthetic represents a clear advantage over intravenous drugs, for which no measure of drug concentration in the central body compartment are available. This advantage was exploited in both control schemes by imposing constraints on end tidal concentrations to prevent overdosing. In our models, ventilation and blood flow are described as nonpulsatile phenomena. Since the equilibration time of the drug is greater than the respiratory cycle and the period of HR, this assumption does not affect performance of the controllers.
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To model the PD effect of Isoflurane on MAP, we assumed that the reaction of the hemodynamic system to the drug does not change during prolonged administration [57]. In other words, no time varying phenomena due to sensitation or tolerance to Isoflurane were considered. Even though HR is known to be strongly coupled with MAP, it was not taken directly into account in our model. Several tachycardic episodes have been reported during Isoflurane anesthesia, and they may suggest the need to model those effects [52]. However, it is not clear whether those episodes depend on beta sympathetic activation of baroreflex activity. In fact, at moderate to deep levels of Isoflurane anesthesia, two clinical investigations have reported contradictory results concerning the activity of the baroreflex, leaving the issue unresolved [12, 31]. January/February 2001
The modeling structure describing the hemodynamic effects of another inhalation anesthetic, Halothane [62], was adapted to the characteristics of Isoflurane. While Halothane decreases cardiac output (CO), reducing the perfusion to internal organs [18, 55], Isoflurane decreases mainly systemic resistance through dilatation of the blood vessels [13]. We assumed that MAP and CO can be described through the following PD relationship: Qa (C)
∑i=1 g i(C) N
(4)
where g i represents the conductivity of the ith organ, increased by the presence of N Isoflurane, and Qa = ∑ i =1 Qi represents CO. Conductivities g i s are assumed to depend exclusively on the anesthetic concentration in the same compartment, whereas Qa is assumed to depend on the arterial (A), gray matter (G), and myocardial (M) concentrations through the affine relationships: Qa = Qa ,0 (1 + a AC A + a G C G + a M C M ) (5) g i = g i ,0 (1 + biC i ).
For a more detailed description of the study design, the reader is referred to [19]. We assumed that the overall dynamic model from Isoflurane-inspired concentrations to BIS is limited by the drug distribution to the organs. Once the drug arrives at the receptor or effect site, we can assume that the binding occurs instantaneously. Then, at the effect site, the relation between BIS and site anesthetic concentrations is represented by a static nonlinearity. In light of these arguments, none of the compartments of the PK model could be considered the effect compartment. Therefore, an artificial effect compartment was added to the model to compensate for this hidden dynamic. The effect compartment can be regarded as an additional compartment with negligible volume, attached to the central compartment. This assumption ensures that its presence does not perturb the mass balance equations of the PK model. Effect site concentrations are related to end tidal concentrations by a first-order delay: dC e = ke 0 dt
(C 1 − C e ).
(7)
(6)
Qa ,0 and g i,0 are the baseline CO and conductivity in the ith organ, respectively. According to the previous discussion, the effects of Isoflurane concentrations are more pronounced in Eq. (6) than in Eq. (5) [14]. MAP must be kept within physiological limits during anesthesia, despite surgical stimulations. Therefore, a physiological model describing the effects of skin incision, skin closure, and tracheal intubation on the systemic circulation was derived [9]. Surgical stimulation activates the sympathetic part of the autonomous nervous system, as do other situations such as stress, infection, and hemorrhage. The sympathetic system triggers a neural and humoral reactions. The former causes the release of norepinephrine in the synaptic cleft, whereas the latter is associated with the discharge of norepinephrine and epinephrine from the adrenal medulla into the blood stream. The two reactions show significantly different time constants, one in the order of few seconds and the other in the order of a minute, which is the characteristic time constant of blood circulation. It is expected that the MAP reactions show the same distinct time constants. These January/February 2001
Modeling for Control of BIS To model the PD effects of Isoflurane on BIS, we enrolled 20 consenting volunteers and put them under general anesthesia with Isoflurane. At the time of the study, there were no published data describing the effect of Isoflurane on BIS.
BIS
MAP =
effects have been experimentally observed during our clinical studies. A typical example where both effects are clearly visible after a tetanus electrical stimulation is shown in Fig. 4. MAP measurements expressed as deviations from the value before stimulation are plotted versus time immediately after the stimulus for a patient. The solid line represents the prediction of the model [5, 6]. This model was validated during clinical studies, and the possibility of suppressing the effects of surgical stimulation by a feedforward compensation with Isoflurane was investigated [15]. Even though the model for MAP was extensively validated, it still contains a great amount of uncertainties, which may result from the different types and sites of surgical stimulation and the different subjects’ sensitivities to pain [41].
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5. PD relationships for two patients who underwent general anesthesia with closed-loop BIS control. In both plots, BIS values versus effect site concentrations are shown. The solid line (——) and the dash dot line (− ⋅ −) represent the optimal fit obtained for the individual and for the population of volunteers, respectively. Note how the patient represented in the right plot differs from the average subject in the population. IEEE ENGINEERING IN MEDICINE AND BIOLOGY
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The parameter ke 0 is referred to as the equilibration constant for the effect site. As the PD relationship, we adopted the classical Emax model: ∆BIS = ∆BIS MAX
C eγ
γ C eγ + EC 50 (8)
where ∆BIS = BIS − BIS 0
(9)
BIS MAX = BIS MAX − BIS 0 .
(10)
BIS 0 is the baseline or awake state value, and BIS MAX represents the minimum BIS. EC 50 represents the concentration at the effect site for which the effect is half of the maximum achievable. γ represents the subject’s sensitivity to small concentration changes at the effect site, and it can be regarded as an index of the model nonlinearity. We assumed BIS 0 = 100 and BIS MAX = 0 since high concentrations of Isoflurane lead to an isoelectric EEG. In such cases BIS = 0. The modeling assumptions together with the available identification procedure for the effect site compartment are discussed with more details in the literature [60, 46]. It is worth mentioning that the variability of the estimated PD parameters in our study is one order of magnitude greater than for the PK parameters [19]. This fact is also confirmed by off-line analysis of the data collected during the clinical evaluation of the BIS controller. Figure 5 displays the effect of Isoflurane concentrations at the effect
MAP Control Control of MAP is performed by means of three observer-based state feedback (OBSF) controllers whose interconnection is illustrated in Fig. 6: where y1 and y 2 represent MAP and end tidal Isoflurane concentrations, respectively. The underlying idea of the control structure is that the main controller C 1 , regulating MAP, is active under normal conditions. However, constraints have to be imposed on y 2 . An upper bound y** 2 , ref is needed because high Isoflurane concentration may lead to hypotonic crisis, cardiac arrhythmias, or even cardiac arrest.
C1
u
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y*2,ref
C2*
6. Block diagram of the override structure to control MAP. y1 and y 2 denote MAP and end tidal concentration measurements, respectively. C 1 regulates MAP under * normal conditions whereas C ** 2 and C 2 enforce the upper and lower limit for end tidal concentrations. u represents the vaporizer setting. 44
To comply with the upper limit, the override controller C ** 2 , which is in itself a complete OBSF controller, was introduced. The minimum selector applied to the control signals of C 1 and C ** 2 ensures is complied. that the upper limit y** 2 , ref A minimum end tidal concentration y*2 , ref must also be guaranteed to prevent light anesthesia and awareness. Therefore, we also introduced an override controller C *2 to ensure a minimum end tidal concentration. The stability analysis of the override structure was done according to the published literature [23, 22]. The classical state-feedback controller with observer [33] was modified with the additional blocks shown in Fig. 16. A feedforward compensation term for MAP, as well as integral action, were added for better setpoint tracking and to compensate for the effect of surgical stimulation and modeling errors, respectively. The input saturation shown in Figs. 6 and 16 limits the fresh gas concentrations betw e e n 0 % a n d 5 % , e xpr e sse d a s Isoflurane volume fraction in the fresh gas flow. Therefore, an anti-windup compensation was added to cope with the input constraints, which is not depicted in Fig. 16 for the sake of simplicity. The parameters of the controller were obtained as the solution of a linear quadratic regulator (LQR) problem [4]. The controllers were parametrized with the fresh gas flow Q0 , the patient weight and the respiratory frequency fR such that it is possible to compute the controller parameters on-line without going through the whole LQR design process.
BIS Control
max
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Controller Design and Testing
C2**
min
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compartment on BIS for two different patients during clinical studies. Together with the single individual’s PD relationships, the PD function identified from the population of volunteers is shown. In the left figure, a patient who behaves very similarly to the population of volunteers is recognizable, whereas in the right plot, a great difference is observed. In particular, it seems to be extremely difficult to achieve BIS values under 40 for the patient in the right plot unless a large amount of Isoflurane is used. On-line estimation of a single individual’s PD characteristics and, in particular, deviations from the behavior of the average subject population would improve the controller performance. Adaptive schemes that would use this information are currently being studied in our research project.
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To control BIS, we adopted the cascaded internal model control (IMC) depicted in Fig. 7, where the master controller regulates BIS and the slave controller regulates end tidal concentrations. The model of the patient is split in ~ two parts: the PK model P2 , relating inputs at the vaporizer u to end tidal conc e n t r a t i o n s y2 , a n d t h e e f f e c t ~ compartment model P1 , relating y 2 to y1 or BIS. The overall model is nonlinear, where the nonlinearity is represented by the PD relationship relating effect site concentrations to BIS [19]. According to Fig. 7, the master controller Q1 provides end tidal concentration reference values y 2 ,ref to the slave controller. This control loop forces y 2 to reach the reference value y 2 ,ref specified by the master loop. January/February 2001
The theoretical background and the tuning guidelines for IMC control systems are given in the literature [39]. Input saturation ~ was also added to the parallel model P2 as an anti-windup prevention. The saturation block after Q1 limits end tidal concentration references between 0.4% and 2.5%. Constraints on y 2 ,ref ensure that the limits for y 2 are not violated but also represent a clear limitation on the controller bandwidth. To compensate for this, anesthesiologists are able to enlarge or narrow the range of the constraints, at their convenience, during administration of anesthesia. ~ The parallel model P1 in the master loop is a linearization of the nonlinear PD model around a reference concentration. This configuration proved to be more robust with respect to PD parametric uncertainties than the full nonlinear model. The offset concentrations in the block diagram were omitted for the sake of simplicity. The ~ transfer ~ functions of the parallel models P2 and P1 were obtained by using the average parameters identified from the population of volunteers. The transfer functions of the IMC blocks Q2 and Q1 were chosen as the ~ filtered ~ inverses of the nominal models P2 and P1 [39]. The choice of a cascaded arrangement with IMC controllers contributed significantly to the acceptance of the controllers in the OR. In fact, the cascade arrangement mimics the procedure adopted by anesthesiologists if they were asked to control BIS manually. Namely, due to lack of clinical experience in controlling hypnosis through BIS values, an anesthesiologist would first target a specific value for end tidal anesthetic concentration. Then, she/he would adjust the end tidal concentration reference on the basis of the BIS values. In the control scheme developed, both tasks are achieved at the
Q2
It is natural to ask whether automatic controllers are capable of taking over and/or improving parts of such a complex decision process.
control performed by anesthesiologists with automatic MAP control. The study was recently completed. The outcomes of the clinical investigation will be published in the medical literature. In all clinical validations of MAP control that we will discuss, the lower y*2 , ref limit for end tidal concentrations was set to 0.4%. The upper limit y** 2 , ref may vary from 1 to 1.5%, depending on the surgical procedure. MAP values around the MAP measured at the arrival of the patient in the OR were used as targets. For half the patients chosen at random, closed-loop administration of Isoflurane is switched off roughly in the middle of the surgery period. From then on, Isoflurane is manually administered by the anesthesiologist. For the other half of the patients, the opposite sequence is done.
Clinical Validation of the Controllers MAP Control For the evaluation of the MAP controller, 40 ASA-class I to III (relatively healthy) patients aged 20 to 65 scheduled for elective abdominal, orthopedic, thoracic, or neurosurgery were enrolled in the study. The goal was to compare MAP
y2,ref
y1,ref −
same time. Also, the design was accomplished by tuning just two parameters, which have a direct clear interpretation. These parameters affect the approximate closed-loop time constant of the slave and master controller, respectively. Further, in the ideal case when there is no plant (physical system)-model mismatch, the closed loop trajectory tracks reference changes with no overshoot, thereby preventing overdosing. The time constants of the IMC filters were set to achieve nominal settling times for such controllers (defined as 90% of the steady-state value) equal to t s = 2 min for the endtidal controller and t s = 4 min for the overall BIS controller. Another advantage of the IMC strategy is that the control transfer functions can be adjusted on-line when the operating conditions of the closed-circuit breathing system are changed. This is not unusual during surgery, since fR , VT , and Q0 are often modified for several reasons. For instance, short periods at high flows ( Q0 ≥ 5 l/min) are normally used when a rapid wash-out of the drug is needed toward the end of the operation. Further, increasing alveolar ventilation fR (VT − ∆) is a standard procedure to reduce high levels of end tidal CO2 resulting from increased metabolism [5]. If respiratory parameters are changed by the anesthesiologist at any time during automatic mode, the supervi~ sory system will update the model P2 and the Q2 block.
u Q1
−
y1
y2 P2
~ P2
P1
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~ P1
k
−
e2 e1
7. Block diagram of the cascaded internal model control (IMC) structure to control BIS. y1 and y 2 denote BIS and end tidal concentration measurements, respectively. The master controller Q1 provides end tidal concentration references y 2 , ref to the slave controller Q2 . The saturation block after Q1 was introduced to enforce upper and lower limits for y 2 . January/February 2001
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8. Automatic MAP regulation during liver surgery. The upper plot depicts MAP and MAP references, respectively. The second plot represents end tidal concentra* tion measurements y 2 together with the upper and lower limits, y ** 2 , ref and y 2 , ref , respectively. The third plot represents the vaporizer settings during the study. In the fourth plot, the active controller is depicted, where −1 denotes C *2 is active, +1 denotes C ** 2 is active, and 0 denotes C 1 is active. Note that the upper override controller becomes active when heavy surgical stimulation starts at t = 50 min. 100 80 60 140
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9. Comparison of manual and automatic regulation of MAP. Automatic control starts at t = 220 min. For a detailed description of the variables in each plot, see the caption of Fig. 8. Note in the second plot that automatic control makes use of a wider bandwidth of end tidal concentrations than does the anesthesiologist. This presumably results from the more intense surgical stimulations in the second part of the operation. 46
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Clinical performance is evaluated based on several criteria such as the duration of periods with MAP within ±10% of the target value, and the numbers and types of critical incidents in both groups. These incidents are periods with MAP < 65 mmHg, systolic BP > 160 mmHg, or HR > 110 bpm. Figures 8, 9, and 10 show a clinical evaluation of the MAP controller. In all the figures, the upper plot represents the MAP profile during the study. The second plot represents the end tidal concentrations y 2 , together with the upper, y** 2 , ref , and lower, y*2 , ref , limits. The third and fourth plots represent the vaporizer settings and the active controller, respectively. According to the notation in Fig. 6, −1 denotes that C *2 is active, +1 denotes that C ** 2 is active, and 0 denotes that C 1 is active. In Fig. 8, the MAP profile under automatic control during a liver surgery is represented. The controller is able to achieve good performance during the periods of light surgical stimulation occurring at t = 38 min and t = 89 min. Note that during the period of light stimulation (t = 20-35 min), the override selector often switches between the MAP controller C 1 and the lower endtidal C *2 , even though end tidal concentrations are within the acceptable range. Presumably, this switching is a result of the particular sensitivity of the patient’s MAP to Isoflurane during the unstimulated period. In this case, the controller C 1 would tend to reduce Isoflurane settings and consequently end tidal concentrations below the accepted limit. At roughly t = 50 min, intense surgical stimulation occurs. To compensate for this, an end tidal concentration larger than y** 2 , ref would be required, which activates the upper override controller C ** 2 , as depicted in the fourth plot of Fig. 8. Figure 9 shows a comparison between manual and automatic control. Up to t = 192 min, anesthesia was conducted manually. According to the anesthesiologist, during this phase just minor adjustments of the vaporizer setting were needed. At t = 210 min automatic control starts. This phase is dominated by an intense disturbance starting at approximately t = 220 min, and a period of good regulation from t = 250 min on. Note from the second plot in Fig. 9 that the controller tends to make more use of the bandwidth of allowed end tidal concentrations than the anesthesiologist, also as a result of the more intense surgical stimulation in the second part of the operation. January/February 2001
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or MAP. Since Isoflurane is a hypnotic, it would seem more natural to use it to regulate BIS. However, this also depends on the anesthesiologists’ confidence in the BIS values. A SIMO controller that regulates BIS and MAP with Isoflurane is now being considered in our research project. The control objective is to administer Isoflurane to regulate BIS, while maintaining MAP within specified limits.
Supervisory Functions The supervisory functionality may be regarded as the superposition of all the necessary functions that have to be wrapped around the basic feedback control algorithms to make them routinely applicable in the OR. Even though the need for supervisory functionality for automatic control application in anesthesia has clearly been recognized by a number of researchers, not all are implemented in real practice [17, 34]. Often, just a brief outline of the necessary supervisory functions is presented [16, 36, 37, 40, 25, 59]. A supervisory system was implemented in our real-time platform according to the scheme represented in Fig. 13. Four main layers can be identified. D - Input and output conditioning: The measurements pass an input conditioning stage as they enter the anesthesia
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BIS Control Forty ASA-class I to III patients age 20 to 65 scheduled for elective abdominal, orthopedic, thoracic or neurosurgery were enrolled in the clinical evaluation of the BIS controller. The goal of the study is to determine whether closed-loop titration of Isoflurane to target specific values of BIS improves the quality of anesthesia. Time-to-eyes opening after interruption of drug administration, and average time spent by the patient in the PACU are recorded, together with episodes where BIS was outside the range 30-70. These periods indicate excessive and insufficient levels of hypnosis, respectively. The study is now in progress. Figure 11 shows the performance of the controller during a discus hernia removal. To the best of the authors’ knowledge, this is the first model-based closed-loop controller for hypnosis assessed with BIS using volatile anesthetics that has been tested on humans. The controller was able to keep BIS in the 40-50 range and to follow changes in the reference signal appropriately. The performance of the slave controller is better than the master, as apparent when comparing the first and second plot in Fig. 11. This is expected, since the model uncertainty is lower for the PK model than for the PD model. Further, end tidal measurements are less noisy than the BIS. Note also that the end tidal reference concentrations that are necessary to maintain BIS = 50 are
lower at the beginning of anesthesia (t = 80-90 min) than in the central period (t = 140-180 min). This may result from either the residuals of the intravenous hypnotic used for induction, from the lower intensity, or from surgical stimulation. Regardless of the reason, the controller was able to adapt the administration profile to the particular situation. Figure 12 shows another clinical validation of the controller. The automatic controller was started at t = 60 min. At t = 80 min the fresh flow rate was decreased from Q0 = 3 l/min to Q0 = 1 l/min to minimize anesthetic consumption. The supervisor recognizes the changes in the breathing system and updates the model in the controller. As a result, the vaporizer setting increased immediately, which compensates for the slower dynamics at low flow conditions. Interesting conclusions can be drawn when comparing the performance of the MAP and the BIS controller. Namely, surgical stimulation does not affect BIS—and therefore the hypnotic state—as much as it affects MAP. This is expected, since consciousness is depressed with lower anesthetic concentrations than is the stress response—particularly hemodynamic variability. The question is then whether Isoflurane should be used to regulate BIS
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Figure 10 shows a clinical evaluation where the controller was able to suppress the effect of surgical stimulation occurring at t = 82 min and t = 115 min, respectively. The period between t = 50 min and t = 80 min was not characterized by any significant stimulation. During this phase, the lower end tidal controller was active to deliver a minimum amount of Isoflurane. The following conclusions can be drawn from the above discussion. The controller is successfully able to compensate for light disturbances, as shown in Fig. 8. The limited control action and the fast disturbance dynamics seriously limit the ability to compensate for intense disturbances. These limitations also apply for manual control. Therefore, we expect that the difference between manual and automatic control will not be substantial. An intuitive way for improving blood pressure regulation is to provide the controller with information about future major disturbances such as skin incision [15]. This approach is now being tested in pilot studies.
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10. Automatic regulation of MAP during neurological surgery, for which no episodes of manual regulation were performed. For a detailed description of the contents in each plot, refer to the caption of Fig. 8. Note that the lower override controller C *2 is active during the first period (t = 50-80 min) of light surgical stimulation to guarantee a minimal anesthetic administration. IEEE ENGINEERING IN MEDICINE AND BIOLOGY
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system. Conditioning includes preprocessing of the signals, selection of the most reliable one out of a set of multiple
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conditioning stage. Typical tasks of this part are the shaping of test inputs for fault detection and isolation (FDI), the min-max selection of an override controller, or the switch from manual to automatic control. C - Process information: At this stage, all the data available about the state of the process are stored, including controller states. Typically, this information is stored in data banks. From there the data are accessed for storage or for display. B - Algorithmic layer: This layer incorporates feedback controllers, supervisor logic control (SLC), FDI algorithms, as well as decision support functions. The division into layers B1 and B2 separates dynamic form logic control. At this stage, for instance, transition conditions are checked to allow the anesthesiologist to switch to automatic control. FDI functions are responsible for detecting faults in the system, such as equipment faults like disconnected sensors or leaks as well as the detection of critical patient physiological states like excessive blood loss. Decision support (DS) makes suggestions to the anesthesiologist on how to optimize the anesthetic procedure. It provides information that cannot be directly read from monitors. Typical examples are the display of the estimated time required for the patient to wake up after the anesthetic is discontinued, or the estimated concentration of anesthetic in the different compartments. A - Man Machine Interface (MMI): This is the most user-oriented layer and is therefore drawn as the top layer of the supervisory structure. All information from the system to the anesthesiologist, and vice versa, must pass through the MMI. The MMI is typically implemented by a graphical user interface (GUI), but acoustic alarms are also part of the MMI. As an example, the control panel adopted during BIS control is depicted in Fig. 14. A detailed discussion of all the supervisory functions is beyond the scope of this article but can be found in the literature [14]. Instead, we will focus on a particular aspect of the supervisory system instead of the treatment of measurement artifacts.
Artifact-Tolerant Controllers Several authors have noted the undesirable implications of improper handling of artifacts during closed-loop control of anesthesia [45, 44, 16]. A minor consequence is illustrated in Fig. 15. Here, a model-based end tidal controller January/February 2001
is supposed to lower end tidal Isoflurane concentration From 1.3% to 0.7%, as indicated by the dashed line. During this maneuver, an automatic calibration of the monitor occurs, resulting in a zero value for the concentration measurement. This sudden change in the controlled output causes the controller to fully open the vaporizer. Although the artifact terminates after 20 s, enough Isoflurane has been supplied to the system to considerably overshoot and prolong the maneuver. Fortunately, this situation only deteriorates the controller performance; there are no critical consequences for the patient here. On the other hand, artifacts in the blood pressure signal might lead to sharp changes of blood pressure during MAP control. An example of such critical transients is documented by Fukui and Musuzawa [16]. Fortunately, we have not encountered such a situation. Before presenting our solution to the artifact problem, we investigate how artifacts deteriorate controller performance. Figure 16 represents a classical OBSF controller, where integral action and the feedforward compensator V have been introduced. In developing the strategy, we work with a linear time invariant approximation of the system represented by the state space matrices A,B,C,D. In Fig. 16, v(t ) and w(t ) represent process and measurement noise, respectively; ␦(t ) represents the artifacts. The observer serves to estimate the states x of the system. The matrix L for update of the observer states can be computed considering process and measurement noise characteristics; e.g., with a Kalman filter design. The artifacts ␦(t ), unlike white, measurement, or process noises, affect the controller in two ways. First, through the output injection matrix L, artifacts lead to a mismatch between observer states and system states. Secondly, they lead to an offset of the integral part of the controller. This mismatch between controller states and reality can be viewed as a controller wind-up [30]. A natural remedy to prevent artifacts from degrading the controller performance is to make sure that the artifacts ␦(t ) do not enter the observer equations. In a stochastic framework, the error signal e y (t ) = y(t ) − y (t ) represents a vector-valued zero mean and white stochastic process [1]. If v(t ) and w(t ) are zero mean white noise processes, and an artifact ocJanuary/February 2001
curs, e y (t ) is not zero mean but has a mean of ␦(t ). Thus, the detection of an artifact based on the innovations signal e y (t ) is equivalent to detecting a sudden shift in
the mean of e y (t ). The test for the zero mean hypothesis may be formulated as a statistical decision based on the actual value of e y (t ).
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14. Operating panel for closed-loop regulation of hypnosis. (a) Central panel, which displays parameters of the breathing system, BIS, and the actual control action; (b) buttons for the switch between passive, manual, and automatic control; (c) buttons to inform the controller about significant events such as skin incision, skin closure, and intubation; (d) BIS controller panel, where the reference BIS is selected together with tolerable limits for the end tidal anesthetic concentration; (e) information about active controller and reliability of both BIS and end tidal concentration measurements. IEEE ENGINEERING IN MEDICINE AND BIOLOGY
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In case of an artifact, the corresponding output injection vector is set to L i = 0, which prevents the artifact from entering the observer equations. The statistical decision may be represented by a diagonal nonlinear block f ( e y (t )), multiplying the innovations e y (t ). That is:
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When it comes to the routine application of automatic controllers to patients, considerable attention must be paid to a proper hardware/software (HW/SW) platform. In the early phase of the project, the controllers were implemented under Modula II on an MS DOS-supported in-
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The controllers for MAP and BIS were also described. The controllers adopt particular schemes to prevent overdosing in clinical practice, and they guarantee safe operation in the presence of measurement artifacts. The controllers are also adaptable to the different operating regimes of the breathing system, guaranteeing adequate performance. The successful application of both controllers in clinical practice has been demonstrated, indicating higher-quality anesthesia for patients who were treated with automatic control. A number of limitations of the actual design must be pointed out at this stage of development. The controllers cannot be used without the anesthesiologist’s close supervision. For example, the feedback systems that were shown are SISO, whereas the goal of the anesthesiologist is to maintain several physiological variables in specified ranges. For instance, under BIS control, no action is taken by the controller if the MAP is too high or too low. Further, the benefits of multidrug anesthesia are not yet exploited. At present, we are using Isoflurane alone, and we are not considering other drugs in our control schemes. Opiates and muscle relaxants—if used in combination with hypnotics—can provide beneficial effects in clinical practice [56, 38].
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Andrea Gentilini was born in 1972 in Italy. He obtained his chemical engineering degree from Politecnico di Milano “summa cum laude” in 1997, winning the award “Premio Pastonesi” for the best presented thesis. He is currently with the Automatic Control Laboratory at the Swiss Federal Institute of Technology, where he obtained postgraduate degrees in information technology and applied statistics. His research
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The first steps toward the development of an autonomous anesthesia system at our laboratory have been described. The controllers are implemented on a real-time platform and tested on humans to quantify the benefits that may result from their use in routine practice. To date, the staff at the University Hospital in Bern can rely on controllers that regulate six different patient outputs. Overall, more than 150 patients were treated with closed-loop controllers during general anesthesia. These controllers regulate O2 , CO2 , and inspired and expired anesthetic gas concentrations in the breathing system, as well as MAP and depth of hypnosis through BIS.
Another open issue is the administration of analgesics, for which an openloop infusion policy is still adopted clinically. As pointed out in the overview, there are no specific measures of the analgesic state of the patient. We have the actuator, but we miss the sensor. The analgesic state is assessed clinically mainly on the basis of the reaction of the hemodynamic system to surgical stimulation. However, this method is of no great help, since the expected reaction of MAP depends on various nonmeasurable variables such as the intensity and location of the stimulation, and the patient’s specific characteristic reaction to pain. These are some of the open issues that will be addressed by our research project in the future.
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dustrial PC with the necessary A/D and D/A conversion boards. This platform suffered from a number of shortcomings, such as poor support of real-time and multitasking features, lack of software components to design adequate user interfaces, and compiler limitations. Currently, a target (VME PowerPC)host (PC) computer system provides the hardware basis for the experimental platform. The operating system XOberon from the Robotics Institute of ETH provides the required real-time and multitask features [58]. The applications are implemented using the object-oriented programming language Oberon, a member of the PascalModula family [32]. Making use of object-oriented technology, a framework has been developed that efficiently allows us to write new control applications. The platform is depicted in Fig. 2. The compact integration of the computer system equipped with a touch screen on a standard CiceroEM anesthesia workstation from Dräger Germany contributes significantly to the general acceptance of this prototype system in the OR. Also, the platform is endowed with an emergency shut-down button that cuts any active controller off and transfers the regulation of the breathing system to the anesthesiologist for manual dosing. Recently, a pump has been integrated for the continuous intravenous infusion of analgesics. The design of the MMI is aimed at reproducing closely the standard monitoring systems for anesthesia. In this way, anesthesiologists are able to run closed-loop controllers without any engineering support. An example of an operating panel is presented in Fig. 14.
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interests include modeling of physiological systems and design of feedback controllers for anesthesia. Christian W. Frei received his first degree in EE from the Engineering School (HTL) Brugg-Windisch (Switzerland). He obtained an MSEE from Northwestern University in 1995 and a PhD from the Swiss Federal Institute of Technology (ETH) in 2000. He has been working for Landis & Gyr Corporation, Zug (Switzerland) since 1994 and is currently with BT&T Asset Management AG, Urdorf (Switzerland). His interests concern modeling and control of non-technical systems. Adolf Hermann Glattfelder received his Diploma in mechanical engineering in 1964 from ETH Zurich/Switzerland, and his Ph.D. degree from the same institution in 1969. His habilitation for automatic control was accepted by ETH Zurich in 1973. From 1976 to 1991 he was research and line manager with Sulzer Limited. In 1991 he returned to the Automatic Control Laboratory. His main research interests are feedback control in anesthesia, design methods adapted to industrial control systems, with input and output constraints. In 1994 Manfred Morari was appointed head of the Automatic Control Laboratory at the Swiss Federal Institute of Technology (ETH) in Zurich. Before that he was the McCollumCorcoran Professor and Executive Officer for Control and Dynamical Systems at the California Institute of Technology. He obtained the diploma from ETH Zurich and the Ph.D. from the University of Minnesota. His interests are in hybrid systems and the control of biomedical systems. In recognition of his research he received numerous awards, among them the Eckman Award of the AACC, the Colburn Award, and the Professional Progress Award of the AIChE, and he was elected to the National Academy of Engineering (US). Professor Morari has held appointments with Exxon R & E and ICI and has consulted interna52
tio n a lly f o r a n u m b e r o f m a jo r corporations. Thomas J. Sieber received his M.D. degree in 1985 from the University of Zurich and is currently working as a staff anesthesiologist at the University Hospital in Bern, Switzerland. His interests include cardiovascular anesthesia, feedback control and general management. Rolf Wymann was born in Switzerland, 1958. He obtained his M.D. from the University of Bern in 1983. In the period 1985-1986 he did research in the field of adverse drug reactions in the team of the Comprehensive Hospital Drug Monitoring in Bern. In the period 1987-1990 he spent his residency in Internal Medicine in Bern and Biel, Switzerland. Since 1991 he is staff anesthesiologist at the University Hospital in Bern. His research interests involve pharmacokinetic-pharmacodynamic modeling of anesthetic drugs and feedback control in anesthesia. Thomas W. Schnider received his M.D. degree from the University of Bern, Switzerland, in 1984, where he is currently working as a staff anesthesiologist. From 1993 to 1995 he worked as a research fellow at the Department of Anesthesiology of Stanford University in clinical pharmacology. His main research interests are in pharmacokinetic/pharmacodynamic modeling and feedback control in anesthesia. Alex M. Zbinden received his first M.D. from the University of Bern and went through his training as a surgeon and anesthesiologist at the University Hospital in Basel and obtained his qualification as anesthesiologist from that institution in 1983. Prof. Zbinden’s first experience with feedback control in anesthesia was obtained in 1985 in Basel. He continued to work on this field after becoming the head of the research department in the Institute of Anesthesiology IEEE ENGINEERING IN MEDICINE AND BIOLOGY
and Intensive Care in the University Hospital of Bern. His main fields of interest are feedback control of anesthesia, dosage of inhaled anesthetics, pain perception, and quality assurance in anesthesia. Address for Correspondence: Manfred Morari, Automatic Control Library, ETH Zentrum, ETH I 29, CH 8092, Zurich Switzerland. Tel: +41 1 632 7626. Fax: +41 632 1211. E-mail:
[email protected].
References 1. Bar-Shalom Y and Fortmann TE: Tracking and Data Association. San Diego, CA: Academic, 1988. 2. Bischoff KB: Some fundamental considerations of the applications of pharmacokinetics to cancer chemotherapy. Cancer Chemotherapy Reports 59: 777-793, 1975. 3. Bradlow HS, Uys PC, and Rametti LB: On-line control of atracurium induced muscle relaxation. J Biomed Eng 8: 72-75, 1986. 4. Bryson AE and Ho Y-Ch: Applied Optimal Control - Optimization, Estimation and Control. New York: Taylor & Francis, 1975. 5. Chapman FW, Neweil JC, and Roy RJ: A feedback controller for ventilatory therapy. Ann Biomed Eng 13: 359-372, 1985. 6. Chilcoat RT: A review of the control of depth of anaesthesia. Trans Institute of Measurement and Control 2(1):38-45, Jan. 1980. 7. Cullen DJ, Eger EI, Stevens WC, Smith NT, Cromwell TH, Cullen BF, Gregory GA, Bahlman SH, Dolan WM, Stoelting RK, and Fourcade HE: Clinical signs of anesthesia. Anesthesiology 36(1): 21-36, Jan. 1972. 8. Derighetti M, Frei C, Glattfelder AH, and Zbinden AM: Fuzzy logic control of mechanical ventilation during anesthesia. In: Proc Fourth European Congress on Intelligent Techniques and Soft Computing, Sept. 1996, Aachen, Germany, 3: 2046-2049, 1996. 9. Derighetti M, Frei CW, Buob M, Zbinden AM, and Schnider TW: Modeling the effect of surgical stimulation on mean arterial blood pressure. In: Proc 19th International Conference IEEE EMBS, Oct. 30 - Nov. 2, 1997, Chicago, IL, pp. 2172-2175, 1997. 10. Derighetti M: Feedback Control in Anaesthesia. PhD dissertation, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland, 1999. 11. Doi M, Gajraj RJ, Mantzaridis H, and Kenny GNC: Relationship between calculated bl ood c onc e nt r a t i on o f p r o p o f o l a n d electrophysiological variables during emergence from anaesthesia: a comparison of bispectral index, spectral edge frequency, median frequency and auditory evoked potential. Br J Anaesthesia, 78: 180-184, 1997. 12. Kotrly KJ, Ebert TJ, Vucins E, Igler FO, Barney JA, and Kampine JP: Baroreceptor reflex control of heart rate during isoflurane anesthesia in humans. Anesthesiology 60(4): 173-179, 1984. 13. Eger II, EI: The pharmacology of Isoflurane. Br J Anaesthesia 56: 71-99, 1984. January/February 2001
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