Hierarchical fuzzy modelling for monitoring depth of anaesthesia

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Hierarchical fuzzy modelling for monitoring depth of anaesthesia D . A . L i n k e n s " ' * , J.S. S h i e h a , J.E. P e a c o c k b "Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1, 3JD, UK b Department of Anaesthesia, University of Sheffield Medical School, Beech Hill Road, Sheffield SI O, 2RX, UK

Abstract

A hierarchical structure, based on fuzzy modelling, which can monitor depth of anaesthesia (DOA) from many clinical signs in the operating theatre, is described. The first level uses numerical clinical signs, such as systolic arterial pressure (SAP) and heart rate (HR), via a rule-base from anaesthetists' experience or a self-organizing learning algorithm to interpret primary depth of anaesthesia (PDOA). The second level is focused on non-numerical clinical signs, such as sweating (SW), lacrimation (LA) and pupil response (PR), which can be merged with the first level of PDOA to decide DOA with more confidence. Furthermore, linguistic rules and a simple fuzzy modelling concept have been used to model a patient during induction and maintenance stages. Not only can this model simulate new ideas and monitoring methods, but it can also be used clinically on-line to give an estimate of the adequacy of DOA. Successful results have given confidence to perform on-line clinical trials in the operating theatre. Two configurations of fuzzy modelling to determine the rule-base are described in this paper. Firstly, a self-organizing fuzzy modelling approach has the ability to generate rules on-line from input and output data. Secondly, if there is no direct measurement for the system output or it is very difficult to interpret, a self-organizing learning system which can learn rules from off-line input and output data can be utilized for modelling such systems. Kevwords: Depth of anaesthesia; Self-organizing fuzzy modelling; Self-organizing learning system

1. Introduction

Modelling a system is very important because it is related to process characterization and design studies. In the past, it has been thought that a complicated mathematical approach can model a system more accurately. But, this still has problems when ill-defined, complicated and non-linear systems are encountered. However, people can easily achieve a good result when they are driving a car, playing golf, cooking a meal and so on. Although

* Corresponding author.

they are not aware of a mathematical description in their brain, people still perform very well using human experience. In 1965, fuzzy set theory proposed by Zadeh [45] offered the possibility of creating models which function more like human thinking. Later, several authors have conducted research into fuzzy modelling which can be divided into several different methods. Firstly, using verbalization or linguistics through interaction with the human operator or domain expert, the system can be modelled [8, 9, 16, 20, 29]. A disadvantage of this method is that it is difficult to find suitable human operators or experts. Secondly, from logical analysis of input and output data, the system can be

0165-0114/96/$15.00 ,~) 1996 - Elsevier Science B.V. All rights reserved SSDI 0 1 6 5 - 0 1 1 4 ( 9 5 ) 0 0 2 9 0 - 1

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D.A. Linkens el al. / Fuzzy Sets and Systems 79 (1996) 43- 57

modelled more accurately by a trial-and-error approach [40, 41]. However, with input and output data it is easy to produce a pair of rules in conflict, and a trial-and-error approach is time-consuming. Thirdly, there are methods based on fuzzy implication and reasoning algorithms to identify a fuzzy model [32 35, 37, 38]. However, this involves traditional identification methods and makes the modelling system more complicated, and like conventional control theory it is difficult to apply to multivariable systems. Fourthly, using identification and self-learning algorithms for modelling of MISO systems, one can identify a fuzzy model with fairly high accuracy, while the self-learning algorithm may further improve the model's accuracy [42-44]. But identification and self-learning algorithms need large calculations which makes them unsuitable for on-line dynamic modelling. Fifthly, using learning signals to create a rulebase, the system can be modelled more generally [22 24]. However, much research is still required to determine appropriate learning signals. Sixthly, by using the method of a self-organizing fuzzy modelling algorithm to model the system via on-line input and output data, Moore has designed a fuzzy controller and applied it to an autonomous guided vehicle (AGV). However, this method of indirect adaptive fuzzy controllers still has problems with non-minimum phase processes [ 19]. Recently, many studies have investigated this field from the point of view of Artificial Intelligence. Cellier [2] developed a new implementation which combines inductive reasoning with fuzzy membership functions to model forecasting behaviour. Shen et al. [28] presented a synthesis of fuzzy sets and qualitative modelling to provide a fuzzy qualitative modelling method for performing a qualitative simulation that offers significant advantages over existing qualitative simulation methods. Grant [5] presented a neural network based implementation of a fuzzy logic controller which is constructed and tuned from logged process data. Linkens and Nyongesa [12] have applied a genetic algorithm to real-time acquisition of fuzzy rules and membership function for multivariable fuzzy control. We believe the same procedures used in these neural network and genetic

algorithm methods can be applied to implement fuzzy modelling. However, it is very difficult to judge which method is the best. The application of these intelligent methods is strongly dependent on different systems situations. Monitoring of DOA is essential to prevent patients' perception of pain, awareness, and recall; to judge autonomic status and prevent untoward effects of excessively light or deep anaesthesia; to minimize stress and its manifestations; and to facilitate prompt emergence when indicated [1]. However, DOA (i.e. unconsciousness) is very hard to define and not readily measurable. In practice, anaesthetists have a number of clinical signs and on-line measurements which can be used selectively for the determination of the patient's state. Therefore, many methods have been used for monitoring DOA based on different clinical measurements such as blood pressure [17, 25, 26], electroencephalograph (EEG) signals [27], minimum alveolar concentration (MAC) values F39], plasma concentration of propofol [36] and auditory evoked response (AER) [7]. The other non-numerical clinical signs such as sweating, lacrimation, pupil response, and movement also have a very important role for determining DOA [6]. However, assessment of DOA still rests on clinically relevant signs which have been in use for more than a century. These signs, which vary with different anaesthetic agents and in the presence of other drugs, complicate the determination of DOA. From the previous section it is clear that monitoring depth of anaesthesia is complex, and dependent on many factors which vary between patients and operating procedures. However, anaesthetists in the operating theatre can monitor and manage patients very well based on their experience and knowledge. In many circumstances where decisions have to be made, the facts are far from precise. A method that can be adapted for handling inexact facts within a computer program is fuzzy set theory. This paradigm seems to be specially suitable for medical processes, since it depends upon expert experiences which are not precisely quantifiable, such as patient's subjective sensations, interpretation of clinical signs and effects of instrumental accuracy. In this paper,

D.A. Linkens et aL / Fuzzy Sets and Systems 79 (1996) 43-57

45

we firstly use fuzzy logic to model the DOA. Different basic configurations of fuzzy modelling to monitor DOA are described. A hierarchical structure, based on fuzzy modelling, which could interpret DOA from many clinical signs during an operation is proposed. The first level, which is based on measuring blood pressure and heart rate, can infer the PDOA. At the second level, which is focused on clinical signs such as sweating, tears, pupil response, the DOA can be determined more completely when it is merged with the PDOA. There are two methods described in this paper to decide the rules of PDOA. One method uses rule-base elicitation from anaesthetists' experience. The other method derives from clinical trials and involves a self-organizing learning system. The basic self-organizing algorithm was proposed by Procyk and Mamdani [21] and used to produce a fuzzy logic controller. In this paper, we propose a self-organizing fuzzy modelling (SOFM) algorithm which can be applied to fuzzy modelling. The ability to generate rules from input and output data is an important feature of SOFM. This is particularly relevant to medical systems which have changeable parameters for different patients. We have also developed a patient model, based on linguistic rules and a simple fuzzy modelling concept, which can be used to simulate anaesthetic procedures during operation from induction to maintenance stages.

2.1. A self-organizing fuzzy modelling system (SOFM)

2. Basic configurations of fuzzy modelling systems

2.1.2. The calculation of rules possibili(v The use of input-output data from the process to estimate the rules is called logical examination and was proposed by Tong [40]. The fuzzification of the corresponding measured values produces a sequence of fuzzy sets, such as positive big (PB), positive medium (PM) and so on. For example, a single input/single output process might be assumed to have an output y(t), which is a function of the last output y(t - 1), and the last input u(t - 1). On the left of Table 1 is part of the input-output data from a hypothetical process, while fuzzification of the fuzzy set values like PS or PM for y(t), y(t - 1) and u ( t - 1) is shown on the right-hand side of the table. Therefore, the rule Q(u(t - 1)) = PS, Q ( y ( t - 1)) = PM ~ Q(y(t)) = PM is identified

A fuzzy modelling system comprises four principal components: a fuzzification interface, a knowledge base, a fuzzy inference engine and a defuzzification interface. The knowledge base also includes two components, i.e. a data base and a fuzzy rule-base [10]. If one fixes all the other parts of these components and just considers the different methods to obtain the rule-base, there are three basic configurations for fuzzy modelling. Firstly, a simple fuzzy modelling system without any adaptation has been implemented with success by many authors as described in the Introduction. The other two methods are proposed in this paper and described as follows.

In contrast to a simple fuzzy modelling system, the S O F M algorithm is derived from a S O F L C algorithm. It can obtain rules automatically from input and output data. Hence, a S O F M is an extension of a simple fuzzy modelling system and incorporates 3 new functional blocks as shown in Fig. 1: (a) the previous rule-base generation, (b) the calculation of rules possibility, and (c) the rules modification. 2.1.1. The previous rule-base generation An adaptive or self-learning modelling system, in order to improve its modelling performance, must be able to assess its own performance. Therefore, the function of the previous rule-base is similar to the performance index of the self-organizing [21]. This rule-base can be generated either from expert experience or from learning via input and output data. Hence, the previous rule-base may have some rules to start with, if it begins from expert experience, or may have no rules initially if it starts from zero knowledge. However, after generating several data from the process, the previous rule-base will be modified by each current input and output data. If the performance of the model is satisfied by the necessary criteria, the rule-base of the model will stop being modified and the previous rule-base will converge to a constant rule-base.

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D.A. Linkens et al. / Fuzzy Sets and Systems 79 (1996) 43-57

ru~-b~o_G, I"IP~I~'I m°d'ne°tl°nl ]GO Input

GI = Input Scaling Factor

GO = Output Scaling Factor

Fig. I. A self-organizing fuzzy modelling system.

Table l An example of logical examination t

u(t)

y(t)

k+l

5

2

2 3 4 5 6 7

2 1 4 3 1 5

4 3 3 2 1 1

8

4

1

Q ( u ( t - 1))

Q ( y ( t - 1))

Q(y(t))

PS

PM

PM

PS PB

PS PS

PS PS

at t = k + 4. The same p r o c e d u r e will be identified by different rules at t = k + 7 a n d t = k + 8. T h a t is to say, each i n p u t a n d o u t p u t d a t a c o r r e s p o n d to fuzzy sets a n d exist as a rule. U s i n g the fuzzy set of current d a t a c o m p a r e d to the previous data, it is easy to o b t a i n the rules possibilities (i.e. the percentage of each rule in the whole rule-base). 2.1.3.

The rule modi#cation

The m e t h o d of logical e x a m i n a t i o n can be applied to o b t a i n the conflicting rules. F o r example, one rule m a y be Q ( u ( t - 1)) = PS, Q ( y ( t - 1)) = P M ~ Q ( y ( t } ) = P M , while a n o t h e r rule c o u l d be

t: time u(t): input data u(t - 1): last input data y(t): output data y(t - 1): last output data Q(u(t - 1)): quantization of the last input data Q ( y ( t - 1)): quantization of the last output data Q(y(t)): quantization of the output data PS: positive small PM: positive medium PB: positive big

- 1)) = PS, Q ( y ( t - 1)) = P M ~ Q ( y ( t ) ) = PB. T h e two rules are in conflict. Conflicts can arise in three different ways. T h e y m a y c o m e from noisy data; they m a y result from u n s u i t a b l e d a t a q u a n t i z ing; o r they m a y arise because the p r o p o s e d structure for the m o d e l is incorrect. T h e r e are two m e t h o d s to solve the conflicts: one a p p r o a c h deletes all the conflicting rules; the o t h e r resolves the conflicts by c h o o s i n g the rule which occurs m o s t often. The latter m e t h o d has been used in this research. W i t h rules o b t a i n e d from i n p u t a n d o u t p u t data, one can calculate the rules possibility for each rule. If there are any conflicting rules, one can Q(u(t

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D.A. Linkens et aL / Fuzzy Sets and Systems 79 (1996) 43-57

compare the rules possibility and retain the one with the largest possibility. Assessing the performance of a SOFM is very similar to that for a simple fuzzy modelling system. The proposed structure for the model is initially very important. A SOFM algorithm can modify the rules according to input and output data but it cannot automatically change the structure of the model. However, the structure of the model such as the input variables, the levels of each variable, or the defuzzification method, can be adjusted off-line by experience to match the criteria. From the description in this section, it is clear that a SOFM has the ability to automatically generate rules from input and output data to model the system. Successful results have been obtained in non-linear modelling and are presented by Linkens and Shieh [131. Further application of this algorithm to a medical system is that of a SOFM for on-line modelling and detection of faults for muscle relaxation anaesthesia [30].

(i.e. anaesthetists) after the off-line analysis. Hence, a self-organizing learning system derived from a SOFM algorithm can learn the rule-base from off-line data as shown in Fig. 2. Obtaining the learned rule-base is difficult because it is strongly dependent on the learning signals. In order to give the model sufficient information to provide identifiability, the learning signal must be chosen to be "persistently exciting". This means that all modes of interest in the process must be excited. However, this learning signal is particularly hard to determine for a medical system because one cannot experiment with the patient. The only way to do this is learning from the results of many patients' operations to obtain the different rule-bases. After discussion with experts (i.e. anaesthetists), a suitable generalized rule-base can be chosen. When the rule-base has been obtained, the simple fuzzy modelling approach can be applied to the system.

2.2. A self-organizing learning system

3. A hierarchical structure for monitoring DOA

The SOFM algorithm shown in Fig. 1 implies a learning ability for rule-base generation. Sometimes, it is difficult to measure directly the monitored variables, and no standard method may be available to interpret them. These variables, such as DOA, need to be discussed with experts

What is a multilevel, hierarchical structure? It cannot be defined by a short concise statement. According to Mesarovic et al. [18], a hierarchical system contains some essential characteristics, i.e. vertical arrangement of subsystems, right of intervention of the higher-level subsystems, and

moclll~caflon

rul~

Input

÷%s'~

I

"1

OuSt

Process output f~edbock

GI ,, Input Scaling Factor GO = Output SealingFactor

Fig. 2. A self-organizinglearningsystem.

.)

48

D.A. Linkens et al. / Fuzzy Sets and Systems 79 (1996) 43-57

performance interdependence of the lower levels. A hierarchical structure using these characteristics to monitor DOA is shown in Fig. 3. The first level uses measured data which can be on-line to the system, such as SAP and HR. The second level is focused on clinical signs which are non-numerical and difficult to apply on-line to the system via a computer. These clinical signs, such as SW, LA and PR, need to be input to the computer manually after observation by the anaesthetist. After the first and second levels have been merged, the DOA can be decided more accurately. 3.1. The first level rule-base

The first level estimates PDOA from on-line signals such as SAP and HR, as shown in Fig. 3. At this level, the rules can come either from anaesthetists' experience, in which case we apply a simple fuzzy modelling system to model PDOA, or they may be derived from self-learning via clinical trials, in which case we apply a self-organizing learning system as shown in Fig. 2.

3.1.1. Rule-base f o r PDOA from anaesthetists' experience The rules to decide PDOA can be expressed verbally. SAP and HR are divided into three different ranges, i.e. High, Medium and Low. High means the SAP and HR values of the patient are higher than normal values and vice versa for Low. Medium means the SAP and HR values of the patient are in the normal range. There are also three states of anaesthesia, i.e. anaesthetic light (AL), anaesthetic O K (AO) and anaesthetic deep (ADj. From discussions with anaesthetists, the rulebase to decide PDOA is shown in Table 2. The baseline of SAP and HR in this table is measured in the induction room before the patient is given any anaesthetic drug. 3.1.2. Rule-base o f PDOA from self-learning via clinical trials A self-organizing learning system can automatically obtain rules from observed input and output data as mentioned before in Section 2.2. In order to

DOA & CDOA 1

J ~OA Expert ] experlencej

I I

T IMo0 .o,I ] T lonomo0] T

T

Model of DOL

~

_~F__xpe~ ] expe~encej

JAnaest hetJist observation

T

Fig. 3. A hierarchicalstructure for monitoring DOA (DOL: degree of lightness).

D.A. Linkens et al. / Fuzzy Sets and Systems 79 (1996) 43-57 Table 2 Anaesthetists' rule-base for PDOA

Table 3 Learning rule-base for PDOA

HR

High Medium Low

49

SAP

HR

High

Medium

Low

AL AL

AO AO AO

AD AD

Note: the range of SAP is: (1) IF baseline of SAP larger than 130 mmHg THEN SAP(Medium): during anaesthesia, the SAP is in 70 80% baseline. SAP(High): during anaesthesia, the SAP is larger than 80% baseline. SAP(Low): during anaesthesia, the SAP is less than 70% baseline. (2) IF baseline of SAP larger than 120 mmHg and smaller than 130 mmHg THEN SAP(Medium): during anaesthesia, the SAP is in 75 85% baseline. SAP(High): during anaesthesia, the SAP is larger than 85% baseline. SAP(Low): during anaesthesia, the SAP is less than 75% baseline. (3) IF baseline of SAP less than 120 mmHg THEN SAP(Medium): during anaesthesia, the SAP is in 90-120 mmHg. SAP(High): during anaesthesia, the SAP is larger than 120 mmHg. SAP(Low): during anaesthesia, the SAP is less than 90 mmHg. Range of HR: HR(Medium): during anaesthesia, the HR is in 80-100% baseline. HR(High): during anaesthesia, the HR is larger than 100% baseline. SAP(Low): during anaesthesia, the HR is less than 80% baseline.

give the rule-base sufficient information and to assist identifiability, the clinical trials must be chosen to include all the situations of D O A . In this learning phase, we designed a suitable trials protocol in collaboration with the anaesthetists. Firstly, the anaesthetist m o n i t o r s S A P and H R from a D i n a m a p instrument and clinical signs from his observations. Then, every 10 min he inputs the estimated states of D O A , i.e. AL, A O and AD, into the data acquisition program. After the experiments, we analyse the data to identify which state of

High Medium Low

SAP High

Medium

Low

AL AL

AO AO

AD AD

D O A was affected by SAP and H R but was not d o m i n a t e d by clinical signs. These experiments comprised five cases at the Royal Hallamshire Hospital, Sheffield. One data file was more complete and included different states of D O A . If one uses the same definition of High, M e d i u m and L o w for SAP and H R and AL, A O and A D for P D O A as in Section 3.1.1, the learning rules from one data file are shown in Table 3. Using fuzzy logic theory, one can obtain a l o o k u p table from either Table 2 or Table 3 to decide P D O A using a triangular shape for the membership functions and centre of area as the defuzzification method.

3.2. Second level o f fuzzy model for degree o f lightness (DOL) The second level to decide D O A is focused on clinical signs, for which there are no automatic methods of measurement. Therefore, it is very difficult to use numeric values to assess them. The best a p p r o a c h is to use qualitative concepts to identify this information. A scoring system is often used in this field [3]. Recently, fuzzy logic applied to the Apgar scoring system has been utilized by S h o n o et al. [31] in Japan. This encouraged us to use fuzzy logic to determine D O A from the qualitative clinical signs. According to anaesthetists' experience, the P D O A can decide anaesthetic O K and deep. But, if the P D O A is anaesthetic light, one should go to the second level to decide the D O L . Hence, from discussions with anaesthetists, the definition of second level scores are shown in Table 4. There are also three states of D O L , i.e. small light (SL) medium light (ML) and very light (VL) and the degrees

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D.A. Linkens et al. /Fuzzv Sets and Systems 79 (1996) 43 57

Table 4 Scoring system for clinical signs

Table 5 The monitoring and assessment of DOA by second level

Index

Condition

Scores

No.

SUM D O L ( % )

DOA

CDOA(%)

Sweating (SW)

Nil Skin moist to touch Visible beads of sweat

0 1 2

Lacrimation (LA)

No tears Tears in angle of eyes Tears in angle of eyes (overflow)

0 1 2

Pupil response (PR)

Small pupil, (no response from the light) Small pupil, (reduction as the light response) Large pupil, (reduction as the light response)

0

1 2 3 4 5 6 7 8 9 10

0 1 2 2 3 3 4 4 5 6

Small light Small light Medium light Medium light Medium light Medium light Very light Very light Very light Very light

84 75 75 50 50 50 50 25 25 0

16 25 25 50 50 50 50 75 75 100

I 2

3.3. Merging first and second levels to decide DOA and CDOA of these three states are 0% for SL, 50% for M L and 100% for VL. The simple linguistic rules used to decide the D O L are as follows: (1) I F no SW, LA and PR T H E N D O L = SL, (2) I F small SW, LA and PR T H E N D O L = ML, (3) IF large SW, LA and PR T H E N D O L = VL. F r o m Table 4 and the three rules above, one can apply fuzzy logic to decide the states of D O L from the different scores of clinical signs in the following way: (1) I F S U M = 0 T H E N D O L = 16%, (2) I F S U M = 1 T H E N D O L = 25%, (3) I F S U M = 2 T H E N D O L = 25%, (4) I F S U M = 2 T H E N D O L = 50%, (5) I F S U M = 3 T H E N D O L = 50%, (6) I F S U M = 3 T H E N D O L = 50%, (7) I F S U M = 4 T H E N D O L = 50%, (8) I F S U M = 4 T H E N D O L = 75%, (9) I F S U M = 5 T H E N D O L = 75%, (lO) I F S U M = 6 T H E N D O L = 100%, where S U M means the sum of scores of SW, LA and PR. Although some values of S U M are the same, the initial clinical signs are different. For example, the S U M of 2 comes either from S W = 1, L A = 1, P R = 0 or S W = 2 , LA=0, PR = 0. Hence, the degree of lightness m a y be different.

Using the previous first level of measuring SAP and H R to decide P D O A , we merge the first and second levels to decide D O A and confidence of depth of anaesthesia (CDOA). The rules for merging the first and second levels are as follows: (1) I F P D O A = A D THEN DOA=AD and C D O A = 100%, (2) I F P D O A = A O T H E N D O A = A O and C D O A = 100%, (3) IF P D O A = AL T H E N G o to 2nd level as shown in Table 5. The C D O A in Table 5 can provide an assessment of the monitoring of D O A using clinical signs. Anaesthetists are concerned about a patient becoming "light" during an operation. F r o m the point of view of controlling a drug, the a m o u n t of the administered drug will keep increasing when the patient is in a "light" situation. Therefore, if these clinical signs cannot actually represent D O A for this patient, too m u c h drug will be given. Hence, if the patient is in a "very light" situation, anaesthetists will need to use other monitoring parameters, e.g. auditory evoked response (AER) signal, to interpret D O A . Because patients vary a great deal, anaesthetists depend on their clinical experience to select monitoring parameters to control a drug. However, something may still happen which the anaesthetist had not

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D.A. Linkens et al. / Fuzzy Sets and Systems 79 (1996) 43-57

anticipated before the operation. Therefore, the CDOA in this method gives an indicator which can help and warn anaesthetists in the operating theatre in special cases.

4. F u z z y model o f a patient

Propofol is a relatively new intravenous anaesthetic induction agent introduced for clinical use in 1986. An emulsion formulation containing soybean oil, glycerol and purified egg phosphatide has gained considerable popularity over other agents such as thiopentone. This popularity is justified by some of its properties such as its good solubility, short time onset, and quick recovery. However, it lacks a strong analgesic effect and therefore it is best combined with an analgesic such as fentanyl or alfentanil. Numerous investigators have evaluated the pharmacokinetics of propofol following a wide range of bolus doses as well as continuous infusion [4, 15]. The kinetics have been described by twoand three-compartment models, the latter in most studies since it reflects more closely the drug metabolism in the body. Furthermore, because it has been argued that under certain circumstances where the presence of pharmacodynamics, usually typified by additional compartments and non-linearities, are known to exist, the plasma concentration is not an adequate variable to be targetted and therefore the pharmacokinetic model is extended to include a pharmacodynamic component [11]. However, it is still very difficult to obtain a suitable quantitative model to represent the relationship between plasma concentration and SAP. Therefore, we use a linguistic model elicited from anaesthetists' experience to describe the relationship of propofol dose to patient's SAP. That is to say we use a linguistic model to replace a pharmacokinetic-pharmacodynamic model for propofol administration. Although a linguistic model is not very precise, it is suitable for the application of fuzzy logic. From discussions with anaesthetists about linguistic model for patients using propofol and fentanyl drugs, the rules for the induction stage (i.e. in the induction room) and the maintenance stage (i.e. in the operating room) are as follows.

4.1. Induction stage

The rapid infusion rate of propofol can be 300, 600 and 1200 ml/h during the induction stage according to anaesthetists' experience. Meanwhile, the fentanyl amount varies in 2 - 4 ~tg/kg in the anaesthetic room, depending on the length of operation. Therefore, the propofol rate and fentanyl dose are divided into three different ranges, i.e. High, Medium and Low. There are also three different ranges for the change of SAP, i.e. Big, Middle and Small. The rule-base to decide the change of SAP is shown in Table 6. Regarding heart rate, the rule-base and the ranges for propofol rate and fentanyl amount are the same as Table 6. However, the ranges for the change of HR are different as shown in the following: AHR(B): during induction, HR decrease is 6-10 beats/2 min. AHR(M): during induction, H R decrease is 3-5 beats/2 min. AHR(S): during induction, HR decrease is - 2-2 beats/2 min. Table 6 Anaesthetists' rule-base for change of SAP at induction stage Fentanyl

High Medium Low

Propofol rate High

Medium

Low

Big Big Big

Big Middle Middle

Middle Middle Small

Note: Range of each parameter is: P(H): during induction, the propofol rate is 1200ml/h. P(M): during induction, the propofol rate is 600 ml/h. P(L): during induction, the propofol rate is 300 ml/h. F(H): during induction, the fentanyl amount is 4 ~tg/kg. F(M): during induction, the fentanylamount is 3 ~tg/kg. F(L): during induction, the fentanyl amount is 2 ~tg/kg. ASAP(B): during induction, SAP decrease is 25-34 mmHg/2 min. ASAP(M): during induction, SAP decrease is 15-24 mmHg/2 rain. ASAP(S): during induction, SAP decrease is 0 14 mmHg/2 min.

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D.A. Linkens et al. / Fuzzy Sets and Systems 79 (1996) 4 3 - 5 7

4.2. Maintenance stage

During the maintenance stage, the propofol rate can be divided into three different cases, i.e. increase (Inc.), constant (Const.) and decrease (Dec.) to prevent hypo- or hypertension which could cause the patient other clinical problems. Meanwhile, the amount of fentanyl is divided into three ranges: 100 lag (High), 50 lag (Low) and 0 lag (ZO). According to anaesthetists' experience, there are five ranges for the change of SAP, i.e. zero change (ZO), small increase (PS), small decrease (NS), medium decrease (NM) and big decrease (NB). The rulebase to decide the change of SAP is shown in Table 7. During the maintenance phase, patients always have disturbances from surgical procedures. Anaesthetists cannot decide accurately the ranges of change for SAP at maintenance stage because they have little experience for the case of no surgical stimulus. Therefore, we set the ranges for the change of SAP to be the same as the induction stage of Table 6 but divided by 10 because the drugs are the same (i.e. propofol and fentanyl) and only the amount is different. The different ranges for the change of SAP are as follows: ASAP(ZO): no change for SAP, ASAP(PS): SAP increase is 0-1.4 mmHg/2 min, ASAP(NS): SAP decrease is 0-1.4 mmHg/2 min, ASAP(NM): SAP decrease is 1.5-2.4 mmHg/2 min, ASAP(NB): SAP decrease is 2.5-3.5 mmHg/2 min. Regarding heart rate, we use the same method to obtain the change of HR as shown in the following: AHR(ZO): no change for HR, AHR(PS): HR increase is 0.2- -0.2 beat/2 min, AHR(NS): HR decrease is 0 . 2 - - 0 . 2 beat/2 min, AHR(NM): HR decrease is 0.3-0.5 beat/2 min, AHR(NB): HR decrease is 0.6-1.0 beat/2 min. After the rule-base for a patient model has been obtained, simple fuzzy modelling can be applied to this system. Choosing a triangular shape for the membership functions and centre of area as

Table 7 Anaesthetists' rule-base for change of SAP at maintenance stage Fentanyl

Propofol rate Increase Constant

High Low ZO

NS

NM NS ZO

Decrease NS NS PS

Note: Range of each parameter is: P(Inc): during maintenance, the propofol rate is increasing. P(Const): during maintenance, the propofol rate is constant. P(Dec): during maintenance, the propofol rate is decreasing. F(H): during maintenance, the fentanyl amount is 100 lag. F(L): during maintenance, the fentanyl amount is 50 lag. F(ZO): during maintenance, the fentanyl amount is 0 lag.

a defuzzification method, one can obtain a lookup table from Tables 6 and 7 to decide the change of SAP and HR during induction and maintenance stages.

5. Patients and methods The self-learning of PDOA to obtain a rule-base has been studied on 5 patients aged 25-78 yr undergoing abdominal surgery in the Royal Hallamshire Hospital, Sheffield, UK. The output had values from 100 to 500 for the three states of anaesthesia, i.e. AL (PDOA less than 200), AO (PDOA between 200 and 400) and AD (PDOA larger than 400) when the SAP and HR were input to the rule-base of PDOA. After this learning phase, we tested 8 patients aged 29-74 yr undergoing operations at the same hospital. All the trials used a Dinamap instrument to measure patients' SAP and HR. Then, SAP and HR were passed through median filters which have been proved suitable for medical signal processing [14]. The length of the filtering window for this system was 5 samples, corresponding to 5 min in real time, and producing a real time delay of 2 min. Regarding clinical signs, such as SW, LA and PR and the state of DOA (i.e. AL, AO and AD), the anaesthetist observed the patients, and input the data manually to the computer at appropriate intervals.

D.A. Linkens et al. / Fuzzy Sets and Systems 79 H996) 43 57

6. Clinical and simulation results The self-organizing rule-base to decide P D O A compared with anaesthetists' rule-base has been used on-line in the operating theatre after the 5 patients learning phase. The results for the patients from clinical trials are shown in Table 8. The second and third columns of this table calculate the root mean square error and percentage error of numerical values of P D O A between anaesthetists' and self-learning rule-base. However, the anaesthetists only want to know the three states of P D O A (i.e. AL, AO and AD) in the operating theatre. If we compare these two rule-bases with states of PDOA, the fourth column shows there is no difference between these two rule-bases. One clinical trial is shown in Fig. 4 to demonstrate the results of P D O A and CDOA. This patient is quite stable initially. The P D O A is O K and no adverse clinical signs are present at the second level. But, after 20min of incision, the patient's SAP was going high and P D O A shows anaesthetic light. Meanwhile, the anaesthetist observed a strong sweating on the head of patient (i.e. the score of SW is 2). According to the rule-base, the DOA was AL and the CDOA was less than 100%. Hence, the

Table 8 The assessment of P D O A compared with anaesthetists' and self-learning rule-base Patient No.

PDOA (RMSD)

PDOA (Dev.) (%)

PDOA State of Anaesthesia

1 2 3 4 5 6 7 8

47.7 30.4 27.0 0.0 61.59 38.4 31.18 25.97

11.9 7.6 6.8 0.0 15.4 9.6 7.8 6.5

0 0 0 0 0 0 0 0

P D O A (RMSD): the root m e a n square deviation of P D O A betwen anaesthetists' experience and self-learning rule-bases, P D O A (Dev. %): the percentage error of P D O A between anaesthetists' and self-learning rule-bases, P D O A (state of anaesthesia): the error of states of P D O A (i.e. 1 for AI, 2 for AD and 3 for AD) from anaesthetists' experience and self-learning rule-bases.

53

anaesthetist watched the patient very carefully, increased the propofol rate, added fentanyl, and used a special drug (labetalol in this case) in order to control the patient back to normal, as shown in Fig. 4(d). The patient model has been used to simulate three types of clinical trials. The first case simulated a situation of small surgical disturbances to the patient. Therefore, the second level (i.e. SW, LA and PR) was O K and patient was under control via SAP and HR signals. The DOA was always in the anaesthetic O K and CDOA was also 100% confidence. The second case simulated a large surgical disturbance and a propofol rate which reached saturation. When a surgical disturbance was added to the patient, the SAP and HR went high and second level was light. After propofol reached saturation, fentanyl was added and the SAP and HR were reduced into the acceptable zone. Therefore, the DOA returned to anaesthetic O K and CDOA returned to 100%. An example of this case study is shown in Fig. 5. The third case simulated a patient who had no response to fentanyl when in a "very light" situation. When surgical disturbances were added to patient, the propofol rate quickly reached saturation and fentanyl was added. However, the patient was still in a situation of high SAP and HR. In this case, P D O A was at anaesthetic light and the second level was at very light. After a special drug was added, all the signals returned to normal. This example is very similar to the clinical trial shown in Fig. 4.

7. Conclusions A hierarchical architecture has been proposed in this paper to make the monitoring of DOA more manageable. The most influential and reliable indicators, such as SAP and HR, were chosen as the system variables in the first level and the next important parameters, such as SW, LA and PR, were chosen as the system variables in the second level. With this hierarchical structure, it is possible to apply fuzzy modelling to large and complicated medical systems such as anaesthesia monitoring. The self-organizing fuzzy modelling algorithm proposed in this paper has the ability to generate

D.A. Linkens et al. / Fuzzy Sets and Systems 79 (1996) 43-57

54

.

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Fig. 4. Hierarchical fuzzy modelling for monitoring D O A in a clinical trial: (a) SAP, SAP (with median filter); (b) HR and HR (with median filter); (c) P D O A from anaesthetists' and self-learning rule-bases; (d) C D O A from anaesthetists" rule-base; notation in (d): F(150), injection fentanyl 150 lag; Ind., induction start; Main., maintenance start; Inc., incision; SW(2), visible beads of sweat; SW(1), skin moist to touch; NiO2, nitrous oxide; S(10), injection special drug (e.g. labetalol) 10 mg; Man(E), m a n u a l control at the emergency state; Man., manual control nearly at the end of operation; Rec., recovery start; Sec*3, 3 s for 1 unit of time scale in the induction period; Min, 1 min for 1 unit of time scale in the maintenance and recovery periods; between the two bars of (a) and (b) m e a n s SAP and H R are OK.

rules on-line from input and output data to model a system. However, if the system output has no direct measurement, or is very difficult to interpret such as DOA, a self-organizing learning system, which can learn rules from off-line input and output data, can be utilized for modelling such systems.

The self-organizing learning rule-base to decide P D O A has been used on-line in the operating theatre to monitor DOA after a clinical trial involving 5 patients comparing P D O A from anaesthetists' and learning rule-bases. It has been shown to give performance similar to that from the anaesthetists'

D.A. Linkens et al. / Fuzzy Sets and Systems 79 (1996) 43-57

I ...........

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Fig. 5. SimulationofalargedisturbanceformonitoringDOAusingapatientmodel:(a)SAP, SAP (with median filter); (b) HR, HR(with median filter); (c) PDOA from anaesthetists' rule-base; (d) CDOA from anaesthetists' rule-base; notation in (d): F(280), injection fentanyl 280 i.tg; Ind., induction start; Main., maintenance start; Int., intubation; Surg. Dist., surgical disturbance (e.g. increasing 24 mmHg of SAP); Man., manual control nearly at the end of operation; Rec., recovery start; Sec*3, 3 s for 1 unit of time scale in the induction period; Min, 1 min for 1 unit of time scale in the maintenance and recovery periods; between the two bars of(a) and (b) means SAP and HR are OK.

rule-base in clinical trials. The second level is focused on non-numerical clinical signs, such as SW, LA and PR, which can be merged with the first level of P D O A to decide D O A with more confidence. Meanwhile, the C D O A gives an indicator which can help and warn anaesthetists in the operating theatre. A linguistic model of patients' responses to

propofol and fentanyl during induction and maintenance stages has been developed and simulated based on anaesthetists' experience in operating theatre. It has been demonstrated successfully as a simulator for the administration of intravenous anaesthetic drugs under three types of clinical situations. Following these studies, the next phase

56

D.A. Linkens et al. / Fuzz~v Sets and Systems 79 (1996) 43 57

involves the use of a fuzzy logic controller to control propofol drug infusion into the patient using this hierarchical structure for monitoring DOA.

[15]

[16]

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