Design of Type-1 and Interval Type-2 Fuzzy PID Control for Anesthesia Using Genetic Algorithms


This paper presents the automatic drug administration for the regulation of bispectral (BIS) index in the anesthesia process during the clinical surgery by controlling the concentration target of two drugs, namely, propofol and remifentanil. To realize the automatic drug administration, real clinical data are collected for 42 patients for the construction of patients’ models consisting of pharmacokinetic and pharmacodynamic models describing the dynamics reacting to the input drugs. A nominal anesthesia model is obtained by taking the average of 42 patients’ models for the design of control scheme. Three PID controllers are employed, namely linear PID controller, type-1 (T1) fuzzy PID controller and interval type-2 (IT2) fuzzy PID controller, to regulate the BIS index using the nominal patient’s model. The PID gains and membership functions are obtained using genetic algorithm (GA) by minimizing a cost function measuring the control performance. The best trained PID controllers are tested under different scenarios and compared in terms of control performance. Simulation results show that the IT2 fuzzy PID controller offers the best control strategy regulating the BIS index while the T1 fuzzy PID controller comes the second.

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Araujo, H. , Xiao, B. , Liu, C. , Zhao, Y. and Lam, H. (2014) Design of Type-1 and Interval Type-2 Fuzzy PID Control for Anesthesia Using Genetic Algorithms. Journal of Intelligent Learning Systems and Applications, 6, 70-93. doi: 10.4236/jilsa.2014.62007.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Croft, R. and Washington, S. (2012) Induction of Anaesthesia. Anaesthesia & Intensive Care Medicine, 13, 401-406.
[2] Mortier, E.P. and Struys, M.M. (2001) Monitoring the Depth of Anaesthesia Using Bispectral Analysis and ClosedLoop Controlled Administration of Propofol. Best Practice & Research Clinical Anaesthesiology, 15, 83-96.
[3] Biebuyck, J.F., O’Hara, D.A., Bogen, D.K. and Noordergraaf, A. (1992) The Use of Computers for Controlling the Delivery of Anesthesia. Anesthesiology, 77, 563-581.
[4] Kern, S.E., Xie, G., White, J.L. and Egan, T.D. (2004) A Response Surface Analysis of Propofol-Remifentanil Pharmacodynamic Interaction in Volunteers. Anesthesiology, 100, 1374-1381.
[5] Struys, M., De Smet, M.T., Greenwald, S., Absalom, A.R., Bingé, S. and Mortier, E.P. (2004) Performance Evaluation of Two Published Closed-Loop Control Systems Using Bispectral Index Monitoring: A Simulation Study. Anesthesiology, 100, 640-647.
[6] Struys, M.M., Mortier, E.P. and Smet, T.D. (2005) Closed Loops in Anaesthesia. Best Practice & Research Clinical Anaesthesiology, 20, 211-220.
[7] Bibian, S., Ries, C.R., Huzmezan, M. and Dumont, G. (2005) Introduction to Automated Drug Delivery in Clinical Anesthesia. European Journal of Control, 11, 535-557.
[8] Moppett, I. (2008) Inhalational Anaesthetics. Anaesthesia & Intensive Care Medicine, 9, 567-572.
[9] Kim, D.W., Joo, J.D., In, J.H., Jeon, Y.S., Jung, H.S., Jeon, K.B., Park, J.S. and Choi, J.W. (2013) Comparison of the Recovery and Respiratory Effects of Aminophylline and Doxapram Following Total Intravenous Anesthesia with Propofol and Remifentanil. Journal of Clinical Anesthesia, 25, 173-176.
[10] Hawthorne, C. and Sutcliffe, N. (2013) Total Intravenous Anaesthesia. Anaesthesia & Intensive Care Medicine, 14, 129-131.
[11] Westrin, P. (1996) 6 Intravenous and Inhalational Anaesthetic Agents. Baillière’s Clinical Anaesthesiology, 10, 687715.
[12] Grieder, P., Gentilini, A., Morari, M. and Schnider, T. (2001) Robust Adaptive Control of Hypnosis during Anesthesia. Proceedings of the 23rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2, 2055-2058.
[13] Kissin, I. (1997) A Concept for Assessing Interactions of General Anesthetics. Anesthesia and Analgesia, 85, 204-210.
[14] Liu, J., Singh, H. and White, P.F. (1997) Electroencephalographic Bispectral Index Correlates with Intraoperative Recall and Depth of Propofol-Induced Sedation. Anesthesia and Analgesia, 84, 185-189.
[15] Glass, P.S., Bloom, M., Kearse, L., Rosow, C., Sebel, P. and Manberg, P. (1997) Bispectral Analysis Measures Sedation and Memory Effects of Propofol, Midazolam, Isoflurane and Alfentanil in Healthy Volunteers. Anesthesiology, 86, 836-847.
[16] Panagopoulos, H., Astrom, K. and Hagglund, T. (2002) Design of PID Controllers Based on Constrained Optimization. IEEE Proceedings of Control Theory and Applications, 149, 32-40.
[17] Dumont, G.A. Martinez, A. and Ansermino, J.M. (2009) Robust Control of Depth of Anesthesia. International Journal of Adaptive Control and Signal Processing, 23, 435-454.
[18] Soltesz, K., Hahn, J.O., Hagglund, T., Dumont, G.A. and Ansermino, J.M. (2013) Individualized Closed-Loop Control of Propofol Anesthesia: A Preliminary Study. Biomedical Signal Processing and Control, 8, 500-508.
[19] Shieh, J.S., Kao, M.H. and Liu, C.C. (2006) Genetic Fuzzy Modelling and Control of Bispectral Index (BIS) for General Intravenous Anaesthesia. Medical Engineering & Physics, 28, 134-148.
[20] Sartori, V., Schumacher, P., Bouillon, T., Luginbuehl, M. and Morari, M. (2005) On-Line Estimation of Propofolpharmacodynamic Parameters. Proceedings of IEEE-EMBS 2005, 27th Annual International Conference of the Engineering in Medicine and Biology Society, 74-77.
[21] De Smet, T., Struys, M.M., Neckebroek, M.M., Van den Hauwe, K., Bonte, S. and Mortier, E.P. (2008) The Accuracy and Clinical Feasibility of a New Bayesian-Based Closed-Loop Control System for Propofol Administration Using the Bispectral Index as a Controlled Variable. Anesthesia and Analgesia, 107, 1200-1210.
[22] Hahn, J.O., Dumont, G.A. and Ansermino, J.M. (2012) Robust Closed-Loop Control of Hypnosis with Propofol Using WAVCNS Index as the Controlled Variable. Biomedical Signal Processing and Control, 7, 517-524.
[23] Haddad, W.M., Hayakawa, T. and Bailey, J.M. (2006) Adaptive Control for Nonlinear Compartmental Dynamical Systems with Applications to Clinical Pharmacology. Systems & Control Letters, 55, 62-70.
[24] Agrawal, D., Kumar, S., Kumar, A., Gombar, S., Trikha, A. and Anand, S. (2012) Design of an Assistive Anaesthesia Drug Delivery Control Using Knowledge Based Systems. Knowledge-Based Systems, 31, 1-7.
[25] Mahfouf, M., Nunes, C.S., Linkens, D.A. and Peacock, J.E. (2005) Modelling and Multivariable Control in Anaesthesia Using Neural-Fuzzy Paradigms: Part II. Closed-Loop Control of Simultaneous Administration of Propofol and Remifentanil. Artificial Intelligence in Medicine, 35, 207-213.
[26] El-Bardini, M. and El-Nagar, A.M. (2011) Direct Adaptive Interval Type-2 Fuzzy Logic Controller for the Multivariable Anaesthesia System. Ain Shams Engineering Journal, 2, 149-160.
[27] Marsh, B., White, M., Morton, N. and Kenny, G.N. (1991) Pharmacokinetic Model Driven Infusion of Propofol in Children. British Journal of Anaesthesia, 67, 41-48.
[28] Minto, C.F., Schnider, T.W., Egan, T.D., Youngs, E., Lemmens, H.J., Gambus, P.L., Billard, V., Hoke, J.F., Moore, K.H., Hermann, D.J., Muir, K.T., Mandema, J.W. and Shafer, S.L. (1997) Influence of Age and Gender on the Pharmacokinetics and Pharmacodynamics of Remifentanil. I. Model Development. Anesthesiology, 86, 10-23.
[29] Absalom, A. and Struys, M. (2007) An Overview of TCI & TIVA. Academia Press, Gent.
[30] Minto, C.F., Schnider, T.W., Short, T.G., Gregg, K.M., Gentilini, A. and Shafer, S.L. (2000) Response Surface Model for Anesthetic Drug Interactions. Anesthesiology, 92, 1603-1616.
[31] Bruhn, J., Bouillon, T.W., Radulescu, L., Hoeft, A., Bertaccini, E. and Shafer, S.L. (2003) Correlation of Approximate Entropy, Bispectral Index, and Spectral Edge Frequency 95 (SEF95) with Clinical Signs of “Anesthetic Depth” during Coadministration of Propofol and Remifentanil. Anesthesiology, 98, 621-627.
[32] Alvis, J.M., Reves, J.G., Spain, J.A. and Sheppard, L.C. (1985) Computer-Assisted Continuous Infusion of the Intravenous Analgesic Fentanyl during Generalanesthesia—An Interactive System. IEEE Transactions Biomedical Engineering, 32, 323-329.
[33] Ang, K.H., Chong, G. and Li, Y. (2005) PID Control System Analysis, Design, and Technology. IEEE Transactions on Control Systems Technology, 13, 559-576.
[34] Carvajal, J., Chen, G. and Ogmen, H. (2000) Fuzzy PID Controller: Design, Performance Evaluation, and Stability Analysis. Information Sciences, 123, 249-270.
[35] Cetin, S. and Akkaya, A.V. (2010) Simulation and Hybrid Fuzzy-PID Control for Positioning of a Hydraulic System. Nonlinear Dynamics, 61, 465-476.
[36] Hagras, H. (2007) Type-2 FLCs: A New Generation of Fuzzy Controllers. IEEE Computational Intelligence Magazine, 2, 30-43.
[37] John, R. and Coupland, S. (2007) Type-2 Fuzzy Logic: A Historical View. IEEE Computational Intelligence Magazine, 2, 57-62.
http://dx.doi. org/10.1109/MCI.2007.357194
[38] Lam, H.K. and Seneviratne, L.D. (2008) Stability Analysis of Interval Type-2 Fuzzy-Model-Based Control Systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 38, 617-628.
[39] Lam, H.K., Li, H., Deters, C., Wuerdemann, H., Secco, E. and Althoefer, K. (2014) Control Design for Interval Type-2 Fuzzy Systems under Imperfect Premise Matching. IEEE Transactions on Industrial Electronics, 61, 956-968.
[40] Mendel, J.M., John, R.I. and Liu, F. (2006) Interval Type-2 Fuzzy Logic Systems Made Simple. IEEE Transactions on Fuzzy Systems, 14, 808-821.
[41] Mendel, J.M. (2007) Type-2 Fuzzy Sets and Systems: An Overview. IEEE Computational Intelligence Magazine, 2, 20-29.
[42] Du, X. and Ying, H. (2010) Derivation and Analysis of the Analytical Structures of the Interval Type-2 Fuzzy-PI and PD Controllers. IEEE Transactions on Fuzzy Systems, 18, 802-814.

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