Three oscillator model of the heartbeat generator

Suchorsky, M. K.; Rand, Richard H.

doi:10.1016/j.cnsns.2008.08.007

Cited by 13 publications

(4 citation statements)

References 5 publications

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“…Since the dynamic evolution of the heart action potential are close to the dynamical response of the Van der Pol oscillator (VdP) [15], this approach has been widely used in the modelling of the heart conduction system [18,20,21,[27][28][29][30][31]. In our model, we modify the heterogeneous oscillator model used for the generation of the ECG signals as proposed by Ryzhii [21].…”

Section: Heart Conduction System and Mathematical Modelsmentioning

confidence: 99%

Improvement of the Cardiac Oscillator Based Model for the Simulation of Bundle Branch Blocks

et al. 2019

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In this paper, we propose an improvement of the cardiac conduction system based on three modified Van der Pol oscillators. Each oscillator represents one of the components of the heart conduction system: Sino-Atrial node (SA), Atrio-Ventricular node (AV) and His–Purkinje system (HP). However, while SA and AV nodes can be modelled through a single oscillator, the modelling of HP by using a single oscillator is a rough simplification of the cardiac behaviour. In fact, the HP bundle is composed of Right (RB) and Left Bundle (LB) branches that serve, respectively, the right and left ventricles. In order to describe the behaviour of each bundle branch, we build a phenomenological model based on four oscillators: SA, AV, RB and LB. For the characterization of the atrial and ventricular muscles, we used the modified FitzHugh–Nagumo (FHN) equations. The numerical simulation of the model has been implemented in Simulink. The simulation results show that the new model is able to reproduce the heart dynamics generating, besides the physiological signal, also the pathological rhythm in case of Right Bundle Branch Block (RBBB) and Left Bundle Branch Block (LBBB). In particular, our model is able to describe the communication interruption of the conduction system, when one of the HP bundle branches is damaged.

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Section: Heart Conduction System and Mathematical Modelsmentioning

confidence: 99%

Improvement of the Cardiac Oscillator Based Model for the Simulation of Bundle Branch Blocks

et al. 2019

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“…There are also multidimensional models of cardiac activity, which represent systems of coupled FitzHugh-Nagumo, Van der Pol, and other equations (see, e.g., [16][17][18]). …”

Section: Application To Modeling Of Cardiac Rhythmsmentioning

confidence: 99%

Blue sky catastrophe as applied to modeling of cardiac rhythms

Glyzin

Kolesov

Розов

2015

Comput. Math. and Math. Phys.

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A new mathematical model for the electrical activity of the heart is proposed. The model represents a special singularly perturbed three dimensional system of ordinary differential equations with one fast and two slow variables. A characteristic feature of the system is that its solution performs nonclassical relaxation oscillations and simultaneously undergoes a blue sky catastrophe bifurcation. Both these factors make it possible to achieve a phenomenological proximity between the time depen dence of the fast component in the model and an ECG of the human heart.

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“…Mathematical modeling of the heart has been widely explored for different purposes [27][28][29][30][31]. Hodgkin and Huxley proposed the first model of electrical signal propagation through a wide variety of excitable cells around the 1950s [32] Later, FitzHugh and Nagumo provided a qualitative description of the Hodgkin-Huxley model, which led to a better understanding of its behavior [33].…”

Section: Introductionmentioning

confidence: 99%

Heart Rhythm Analysis Using Nonlinear Oscillators with Duffing-Type Connections

Fonkou,

Savi

2023

Fractal Fract

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Heartbeat rhythms are related to a complex dynamical system based on electrical activity of the cardiac cells usually measured by the electrocardiogram (ECG). This paper presents a mathematical model to describe the electrical activity of the heart that consists of three nonlinear oscillators coupled by delayed Duffing-type connections. Coupling alterations and external stimuli are responsible for different cardiac rhythms. The proposed model is employed to build synthetic ECGs representing a variety of responses including normal and pathological rhythms: ventricular flutter, torsade de pointes, atrial flutter, atrial fibrillation, ventricular fibrillation, polymorphic ventricular tachycardia and supraventricular extrasystole. Moreover, the sinoatrial rhythm variations are described by time-dependent frequency, representing transient disturbances. This kind of situation can represent transitions between different pathological behaviors or between normal and pathological physiologies. In this regard, a nonlinear dynamics perspective is employed to describe cardiac rhythms, being able to represent either normal or pathological behaviors.

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Three oscillator model of the heartbeat generator

Cited by 13 publications

References 5 publications

Improvement of the Cardiac Oscillator Based Model for the Simulation of Bundle Branch Blocks

Improvement of the Cardiac Oscillator Based Model for the Simulation of Bundle Branch Blocks

Blue sky catastrophe as applied to modeling of cardiac rhythms

Heart Rhythm Analysis Using Nonlinear Oscillators with Duffing-Type Connections

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