Unconstrained and constrained generalised predictive control of depth of anaesthesia during surgery

Abstract

The unconstrained and constrained versions of generalised predictive control (GPC) are evaluated for on-line administration of anaesthetic drugs during surgery. First, a patient simulator was developed using a physiological model of the patient and the necessary control software was validated via a series of extensive simulation studies. The validated system was then transferred into the operating theatre for a series of clinical evaluation trials. The trials were performed with little involvement of the design engineers and good regulation of the blood pressure has been achieved using fixed-parameter as well the adaptive versions of the algorithm. Following such trials, the design engineer's assessment was that better regulation and control were obtained with the constrained algorithm and the anaesthetist's assessment was that good anaesthesia was achieved, with all patients recovering well after the operations. Furthermore, the constrained algorithm displayed good robustness properties against disturbances such as high stimulus levels and allowed for safe and economically effective administration of the drug isoflurane.

Introduction

Anaesthesia can be defined as the lack of response and recall to noxious stimuli. It comprises muscle relaxation, analgesia and unconsciousness (i.e. depth of anaesthesia). In other words, depth of anaesthesia (DOA) is one of the components of anaesthesia. Anaesthetists use a variety of observations, such as blood pressure, heart rate, lacrimation, movement, sweating, and pupil response, to make a judgement on DOA levels.

The measure of anaesthetic depth during surgical anaesthesia has always represented a tough challenge and the experience of the anaesthetist is required to control the patient's anaesthetic state. Controlling anaesthesia means that the patient is maintained at a suitable level of sedation in order to allow the surgeon to proceed with the operation without causing awareness in the patient. Hence, a number of drugs have to be administered carefully to achieve an appropriate DOA level without compromising the patient's health. There have been reports of incomplete general anaesthesia (Jessop & Jones, 1991) by patients who were pharmacologically paralysed while under anaesthesia (Kulli & Koch, 1991):

The feeling of helplessness was terrifying. I tried to let the staff know I was conscious but I could not move even a finger nor eyelid. It was like being held in a vice and gradually I realised that I was in a situation from which there was no way out. I began to feel that breathing was impossible and I just resigned myself to dying.

Nowadays, safer drugs are used with patients, and better monitoring machines help the anaesthetist make an informed decision during surgery, and state-of-the-art delivery equipment have also helped him/her maintain a more stable anaesthetic depth. Such clinical measures, however, are still open to the anaesthetist's scrutiny as patients react differently with drugs, and as a result, different patients at the same anaesthetic depth can present different clinical measures.

Several researchers have argued that if automatic control of anaesthetic depth relies on its accurate measurement, then more efforts must be directed towards devising ways of measuring DOA directly. Previous research work by Schwilden, Stoeckel, and Schuttler (1989) used quantitative EEG analysis in humans to give an indication of the anaesthetic state. However, the interpretation of the tracings proved difficult and a subjective task. The information proved unreliable even when interpreted by experienced staff, since the characteristic patterns are often disturbed by factors such as anoxia, surgical stimulations. Recently, auditory evoked potentials (AEP) have been shown to be good indicators of anaesthetic depth (Kenny, Fadzean, Mantzaridis, & Fisher, 1992; Linkens, Abbod, & Backory, 1996); they are said to have a graded response with changing anaesthetic depth, they demonstrate little inter-patient variability, and they measure the underlying anaesthetic depth as opposed to the anaesthetic concentration in the blood. However, the extraction, analysis, and the on-line use of such signals in the operating theatre are not a straightforward task.

An alternative to direct measurement of DOA has been the merger of several clinical signs such as blood pressure, heart, respiration, etc. to obtain the closest possible indication of how well the patient is anaesthetised. Indeed, in a study which was conducted by the second author, anaesthetists were asked to rank the relative importance of ten clinical signs. These signs were ranked on a scale of 1 to 10 based on the mean values provided by these anaesthetists. From these 10 clinical signs, blood pressure (ranked 6- the lowest ranked having been given to non-measurable signs or variables which are not easy to model) has been selected as one variable to give an indication of anaesthetic depth. Hence, the use of arterial blood pressure, monitored via an inflatable cuff using a DINAMAP instrument, has been investigated for feedback control with simple PI strategies (Robb, Asbury, Gray, & Linkens, 1988). In this case, the control actuation was via a stepper motor driving the dial on a gas vaporiser. It has been concluded from this study and others that when no emergency conditions occur, blood pressure can be used to provide a good indication of the patient's anaesthetic state. More recently, a multitasked closed-loop control system consisting of two controllers, was presented by Gentilini et al. (2001). In this work, the authors controlled mean arterial pressure (MAP) and hypnosis through the bi-spectral index (BIS), which is a measure of the EEG, via isoflurane administration.

The Research Group at the University of Sheffield, now led by the first author, has worked in the area of anaesthesia monitoring for a number of years. Analytical as well as hierarchical fuzzy modelling and control techniques of anaesthesia were investigated. From a purely analytical viewpoint, the control theme at the heart of this study is that of Model-Based Predictive Control, particularly generalised predictive control (GPC) (Clarke, Mohtadi, & Tuffs, 1987), which is seen by many as the control strategy that has had the most significant impact on solving a wide range of complex industrial problems, including those within the realm of biomedicine (Mahfouf & Linkens, 1998). In this paper, hard constraints are introduced as part of the optimisation problem. Hence, this paper is organised as follows: Section 2 will review the re-circulatory physiological model relating to the drug isoflurane (Derighetti, 1999), together with our own modification in terms of the control actuation being via a syringe pump rather than a gas vaporiser. In Section 3, the development of constrained GPC is briefly reviewed, while in Section 4 results of the simulation experiments are presented and discussed. In Section 5 the transfer of the overall control system to the operating theatre is described, the subsequent real-time experiments are presented, and the discussions and analyses of the various results obtained are given. Finally, Section 6 gives the conclusions relating to this study.