We propose a model to generate electrocardiogram signals based on a discretized reaction-diffusion system to produce a set of three nonlinear oscillators that simulate the main pacemakers in the heart. The model reproduces electrocardiograms from healthy hearts and from patients suffering various well-known rhythm disorders. In particular, it is shown that under ventricular fibrillation, the electrocardiogram signal is chaotic and the transition from sinus rhythm to chaos is consistent with the Ruelle-Takens-Newhouse route to chaos, as experimental studies indicate. The proposed model constitutes a useful tool for research, medical education, and clinical testing purposes. An electronic device based on the model was built for these purposes
We present an extended heterogeneous oscillator model of cardiac conduction system for generation of realistic 12 lead ECG waveforms. The model consists of main natural pacemakers represented by modified van der Pol equations, and atrial and ventricular muscles, in which the depolarization and repolarization processes are described by modified FitzHugh-Nagumo equations. We incorporate an artificial RR-tachogram with the specific statistics of a heart rate, the frequency-domain characteristics of heart rate variability produced by Mayer and respiratory sinus arrhythmia waves, normally distributed additive noise and a baseline wander that couple the respiratory frequency. The standard 12 lead ECG is calculated by means of a weighted linear combination of atria and ventricle signals and thus can be fitted to clinical ECG of real subject. The model is capable to simulate accurately realistic ECG characteristics including local pathological phenomena accounting for biophysical properties of the human heart. All these features provide significant advantages over existing nonlinear cardiac models. The proposed model constitutes a useful tool for medical education and for assessment and testing of ECG signal processing software and hardware systems.
This work considers the stabilization problem for unstable linear input-delay systems. The main idea of the
paper is to use a finite-dimensional approximation for the delay operator, which is based on non-overlapping
partitions of the time delay. Subsequently, each individual delay is approximated by means of a classical
Pade approximation, where the overall approximation results in a high-order Pade approximation that converges
to the original delay operator. By departing from a state-space realization of the approximate process, a linear
observer is used to estimate the delay-free output, which is used within a compensation scheme to stabilize
the process output. The resulting control strategy has the structure of an observer-based Smith prediction
scheme. Numerical results on three examples show that (i) the finer the time delay partition, the better the
control performance and (ii) high-order compensators can be required to stabilize certain unstable processes.
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