**8. Conclusion**

In this chapter both results on modelling and control of patients under general anaesthesia with propofol is presented. First results presented refer to the synthesis of linear models for use in model-based controllers. The anaesthetic process was segmented into several phases, according to the state of the surgery (consciousness, hypnosis, intubation, incision, etc.). The propofol infusion rate in ml/h was used as the input variable *u(t)*, while the BIS represented the output. Validation of the proposed model was done with real data patients.

For simulation purposes a PK/PD model based on compartmental approaches as obtained. The model was adjusted using information of real data from patients. The obtained model was used to simulate the response of the patients with the different controllers.

Concerning hypnosis control, this chapter presents a review of the state of the art of the closed-loop control of anaesthesia. Then, a description of approaches based on signal feedback and model based controllers are presented.

The chapter proposed an advanced PI controller with several important features. First, an adaptive module is included that adapts the controller to the specific patient behaviour. On the other hand, the controller incorporates a dead-time compensation system that improves notably the performance of the controller. The performance of this compensation is

Closed-Loop Control of Anaesthetic Effect 475

Kazama, T.; Ikeda, K.; Morita, K.; Kikura, M.; Doi, M.; Ikeda, T.; Kurita, T.; Nakajima, Y.

Liu, N.; Chazot, T.; Genty, A.; Landais, A.; Restoux, A.; McGee, K.; Laloë, P.A.; Trillat, B.;

Morley, A., Derrick, J., Mainland, P., Lee, B. B. and Short, T. G. (2000). *Closed loop control of* 

Niño J.; De Keyser, R.; Syafiie, S.; Ionescu, C.; Struys, M.M. (2009). *EPSAC-controlled* 

Sawaguchi, Y.; Purutani, E.; Shirakami, G.; Araki, M.; Fukuda, K. (2003). *A model predictive* 

EMBS Asian-Pacific Conference on Biomedical Engineering, pp. 358- 359. Sakai, T.; Matsuki A.; White P.F.; Giesecke A.H. (2000). *Use of an EEG-bispectral closed-loop* 

Schnider, T.W.; Minto, C.F.; Gambus, P.L.; Anderson, C.; Goodale, D.B.; Shafer S.L.; Youngs,

Sigl, J.C.; Chamoun, N.G. (1994). *An introduction to bispectral analysis for the electroencephalogram*. Journal of Clinical Monitoring, Vol. 10, No.6, pp. 392-404. Smith, C. (1972). *Digital Computer Process Control*. Intext Education Publishers. Scranton PA. Sreenivas, Y.; Samavedham, L.; Rangaiah, G. P. (2008). *Advanced Regulatory Controller for* 

International Federation of Automatic Control, Seoul, Korea, July, pp. 6-11. Sreenivas, Y.; Samavedham, L. Rangaiah, G. P. (2009). *Advanced Control Strategies for* 

Struys, M.M.; De Smet, T.; Depoorter, B.; Versichelen, L.F.; Mortier, E.P.; Dumortier, F.J.;

Struys, M.M.; De Smet, T.; Versichelen, L.F.; Van De Velde, S.; Van den Broecke, R.; Mortier,

*infusion of propofol in children*. Br J Anaesth., Vol. 67, pp. 41-48.

and Signal Processing, No. 23, pp. 455–471.

pp. 1517-1527.

pp. 953-959.

1007-1010.

3880–3897.

Vol. 92, No. 2, pp. 399–406.

*Administration.* Anesthesiology, No. 95. pp. 6–17.

1182.

(1999). *Comparison of the Effect-site keO s of Propofol for Blood Pressure and EEG Bispectral Index in Elderly and Younger Patients*. Anesthesiology, Vol. 90, No. 6, June,

Barvais, L.; Fischler, M. (2006). *Titration of Propofol for Anesthetic Induction and Maintenance Guided by the Bispectral Index: Closed-loop versus Manual Control*. *A Prospective, Randomized, Multicenter Study*. Anesthesiology, No. 104. pp. 686–695. Marsh, B. ; White, M. ; Morton N. ; Kenny, G.N.C. (1991). *Pharmacokinetic model driven* 

*anaesthesia: an assessment of the bispectral index as the target of control*. Anaesthesia, 55.

*anesthesia with online gain adaptation*. International Journal of Adaptative Control

*sedation control system under total intravenous anesthesia*. Proceedings of the IEEE

*delivery system for administering propofol*. Anaesthesiologica Scandinavica, 44. pp.

E.J. (1998). *The Influence of method of administration and covariates on the pharmacokinetics of propofol in adult volunteer*. Anesthesiology, Vol. 88, pp. 1170–

*Automatic Control of Anesthesia*. Proceedings of the 17th World Congress of The

*the Regulation of Hypnosis with Propofol*. Ind. Eng. Chem. Res., No. 48, pp.

Shafer, S.L.; Rolly, G. (2000). *Comparison of plasma compartment versus two methods for effect compartment-controlled target controlled infusion for propofol*. Anesthesiology,

E.P. (2001). *A Comparison of Closed-loop Controlled Administration of Propofol Using Bispectral Index as the Controlled Variable versus "Standard Practice" Controlled* 

improved by self-adapting the approximation of the patient model used in the Smith Predictor scheme.

The last part of the chapter is devoted to the design of model-based controllers. In particular, a model-based predictive controller is presented that corrects efficiently the transient evolution of the BIS, offering a smooth evolution of this signal to the reference value.

#### **9. Acknowledgment**

This work is under the auspicious of the Research Project DPI2010-18278 supported by "Ministerio de Educación y Ciencia" of the Spanish Government.

#### **10. References**


improved by self-adapting the approximation of the patient model used in the Smith

The last part of the chapter is devoted to the design of model-based controllers. In particular, a model-based predictive controller is presented that corrects efficiently the transient evolution of the BIS, offering a smooth evolution of this signal to the reference

This work is under the auspicious of the Research Project DPI2010-18278 supported by

Absalom, A.R., Sutcliffe, Kenny, G.N.C., (2002a). *Closed-loop Control of Anesthesia Using* 

Absalom, A.R.; Leslie, K.; Kenny, G.N.C. (2002b). *Closed loop control of sedation for colonoscopy* 

Absalom, A.R.; Kenny, G.N.C. (2003). *Closed-loop control of propofol anaesthesia using bispectral* 

Åström, K.J.; Wittenmark, B. (1994). *Adaptive Control (2nd ed.)*. Addison-Wesley Publishing

Bressan, N.; Moreira, A.P.; Amorim, P.; Nunes, C.S. (2009). *Target controlled infusion* 

Dumont, G.A.; Martinez, A.; Ansermino, J.M. (2009). *Robust control of depth of anesthesia*.

Furutani, E.; Sawaguchi, Y.; Shirakami, G.; Araki, M.; Fukuda, K. (2005). *A hypnosis control* 

Gil, F.G. (2004). *Sistema de ayuda a la toma de decisiones mediante logica fuzzy en anestesia* 

Ionescu, C.M.; De Keyser, R.; Torrico, B.C.; De Smet, T.; Struys, M.M.; Normey-Rico, J.E.

*Bispectral Index. Performance Assessment in Patients Undergoing Major Orthopedic Surgery under Combined General and Regional Anesthesia.* Anesthesiology; 96. pp.67–

*indexTM: performance assessment in patients receiving computer controlled propofol and manually controlled remifentanil infusions for minor surgery.* British Journal of

*algorithms for anesthesia: Theory vs practical implementation.* Engineering in Medicine and Biology Society, EMBC 2009. Annual International Conference of the IEEE, pp.

International Journal of Adaptive Control and Signal Processing, No. 23. pp. 435–

*system using a model predictive controller with online identification of individual parameters*. Proceedings of the 2005 IEEE Conference on Control Applications.

*intravenosa: modelo farmacocinetico/farmacodinamico del propofol.* PhD. Thesis,

(2008). *Robust Predictive Control Strategy Applied for Propofol Dosing Using BIS as a Controlled Variable During Anesthesia*. IEEE Transactions On Biomedical

"Ministerio de Educación y Ciencia" of the Spanish Government.

*using the Bispectral Index*. Anaesthesia, 57. pp. 690–709.

Anaesthesia 90, No. 6. pp. 737-741.

Toronto, Canada, August, pp. 28-31.

Engineering, Vol. 55, No. 9, pp. 2161-2170.

Universidad de Murcia, España.

Predictor scheme.

**9. Acknowledgment** 

**10. References** 

73.

Company, Inc.

6234-6237.

454.

value.


**Part 6** 

**Ethnopharmacology and Toxicology** 

Syafiie, S.; Niño, J.; Ionescu, C.; De Keyser, R. (2009). *NMPC for Propofol Drug Dosing during Anesthesia Induction*. L. Magni et al. (Eds.): Nonlinear Model Predictive Control, LNCIS, No. 384, pp. 501–509.
