Nonlinear dynamics of the patient’s response to drug effect during general anesthesia

In today’s healthcare paradigm, optimal sedation during anesthesia plays an important role both in patient welfare and in the socio-economic context. For the closed-loop control of general anesthesia, two drugs have proven to have stable, rapid onset times: propofol and remifentanil. These drugs are related to their effect in the bispectral index, a measure of EEG signal. In this paper wavelet time–frequency analysis is used to extract useful information from the clinical signals, since they are time-varying and mark important changes in patient’s response to drug dose. Model based predictive control algorithms are employed to regulate the depth of sedation by manipulating these two drugs. The results of identification from real data and the simulation of the closed loop control performance suggest that the proposed approach can bring an improvement of 9% in overall robustness and may be suitable for clinical practice.

Nonlinear dynamics of the patient’s response to drug effect during general anesthesia

In today’s healthcare paradigm, optimal sedation during anesthesia plays an important role both in patient welfare and in the socio-economic context. For the closed-loop control of general anesthesia, two drugs have proven to have stable, rapid onset times: propofol and remifentanil. These drugs are related to their effect in the bispectral index, a measure of EEG signal. In this paper wavelet time–frequency analysis is used to extract useful information from the clinical signals, since they are time-varying and mark important changes in patient’s response to drug dose. Model based predictive control algorithms are employed to regulate the depth of sedation by manipulating these two drugs. The results of identification from real data and the simulation of the closed loop control performance suggest that the proposed approach can bring an improvement of 9% in overall robustness and may be suitable for clinical practice.

Dynamical behaviour of multi-particle large-scale systems

Collective behaviours can be observed in both natural and man-made systems composed of a large number of elemental subsystems. Typically, each elemental subsystem has its own dynamics but, whenever interaction between individuals occurs, the individual behaviours tend to be relaxed, and collective behaviours emerge. In this paper, the collective behaviour of a large-scale system composed of several coupled elemental particles is analysed. The dynamics of the particles are governed by the same type of equations but having different parameter values and initial conditions. Coupling between particles is based on statistical feedback, which means that each particle is affected by the average behaviour of its neighbours. It is shown that the global system may unveil several types of collective behaviours, corresponding to partial synchronisation, characterised by the existence of several clusters of synchronised subsystems, and global synchronisation between particles, where all the elemental particles synchronise completely.

Fractional order inductive phenomena based on the skin effect

The Maxwell equations play a fundamental role in the electromagnetic theory and lead to models useful in physics and engineering. This formalism involves integer-order differential calculus, but the electromagnetic diffusion points towards the adoption of a fractional calculus approach. This study addresses the skin effect and develops a new method for implementing fractional-order inductive elements. Two genetic algorithms are adopted, one for the system numerical evaluation and another for the parameter identification, both with good results.

Entropy analysis of integer and fractional dynamical systems

This paper investigates the adoption of entropy for analyzing the dynamics of a multiple independent particles system. Several entropy definitions and types of particle dynamics with integer and fractional behavior are studied. The results reveal the adequacy of the entropy concept in the analysis of complex dynamical systems.

Exciting dynamical behavior in a network of two coupled rings of Chen oscillators

We study exotic patterns appearing in a network of coupled Chen oscillators. Namely, we consider a network of two rings coupled through a “buffer” cell, with Z3×Z5 symmetry group. Numerical simulations of the network reveal steady states, rotating waves in one ring and quasiperiodic behavior in the other, and chaotic states in the two rings, to name a few. The different patterns seem to arise through a sequence of Hopf bifurcations, period-doubling, and halving-period bifurcations. The network architecture seems to explain certain observed features, such as equilibria and the rotating waves, whereas the properties of the chaotic oscillator may explain others, such as the quasiperiodic and chaotic states. We use XPPAUT and MATLAB to compute numerically the relevant states.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.