Modeling and Closed-loop Control of Depth of Anaesthesia

Scientific background

An increasing degree of automation and informatisation of dynamical processes enables higher quality of achieved goals, lower costs and lower eventual impact on humans and nature alike. Automatic control is an infrastructural field that comprises mathematical modelling, simulation of dynamical systems and automatic control methods. The systematic approach enables the use of control methods in various technical and nontechnical fields, therefore, the advances in automatic control are very useful in interdisciplinary projects.

Likewise, there are many processes in medicine that can be improved by automatic control. In the literature, there have been some approaches to closed-loop control of depth of anaesthesia, but none seem to have influenced clinical practice. Within the project the investigators will develop a system for closed-loop control of depth of anaesthesia using BIS index, which will be based on a predictive model and will consider individual properties of each patient that are obtained from the measurements.

Problem identification

To perform a general anaesthesia, it is necessary to use substances, which enable deep unconsciousness, analgesia, amnesia and muscle relaxation, all required for performing a surgery or a diagnostic procedure. General anaesthesia and related dynamic activities in the human body is a complicated process, which includes pharmacokinetic and pharmacodynamic mechanisms, which have not been fully studied yet.

During the general anaesthesia the anaesthesiologist needs to monitor the patient's vital functions and maintain the functions of vital organs. To achieve anaesthesia, substances are introduced in different manners into the patient's body. In clinical practice, the most commonly used methods are the intravenous induction of an anaesthetic agent, i.e., injection of the anaesthetic into a vein, and inhalation induction of anaesthesia, whereby the patient inhales the substance from the breathing mixture. Total intravenous anaesthesia (TIVA) is an anaesthesiologic technique, where substances are injected intravenously.

The anaesthesiologist needs to adjust the dosage of anaesthetic to maintain the appropriate depth of general anaesthesia according to pharmacokinetics and pharmacodynamics of the anaesthetic agent and considering the type of procedure. Inadequate depth of anaesthesia is manifested with the activation of sympathetic nerves or in the most unlikely event with the patient awakening. Too deep anaesthesia is manifested with a drop in blood pressure level and heart rate frequency as well as slow post-operative awakening of the patient from general anaesthesia. In modern clinical practice, the depth of anaesthesia is determined by assessing the relevant clinical signs (iris, sweating, movements), by interpreting hemodynamic measurements and by estimating the depth of anaesthesia from EEG signals, for which several established measurement systems already exist, e.g. BIS index, Narcotrend, Scale Entropy, Response Entropy, Cerebral State Index, Patient State Analyser, Similarity index, Surgical Stress Index, Auditory Evoked Potential, Patient State index (PSi). BIS index measurement is a non-invasive method, where a BIS monitor is connected to electrodes on the patient's head. By measuring the EEG signals the bispectral index is defined, representing the depth of anaesthesia. The BIS monitor provides a single dimensionless number, which ranges from 0 (equivalent to EEG silence) to 100. A BIS value between 40 and 60 indicates an appropriate level for general anaesthesia, whereas for long-term sedation due to head injuries a value below 40 is appropriate. The reference can thus be set to the applicable value; the manner and speed of approaching the reference value depend on the specific characteristics of the procedure and the pharmacokinetics and pharmacodynamics of the substance in the patient's body. A novel very promising depth-of-anaesthesia measuring method based on EEG signals is Patient State Index (PSi). The forehead sensor collects the patient's EEG data from the frontal lobe on both sides of the brain, which is an advantage of the PSi method. The PSi measuring system features an enhanced signal-processing engine, which provides the PSi calculation with a minimal delay. The calculated index represents a processed EEG-based variable related to the effect of the anaesthetic agents. For general anaesthesia, a PSi value between 25 and 50 is considered appropriate.

Objective of the proposed research with particular emphasis on the originality of the proposed research and its potential impact for the development of new research directions

The anaesthesiologist adjusts the injection of intravenous anaesthetic agents regarding the depth of anaesthesia. The closed-loop system for administration of intravenous anaesthetic agent will enable immediate reaction and adjustment of the intravenous anaesthetic flow. In this project the investigators will focus on the closed-loop control of flow in intravenous administration of propofol . Induction of propofol affects the EEG index and an adequate controller sets the infusion pump so that the EEG index follows as closely as possible the trajectory, prescribed by the anaesthesiologist.

The proposed research project is divided in two parts:

• the development of a mathematical model describing the impact of anaesthetic-agent administration on the depth of anaesthesia (EEG index);
• the development of a closed-loop control system for depth of anaesthesia.

The first phase will begin with the modelling of dynamics of anaesthetic-agent administration impacting the anaesthetic depth. The advantages of developing a mathematical dynamical model are as follows: better comprehension of the process and its dynamics; the model presents the basis for developing a simulator and for running simulation experiments that are useful in the closed-loop control-system design phase; the dynamical mathematical model can be employed in the control algorithm, especially for predictive control approaches.

The input of the controller is represented by two signals: the reference value of EEG index and the actual value of EEG index. The controller uses these two signals to calculate the suitable input signal of the infusion pump, which administers propofol with a flow set by the controller. Once the propofol is administered into the body, its level in blood increases and consequently the concentration at the effect site, i.e. central nervous system, increases, too. Changing of the propofol concentration is a dynamic process, which depends on the pharmacokinetic system of the patient. The concentration level of propofol at the effect site represents the input of pharmacodynamic system, describing the depth of anaesthesia, which could be treated as the output of pharmacodynamic system. The depth of anaesthesia affects the brain waves, measured by electrodes for measuring EEG signals. The EEG monitor measures the signals and uses these measurements to establish the EEG index. The induction of other anaesthetic agents (e.g. remifentanil analgesic), which also partially impacts the EEG index, is considered as a disturbance.

The originality of the expected results

In this project, the depth of anaesthesia will be treated from 3 perspectives: modelling, simulation, and control.

The problem of modelling the effect of propofol is described in literature in various ways. Pharmacokinetic and pharmacodynamic models, such as Marsh, Schneider, Kataria, Schüttler, White-Kenny have been developed for such purposes. The models typically define the basic structure of the dynamic operating system of propofol and the parameters depend on individual patients. The values of model's parameters are affected by the patient and his characteristics (weight, height, age, sex etc.) as well as individual sensitivity to propofol and the ability to excrete propofol.

A mathematical model of propofol affecting the dynamics of depth of anaesthesia will be developed based on the existing models in literature. The investigators will develop the model using classic modelling approaches, such as differential equations with the Laplace-domain and state-space representations, as well as advanced approaches: nonlinear dynamics will be treated using fuzzy logic, namely Takagi-Sugeno models. An appropriately validated dynamical model for propofol activity will be the basis for developing a simulator assisting the anaesthesiologist in safe study of anesthesiologic procedures. It will simplify the understanding of the operating mechanism of propofol and enable testing of different scenarios of administering propofol.

Several developed pharmacokinetic models are used in certain infusion pumps for target controlled infusion (TCI), where the pump sets the proper flow of the medication with regard to the model. The problem with these models is that they often do not reflect the real dynamics, which also depends on individual sensitivity of the patients to the substance, therefore such approaches, based on open-loop induction, often do not yield the best performance.

The algorithm for closed-loop control of anaesthetic depth will be based on 2-DOF control, which means that it can be functionally divided into two parts: the feedforward and the feedback part. Hence, the algorithm merges the advantages of both open-loop and closed-loop control. The feedforward part will use the model of propofol to calculate the flow according to EEG index reference trajectory. On the other hand, the feedback part will provide the appropriate flow corrections based on EEG index measurements. The advantage of the proposed approach is that the feedforward part of the control algorithm can bring the actual EEG index value close to the reference trajectory, whereas the feedback part compensates the control error, which occurs due to inaccurate modelling, noise and eventual disturbances on the real system, such as for instance the induction of remifentanil.

The control algorithm will be based on the developed dynamic model of propofol that will be used for predicting the depth of anaesthesia. By online adaptation of the parameters of the internal dynamic model, the algorithm will consider the individual patient's response to propofol, estimated from the measurements during the procedure.

Working methods

The project work will begin with modelling and simulation studies of propofol effects. The modelling procedure will involve theoretical and experimental approaches. Within the theoretical modelling framework, the investigators will use the knowledge on pharmacokinetic and pharmacodynamic mechanisms, whereas the experimental approach will complement the theoretical one by using the appropriate measurements for identifying the structure and the parameters of the model. Mathematical modelling of complex systems is an iterative procedure, requiring verification and validation of the developed model in every consecutive step. The quality of the data, obtained from suitably designed experiments, is of utmost importance. The measured signals must be properly synchronized, appropriately filtered, sampled and informationally-adequate segments have to be selected for identification.

The developed model will be tested in the Matlab-Simulink environment. The virtual simulation environment will enable various experiments for validation of the model behaviour and comparison to the measured dynamics of depth of anaesthesia. The investigators will develop a user interface that will facilitate the conduction of simulation experiments. The developed system for closed-loop control of depth of anaesthesia will be first tested in a virtual environment. Finally, the investigators will also test it - under anaesthesiological supervision - in clinical practice.

The anaesthesiological protocol with detailed descriptions of the course of operation and induction of particular agents is described in the application that is being considered at the National Medical Ethics Committee of Slovenia. Due to space restrictions the aforementioned details are not stated here.

Relevance and potential impact of the results

Despite the obvious advantages of closed-loop control of anaesthetic depth, such approaches are not yet used in clinical practice. Hence, the main result of this project will be the development and the study of implementation potential of closed-loop control system for depth of anaesthesia, based on EEG index measurements. In the first part of the project the investigators will develop dynamical model dealing with the effects of anaesthesiological agents on the depth of anaesthesia, whereas the second part will be devoted to the development of a system for closed-loop control of depth of anaesthesia. The developed model will be validated by comparing its outputs it to the measurements of dynamical processes on real patients. Finally, the performance of the closed-loop control system will be assessed in clinical practice.

We expect that by using the proposed concept of closed-loop control of depth of anaesthesia, which is measured by EEG index and controlled by propofol administration, a better course of depth anaesthesia than in manual operation will be achieved. The control system will avoid excessive overshoots of EEG index trajectory, react instantly to unexpected dynamic behaviour, effectively compensate disturbances and consider a priori unknown pharmacokinetic and pharmacodynamic properties of a particular patient. On the other hand, the anaesthesiologist will be notified only in cases of unpredicted value of EEG index or propofol flow outside the prescribed constraints. In such a manner, the anaesthesiologist will be able to devote his attention to other critical aspects of anaesthesia. Although the anaesthesiologist will not have to continuously monitor the EEG index value, the automatic system will decrease the deviation of depth of anaesthesia from the desired value. Improved tracking of the reference trajectory will certainly be beneficial for the patients as it will decrease the possibility of being awake during the procedure and at the same time prevent excessive administration of propofol, which will ease the postoperative recovery and adverse events of propofol. It will also decrease the amount of propofol used during the procedure.

Exceptional socio-economic or culturally relevant achievements of the project leader

The main field of research of the project leader Assist. Prof. Dr. Gorazd Karer are modelling, simulation and control of dynamical systems. Since his PhD defence in 2009 he has been intensively working especially on advanced approaches to mathematical modelling and on control of dynamical processes. He is the author or co-author of 16 scientific papers, 28 conference papers, 1 scientific monograph, 1 chapter in a scientific monograph, 1 terminological dictionary, 3 studies and the supervisor of 14 successfully defended bachelor theses.

He is involved in several courses in the field of modelling, system theory and automatic control at the Faculty of Electrical Engineering, University of Ljubljana. The courses Automatic Control Systems and Automatic Control are the basic courses in the Control Engineering study programme. The courses Control Systems Instrumentation and Control Technology Instrumentation deal with technological aspects and sensors. The courses Modelling and Signal Processing and Modelling Methods treat modelling of dynamical systems. The approaches from the latter will be useful especially for the first stage of the research project.

In 2013, he published a scientific monograph with Springer Verlag titled Predictive Approaches to Control of Complex Systems with his co-author Prof. Dr. Igor Škrjanc. The monograph has been favourably accepted in the scientific community as it has been downloaded in electronic form more than 11.000 times since it had been made available online at Springer. The monograph deals with advanced control algorithms for systems with complex dynamics, which also include the dynamic processes during anaesthesia. Therefore, the approaches described in the monograph represent an excellent basis for the development of a system for closed-loop control of depth of anaesthesia proposed in this project.

He was the initiator and one of the authors of the Dictionary of automatic control, systems and robotics, published in 2014. In the preparation phase, the Terminological Section of the Fran Ramovš Institute of the Slovenian Language at the Research Centre of the Slovenian Academy of Sciences and Arts (ZRC SAZU) was involved. During the project he was intensively working on the terminological definitions of concepts from his research field. Such a terminological experience facilitates the communication in interdisciplinary teams, especially with co-workers that are not familiar with the field of automatic control. Therefore, it will also benefit the cooperation with anaesthesiologist involved in the proposed project.

He was the secretary of the Automatic Control Society of Slovenia from 2010 to 2014 and has been a member of the Executive Committee since 2014. The contacts within the society enable connections to the experts working in the field of automatic control both in academia and in industry, which provides a good overview of the state of automatic control in Slovenia.

He was involved in the Competence Centre for Advanced Control Technologies, where a control approach, based on key performance indicators (KPI) and dynamic model identification was developed. The approach is conceptually related to the proposed closed-loop control system for depth of anaesthesia. The methods for acquiring knowledge from the history of KPI will also be useful for developing the proposed control system, of course by considering the anaesthesia-related particularities and by involving the knowledge of the collaborating anaesthesiologists.

Organisational structure and feasibility of the project

The project will be realized in collaboration with a research group at the Department of Anaesthesiology and Surgical Intensive Therapy (KOAIT) at the University Medical Centre (UKC) Ljubljana, led by Boris Počkar. The group consists of anaesthesiologists that have access to the equipment needed for the theoretical results of the project and the simulation studies to be clinically validated. The clinical part of the research will be carried out at the Department of Ophthalmology UKC Ljubljana for vitroretinal surgeries, at the Neurosurgical Department UKC Ljubljana for patients undergoing surgery due to expansive processes in the head, and at the Intensive Care Unit KOAIT UKC Ljubljana for patients needing long-term sedation due to head injuries. For establishing the plasmatic concentrations of anaesthetic agents the investigators will cooperate with the Institute of Clinical Chemistry and Biochemistry UKC Ljubljana. The first measurements will be conducted after obtaining the approval from the National Medical Ethics Committee of Slovenia.