Dana Copot

A two-compartment fractional derivative model for Propofol diffusion in anesthesia

This paper presents the initial steps towards the development of a compartmental model for Propofol diffusion in the human body using concepts from fractional calculus. The model presented here preserves the mass balance, therefore it maintains the link between physiological and mathematical parameters. The final purpose of this model is to predict drug pharmacokinetics and pharmacodynamics during general anesthesia. A comparison of the proposed a fractional order model and the integer order compartmental model of Propofol shows good agreement between them.

Modelling drug interaction using a fractional order pharmacokinetic model

Modeling the effect of anaesthetic drugs on the electrical activity in the brain Bispectral Index is of great importance to obtain optimal control of the drug infusion during general anesthesia. In this paper, we present a first attempt in using a fractional order pharmacokinetic model (FOPK) to model drug interactions. The FOPK model preserves mass balance and maintains the link between physiological and mathematical parameters. The final use of this model is to predict drug pharmacokinetics and pharmacodynamics during general anaesthesia that will capture accurately the inter-patient variability and enable patient individualized drug dosing control.

Evaluation of respiratory properties by means of fractional order models

Abstract The goal of this paper is to model and analyze the properties of the respiratory system by means of fractional calculus. A linear fractional order system of commensurate order is obtained using the real and the imaginary parts of the measured respiratory impedance through an identification technique. In this context, the features used for the classification of some respiratory diseases are the identified parameters of the linear fractional order system of commensurate order. These features are then classified using the K-Nearest Neighbors (KNN) classifier. The proposed method has achieved an accuracy of 40% using only the first feature, however by using all the features the accuracy has increased up to 100%. The proposed classification technique is validated on 15 patients: healthy, asthma and chronic obstructive pulmonary disease (COPD).

Modelling for control of depth of hypnosis - a patient friendly approach

This paper presents a mathematical framework for over-simplification of pharmacodynamic models to capture drug effects in humans. A large representative class of drugs are classically modelled by Hill equations, and a specific case is discussed in this paper. The proposed model is validated in simulation against a classical model of drug effect for a specific case of hypnotic drug used in general anaesthesia: Propofol. The results support the validity of the proposed model and allow further improvements in the current use of such models. An important property of the model is that it allows prediction of the patients response to drug infusion dynamic profiles and allows a smoother control sequence of drug profiles, i.e. a more suitable approach for model based predictive control strategies. A manifold of 1000 Monte Carlo simulations from generated data in closed loop control indicate the suitability of the model for continuous infusion drug management during hypnosis.

Reducing bias in fractional order impedance estimation for lung function evaluation

Abstract Forced oscillation technique (FOT) emerged as a non-invasive, computationally efficient, fast and reliable method used in clinical practice for lung evaluation by means of fractional order impedance. Only recently, FOT has been employed to assess respiratory properties at low frequencies. When measuring at low frequencies interference between the imposed pressure oscillations and the breathing signal of the subject occurs. To deal with these challenges filtering techniques have been proposed to avoid biased correlates in the impedance, but none proved to successfully separate this disturbance signal. Hence, in this paper we are investigating the usefulness of empirical mode decomposition techniques to eliminate the bias introduced by the breathing signal. Respiratory data from patients diagnosed with chronic obstructive pulmonary disease (COPD) were analyzed and the results indicate that the method can successfully fill the gap in reducing the bias in the estimated impedance. The preliminary results show that by using the decomposed signals to estimate the fractional order impedance a bias reduction of respiratory impedance evaluation can be achieved.

Fractional order impedance model to estimate glucose concentration : in vitro analysis

This paper uses tools from fractional calculus such as Cole-Cole and fractional order impedance models for estimation of glucose concentration. The measured impedance is compared with two fractional order models and the simulation results show that Cole-Cole model has limitation and cannot capture the dynamics of the simulated environment. On the other hand, the fractional order model can follow the changes in impedance for several study cases. Model parameters are correlated with various conditions of the test environment. The results of these study cases show that the fractional order model is a suitable candidate for this particular application. The hypothesis tested in this paper provides new tools for glucose concentration monitoring and measurement.

Comparative analysis and exprimental results of advanced control strategies for vibration suppression in aircraft wings

The smart beam is widely used as a means of studying the dynamics and active vibration suppression possibilities in aircraft wings. The advantages obtained through this approach are numerous, among them being aircraft stability and manoeuvrability, turbulence immunity, passenger safety and reduced fatigue damage. The paper presents the tuning of two controllers: Linear Quadratic Regulator and Fractional Order Proportional Derivative controller. The active vibration control methods were tested on a smart beam, vibrations being mitigated through piezoelectric patches. The obtained experimental results are compared in terms of settling time and control effort, experimentally proving that both types of controllers can be successfully used to reduce oscillations. The analysis in this paper provides for a necessary premise regarding the tuning of a fractional order enhanced Linear Quadratic Regulator, by combining the advantages of both control strategies.

Drug delivery system for general anesthesia: where are we?

This paper provides an up-to-date review from the intersecting point of both clinical and engineering frameworks. The text interwoves available measures, models and control algorithms for general anesthesia. The three main parts of general anesthesia: neuromuscular blockade (NMB), hypnosis and analgesia are critically observed and perused from a global objective perspective. The outcome of this review is that quantifying and controlling depth of anesthesia is a challenging process and that current bottlenecks are singularly due to lack of direct measurement of analgesia during general anesthesia. Some ongoing efforts are recognized towards the development of a pain transmission model, possibly leading to the breakthrough required for analgesia sensor availability.

Emerging Tools for Quantifying Unconscious Analgesia: Fractional-Order Impedance Models

This paper presents the application of model-based predictive control (MPC) in combination with a sensor for the measurement of analgesia (pain relief) in an unconscious patient in order to control the level of anesthesia. The MPC strategy uses fractional-order impedance models (FOIMs) to model the diffusion process that occurs in the human body when an analgesic drug is taken up. Based on this control strategy an early dawn concept of the pain sensor is developed. The grand challenges that coincide with this development include identification of the patient model, validation of the pain sensor, and validation of the effect of the analgesic drug.

Fractional order modeling of diffusion processes: A new approach for glucose concentration estimation

This paper presents the application of fractional calculus tools, i.e. fractional order impedance and Cole-Cole elements to detect, measure and estimate glucose concentrations by means of electrochemistry. Fractional calculus can provide a concise model for the description of the dynamic events that occur in biological tissues. The concepts of fractional calculus has been successfully applied in physics, chemistry and material science, electrodes and viscolelastic materials over extended ranges of time and frequency. In this paper, the fractional order impedance model is presented and compared with the measured impedance. The model parameters are related to various physical conditions of the test-cells and a baseline measurements along with blind evaluation are presented. The results indicate that the proposed model is valid in a limited range of frequencies and generalization for higher order models is possible.