General anaesthesia, in which a hypnotic, analgesic and muscle relaxant are administered into the patient intravenously, is called total intravenous anaesthesia (TIVA). To help in assessing the depth of anaesthesia, bispectral index (BIS) monitors have become established in clinical practice. BIS index is calculated from an analysis of electroencephalographic (EEG) signals in the time and frequency domain. The infusion of a hypnotic such as propofol reduces BIS index values appropriately but is not the only factor that affects BIS index values. The movement of facial muscles, the presence of muscle relaxants in the body, various pathological conditions and noxious stimuli during surgery can impact the values of the BIS index. In addition, BIS index calculated during surgery is subject to noise and may have a variable time delay (i.e., dead time). In clinical practice, infusion pumps with target-controlled infusion (TCI) are established for computer control of the depth of anaesthesia. TCI infusion pumps work on the basis of a linear dynamic model that model the course of drug concentration in the body. These models are often 3-compartment models with a virtual effect site compartment (i.e., biophase) in which the drug concentration correlates with the drug effect. For propofol, there are non-linear static functions that map propofol concentration in the biophase a BIS index value. In order to relieve the anaesthesiologist, various methods of closed-loop control of the depth of anaesthesia have been developed, which regulate BIS index values by adjusting the rate of propofol infusion, but they have not yet been established in clinical practice.
In the master's thesis, we presented two versions of a new closed-loop method of controlling the depth of anaesthesia. The new method uses a TCI infusion pump as feedforward control. Due to the difference between the nominal patient model used in the TCI infusion pump and the dynamics of the actual patient, there remains an error between the reference and the BIS index measurements. We eliminate this with a regulator. The first version uses a PI controller and the second uses model predictive control (MPC). To implement the TCI infusion pump, we detailed the STANPUMP algorithm and the structure of the propofol patient models used by the TCI infusion pump in clinical practice. Both versions of the new control method were compared by simulation in the MATLAB Simulink environment with each other and against the most common and simple control method the PI controller. We tested the quality of control in the case where we consider the deviation between the nominal patient model and the dynamics of the actual patient, when there is noise at the output, when the dead time at the output is considered, and when there are disturbances at the output due to noxious stimuli. We found that we can get better results than the classical approach used in clinical practice, especially when using MPC. Both versions are able to reject disturbances from noxious stimuli. We found that it makes sense to explicitly compensate for noise and dead time. If they are not compensated, we get large and rapid changes in the rate of propofol infusion and an oscillatory response of the BIS index, both of which are detrimental to the quality of control.
In order to better predict the response of the BIS index in MPC, a non linear residual model of the patient was identified. A neuro-fuzzy Takagi Sugeno model and a non linear autoregressive neural network with exogenous inputs were used, which we tested on real data collected during surgery and on a simulated example. The two identified non linear residual models improved the prediction of the BIS index of the nominal patient model. In the case of the simulated example, it was shown that Schnider's patient model is a stiff system and autoregressive models with exogenous input fail to identify stiff systems well. The results of the simulation case still indicate that the used residual model identification methods can be improved by using more advanced identification methods.
In the future, we will therefore investigate the use of various methods for the on line identification of stiff systems, for the identification of the patient's residual model. This will allow further improvement of predictions in MPC. In addition, we will also focus on the development of new advanced methods for the implementation of observers for nonlinear systems.
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