Liénard-type models for the simulation of the action potential of cardiac nodal cells

Podziemski, Piotr; Żebrowski, Jan J.

doi:10.1016/j.physd.2013.06.007

Cited by 9 publications

(7 citation statements)

References 39 publications

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“…In addition to animal experiments and clinical studies on humans, mathematical modeling at different levels of detalization and complexity may offer insight into the AVN "black box". Currently, very few AVN models or atrial models incorporating AVN with dual conduction pathways exist (Inada et al, 2009;Climent et al, 2011;Masè et al, 2012;Podziemski and Żebrowski, 2013;Li et al, 2014;Ryzhii and Ryzhii, 2019). The rabbit cardiac biophysically-detailed multicellular ion-channel model (Inada et al, 2009) is quite complex and requires reconfiguration, e.g., changing the number of model cells for simulation of different AVN phenomena.…”

Section: Introductionmentioning

confidence: 99%

A compact multi-functional model of the rabbit atrioventricular node with dual pathways

Ryzhii

2023

Front. Physiol.

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The atrioventricular node (AVN) is considered a “black box”, and the functioning of its dual pathways remains controversial and not fully understood. In contrast to numerous clinical studies, there are only a few mathematical models of the node. In this paper, we present a compact, computationally lightweight multi-functional rabbit AVN model based on the Aliev-Panfilov two-variable cardiac cell model. The one-dimensional AVN model includes fast (FP) and slow (SP) pathways, primary pacemaking in the sinoatrial node, and subsidiary pacemaking in the SP. To obtain the direction-dependent conduction properties of the AVN, together with gradients of intercellular coupling and cell refractoriness, we implemented the asymmetry of coupling between model cells. We hypothesized that the asymmetry can reflect some effects related to the complexity of the real 3D structure of AVN. In addition, the model is accompanied by a visualization of electrical conduction in the AVN, revealing the interaction between SP and FP in the form of ladder diagrams. The AVN model demonstrates broad functionality, including normal sinus rhythm, AVN automaticity, filtering of high-rate atrial rhythms during atrial fibrillation and atrial flutter with Wenckebach periodicity, direction-dependent properties, and realistic anterograde and retrograde conduction curves in the control case and the cases of FP and SP ablation. To show the validity of the proposed model, we compare the simulation results with the available experimental data. Despite its simplicity, the proposed model can be used both as a stand-alone module and as a part of complex three-dimensional atrial or whole heart simulation systems, and can help to understand some puzzling functions of AVN.

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Section: Introductionmentioning

confidence: 99%

A compact multi-functional model of the rabbit atrioventricular node with dual pathways

Ryzhii

2023

Front. Physiol.

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“…Implementing the oscillating APm cells simplifies the model description, providing easy control of intrinsic oscillation frequency and reliable overdrive suppression 29 . That substitutes a significant advantage of the cardiac APm over the FitzHugh-Nagumo and modified Van der Pol models and their combinations, used in the modeling of the simplified cardiac conduction system 13, 30 , due to the absence of the quiescent state in the modified Van der Pol model and the absence of well-defined threshold potential in both FitzHugh-Nagumo and modified Van der Pol models. Also, close values of the minimal diastolic potential of both non-pacemaking and pacemaking APm cells allow the driving of a relatively big number of non-pacemaking cells by a single pacemaking APm cell 28 .…”

Section: Methodsmentioning

confidence: 99%

“…There were also attempts to develop AVN models based on more computationally effective simplified nonlinear two-variable models. In the work 13 the AVN model based on hundreds of Lienard-transformed modified Van der Pol 17 and FitzHugh-Nagumo 18,19 equations, reproduces normal sinus rhythm and AVNRT. The three-dimensional anatomically-detailed model of the rabbit right atrium 14 includes the AVN with dual pathways and utilizes the cellular automaton method and modified FitzHugh-Nagumo and Rogers 20 two-variable models.…”

Section: Introduction 1 Introductionmentioning

confidence: 99%

Section: Introduction 1 Introductionmentioning

confidence: 99%

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A compact multifunctional model of the rabbit atrioventricular node with dual pathways

Ryzhii¹,

Ryzhii²

2023

Preprint

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The atrioventricular node (AVN) is considered a "black box", and the functioning of its dual pathways remains controversial and not fully understood. In contrast to numerous clinical studies, there are only a few mathematical models of the node. In this paper, we present a compact, computationally lightweight multifunctional rabbit AVN model based on the Aliev-Panfilov two-variable cardiac cell model. The AVN model includes fast (FP) and slow (SP) pathways, primary pacemaking in the sinoatrial node, subsidiary pacemaking in the SP, and takes into account the asymmetry of coupling between model cells. At the same time, the model is accompanied by a visualization of electrical conduction in the AVN, revealing the interaction between SP and FP in the form of ladder diagrams. The AVN model demonstrates broad functionality, including normal sinus rhythm, AVN automaticity, filtering of high-rate atrial rhythms during atrial fibrillation and atrial flutter with Wenckebach periodicity, direction-dependent properties, and realistic anterograde and retrograde conduction curves in the control case and the cases of FP and SP ablation. To show the validity of the proposed model, we compare the simulation results with the available experimental data. Despite its simplicity, the proposed model can be used both as a stand-alone module and as a part of complex three-dimensional atrial or whole heart simulation systems and can help to understand some puzzling functions of AVN.

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“…Most of the above mentioned models are included into the modeling software packages and repositories, such as openCARP [16] and Physiome Project [1,17]. The VDP and FHN models and their modifications are being predominantly used as simple models of natural pacemakers in physiological simulations of different levels of complexity (see, for example, [18][19][20][21][22]). The VDP model of relaxation oscillator was proposed to describe general heartbeat dynamics and by its nature does not have the quiescent excitable form.…”

Section: Introductionmentioning

confidence: 99%

Pacemaking function of two simplified cell models

Ryzhii

2021

Preprint

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Simplified nonlinear models of biological cells are widely used in computational electrophysiology. The models reproduce qualitatively many of the characteristics of various organs, such as the heart, brain and intestine. In contrast to complex cellular ion-channel models, the simplified models usually contain a small number of variables and parameters which facilitates nonlinear analysis and reduces computational load. In this paper, we consider pacemaking variants of the Aliev-Panfilov and Corrado two-variable excitable cell models. We conducted numerical simulation study of these models, and investigated main nonlinear dynamic features of both isolated cells and 1D coupled pacemaker-excitable systems. Simulations of 2D sinoatrial node and 3D intestine tissue as application examples of combined pacemaker-excitable systems demonstrated results similar to obtained previously. The uniform formulation for the conventional excitable cell models and proposed pacemaker models allows a convenient and easy implementation for the construction of personalized physiological models, inverse tissue modeling, and development of real-time simulation systems for various organs that contain both pacemaker and excitable cells.

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Liénard-type models for the simulation of the action potential of cardiac nodal cells

Cited by 9 publications

References 39 publications

A compact multi-functional model of the rabbit atrioventricular node with dual pathways

A compact multi-functional model of the rabbit atrioventricular node with dual pathways

A compact multifunctional model of the rabbit atrioventricular node with dual pathways

Pacemaking function of two simplified cell models

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