Modeling of calcium dynamics in excitable and non-excitable cells

Tato bakalářská práce se zabývá elektrofyziologickými jevy na molekulární úrovni a úrovni buněk. Cílem je podat základní informace pro pochopení jednoduchých buněčných modelů. Práce také pojednává o principech modelování dynamiky kalcia v buňkách. V prostředí Matlab jsou realizovány modely Luo-Rudy z roku 1991, Luo Rudy z roku 1994 a model oscilačního chování ß-buněk pankreatu. Pomocí rozhraní GUI je vytvořen přehledný program pro simulaci elektrofyziologickými jevu.This bachelor thesis deals with electrophysiologic phenomenons on molecular and cellular level. The aim is to provide basic information for better understanding of simple cellular models. This work also discusses principles of calcium dynamic modelling in cells. In Matlab environment the Lou-Rudy model from 1991, Lou-Rudy model from 1994 and the phantom burster model for pancreatic ß-cells are implemented. Using the GUI interface a clear program for simulation electrophysiologic phenomenons is created.

Reaction-Diffusion systems for the macroscopic Bidomain model of the cardiac electric field

The paper deals with a mathematical model for the electric activity of the heart at macroscopic level. The membrane model used to describe the ionic currents is a generalization of the phase-I Luo-Rudy, a model widely used in 2-D and 3-D simulations of the action potential propagation. From the mathematical viewpoint the model is made up of a degenerate parabolic reaction diffusion system coupled with an ODE system. We derive existence, uniqueness and some regularity results

The role of M cells and the long QT syndrome in cardiac arrhythmias: simulation studies of reentrant excitations using a detailed electrophysiological model

In this numerical study, we investigate the role of intrinsic heterogeneities of cardiac tissue due to M cells in the generation and maintenance of reentrant excitations using the detailed Luo-Rudy dynamic model. This model has been extended to include a description of the long QT 3 syndrome, and is studied in both one dimension, corresponding to a cable traversing the ventricular wall, and two dimensions, representing a transmural slice. We focus on two possible mechanisms for the generation of reentrant events. We first investigate if early-after-depolarizations occurring in M cells can initiate reentry. We find that, even for large values of the long QT strength, the electrotonic coupling between neighboring cells prevents early-after-depolarizations from creating a reentry. We then study whether M cell domains, with their slow repolarization, can function as wave blocks for premature stimuli. We find that the inclusion of an M cell domain can result in some cases in reentrant excitations and we determine the lifetime of the reentry as a function of the size and geometry of the domain and of the strength of the long QT syndrome

Spiral-wave Dynamics Depends Sensitively on nhomogeneities in Mathematical Models of Ventricular Tissue

Every sixth death in industrialised countries occurs because of cardiac arrhythmias like ventricular tachycardia (VT) and ventricular fibrillation (VF). There is growing consensus that VT is associated with an unbroken spiral wave of electrical activation on cardiac tissue but VF with broken waves, spiral turbulence, spatiotemporal chaos and rapid, irregular activation. Thus spiral-wave activity in cardiac tissue has been studied extensively. Nevertheless many aspects of such spiral dynamics remain elusive because of the intrinsically high-dimensional nature of the cardiac-dynamical system. In particular, the role of tissue heterogeneities in the stability of cardiac spiral waves is still being investigated. Experiments with conduction blocks in cardiac tissue yield a variety of results: some suggest that blocks can eliminate VF partially or completely, leading to VT or quiescence, but others show that VF is unaffected by obstacles. We propose theoretically that this variety of results is a natural manifestation of a fractal boundary that must separate the basins of the attractors associated, respectively, with VF and VT. We substantiate this with extensive numerical studies of Panfilov and Luo-Rudy I models, where we show that the suppression of VF depends sensitively on the position, size, and nature of the inhomogeneity.Comment: 9 pages, 5 figures

Procesos fisicoquímicos asociados con isquemia en miocardio y su influencia en arritmias: un estudio de simulación

Los fuertes cambios fisicoquímicos sufridos por el miocardio en eventos isquémicos componen el sustrato funcional para la formación de reentradas de potencial eléctrico en superficie. Estas alteraciones son modeladas en mallas bidimensionales, utilizando modelo biofísico de Luo-Rudy en tejido epicárdico. Se obtienen reentradas en forma de ocho que representa un desbalance eléctrico de tipo fuente-sumidero. Se cree que este desbalance es clave en fibrilación ventricular

Procesos fisicoquímicos asociados con isquemia en miocardio y su influencia en arritmias: un estudio de simulación

Los fuertes cambios fisicoquímicos sufridos por el miocardio en eventos isquémicos componen el sustrato funcional para la formación de reentradas de potencial eléctrico en superficie. Estas alteraciones son modeladas en mallas bidimensionales, utilizando modelo biofísico de Luo-Rudy en tejido epicárdico. Se obtienen reentradas en forma de ocho que representa un desbalance eléctrico de tipo fuente-sumidero. Se cree que este desbalance es clave en fibrilación ventricular