相关论文: Modeling Excitable Systems: Reentrant Tachycardia

The Extracellular-Membrane-Intracellular (EMI) model is a novel mathematical framework for cardiac electrophysiology simulations. The EMI model provides a more detailed description of the heart's electrical activity compared to traditional…

In this paper, the transport phenomena of synaptic electric impulses are considered. The FitzHugh--Nagumo and FitzHugh--Rinzel models appear mathematically appropriate for evaluating these scientific issues. Moreover, applications of such…

The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation…

A general framework for performing event-driven simulations of systems with semi-flexible or rigid bodies interacting under impulsive torques and forces is outlined. Two different approaches are presented. In the first, the dynamics and…

This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated systems experiencing multiple excitations. The aim of such an approach is to focus on the evolution of a signal (e.g., heart…

A bio tissue model consisting of multilayer spherical cells including four nested radial domains (nucleus, nuclear membrane, cytoplasm and plasma membrane) is worked out to derive the cell heating dynamics in presence of membrane…

We give a constructive method for realizing an arbitrary directed graph (with no one-cycles) as a heteroclinic or an excitable dynamic network in the phase space of a system of coupled cells of two types. In each case, the system is…

The extracellular space has an ambiguous role in neuroscience. It is present in every physiologically relevant system and often used as a measurement site in experimental recordings, but it has received subordinate attention compared to the…

A minimalistic model of the half-center oscillator is proposed. Within it, we consider dynamics of two excitable neurons interacting by means of the excitatory coupling. In the parameter space of the model, we identify the regions of…

The Hubbard model is a prototype for strongly correlated electrons in condensed matter, for molecules and fermions or bosons in optical lattices. While the equilibrium properties of these systems have been studied in detail, the excitation…

Computer-based simulations of non-invasive cardiac electrical outputs, such as electrocardiograms and body surface potential maps, usually entail severe computational costs due to the need of capturing fine-scale processes and to the…

Since Noble adapted in 1962 the model of Hodgkin and Huxley to fit Purkinje fibres the refinement of models for cardiomyocytes has continued. Most of these models are high-dimensional systems of coupled equations so that the possible…

Formation of feedback loops of excitation waves (reentrant circuit) around non-conducting ventricular scar tissue is a common cause of lethal cardiac arrhythmias, such as ventricular tachycardia. This is typically treated by rapid…

Reentry around non-conducting ventricular scar tissue, which often causes lethal arrhythmias, is typically treated by rapid stimulation from an implantable defibrillator. However, the mechanisms of termination (success and failure) are…

The analytically tractable model employing Quantum Markovian Master Equations, derived by weak coupling procedure and satisfying complete positivity, is proposed to describe a model of molecular battery charged by a non-equilibrium…

This thesis is concerned with modeling and simulation of the mitral valve, one of the four valves in the human heart. The valve is composed of leaflets attached to a ring, the free edges of which are supported by a system of chordae, which…

The elapsed time model has been widely studied in the context of mathematical neuroscience with many open questions left. The model consists of an age-structured equation that describes the dynamics of interacting neurons structured by the…

This work aims to describe a mathematical model and a numerical method to simulate a thin anisotropic composite membrane moving and deforming in 3D space under a dynamic load of an arbitrary time and space profile. The model and the method…

Inhibitory circuits of relaxation oscillators are often-used models for the dynamics of biological networks. We present a qualitative and quantitative stability analysis of such a circuit constituted by three reciprocally coupled…

Temporal modulation unlocks possibilities to dynamically control and modify the response of electromagnetic systems. Employing explicit dependencies of circuit or surface parameters on time enables the engineering of systems with…