Modelling and multivariable control in anaesthesia using neural-fuzzy paradigms: Part II. Closed-loop control of simultaneous administration of propofol and remifentanil

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Summary

Objective

Part II of this research study is concerned with the development of a closed-loop simulation linking the patient model as well as the fuzzy relational classifier already introduced in Part I with a control algorithm. The overall architecture is in fact a system advisor, which provides information to the anaesthetist about the adequate infusion-rates of propofol and remifentanil simultaneously.

Methods and material

The developed fuzzy multivariable controller includes three rule-bases and takes into account the synergetic interactions between the above drugs and uses such knowledge to achieve rapidly the desired depth of anaesthesia (DOA) level.

Results

The result of the study is a closed-loop control scheme, which adjusts efficiently the infusion-rates of two drugs in response to DOA changes. This controller can either be used in an advisory mode or closed-loop feedback mode in the operating theatre during surgery.

Conclusion

It is hoped that this control scheme coupled with the patient model presented in Part I of this study will be used routinely in the operating theatre in the very near future.

Introduction

The infusion-rate of the anaesthetic drug is titrated according to the patient's requirements, so as to maintain a certain level of depth of anaesthesia (DOA). The patient's clinical signs and/or brain signals are used by the anaesthetist to determine the adequate infusion-rate. In addition, the anaesthetist also establishes the required infusion-rate of the analgesic drug, based on the patient's response to surgical stimuli. A closed-loop control system of DOA will help the anaesthetist adjust simultaneously the infusion-rates of the anaesthetic and analgesic drugs. The majority of the researches in the area are mainly concerned with the automatic control of the anaesthetic drug, whereas the analgesic is controlled manually by the anaesthetist. However, in this research the objective is a multivariable control structure for both drugs. The patient model presented in Part I of this research study [1], described adequately the effects and interactions of the two drugs in the presence of surgical stimuli. This model will be used to develop a control algorithm relating to the administration of both drugs. The study of the interactions between the anaesthetic propofol and the analgesic remifentanil helps to determine the ideal combination of infusion-rates. This study will also represent a practical guide for the anaesthetist, which would help him/her learn how to adjust the amount of drug infused and hence improve the patient's comfort. First, the patient model will be tested using a series of open-loop simulations with different infusion profiles. Second, the closed-loop structure will be presented, showing the links between the patient model, the DOA classifier, i.e. the fuzzy relational classifier (FRC) presented in Part I of this study, and the controller. Third, a multivariable fuzzy controller, developed with the anaesthetist's cooperation, is also described. This controller establishes the infusion-rates of propofol and remifentanil simultaneously based on the level of DOA, the concentrations of the drugs and the surgical stimuli. The performance of the controller is tested under different conditions.

Section snippets

Open-loop simulation results using the patient model

The patient model developed in Part I was tested in open-loop simulations with different infusion profiles for propofol and remifentanil. Although three different infusion profiles were studied only one profile will be presented and discussed here expressing lessons learned from the experiment. The simulations were performed for 7200 s (120 min) with a sampling-time of 30 s. The first 1500 s relate to the induction-phase, followed by the maintenance-phase. It is worth noting that the recovery-phase

Closed-loop structure

The closed-loop simulation system links the patient model, the FRC of DOA and the control algorithm. Fig. 4 shows the block diagram comprising the different components of the closed-loop system during the maintenance-phase of anaesthesia. The FRC uses the parameters from the patient model to classify DOA. Finally, a control structure maintains an adequate DOA level by adjusting the infusion-rates of propofol and remifentanil, which are the inputs of the patient model. The fuzzy controller

Simulation results

The multivariable fuzzy controller was used in the closed-loop simulations with the patient model. Note that the controller only starts acting at 1500 s (i.e. after the induction-phase).

Discussions and conclusions

The objective of a control system for DOA is to determine the best infusion-rates of the anaesthesiologist and analgesic drugs, helping the anaesthetist to decide which drug should be changed in response to different events. The developed patient model was used to construct and test a multivariable controller for simultaneous administration of remifentanil and propofol during the maintenance-phase. Anaesthesiologists’ experience was incorporated into the control structure using linguistic

Acknowledgements

The authors would like to thank the anonymous reviewers for their comments, which helped to improve the quality of this paper. In addition, the second author wishes to acknowledge the Portuguese Foundation for Science and Technology for their financial support during the course of this project: Fundação para a Ciência e a Tecnologia, Ministério da Ciência e da Tecnologia, Portugal.

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    Modelling and multivariable control in anaesthesia using neural-fuzzy paradigms: Part I—classification of depth of aneasthesia and development of a patient model

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