Editorial

FUZZY CONTROLIN ANESTHESIA James F. Martin, PhD

Martin JF. Fuzzycontrol in anesthesia. J Clin Monit 1994;10:77-80

The term "fuzzy logic" arouses a bit of amusement in those who don't know what it is and sometimes a bit of apprehension in those who do. Yet this is an area with great potential for affecting our daily lives, both as health care providers and as just ordinary consumers. While it has been treated as an outcast in the United States, fuzzy logic has been embraced in Japan, where consumers can purchase a variety of fuzzy appliances. In Japan, you can toss a load of clothes into a fuzzy washer, press a single button, and the machine automatically chooses the best cycle based on load size, fabric, and the kind of dirt or stain on the clothes. You can place a variety of frozen dinners or leftovers into a fuzzy microwave, push a single button, and it cooks for the right time at the proper power, based on temperature, humidity, and change in food shapes. They also have fuzzy camcorders, fuzzy televisions, and cars that employ fuzzy logic. This editorial describes fuzzy logic and some of its uses in anesthesia. In particular, it discusses the paper by Tsutsui and Arita [1], published in this issue of Journal of Clinical Monitoring. To understand fuzzy logic, we must first understand a fuzzy set. What is a fuzzy set? The following gives a simple numerical example. Most people would find it easy to determine membership in the set "positive integers" (PosInt). Clearly 1, 100, 10,000, 1,000,000, and 109 are all members of PosInt, while - 1 , 37.4, and 3/8 are not. Now, consider three other sets: small positive integers (SmPoslnt), medium positive integers (MdPoslnt), and large positive integers (LgPoslnt). Obviously, 1 is a member of the set SmPoslnt; it is pretty safe to include 109 in the set LgPoslnt. What about 100, 10,000, or even 1,000,000? Are they all members of MdPoslnt, or is 100 a member of SmPoslnt and 1,000,000 a member of LgPoslnt? There is some vagueness regarding membership to these different sets. This vagueness is caused by the words "small," "medium," and "large." In everyday conversation, such simple adjectives may be interpreted in many ways. To resolve this problem, classical set theory requires dictating upper and lower bounds for each of the three sets: From the Medical Devices and Diagnostics Division, Eli Lilly and Company, Lilly Corporate Center, Indianapolis, IN. Received Oct 1, 1993, and in revised form Oct 17, 1993. Accepted for publication Oct 20, 1993. Address correspondenceto Dr Martin, MedicalDevices and Diagnostics Division, Eli Lilly and Company, LillyCorporate Center, Indianapolis, IN 46285.

SmPoslnt = {1, 2, 3 . . . . . 100} MdPoslnt = {101, 102 . . . . . 1,000,000} LgPoslnt = {1,000,001 . . . . . infinity} Now each positive integer either is or is not a member of a specific set. Yet, why should 100 be considered small, while 101 is medium? Copyright 9 1994 by Little, Brown and Company 77

78 Journal of Clinical Monitoring Vol 10 No 2 March 1994

In 1965, Zadeh [2] introduced the concepts of fuzzy logic and fuzzy set theory to deal better with these concerns. Zadeh's key notion was graded membership. A set could have members that belonged to it in varying degrees, and each member could be a member of other sets. Thus, both 100 and 101 could be considered members of SmPoslnt and MdPoslnt with different membership grades. In classical set theory, using binary logic, there are only two possible membership grades: 1 if something belonged to the set, and 0 if it did not. In fuzzy set theory, using fuzzy logic, the membership grades can range from 0 to 1, inclusive. Applying fuzzy set theory to the previous example could yield the following memberships: Integer

SmPoslnt

MdPoslnt

LgPoslnt

1 100 300 700 1 * lO s 1 * 107 1 * I08 1 * 109

1 0.95 0.74 0.32

0 0.05 0.26 0.68

0 0 0 0

0

1

0

0

0.99 0.2

0.01 0.8

0

1

0 0

In 1973 Zadeh [3] published yet another very influential article, which laid the groundwork for fuzzy control. In classical control, mathematical formulas are used to achieve specified targets or goals. The most common types of controllers are proportional-integralderivative (PID) based devices that may include some adaptive capability. These classical controllers work extremely well when the systems to be controlled are well defined. However, these controllers run into difficulty with ill-defined systems. Zadeh proposed that the tools developed in fuzzy logic to deal with vagueness (such as small, medium, and large) allow for a systematic description of the "rules-of-thumb" that experts use in manually controlling ill-defined systems. He thought to capture human judgment with a string of IF-THENs. As an example, let's consider an application in anesthesiology: controlling depth of anesthesia. The anesthesiologist appropriately adjusts the level of anesthetic, either inhalation agent or intravenous infusion, based on his observations of the patient. Currently, there is no "depth of anesthesia" monitor; rather, the anesthesiologist tries to control an ill-defined system using multiple sources of data. Heart rate, blood pressure, EEG, and even skin tone are frequently used to judge depth of anesthesia--yet, there is not a direct (1:1) correlation between any of these variables and the depth ofanesthe-

sia. The anesthesiologist may make a "large" increase in the level of anesthetic if the patient's blood pressure is increasing "rapidly" and the EEG shows "significant" alpha and beta waves. While this might be a typical control rule used by an anesthesiologist--or expert--it is rather vague to nonexperts and computers. The phrases that generate this vagueness include words that are difficult to quantize: large, rapidly, and significant. Given the nature of the anesthesiologist control actions and that this is an ill-defined system, it would appear that the automated control of the depth of anesthesia seems appropriate for a fuzzy controller. A typical fuzzy controller consists of three elements: data fuzzification, rule base, and data defuzzification (Fig 1). The first step of a fuzzy controller is to fuzzify the input data. This is done by constructing membership functions that convert precise numbers or measurements, such as 100, into fuzzy numbers or sets, such as small, medium, or large. Figure 2 shows possible membership functions for defining membership in the three sets SmPoslnt, MdPoslnt, and LgPoslnt. These membership functions represent the degree, or membership grade, to which elements, in this case integers, are members of each set. The rule base of a fuzzy controller contains the experts' rules-of-thumb for determining control action, also specified in fuzzy hum-

i n p ~ ~ ' ~ ~ signal -I data I - Ibaset

I

defuzzify ~ . control data I - signal

Fig 1. Block diagram offuzzy controller.

Membership Grade 1

m

0.75

MdPoslnt

oJ

025

P

0 1.00E§

I .OOE+06

1.00E§

Integer

1.00E+09

Value

Fig 2. Possible membershipfunctions for SmPoslnt, MdPoslnt, and LgPoslnt usingfuzzy logic.

Editorial: Martin: Fuzzy Control in Anesthesia 79

bers, based on the fuzzified input. These are the IF-THEN statements proposed by Zadeh. For example: IF input #1 is X and input #2 is M, THEN change the control to A. Because each input, when fuzzified, can have membership in multiple fuzzy sets, there will be multiple control values, of different degrees, from the rule base. The last step in the fuzzy controller is to defuzzify these multiple control values into one crisp value, or the actual control signal. Mathematically, this step involves finding the center of gravity of the multiple control values. In summary, a fuzzy controller operates like a committee. While every member of a committee may be equally well-informed, each one may view the input differently (fuzzify). Then, based on their view of the input, and their confidence level, each member makes a recommendation (rule base). Lastly, the committee chairman, if sensible, assesses each recommendation and merges them into a crisp command (defuzzify). Tsutsui and Arita [1] present a fuzzy controller for the regulation of arterial pressure through enflurane anesthesia. The automated regulation of blood pressure has been studied extensively for over 15 years [4], yet only a handful of publications document the clinical use of controllers [5-9]. Many investigators appear content to publish the results of their controllers, claiming success, based on animal studies, or even simple computer simulations. There are substantial differences between the uncontrolled clinical environment and controlled animal studies or computer simulations. Therefore, it is refreshing to see Tsutsui and Arita present the clinical use of their fuzzy controller. Instead of discussing the merits of Tsutsui and Arita's fuzzy controller (the readers can judge for themselves), we should address the broader issue: the use of fuzzy control in the regulation of arterial blood pressure. As stated previously, there has been extensive research in the area of automated blood pressure regulation. This research not only includes analyzing different control approaches, but also the modeling of the response of mean arterial pressure (MAP) to the various vasoactive agents [10,11]. Thus, the relationship between the vasoactive agents and blood pressure is fairly well defined. Therefore, the main criterion for using fuzzy control does not exist and it does not appear to be logical to apply fuzzy control to the problem of automated blood pressure regulation. However, there is room for fuzzy logic in the problem of regulating blood pressure. Many controllers have been developed that performed sufficiently in con-

trolled animal studies, yet there are only a handful of published clinical results. Most of the controllers developed, and tested only on animals, will fail in the clinical environment. This is not because the vasoactive agent/ MAP system is ill defined, but because there exist intermittent periods in which the system is caused to be ill defined, due to some external or internal disturbance. These disturbances can be pain, hemorrhage, injection of other vasoactive agents, patient position changes, and manipulation of the arterial line. These types of problems have been the cause of most of the difficulties encountered clinically by automatic controllers. Tsutsui and Arita did not address these problems in the design of their controller. In fact, in their discussion they mention that other controllers have difficulty with disturbances and that their "technique may have similar problems." Recently, the concept of a supervisor, or safety shell, has been developed to oversee the performance of a controller and to direct the controller to take specific actions in the case of special situations, such as disturbances [6,12]. The supervisor can reject artifact data, introduce learning signals, make the controller more aggressive or conservative, or even take over completely for periods of time. These supervisors are expert, or rulebased, systems that assume the data for decision making is well defined. However, in this case the input may not be that well defined and no reasonable model is available. Because fuzzy systems are, in essence, expert systems dealing with uncertainty, perhaps the most appropriate application for them in automatic blood pressure regulation is in the design of the supervisor, or safety shell. Fuzzy logic is controversial. There exists widespread debate about its accomplishments--even about its role in science. Respected scholars, including Kalman, inventor of the Kalman filter, have warned against it. It has been called a fad and a sham. Yet, fuzzy logic does provide methods of representing human knowledge, and the ability to introduce notions of continuity into deductive thinking. This editorial will not end the debate; instead, it will likely inflame all parties, pro and con. Those who champion fuzzy logic will cry foul at the suggestion that a fuzzy controller may not be the best controller for regulating arterial pressure. Yet, those opposed to fuzzy logic will cringe at the suggestion that it has any role in anesthesiology. Does fuzzy logic have a role in anesthesiology? Yes. There are illdefined systems in anesthesiology where applications of fuzzy logic could be beneficial, such as controlling the depth of anesthesia, safety shells, and intelligent alerts and alarms. However, fuzzy logic, like any other scientific tool, should not be considered the holy grail. It

80 Journal of Clinical Monitoring Vol 10 No 2 March I994

should be applied only when, and where, it is appropriate.

EDITOR'SNOTE

REFERENCES

The Journal of Clinical Monitoring is grateful to the following people for their translation of the article abstracts into French, German, and Spanish, respectively:

1. Tsutsui T, Arita S. Fuzzy-logic control of blood pressure through enflurane anesthesia. J Clin Monit 1994;10:110117 2. Zadeh LA. Fuzzy sets. Inform Contr 1965;8:338-353 3. Zadeh LA. Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans on Sys Man Cybern 1973;SMC-3(1):28-44 4. Isaka S, Sebald AV. Control strategies for arterial blood pressure regulation. IEEE Trans Biomed Eng 1993;BME40:353-363 5. Sheppard LC. Computer control of the infusion of vasoactive drugs. Ann Biomed Eng 1980;8:431-444 6. MartinJF, Smith NT, Quinn ML, Schneider AM. Automatic control of arterial pressure during cardiac surgery. IEEE Trans Biomed Eng 1992;BME-39:389-393 7. Cosgrove DM, Petre JH, Waller JL, et al. Automated control of postoperative hypertension: A prospective randomized multicenter study. Ann Thorac Surg 1989;47: 678-683 8. PackerJS, Mason DG, CadeJF, McKinley SM. An adaptive controller for closed-loop management of blood pressure in seriously ill patients. IEEE Trans Biomed Eng 1987;BME-34:612-616 9. Reid JA, Kenny GNC. Evaluation of closed-loop control of arterial pressure after cardiopulmonary bypass. Brit J Anaesth 1987;59:247-255 10. SlateJB, Sheppard LC, Rideout VC, Blackstone EH. A model for the design of a blood pressure controller for hypertensive patients. IEEE Front Eng Health Care 1979: 285-289 11. MartinJF, Scheider AM, MandelJE, et al. A new cardiovascular model for real-time applications. Trans Soc Com Simul 1986;3:31-66 12. Martin JF, Scheider AM, Quinn ML, Smith NT. Improved safety and efficacy in adaptive control of arterial pressure through the use of a supervisor. IEEE Trans Biomed Eng 1992;BME-39:381-388

Yves Louville, MD, J. B. Cazalaa, MD, and B. Clero, MD, D~partement d'Anesth~sie, Groupe Hospitalier Necker-Enfants Malades, Paris, France. Sylvia Klatt Gippert (Office of English-German Translations) and Dr Karl-Ludwig Gippert (Technical), funded by Dr Carl-F Wallroth, Dragerwerk Aktiengesellschaft; Dr Wolfgang Friesdorf et al, ATV Section, University of Ulm, Germany; and Hans J. Popp, MSEE, Helmholtz-Institute for Biomedical Engineering at Aachen University of Technology, Aachen, Germany. DrJorge Urzua, Professor of Anesthesiology and Engineering, Pontifica Universidad Catolica de Chile, Santiago, Chile.