Margarida Martins da Silva

Online nonlinear identification of the effect of drugs in anaesthesia using a minimal parameterization and BIS measurements

This paper addresses the problem of modeling and identification of the Depth of Anaesthesia (DoA). It presents a new MISO Wiener model for the pharmacokinetics and pharmacodynamics of propofol and remifentanil, when jointly administered to patients undergoing surgery. The models most commonly used to describe the effect of drugs in the human body are overparameterized Wiener models. In particular, in an anaesthesia environment, the high number of patient-dependent parameters coupled with the insufficient excitatory pattern of the input signals (drug dose profiles) and the presence of noise make robust identification strategies difficult to find. In fact, in such clinical application the user cannot freely choose the input signals to enable accurate parameter identification. A new MISO Wiener model with only four parameters is hence proposed to model the effect of the joint administration of the hypnotic propofol and the analgesic remifentanil. An Extended Kalman Filter (EKF) algorithm was used to perform the nonlinear online identification of the system parameters. The results show that both the new model and the identification strategy outperform the currently used tools to infer individual patient response. The proposed DoA identification scheme was evaluated in a real patient database, where the DoA is quantified by the Bispectral Index Scale (BIS) measurements. The results obtained so far indicate that the developed approach will be a powerful tool for modeling and identification of anaesthetic drug dynamics during surgical procedures.

Prediction error identification of minimally parameterized Wiener models in anesthesia

Abstract Patient modeling is a necessary step towards the achievement of successful control strategies that guarantee adequate drug dosing in patients subject to anesthesia. In this paper, Prediction Error Method algorithms for the identification of Wiener models describing the effect of drugs in those patients are derived. The proposed methods are general for cases where the effect of drugs in the human body is modeled by pharmacokinetic/pharmacodynamic models. In order to exemplify the performance of the proposed Prediction Error Method algorithms a database with real records collected from patients undergoing general anesthesia is used. The two parameters of a SISO Wiener model describing the effect of the muscle relaxant atracurium in the NeuroMuscular Blockade are identified. Regarding the Depth of Anesthesia, the four parameters of a MISO Wiener model describing the joint effect of the hypnotic propofol and the opioid remifentanil in the Bispectral Index are also identified. The results show that the identified parameters give rise to predicted output signals that follow the main trends of the real signals, discarding the noise that highly corrupts the measurements. This fact supports the use of these minimally parameterized models to model the aforementioned systems since they correctly describe the real dynamics of the systems.

Total Mass TCI driven by parametric estimation

This paper presents the Total Mass Target Controlled Infusion algorithm. The system comprises an On Line tuned Algorithm for Recovery Detection (OLARD) after an initial bolus administration and a Bayesian identification method for parametric estimation based on sparse measurements of the accessible signal. To design the drug dosage profile, two algorithms are here proposed. During the transient phase, an Input Variance Control (IVC) algorithm is used. It is based on the concept of TCI and aims to steer the drug effect to a predefined target value within an a priori fixed interval of time. After the steady state phase is reached the drug dose regimen is controlled by a Total Mass Control (TMC) algorithm. The mass control law for compartmental systems is robust even in the presence of parameter uncertainties. The whole system feasibility has been evaluated for the case of Neuromuscular Blockade (NMB) level and was tested both in simulation and in real cases.

Local identifiability and sensitivity analysis of neuromuscular blockade and depth of hypnosis models

This paper addresses the local identifiability and sensitivity properties of two classes of Wiener models for the neuromuscular blockade and depth of hypnosis, when drug dose profiles like the ones commonly administered in the clinical practice are used as model inputs. The local parameter identifiability was assessed based on the singular value decomposition of the normalized sensitivity matrix. For the given input signal excitation, the results show an over-parameterization of the standard pharmacokinetic/pharmacodynamic models. The same identifiability assessment was performed on recently proposed minimally parameterized parsimonious models for both the neuromuscular blockade and the depth of hypnosis. The results show that the majority of the model parameters are identifiable from the available input-output data. This indicates that any identification strategy based on the minimally parameterized parsimonious Wiener models for the neuromuscular blockade and for the depth of hypnosis is likely to be more successful than if standard models are used.

Comparing different identification approaches for the depth of anesthesia using BIS measurements

Depth of anesthesia is usually quantified by the Bispectral Index (BIS) and refers to both loss of consciousness, resulting from the administration of a hypnotic like propofol, and inhibition of pain, resulting from the administration of an analgesic like remifentanil. This paper addresses the mathematical modeling of the joint effect of propofol and remifentanil in the depth of anesthesia, using BIS measurements. Two models and identification strategies are considered. The first model is based on standard pharmacokinetic/pharmacodynamic models and the associated identification strategy corresponds to the application of a hybrid method. The second model has a minimal number of parameters and the associated identification strategy corresponds to the application of a prediction error method. These two approaches are tested and compared on real data.

Nonlinear estimation of a parsimonious Wiener model for the neuromuscular blockade in closed-loop anesthesia

Nonlinear estimation of a parsimonious Wiener model for the neuromuscular blockade in closed-loop anesthesia

Exactly linearizing adaptive control of propofol and remifentanil using a reduced Wiener model for the depth of anesthesia

A closed-loop adaptive controller for propofol and remifentanil administration using BIS measurements is proposed in this paper. The controller design relies on a reduced MISO Wiener model for the depth of anesthesia. The exact linearization of this minimal Wiener structure using the model continuous-time parameter estimates calculated online by an extended Kalman filter is a key point in the design. A linear quadratic gaussian controller is developed for the exactly linearized system. Good results were obtained when the robustness of the proposed controller was assessed with respect to inter and intrapatient variability through Monte Carlo simulations on a database of 500 patients.

Personalized neuromuscular blockade through control: Clinical and technical evaluation

This paper presents a statistical analysis of clinical data collected in surgeries under automatic closed-loop control of neuromuscular blockade. Four different control strategies have been applied in patients undergoing elective surgeries and clinical and technical evaluations of the control system were performed. Both transient and steady-state behaviour were analysed in detail and clearly suggest an automatic control approach relying on the information about the patient dynamics. The results can be a valuable start point to design personalized drug infusion control in anaesthesia.

Bifurcation analysis for PID-controller tuning based on a minimal neuromuscular blockade model in closed-loop anesthesia

The problem of PID-controller tuning in an automatic drug administration system for neuromuscular blockade (NMB) in closed-loop anesthesia is considered. Contrary to the usual practice of tuning PID-controllers on the basis of a linearized model or online tests, bifurcation analysis based on a minimally-parametrized Wiener model for NMB is utilized. The parsimony of the mathematical model is instrumental in minimizing the number of bifurcation parameters. It appears that the equilibrium of the closed-loop system defined by the setpoint of the controller undergoes Andronov-Hopf bifurcation at a point in the model parameter space giving rise to sustained nonlinear oscillations. A model-based PID-controller tuning procedure is suggested that guarantees a certain settling time and robustness margin of the resulting loop. The tuning procedure is illustrated on mathematical models identified from patient data.

A compartmental model-based control strategy for NeuroMuscular Blockade level

Abstract This paper presents a compartmental model-based control strategy to drive the NeuroMuscular Blockade level of patients undergoing general anesthesia to a predefined target. For that purpose, a compartmental realization of a minimally parameterized nonlinear Wiener model was derived and used on an adapted version of the standard compartmental control law for linear systems. The identification of the model parameters was recursively performed by one Extended Kalman Filter during the initial bolus induction period and stopped afterwards. To overcome the fact that this identification is stopped during the closed-loop control period, uncertainties in the parameters are assumed to be present and included in the control law. Information taken from the identification of real collected cases was used to tune the parameter uncertainties. The feasibility of the whole strategy was evaluated in a bank of simulated models, giving rise to good reference tracking results even in the presence of noise.