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.

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

A comparative study fourth order runge kutta-tvd Scheme and fluent software case of inlet flow problems

Inlet as part of aircraft engine plays important role in controlling the rate of airflow entering to the engine. The shape of inlet has to be designed in such away to make the rate of airflow does not change too much with angle of attack and also not much pressure losses at the time, the airflow entering to the compressor section. It is therefore understanding on the flow pattern inside the inlet is important. The present work presents on the use of the Fourth Order Runge Kutta – Harten Yee TVD scheme for the flow analysis inside inlet. The flow is assumed as an inviscid quasi two dimensional compressible flow. As an initial stage of computer code development, here uses three generic inlet models. The first inlet model to allow the problem in hand solved as the case of inlet with expansion wave case. The second inlet model will relate to the case of expansion compression wave. The last inlet model concerns with the inlet which produce series of weak shock wave and end up with a normal shock wave. The comparison result for the same test case with Fluent Software [1, 2] indicates that the developed computer code based on the Fourth Order Runge Kutta – Harten – Yee TVD scheme are very close to each other. However for complex inlet geometry, the problem is in the way how to provide an appropriate mesh model

Negative tension of scroll wave filaments and turbulence in three-dimensional excitable media and application in cardiac dynamics

Scroll waves are vortices that occur in three-dimensional excitable media. Scroll waves have been observed in a variety of systems including cardiac tissue, where they are associated with cardiac arrhythmias. The disorganization of scroll waves into chaotic behavior is thought to be the mechanism of ventricular fibrillation, whose lethality is widely known. One possible mechanism for this process of scroll wave instability is negative filament tension. It was discovered in 1987 in a simple two variables model of an excitable medium. Since that time, negative filament tension of scroll waves and the resulting complex, often turbulent dynamics was studied in many generic models of excitable media as well as in physiologically realistic models of cardiac tissue. In this article, we review the work in this area from the first simulations in FitzHugh-Nagumo type models to recent studies involving detailed ionic models of cardiac tissue. We discuss the relation of negative filament tension and tissue excitability and the effects of discreteness in the tissue on the filament tension. Finally, we consider the application of the negative tension mechanism to computational cardiology, where it may be regarded as a fundamental mechanism that explains differences in the onset of arrhythmias in thin and thick tissue