“…4 we show ECG’s corresponding to ( a ) normal rhythm ( H = 3), ( c ) quasiperiodicity ( H = 2.729) and ( e ) VF ( H = 2.164), with their corresponding power spectra in the right hand side. For all rhythms in this subsection, the numerical simulations of (4) were carried out with C = 1.35, β = 4, and scaling coefficients: α 1 = −0.024, α 2 = 0.0216, α 3 = −0.0012, and α 4 = 0.12. α i coefficients were calculated using a modification of the supervised learning algorithm called perceptron 38,39 . The time scaling factors, Γ t = 7, for normal and period doubling rhythms, and Γ t = 17 for VF were computed using (5), in order to recover the physiological times.Figure 4ECG’s corresponding to: ( a ) normal rhythm ( H = 3), ( c ) quasiperiodicity ( H = 2.729) and ( e ) VF ( H = 2.164).…”
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
“…4 we show ECG’s corresponding to ( a ) normal rhythm ( H = 3), ( c ) quasiperiodicity ( H = 2.729) and ( e ) VF ( H = 2.164), with their corresponding power spectra in the right hand side. For all rhythms in this subsection, the numerical simulations of (4) were carried out with C = 1.35, β = 4, and scaling coefficients: α 1 = −0.024, α 2 = 0.0216, α 3 = −0.0012, and α 4 = 0.12. α i coefficients were calculated using a modification of the supervised learning algorithm called perceptron 38,39 . The time scaling factors, Γ t = 7, for normal and period doubling rhythms, and Γ t = 17 for VF were computed using (5), in order to recover the physiological times.Figure 4ECG’s corresponding to: ( a ) normal rhythm ( H = 3), ( c ) quasiperiodicity ( H = 2.729) and ( e ) VF ( H = 2.164).…”
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
“…The literature dealing with dipole models for the electric activity of the heart is very extensive 5,6,7,8,9,10,11,12,13,14,15 . Alternative approaches dealing with specific aspects of the heart's electric activity are also too many to be easily summarised 16,17,18,19,20,21 .…”
Mathematical models of cardiac electrical activity are one of the most important tools for elucidating information about the heart diagnostic. Even though it is one of the major problems in biomedical research, an efficient mathematical formulation for this modelling has still not been found. In this paper, we present an outstanding mathematical model. It relies on a five dipole representation of the cardiac electric source, each one associated with the well-known waves of the electrocardiogram signal. The mathematical formulation is simple enough to be easily parametrized and rich enough to provide realistic signals. Beyond the physical basis of the model, the parameters are physiologically interpretable as they characterize the wave shape, similar to what a physician would look for in signals, thus making them very useful in diagnosis. The model accurately reproduces the electrocardiogram and vectocardiogram signals of any diseased or healthy heart, bringing together different systems in a single model. Furthermore, a novel algorithm accurately identifies the model parameters. This new discovery represents a revolution in electrocardiography research, solving one of the main problems in this field. It is especially useful for the automatic diagnosis of cardiovascular diseases, patient follow-up or decision-making on new therapies.
“…The process over described is the generation of a heartbeat. The propagation of the pulse from the AV node to the ventricles is guaranteed by His Purkinje complex [18], which divides the signal in two branches: one branch goes to the left ventricle, and the other one goes to the right. After each electrical excitation (depolarization), the cardiac tissue starts a process of recovery (repolarization), to prepare the cardiac muscle for the next electrical stimulation.…”
Section: Physiology Of the Heart: The State Of The Art Of The Mathemamentioning
The hardware in the loop technologies allow to simulate physical models in combination with real devices in order to validate the behavior of the latter under different conditions, not easily reproducible in the real world. They are widely used in various industrial applications. In this work we want to extend the methodology to medical devices. These must interact with the patient to obtain the desired clinical result, however, during the development and validation phase of medical devices, the patient cannot be involved in the testing process. In this article the hardware in the loop methodology is proposed starting from a mathematical model of the heart, based on oscillators, that can be used to validate pacemakers or other medical devices.
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