**Closed-Loop Control of Anaesthetic Effect**

Santiago Torres, Juan A. Méndez, Héctor Reboso, José A. Reboso and Ana León *Universidad de La Laguna* 

*Spain* 

## **1. Introduction**

452 Pharmacology

Taira, S., Sugiura, Y., Moritake, S., Shimma, S., Ichiyanagi, Y., & Setou, M. (2008).

Tanaka, H., Zaima, N., Yamamoto, N., Sagara, D., Suzuki, M., Nishiyama, M., Mano, Y.,

Tanaka, H., Zaima, N., Yamamoto, N., Suzuki, M., Mano, Y., Konno, H., Unno, N., & Setou,

Tanaka, K., Ido, Y., Akita, S., Yoshida, Y., & Yoshida, T. (1987). Detection of High Mass

Vrkoslav, V., Muck, A., Cvacka, J., & Svatos, A. (2010). MALDI imaging of neutral cuticular

Wiseman, J. M., Ifa, D. R., Song, Q., & Cooks, R. G. (2006). Tissue imaging at atmospheric

Woods, A. S., & Jackson, S. N. (2006). Brain tissue lipidomics: direct probing using matrixassisted laser desorption/ionization mass spectrometry. *AAPS J* 8.2, pp.E391-5 Yates, J. R., 3rd (1998). Mass spectrometry and the age of the proteome. *J Mass Spectrom* 33.1,

Zaima, N., Goto-Inoue, N., Adachi, K., & Setou, M. (2011a). Selective analysis of lipids by

Zaima, N., Goto-Inoue, N., Hayasaka, T., Enomoto, H., & Setou, M. (2011b). Authenticity

Zaima, N., Goto-Inoue, N., Hayasaka, T., & Setou, M. (2010a). Application of imaging mass

Zaima, N., Hayasaka, T., Goto-Inoue, N., & Setou, M. (2010b). Matrix-assisted laser desorption/ionization imaging mass spectrometry. *Int J Mol Sci* 11.12, pp.5040-55 Zaima, N., Matsuyama, Y., & Setou, M. (2009). Principal component analysis of direct

Zaima, N., Sasaki, T., Tanaka, H., Cheng, X. W., Onoue, K., Hayasaka, T., Goto-Inoue, N.,

Zhang, X., Leung, S. M., Morris, C. R., & Shigenaga, M. K. (2004). Evaluation of a novel,

lipids in insects and plants. *J Am Soc Mass Spectrom* 21.2, pp.220-31

cellular resolution. *Anal Chem* 80.12, pp.4761-6

*China Joint Symp. Mass Spectrom.*, pp.185

*Angew Chem Int Ed Engl* 45.43, pp.7188-92

imaging mass spectrometry. *J Oleo Sci* 60.2, pp.93-8

metabolites of fatty liver. *J Oleo Sci* 58.5, pp.267-73

*Atherosclerosis* 217.2, pp.427-32

*Chem* 400.7, pp.1873-80

pp.1-19

24.18, pp.2723-9

varicose veins. *Eur J Vasc Endovasc Surg* 40.5, pp.657-63

Nanoparticle-assisted laser desorption/ionization based mass imaging with

Sano, M., Hayasaka, T., Goto-Inoue, N., Sasaki, T., Konno, H., Unno, N., & Setou, M. (2010). Imaging mass spectrometry reveals unique lipid distribution in primary

M. (2011). Distribution of phospholipid molecular species in autogenous access grafts for hemodialysis analyzed using imaging mass spectrometry. *Anal Bioanal* 

Molecules by Laser Desorption Time-Of-Flight Mass Spectrometry. *Proc. Japan-*

pressure using desorption electrospray ionization (DESI) mass spectrometry.

thin-layer chromatography blot matrix-assisted laser desorption/ionization

assessment of beef origin by principal component analysis of matrix-assisted laser desorption/ionization mass spectrometric data. *Anal Bioanal Chem* 400.7, pp.1865-71

spectrometry for the analysis of Oryza sativa rice. *Rapid Commun Mass Spectrom*

matrix-assisted laser desorption/ionization mass spectrometric data related to

Enomoto, H., Unno, N., Kuzuya, M., & Setou, M. (2011c). Imaging mass spectrometry-based histopathologic examination of atherosclerotic lesions.

integrated approach using functionalized magnetic beads, bench-top MALDI-TOF-MS with prestructured sample supports, and pattern recognition software for profiling potential biomarkers in human plasma. *J Biomol Tech* 15.3, pp.167-75

The interest in automation technologies applied to anaesthesia has been grown exponentially in last decade. The main difference with other fields of automation is that the presence of a human supervisor has been never questioned. In spite of this, the use of automation tools to monitor and control the main variables during surgery notably helps the anaesthetist during surgery. The basic functions of the automation systems in anaesthesia are monitoring and control of the main variables of the process. This leads to two expected benefits. First, the anaesthetist will be freed of some routinary tasks so that he can concentrate more on the state of the patient. On the other hand, using these tools contributes to improve the global performance of the process in terms of safety, costs reduction and patient comfort.

During the surgery operation three main variables have to be regulated: hypnosis, analgesia and muscle relaxation. To achieve this, drugs have to be properly administered to the patient. In recent years many efforts have been made in the development of new drug delivery technologies (Bressan et al., 2009). Most of the difficulties to calculate the proper drug rate to each patient were the inexistence of precise methods to monitor the anaesthetic state of the patient. In the past, patient monitoring was performed just by observing several patient signs (sweat, head lifting, movement, etc.). Nowadays the way that anaesthesia is monitored has changed considerably.

Concerning hypnosis regulation, many efforts have been made to provide the anaesthesiologist with reliable methods for monitoring. In particular, the introduction of the Bispectral Index (BIS) to measure the depth of anaesthesia was one of the key elements in the development of new ways of drug administration (Sigl and Chamoun, 94).

The other main problem in designing control algorithms to regulate hypnosis arises from the complexity of the patient response to drug infusion. This response can be divided in two subsystems. One is the Pharmacokinetics (PK) that refers to the adsorption, distribution, biotransformation and excretion of the drug. And the other is the Pharmacodynamics (PD) that describes the equilibrium relationship between concentration in the body and visible effect produced in the patient. In practice a linear model has been accepted to describe the PK and a nonlinear model for the PD part.

Closed-Loop Control of Anaesthetic Effect 455

The drug distribution in the body depends on transport and metabolic processes, which in many cases are not clearly understood. However, dynamical models based on conservation laws that capture the exchange of material between coupled macroscopic subsystems or

compartments, are widely used to model these processes.

Fig. 1. Input-output description of the anaesthetic process.

with a poor blood supply (such as adipose tissue).

Figure 2 shows a model based in three compartments: central, fast and slow. The central compartment is the volume in which initial mixing of the drug occurs, and thus can be thought to include the vascular system (blood volume) and for some drugs the interstitial fluid. The fast peripheral compartment represents a compartment of the body that absorbs drug rapidly from the central compartment, and thus can be thought of as comprising tissues of the body that are well-perfused (such as muscles and vital organs). Finally the slow peripheral compartment is used to mathematically represent a compartment into which re-distribution occurs more slowly, and thus can be thought of as including tissues

**2.1 The compartmental model** 

First works involved with anaesthesia control were focused in checking the performance of a fully automated controller compared with the results obtained in a process guided by an anaesthetist. In (Sakai et al., 2000) and (Morley et al., 2000) it is showed that proposed PID controller can assure intraoperative hemodynamic stability and a fast recover of the patient from the hypnosis effects of the drug using closed-loop techniques. In these works and in the works of Absalom (Absalom et al., 2002a, Absalom et al., 2002b, Absalom et al., 2003), it can be shown that the performance of the closed-loop system was as efficient as the observed in the process guided by the specialist, without demonstrating any clinical advantages over the manual techniques.

In the last decade, a lot of research related with automatic control of anaesthesia has been made. Most of them use the intravenous drug propofol as the hypnotic agent. It is important to mention the works that follow a signal-based control, as PID (Liu et al., 2006; Dumont et al., 2009) and fuzzy controllers (Gil, 2004), and the works that follow a model-based control. In this way, many different proposals have been made depending on the controller structure, the controlled variable and the prediction model used. In (Struys. et al., 2001; Sawaguchi et al., 2003; Furutani et al., 2005) the drug concentration in brain is used as controlled variable. In (Ionescu et al., 2008) and (Niño et al., 2009), were EPSAC tecniques are used as controller structure, in (Screenivas et al., 2008), were robust characteristics are added in the design of the controller, and in (S. Syafiie et al., 2009), were nonlinear techinques are used, the authors use predictive control techniques. In (Screenivas et al., 2009) a comparative study between predictive control and PID techniques applied to the control of anaesthetic is done.

The focus of this chapter will be in the regulation of depth of consciousness of patients under general anaesthesia with intravenous propofol.

#### **2. Anaesthetic process: The control problem**

The main variables that describe the anaesthetic process are depicted in figure 1. In this figure an input-output description of the system is shown. As can be observed, manipulated variables are anaesthetics, relaxants or serums. Perturbations in the system are signals that can occur at any time (surgical stimulation, blood loss, etc.). The output variables can be measurable and not measurable. The main interest in anaesthesia is focused in nonmeasurable variables: hypnosis, analgesia and muscular relaxation. Although these variables are not directly measurable, there are methods to estimate them that are used in clinical practice. These methods are based on the use of alternative variables whose behaviour allows the estimation of the non-measurable ones.

Hypnosis is a general term indicating loss of consciousness and absence of the memory of the intervention after awake. Currently, the techniques that have been considered more efficient for this are based in the processing of the patient electroencephalogram (EEG), (Kazama et al., 1999; Struys et al., 2000).

The description of the BIS dynamics has been done mainly with physiological based models. These models consist of a PK part to describe the drug distribution in the internal organs and a PD part to describe the drug effect on the physiological variables of interest.

First works involved with anaesthesia control were focused in checking the performance of a fully automated controller compared with the results obtained in a process guided by an anaesthetist. In (Sakai et al., 2000) and (Morley et al., 2000) it is showed that proposed PID controller can assure intraoperative hemodynamic stability and a fast recover of the patient from the hypnosis effects of the drug using closed-loop techniques. In these works and in the works of Absalom (Absalom et al., 2002a, Absalom et al., 2002b, Absalom et al., 2003), it can be shown that the performance of the closed-loop system was as efficient as the observed in the process guided by the specialist, without demonstrating any clinical

In the last decade, a lot of research related with automatic control of anaesthesia has been made. Most of them use the intravenous drug propofol as the hypnotic agent. It is important to mention the works that follow a signal-based control, as PID (Liu et al., 2006; Dumont et al., 2009) and fuzzy controllers (Gil, 2004), and the works that follow a model-based control. In this way, many different proposals have been made depending on the controller structure, the controlled variable and the prediction model used. In (Struys. et al., 2001; Sawaguchi et al., 2003; Furutani et al., 2005) the drug concentration in brain is used as controlled variable. In (Ionescu et al., 2008) and (Niño et al., 2009), were EPSAC tecniques are used as controller structure, in (Screenivas et al., 2008), were robust characteristics are added in the design of the controller, and in (S. Syafiie et al., 2009), were nonlinear techinques are used, the authors use predictive control techniques. In (Screenivas et al., 2009) a comparative study between predictive control and PID techniques applied to the

The focus of this chapter will be in the regulation of depth of consciousness of patients

The main variables that describe the anaesthetic process are depicted in figure 1. In this figure an input-output description of the system is shown. As can be observed, manipulated variables are anaesthetics, relaxants or serums. Perturbations in the system are signals that can occur at any time (surgical stimulation, blood loss, etc.). The output variables can be measurable and not measurable. The main interest in anaesthesia is focused in nonmeasurable variables: hypnosis, analgesia and muscular relaxation. Although these variables are not directly measurable, there are methods to estimate them that are used in clinical practice. These methods are based on the use of alternative variables whose

Hypnosis is a general term indicating loss of consciousness and absence of the memory of the intervention after awake. Currently, the techniques that have been considered more efficient for this are based in the processing of the patient electroencephalogram (EEG),

The description of the BIS dynamics has been done mainly with physiological based models. These models consist of a PK part to describe the drug distribution in the internal organs

and a PD part to describe the drug effect on the physiological variables of interest.

advantages over the manual techniques.

control of anaesthetic is done.

under general anaesthesia with intravenous propofol.

**2. Anaesthetic process: The control problem** 

behaviour allows the estimation of the non-measurable ones.

(Kazama et al., 1999; Struys et al., 2000).

The drug distribution in the body depends on transport and metabolic processes, which in many cases are not clearly understood. However, dynamical models based on conservation laws that capture the exchange of material between coupled macroscopic subsystems or compartments, are widely used to model these processes.

Fig. 1. Input-output description of the anaesthetic process.

#### **2.1 The compartmental model**

Figure 2 shows a model based in three compartments: central, fast and slow. The central compartment is the volume in which initial mixing of the drug occurs, and thus can be thought to include the vascular system (blood volume) and for some drugs the interstitial fluid. The fast peripheral compartment represents a compartment of the body that absorbs drug rapidly from the central compartment, and thus can be thought of as comprising tissues of the body that are well-perfused (such as muscles and vital organs). Finally the slow peripheral compartment is used to mathematically represent a compartment into which re-distribution occurs more slowly, and thus can be thought of as including tissues with a poor blood supply (such as adipose tissue).

Closed-Loop Control of Anaesthetic Effect 457

To include this dynamics in the model a fourth compartment is added. This compartment is known as effect site. It is assumed that this compartment is attached to the central compartment and has negligible volume. The diffusion constant of the effect site is *ke0*.

*k***10(min-1)** 0.119 0.0443+0.0107\*(BW-77)-0.0159\*(LBM-

Table 1. Comparison of Marsh and Schnider models for PK of propofol. BW stands for Body

On the other hand, the drug's pharmacodynamics, that represents the BIS in terms of the

The *f* function is usually taken as an EMAX model whose profile suits the described process:

max

BIS0 corresponds to the awake state, *BISmax* represents the minimum achievable BIS and *EC50* represents the concentration in the effect site for which the effect is half the maximum value, represents the sensitivity of the patient to mall concentration variations in the effect site. This parameter can be seen as index that measures the degree of nonlinearity of the model.

From the perspective of the control system three level of complexity can be distinguished. The basic procedure is the open-loop practice in which the anaesthetist, according to the parameters of the patient (age, weight, sex, ASA) directly uses predefined infusion rates of drugs. According to the response observed through his vital signs the drug rates can be

In the next level, it appears the Target Controlled Infusion systems (TCI). In TCI the infusion rate is calculated from models of the pharmacokinetic of the patient, as can be seen in figure

*<sup>C</sup> BIS BIS*

*V***1** 0.228 L/Kg 4.27L

*k***13(min-1)** 0.0419 0.196

*k***31(min-1)** 0.0033 0.0035 *ke***0(min-1)** 1.21 0.456

Weight, LBM is Lean Body Mass and HT is Height.

effect site concentration, is governed by:

**2.2 The control problem** 

modified (the anaesthetist is the controller).

*k***12(min-1)** 0.112 0.302-0.0056\*(Age-53)

*k***21(min-1)** 0.005 1.29-0.024\*(Age-53)

**Marsh Model Schnider Model** 

59)+0.0062\*(HT-177)

( ) *BIS f C <sup>e</sup>* (5)

*BIS BIS BIS* 0 (7)

*BIS BIS BIS* max max 0 (8)

(6)

50

*e*

*C EC*

*e*

Fig. 2. Compartmental model.

The drug is infused in central compartment and then distributed to the slow and fast compartment and eliminated trough metabolism. Defining the drug concentration variable of the i-th compartment as *Ci*, the propofol distribution can be described as:

$$V\_1 \frac{\partial \mathbb{C}\_1}{\partial t} = V\_2 \mathbb{C}\_2(t) k\_{21} + V\_3 \mathbb{C}\_3(t) k\_{31} - V\_1 \mathbb{C}\_1(t) (k\_{10} + k\_{12} + k\_{13}) + \mu(t) \tag{1}$$

$$V\_2 \frac{\partial \mathcal{C}\_2}{\partial t} = V\_1 \mathcal{C}\_1(t)k\_{12} - V\_2 \mathcal{C}\_2(t)k\_{21} \tag{2}$$

$$V\_3 \frac{\partial \mathcal{C}\_3}{\partial t} = V\_1 \mathcal{C}\_1(t)k\_{13} - V\_3 \mathcal{C}\_3(t)k\_{31} \tag{3}$$

$$\frac{\partial \mathbb{C}\_{\epsilon}}{\partial t} = \mathbb{C}\_{1}(t)k\_{\epsilon 0} - \mathbb{C}\_{\epsilon}(t)k\_{\epsilon 0} \tag{4}$$

where *u(t*) represents the drug infusion rate in the central compartment and *Vi* is the volume of the i-th compartment. The dynamics of the compartmental model is defined by the following diffusion constants: *k10* (rate constant for drug metabolism), *k12* (rate constant for re-distribution of drug from central to fast peripheral compartment), *k21* (rate constant for redistribution of drug from fast to central compartment), *k13* (rate constant for redistribution of drug from central to slow compartment) and *k31* (rate constant for redistribution of drug from slow to central compartment). Common PK models for propofol are the Marsh model (Marsh et al., 1991) and the Schnider model (Schnider et al., 1998). Differences between both models can be seen in table 1.

From the point of view of hypnosis control, the variable of interest is not the blood concentration but the concentration in the place where the effect on the controlled variable is produced (effect site concentration). Thus, when there is a simultaneous measure of the drug concentration in blood and its effect on the brain, drug latency can be observed that produces a temporal displacement between the peak of blood concentration and the drug effect.

Propofol

Central Compartment V1

*k*<sup>12</sup>

*k*<sup>21</sup>

*k*e0

Effect Site

The drug is infused in central compartment and then distributed to the slow and fast compartment and eliminated trough metabolism. Defining the drug concentration variable

1 22 21 33 31 11 10 12 13 ( ) ( ) ( )( ) () *<sup>C</sup> V VC t k VC t k VC t k k k ut*

<sup>2</sup> 1 1 12 2 2 21 () () *<sup>C</sup> V VC t k VC t k*

<sup>3</sup> 1 1 13 3 3 31 () () *<sup>C</sup> V VC t k VC t k*

10 0 () () *<sup>e</sup> e ee <sup>C</sup> C tk C tk*

where *u(t*) represents the drug infusion rate in the central compartment and *Vi* is the volume of the i-th compartment. The dynamics of the compartmental model is defined by the following diffusion constants: *k10* (rate constant for drug metabolism), *k12* (rate constant for re-distribution of drug from central to fast peripheral compartment), *k21* (rate constant for redistribution of drug from fast to central compartment), *k13* (rate constant for redistribution of drug from central to slow compartment) and *k31* (rate constant for redistribution of drug from slow to central compartment). Common PK models for propofol are the Marsh model (Marsh et al., 1991) and the Schnider model (Schnider et al., 1998). Differences between both

From the point of view of hypnosis control, the variable of interest is not the blood concentration but the concentration in the place where the effect on the controlled variable is produced (effect site concentration). Thus, when there is a simultaneous measure of the drug concentration in blood and its effect on the brain, drug latency can be observed that produces a

temporal displacement between the peak of blood concentration and the drug effect.

(1)

(2)

Fast Compartment V2

(3)

(4)

of the i-th compartment as *Ci*, the propofol distribution can be described as:

*k*<sup>13</sup>

*k*<sup>31</sup>

Metabolism

 *k*<sup>10</sup>

2

3

*t*

*t*

*t*

Fig. 2. Compartmental model.

1

Slow Compartment V3

*t* 

models can be seen in table 1.

To include this dynamics in the model a fourth compartment is added. This compartment is known as effect site. It is assumed that this compartment is attached to the central compartment and has negligible volume. The diffusion constant of the effect site is *ke0*.


Table 1. Comparison of Marsh and Schnider models for PK of propofol. BW stands for Body Weight, LBM is Lean Body Mass and HT is Height.

On the other hand, the drug's pharmacodynamics, that represents the BIS in terms of the effect site concentration, is governed by:

$$BIS = f(\mathbb{C}\_{\varepsilon}) \tag{5}$$

The *f* function is usually taken as an EMAX model whose profile suits the described process:

$$
\Delta BIS = \Delta BIS\_{\text{max}} \frac{C\_e^{\gamma}}{C\_e^{\gamma} + EC\_{50}^{\gamma}} \tag{6}
$$

$$
\Delta BIS = BIS - BIS\_0 \tag{7}
$$

$$
\Delta BIS\_{\text{max}} = BIS\_{\text{max}} - BIS\_0 \tag{8}
$$

BIS0 corresponds to the awake state, *BISmax* represents the minimum achievable BIS and *EC50* represents the concentration in the effect site for which the effect is half the maximum value, represents the sensitivity of the patient to mall concentration variations in the effect site. This parameter can be seen as index that measures the degree of nonlinearity of the model.

#### **2.2 The control problem**

From the perspective of the control system three level of complexity can be distinguished. The basic procedure is the open-loop practice in which the anaesthetist, according to the parameters of the patient (age, weight, sex, ASA) directly uses predefined infusion rates of drugs. According to the response observed through his vital signs the drug rates can be modified (the anaesthetist is the controller).

In the next level, it appears the Target Controlled Infusion systems (TCI). In TCI the infusion rate is calculated from models of the pharmacokinetic of the patient, as can be seen in figure

Closed-Loop Control of Anaesthetic Effect 459

predict the behaviour of the patient and anticipate the changes in drug infusion to avoid

In order to develop an adequate model-based control strategy, it is necessary to obtain a suitable model for the patient behaviour. One common practice is to simplify the model by means of linear approximations around a nominal state (corresponding to BIS target). On the other hand, models are also necessary for offline simulation of the controller structure. The most accepted models for patient representation are those based on compartments to represent the pharmacokinetic together with a nonlinear modelling that

The main elements that constitute the control system are depicted in figure 5. As can be observed there is a computer that centralizes the monitoring and control task in the system. The BIS monitor is a passive analyser of EEG, that allows monitor the deep of anaesthesia, and has the first objective of adjust in real time the dose of drugs administered to one patient to the actual need. The BIS correlated well with the level of responsiveness and provided an excellent prediction of the level of sedation and loss of consciousness for propofol and midazolam. In this work the Aspect® A-2000 monitor was used. The communication with the computer was implemented via a RS-232 serial interface. Concerning the actuator, the Graseby® infusion pump was used for drug infusion in the

Apart from sending commands to the pump, the program in the PC reads continuously its state to detect eventual failures of any of the elements in the control loop, like missing BIS

Patient Computer

Infusion of drug (propofol)

Graseby 3500

EEG processing BIS calculation

BIS Monitor

with monitor and control software

**Serial Interface** 

**Serial Interface** 

**3. Implementation of the closed-loop control of anaesthesia** 

patient. The pump is also governed via a RS-232 serial interface.

Fig. 5. Main elements of the closed-loop control system.

**Sensors** 

undesirable responses.

describes the PD.

3. Thus, the objective in TCI is to achieve a pre-set target plasma concentration. According to the model of the patient the TCI system (normally implemented in the infusion pump) delivers the adequate drug doses to achieve the objective.

#### Fig. 3. Hypnosis control with TCI

There is a clear weakness in TCI related to the fact that the real plasma concentration cannot be online measured to compute the infusion rate. That is, TCI is also an open-loop control strategy. Closed-loop strategies appear to solve this problem. The main idea in closed-loop control is to use information of the state of the patient to automatically adjust the drug dosing. Many efforts have been made to provide the anaesthetist with more reliable methods for monitoring this state. In particular, the introduction of the Bispectral Index (BIS) to measure the depth of anaesthesia was one of the key elements in the development of new ways of drug administration (Sigl and Manchoun, 94). BIS has been demonstrated to correlate well with the depth of consciousness of the patient. Thus, it can be used as a feedback system to the controller in order to compute the adequate infusion rate, as can be seen in figure 4.

Fig. 4. Hypnosis control with closed-loop controller.

The controller algorithm used for anaesthesia control can be based on signals or in models. Signal based controllers are basically PID algorithms. The key feature of this algorithm is that no model is necessary to compute the infusion rate. Instead, the measured BIS is used to compute an error signal from which the drug dose is calculated. Model based controllers are an alternative to PID controller. The advantage of model-based controller is its ability to

3. Thus, the objective in TCI is to achieve a pre-set target plasma concentration. According to the model of the patient the TCI system (normally implemented in the infusion pump)

There is a clear weakness in TCI related to the fact that the real plasma concentration cannot be online measured to compute the infusion rate. That is, TCI is also an open-loop control strategy. Closed-loop strategies appear to solve this problem. The main idea in closed-loop control is to use information of the state of the patient to automatically adjust the drug dosing. Many efforts have been made to provide the anaesthetist with more reliable methods for monitoring this state. In particular, the introduction of the Bispectral Index (BIS) to measure the depth of anaesthesia was one of the key elements in the development of new ways of drug administration (Sigl and Manchoun, 94). BIS has been demonstrated to correlate well with the depth of consciousness of the patient. Thus, it can be used as a feedback system to the controller in order to compute the adequate infusion rate, as can be

Concentration Target *<sup>u</sup>*(*t*) Hypnosis

Pump

Infusion Patient

The controller algorithm used for anaesthesia control can be based on signals or in models. Signal based controllers are basically PID algorithms. The key feature of this algorithm is that no model is necessary to compute the infusion rate. Instead, the measured BIS is used to compute an error signal from which the drug dose is calculated. Model based controllers are an alternative to PID controller. The advantage of model-based controller is its ability to

Pump

BIS Target *u*(*t*) Hypnosis

Measuring unit

Infusion **Patient** 

delivers the adequate drug doses to achieve the objective.

TCI Algorithm

**PK Model**

Fig. 3. Hypnosis control with TCI

Plasma

Fig. 4. Hypnosis control with closed-loop controller.

Measured BIS

Controller

seen in figure 4.

predict the behaviour of the patient and anticipate the changes in drug infusion to avoid undesirable responses.

In order to develop an adequate model-based control strategy, it is necessary to obtain a suitable model for the patient behaviour. One common practice is to simplify the model by means of linear approximations around a nominal state (corresponding to BIS target). On the other hand, models are also necessary for offline simulation of the controller structure. The most accepted models for patient representation are those based on compartments to represent the pharmacokinetic together with a nonlinear modelling that describes the PD.
