scholarly journals Cell-to-cell Mathematical modeling of arrhythmia phenomena in excitable media

2019 ◽  
Author(s):  
Gabriel López Garza
Keyword(s):  
Mathematical Modeling ◽  
Differential Equations ◽  
Cellular Automaton ◽  
Ordinary Differential Equations ◽  
Excitable Media ◽  
Similar Distribution ◽  
Two Dimensional ◽  
Self Similar

AbstractIn this document are modeled arrhythmias with cellular automaton and ordinary differential equations systems. With an aperiodic, self-similar distribution of two-dimensional arrangement of cells, it is possible to simulate such phenomena as fibrillation, fluttering and a sequence of fibrillation-fluttering. The topology of the cytoarchitecture of a network of cells may determine the initiation and development of arrhythmias.

scholarly journals Cell-to-cell Mathematical Modeling of Arrhythmia Phenomena in the Heart

2020 ◽  
Author(s):  
Gabriel López Garza ◽  
A. Nicolás Mata ◽  
G. Román Alonso ◽  
J. F. Godínez Fernández ◽  
M. A. Castro García
Keyword(s):  
Mathematical Modeling ◽  
Initial Conditions ◽  
Parallel Architecture ◽  
Similar Distribution ◽  
Two Dimensional ◽  
Fractal Distribution ◽  
Basic Cell ◽  
Atrial Cells ◽  
Self Similar

AbstractWith an aperiodic, self-similar distribution of two-dimensional arrangement of atrial cells, it is possible to simulate such phenomena as Fibrillation, Fluttering, and a sequence of Fibrillation-Fluttering. The topology of a network of cells may facilitate the initiation and development of arrhythmias such as Fluttering and Fibrillation. Using a GPU parallel architecture, two basic cell topologies were considered in this simulation, an aperiodic, fractal distribution of connections among 462 cells, and a chessboard-like geometry of 60×60 and 600×600 cells. With a complex set of initial conditions, it is possible to produce tissue behavior that may be identified with arrhythmias. Finally, we found several sets of initial conditions that show how a mesh of cells may exhibit Fibrillation that evolves into Fluttering.

THE FLUX CREEP AUTOMATON

2004 ◽  
Vol 14 (03) ◽  
pp. 1155-1175 ◽  
Author(s):  
JOHN F. LINDNER ◽  
SCOTT B. HUGHES ◽  
DAVID J. MILLER ◽  
BRADLEY C. THOMAS ◽  
KURT WIESENFELD
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Differential Equations ◽  
Cellular Automaton ◽  
Ordinary Differential Equations ◽  
Flux Creep ◽  
Square Lattice ◽  
Discrete Dynamics ◽  
Two Dimensional ◽  
Granular Superconductors

We study a cellular automaton derived from the phenomenon of magnetic flux creep in two-dimensional granular superconductors. We model the superconductor as an array of Josephson junctions evolving according to a set of coupled ordinary differential equations. In the limit of slowly increasing magnetic field, we reduce these equations to a simple cellular automaton. The resulting discrete dynamics, a stylized version of the continuous dynamics of the differential equations, is equivalent to the dynamics of a gradient sand pile automaton. We study the dynamics as we vary the symmetry of the underlying lattice and the shape of its boundary. We find that the "simplest" realization of the automaton, on a square lattice with commensurate boundaries, results in especially simple dynamics, while "generic" realizations exhibit more complicated dynamics characterized by statistics with broad distributions, even in the absence of noise or disorder.

A Simple Three-States Cellular Automaton for Modelling Excitable Media

1998 ◽  
Vol 12 (05) ◽  
pp. 601-607 ◽  
Author(s):  
M. Andrecut
Keyword(s):  
Wave Propagation ◽  
Partial Differential Equations ◽  
Cellular Automata ◽  
Differential Equations ◽  
Cellular Automaton ◽  
Cellular Automaton Model ◽  
Excitable Media ◽  
Self Organization ◽  
Partial Differential ◽  
Bz Reaction

Wave propagation in excitable media provides an important example of spatiotemporal self-organization. The Belousov–Zhabotinsky (BZ) reaction and the impulse propagation along nerve axons are two well-known examples of this phenomenon. Excitable media have been modelled by continuous partial differential equations and by discrete cellular automata. Here we describe a simple three-states cellular automaton model based on the properties of excitation and recovery that are essential to excitable media. Our model is able to reproduce the dynamics of patterns observed in excitable media.

Some Invariant Solutions of Two-Dimensional Elastodynamics in Linear Homogeneous Isotropic Materials

2013 ◽  
Vol 5 (2) ◽  
pp. 212-221
Author(s):  
Houguo Li ◽  
Kefu Huang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Theoretical Method ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
Partial Differential ◽  
Isotropic Materials ◽  
Group Theoretical Method ◽  
Infinitesimal Operators

AbstractInvariant solutions of two-dimensional elastodynamics in linear homogeneous isotropic materials are considered via the group theoretical method. The second order partial differential equations of elastodynamics are reduced to ordinary differential equations under the infinitesimal operators. Three invariant solutions are constructed. Their graphical figures are presented and physical meanings are elucidated in some cases.

Ordinary differential equations and calculus of variations

2020 ◽  
Author(s):  
Efim Kogan
Keyword(s):  
Mathematical Modeling ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Calculus Of Variations ◽  
Applied Mechanics ◽  
Technological Systems ◽  
Technological Means ◽  
Independent Work

The textbook contains theoretical information in a volume of the lecture course are discussed in detail and examples of typical tasks and test tasks and tasks for independent work. Designed for students enrolled in directions of preparation 15.03.03 "Applied mechanics" 01.03.02 "mathematics" (specialization "Mathematical modeling"), major 23.05.01 "Land transport and technological means" (specialization "Dynamics and strength of transport and technological systems"). Can be used by teachers for conducting practical classes.

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