BioMed Research International

Volume 2014 (2014), Article ID 379090, 19 pages

http://dx.doi.org/10.1155/2014/379090

## Performance Analysis of Extracted Rule-Base Multivariable Type-2 Self-Organizing Fuzzy Logic Controller Applied to Anesthesia

^{1}Department of Mechanical Engineering and Innovation Center for Big Data and Digital Convergence, Yuan Ze University, Chungli 320, Taiwan^{2}Department of Computing, Faculty of Engineering and Computing, Coventry University, Priory Street, Coventry CV1 5FB, UK^{3}Department of Anesthesiology, National Taiwan University Hospital, Taipei 100, Taiwan^{4}Center for Dynamical Biomarkers and Translational Medicine, National Central University, Chung-Li 32001, Taiwan

Received 19 December 2013; Revised 12 September 2014; Accepted 7 October 2014; Published 21 December 2014

Academic Editor: Paul M. Tulkens

Copyright © 2014 Yan-Xin Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We compare type-1 and type-2 self-organizing fuzzy logic controller (SOFLC) using expert initialized and pretrained extracted rule-bases applied to automatic control of anaesthesia during surgery. We perform experimental simulations using a nonfixed patient model and signal noise to account for environmental and patient drug interaction uncertainties. The simulations evaluate the performance of the SOFLCs in their ability to control anesthetic delivery rates for maintaining desired physiological set points for muscle relaxation and blood pressure during a multistage surgical procedure. The performances of the SOFLCs are evaluated by measuring the steady state errors and control stabilities which indicate the accuracy and precision of control task. Two sets of comparisons based on using expert derived and extracted rule-bases are implemented as Wilcoxon signed-rank tests. Results indicate that type-2 SOFLCs outperform type-1 SOFLC while handling the various sources of uncertainties. SOFLCs using the extracted rules are also shown to outperform those using expert derived rules in terms of improved control stability.

#### 1. Introduction

Anesthesia is a branch of medical science involved in the administration of anesthetic agents whose aim is to keep patients in a state of insensitivity during surgical procedures. Modern balanced general anesthesia includes muscle relaxation, unconsciousness (i.e., depth of anesthesia), and analgesia (blocking response to pain). The first two are regulated by the anesthetist in the operating theater, while the third is related to postoperative conditions [1–4]. In the past two decades, there have been several studies on applying intelligent systems to regulate and control anesthetic delivery [5–14]. The human body is a highly nonlinear and multivariable system with many sources of uncertainty that make designing such an automatic controller challenging, specifically:(i)physiological differences in age, gender, and preoperative health conditions from one person to another (interpatient variability) can all have an effect on the concentration and duration of anesthetic drug that is required to be administered during surgery [1];(ii)differences in the anesthetic drug concentration required to be infused due to variability in the physiological effects of drugs on the body (pharmacodynamics) and variability in the drugs metabolism in the body (pharmacokinetics);(iii)dynamic multivariable changes and interactions in the patient’s physiological parameters such as heart rate, respiration, blood pressure (BP), and muscle relaxation (EMG) need to be monitored and controlled by the anesthetist during surgery (intrapatient variability);(iv)noise and variability in signals are sensed and monitored from the human body such as data collected from EMG and BP monitors.

The above sources of uncertainties translate into a high degree of nonlinearity; complex input output relationships; and encountered uncertainties within the control process. Fuzzy logic controllers (FLC) provide a methodology for designing robust controllers that are able to deliver a satisfactory performance while contending with the uncertainty and imprecision attributed to the real world [15, 16]. FLCs transform numerical information into linguistic values and infer output control responses by using fuzzy rules that encapsulate nonlinear relationships between the system inputs and controlled outputs without the need for any mathematical model. FLCs are therefore able to exhibit robustness with regard to noise and variation of system parameters in complex highly nonlinear problem domains such as biomedical control systems [17, 18]. There have been a number of previous applications of FLCs for automated drug infusion control as described in [10, 19, 20]. These systems have used FLCs to control the infusion rates of different drugs based on approximating the outputs of a reference model in a closed loop design. Previous works [6] on applying FLC in anesthesia have mainly use type-1 fuzzy sets, whose grades of membership are crisp and therefore unable to fully handle the uncertainties affecting parameter variability associated with biomedical control processes and in particular controlling anesthesia delivery during surgical procedures. In order to solve the drawbacks of type-1 systems, type-2 fuzzy systems which use type-2 fuzzy sets have been applied to control anesthesia [2]. Type-2 FLCs have the potential to outperform type-1 FLCs and have been shown under specific conditions to produce more accurate and stable control performances in face of different sources of uncertainties [21–24].

Due to the dynamic changes caused by external stimuli’s and the effect of different drugs on patients during surgical operations, the fuzzy logic controller also has to adapt its control rules to facilitate regulation and adjustment of administered anesthetic in response to physiological indicators such as BP and level of paralysis to maintain depth of anesthesia (DoA). This is especially important during multistage operation procedures where the DoA is not always kept at the same level and the maintained set points for parameters such as muscle relaxation and BP are changed during surgery. The self-organizing fuzzy logic controller (SOFLC) proposed by Shieh et al. and Procyk and Mamdani [6, 25] is a successful approach that uses a learning algorithm which can generate and modify rules based on the performance of the control system and is well suited to deal with multivariable adaptive control of drug delivery during surgical operations [6]. In an SOFLC, the initial rule-base is an important factor for determining its control behavior and performance. Traditional methods to obtain fuzzy rules have been through consultation with experts (e.g., doctors) [8, 26]. In recent years, there have been some studies on extracting fuzzy rules using machine learning approaches such as genetic algorithm, neural network, and from initial pretraining an SOFLC to determine the most frequently used control rules [27–31]. Extracted rules by SOFLC are proved to have better control performance than the original expert rules under a single variable environment [29]. In [30], Liu et al. extracted a multivariable rule-base for anesthesia control; however, its performance was not fully verified.

In this paper, we propose the use of type-2 SOFLCs for the automatic control of anesthesia during multistage surgical procedures, where the type-2 fuzzy sets are constructed using data acquired from real patients during surgical procedures. We perform unique simulated experiments under signal noise and model uncertainties in which we evaluate the ability of the type-2 SOFLCs in controlling anesthetic drug delivery to maintain physiological set points for muscle relaxation and BP (used in assessing consciousness) based on a nonfixed multivariable patient model for regulating intravenous administration of atracurium and inhaled isoflurane. The control performance of the type-2 SOFLC is evaluated by comparing the pretrained extracted rule-bases based on analyzing rule usage, with the expert designed rule-bases for a simulated multistage surgical procedure. The experiments show how our type-2 SOFLCs produce a better control performance in the face of uncertainties compared to the type-1 SOFLC. The type-2 SOFLCs with the pretrained extracted rules also produce smoother control behavior than that using the expert derived rules.

The rest of paper is organized as follows. In Section 2, we describe the patient anesthetic model used in our simulations. In Section 3, we present the structure and theory of type-2 SOFLC. In Section 4, we present our experiments and results. Finally, the conclusions are given in Section 5.

#### 2. Patient Anesthetic Model

Clinically, anesthetists measure the patient’s level of sensation based on muscle relaxation measured from electromyogram (EMG) signals. To assess unconsciousness, anesthetists generally use the signal of BP as a reliable source to define the anesthesia level that relates to the DoA [32, 33]. In this paper, in order to maintain these two physiological signals, we use two common drugs, atracurium for controlling muscle relaxation and isoflurane for controlling BP, which follows previous studies [2, 6, 30].

In practice, anesthetists use a pharmacological model to describe and understand the drug’s metabolic effects [24]. Modern pharmacological modeling consists of two categories: pharmacokinetics (PK) and pharmacodynamics (PD). The former describes the concentration of drugs in tissue as a function of time and dose schedule, whereas the latter describes the relationship between drugs concentration in blood and its effect [34]. The pharmacological models of atracurium and isoflurane are described as follows.

##### 2.1. The Atracurium Mathematical Model

According to previous studies [33, 34], the atracurium pharmacokinetics can be expressed by the following transfer function (1) which describes the pharmacokinetics of the muscle relaxation relating to atracurium:
The drug’s pharmacodynamics effect can be expressed as the following transfer function [35]:
where is a dead time (time elapsed until the drug takes effect), is a coefficient, and , , , and are time constants with the values: min, , min, min, min, and min. In addition, the following Hill equation is used to relate the effect of a specific drug concentration as described in (3) [36, 37]:
where is the drug concentration, is the power, and is the drug concentration at 50% effect with the following values: , *μ*g/mL, and .

##### 2.2. The Isoflurane Unconsciousness Model

Up till now there is still no direct method to measure DoA since the brain activity is too complicated to observe. Clinically, BP is one of the signs that are commonly used to indicate DoA. Based on previous studies in [6, 38], the responses of BP to inhaled isoflurane concentration is approximately linear when the changes in isoflurane concentration are less than 5%. However, the responses are in general nonlinear and time varying if the changes become large. Therefore, a first-order linear model with a dead time of 0.42 minutes and a time constant of 2 minutes is used. In addition, in order to estimate the steady-state gain, it is assumed that a relatively sensitive patient needs 2% isoflurane for a 30 mmHg reduction in mean arterial pressure. Therefore, the model describing variations of BP to inhaled isoflurane concentration can be written as follows [6]: where MAP is mean arterial pressure, is a dead time, is a time constant, and is a coefficient with the following values: min, min, and mmHg/percent.

##### 2.3. The Interactive Component Model

According to previous studies, the interaction of atracurium to BP is so small that can be ignored [26, 33]. The interaction of isoflurane to muscle relaxation is significant and is expressed by the following equation [39]: where is dead time, and are time constants, and is a coefficient having the values: min, min, min, and .

##### 2.4. The Multivariable Anesthetic Model

Based on (1)–(5) described in previous sections, the overall multivariable anesthetic model combining muscle relaxation (based on the pharmacokinetics and nonlinear pharmacodynamics of atracurium) and unconsciousness (based on the effects of isoflurane on BP) can be summarized as follows: where is the atracurium infusion and is the isoflurane concentration.

##### 2.5. Nonfixed Anesthetic Model

The traditional fixed patient mathematical model is based on clinical data [33, 34] and cannot represent the dynamic changes of the patient during surgical operations (intrapatient uncertainties) and the difference from one person to another (interpatient uncertainties). Following on from our previous study [30], we added 1% white noise where this value was obtained by trial and error and consultation with experts to approximate the maximum value of possible parametric uncertainty affecting all parameters in (1) to (5) used in our multivariable anesthetic model. By using this nonfixed patient anesthetic model we can account for the possible patient drug interaction uncertainties during our simulations and more suitably test the features of type-2 SOFLCs, in their ability to handle these encountered uncertainties.

#### 3. Type-2 SOFLC

A type-2 SOFLC has a closed loop hierarchical adaptation and control structure which consists of a type-2 fuzzy logic controller (FLC) based on type-2 fuzzy sets and a self-organizing (SO) mechanism as shown in Figure 1. Each of these components will now be described in the following sections.