Department of Theoretical Biology, Utrecht University, Utrecht, The Netherlands
Submitted 30 January 2006
; accepted in final form 5 March 2006
Ventricular fibrillation (VF) is one of the main causes ...of death in the Western world. According to one hypothesis, the chaotic excitation dynamics during VF are the result of dynamical instabilities in action potential duration (APD) the occurrence of which requires that the slope of the APD restitution curve exceeds 1. Other factors such as electrotonic coupling and cardiac memory also determine whether these instabilities can develop. In this paper we study the conditions for alternans and spiral breakup in human cardiac tissue. Therefore, we develop a new version of our human ventricular cell model, which is based on recent experimental measurements of human APD restitution and includes a more extensive description of intracellular calcium dynamics. We apply this model to study the conditions for electrical instability in single cells, for reentrant waves in a ring of cells, and for reentry in two-dimensional sheets of ventricular tissue. We show that an important determinant for the onset of instability is the recovery dynamics of the fast sodium current. Slower sodium current recovery leads to longer periods of spiral wave rotation and more gradual conduction velocity restitution, both of which suppress restitution-mediated instability. As a result, maximum restitution slopes considerably exceeding 1 (up to 1.5) may be necessary for electrical instability to occur. Although slopes necessary for the onset of instabilities found in our study exceed 1, they are within the range of experimentally measured slopes. Therefore, we conclude that steep APD restitution-mediated instability is a potential mechanism for VF in the human heart.
reentrant arrhythmias; human ventricular myocytes; restitution properties; spiral waves; computer simulation
Address for reprint requests and other correspondence: K. H. W. J. ten Tusscher, Utrecht Univ., Dept. of Theoretical Biology, Padualaan 8, 3584 CH Utrecht, The Netherlands (e-mail: khwjtuss{at}hotmail.com )
Cardiac fibrosis occurs in many forms of heart disease. It is well established that the spatial pattern of fibrosis, its texture, substantially affects the onset of arrhythmia. However, in most ...modelling studies fibrosis is represented by multiple randomly distributed short obstacles that mimic only one possible texture, diffuse fibrosis. An important characteristic feature of other fibrosis textures, such as interstitial and patchy textures, is that fibrotic inclusions have substantial length, which is suggested to have a pronounced effect on wave propagation. In this paper, we study the effect of the elongation of inexcitable inclusions (obstacles) on wave propagation in a 2D model of cardiac tissue described by the TP06 model for human ventricular cells. We study in detail how the elongation of obstacles affects various characteristics of the waves. We quantify the anisotropy induced by the textures, its dependency on the obstacle length and the effects of the texture on the shape of the propagating wave. Because such anisotropy is a result of zig-zag propagation we show, for the first time, quantification of the effects of geometry and source-sink relationship, on the zig-zag nature of the pathway of electrical conduction. We also study the effect of fibrosis in the case of pre-existing anisotropy and introduce a procedure for scaling of the fibrosis texture. We show that fibrosis can decrease or increase the preexisting anisotropy depending on its scaled texture.
Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of ...electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as Formula: see text, the fibroblast resting-membrane potential, the fibroblast conductance Formula: see text, and the MF gap-junctional coupling Formula: see text. Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as Formula: see text, and Formula: see text, and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity Formula: see text decreases as a function of Formula: see text, for zero-sided and one-sided couplings; however, for two-sided coupling, Formula: see text decreases initially and then increases as a function of Formula: see text, and, eventually, we observe that conduction failure occurs for low values of Formula: see text. In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling Formula: see text or Formula: see text. Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
One of the important questions in cardiac electrophysiology is to characterise the arrhythmogenic substrate; for example, from the texture of the cardiac fibrosis, which is considered one of the ...major arrhythmogenic conditions. In this paper, we perform an extensive in silico study of the relationships between various local geometric characteristics of fibrosis on the onset of cardiac arrhythmias. In order to define which texture characteristics have better predictive value, we induce arrhythmias by external stimulation, selecting 4363 textures in which arrhythmia can be induced and also selecting 4363 non-arrhythmogenic textures. For each texture, we determine such characteristics as cluster area, solidity, mean distance, local density and zig-zag propagation path, and compare them in arrhythmogenic and non-arrhythmogenic cases. Our study shows that geometrical characteristics, such as cluster area or solidity, turn out to be the most important for prediction of the arrhythmogenic textures. Overall, we were able to achieve an accuracy of 67% for the arrhythmogenic texture-classification problem. However, the accuracy of predictions depends on the size of the region chosen for the analysis. The optimal size for the local areas of the tissue was of the order of 0.28 of the wavelength of the arrhythmia. We discuss further developments and possible applications of this method for characterising the substrate of arrhythmias in fibrotic textures.
A model for human ventricular tissue ten Tusscher, K. H. W. J; Noble, D; Noble, P. J ...
American journal of physiology. Heart and circulatory physiology,
04/2004, Letnik:
286, Številka:
4
Journal Article
Recenzirano
1 Department of Theoretical Biology, Utrecht University, 3584 CH Utrecht, The Netherlands; and 2 University Laboratory of Physiology, University of Oxford, Oxford OX1 3PT; and 3 Division of ...Mathematics, University of Dundee, Dundee DD1 4HN, United Kingdom
Submitted 9 August 2003
; accepted in final form 2 December 2003
The experimental and clinical possibilities for studying cardiac arrhythmias in human ventricular myocardium are very limited. Therefore, the use of alternative methods such as computer simulations is of great importance. In this article we introduce a mathematical model of the action potential of human ventricular cells that, while including a high level of electrophysiological detail, is computationally cost-effective enough to be applied in large-scale spatial simulations for the study of reentrant arrhythmias. The model is based on recent experimental data on most of the major ionic currents: the fast sodium, L-type calcium, transient outward, rapid and slow delayed rectifier, and inward rectifier currents. The model includes a basic calcium dynamics, allowing for the realistic modeling of calcium transients, calcium current inactivation, and the contraction staircase. We are able to reproduce human epicardial, endocardial, and M cell action potentials and show that differences can be explained by differences in the transient outward and slow delayed rectifier currents. Our model reproduces the experimentally observed data on action potential duration restitution, which is an important characteristic for reentrant arrhythmias. The conduction velocity restitution of our model is broader than in other models and agrees better with available data. Finally, we model the dynamics of spiral wave rotation in a two-dimensional sheet of human ventricular tissue and show that the spiral wave follows a complex meandering pattern and has a period of 265 ms. We conclude that the proposed model reproduces a variety of electrophysiological behaviors and provides a basis for studies of reentrant arrhythmias in human ventricular tissue.
reentrant arrhythmias; human ventricular myocytes; restitution properties; spiral waves; computer simulation
Address for reprint requests and other correspondence: K. H. W. J. ten Tusscher, Utrecht Univ., Dept. of Theoretical Biology, Padualaan 8, 3584 CH Utrecht, The Netherlands (E-mail: khwjtuss{at}hotmail.com ).
Cardiovascular diseases remain one of the largest causes of death worldwide. The lethal pathologies often occur due to atherosclerosis, clot formation and cardiac arrhythmia. It turns out that all ...these pathologies can be described using the generic framework of multi-component reaction–diffusion equations. These parabolic partial differential equations sustain waves and pattern formation that are relevant in the study of all those processes. Here we present the first review which combines the description of these fields: atherosclerosis, clot formation and cardiac arrhythmias, and includes classic and recent developments in these areas. We show how mathematical models for the underlying physiological processes have been constructed, and which generic properties follow from their analytical or numerical study. Finally, we discuss the possibility of integrative studies of cardiovascular disease which will include both clot formation and cardiac arrhythmias. Such approach will be highly relevant to atrial fibrillation, a common cardiac arrhythmia whose main complication is clot formation and stroke.
•Cardiovascular diseases are reviewed from joint grounds of reaction–diffusion waves.•Atherosclerosis is modeled as chronic inflammation of blood vessel walls.•The state-of-the-art models of thrombus formation are considered.•Cardiac arrhythmia modeling via reaction–diffusion equations is discussed.•Response function perturbation theory for cardiac arrhythmias is presented.
Models of cardiac tissue electrophysiology are an important component of the Cardiac Physiome Project, which is an international effort to build biophysically based multi-scale mathematical models of ...the heart. Models of tissue electrophysiology can provide a bridge between electrophysiological cell models at smaller scales, and tissue mechanics, metabolism and blood flow at larger scales. This paper is a critical review of cardiac tissue electrophysiology models, focussing on the micro-structure of cardiac tissue, generic behaviours of action potential propagation, different models of cardiac tissue electrophysiology, the choice of parameter values and tissue geometry, emergent properties in tissue models, numerical techniques and computational issues. We propose a tentative list of information that could be included in published descriptions of tissue electrophysiology models, and used to support interpretation and evaluation of simulation results. We conclude with a discussion of challenges and open questions.
Using a reaction-diffusion-mechanics model we identify a mechanism for mechanical wave break in the heart muscle. For a wide range of strengths and durations an external mechanical load causes wave ...front dissipation leading to formation and breakup of spiral waves. We explain the mechanism, and discuss under which conditions it can cause or abolish cardiac arrhythmias.
One of the most recent trends in cardiac electrophysiology is the development of integrative anatomically accurate models of the heart, which include description of cardiac activity from sub-cellular ...and cellular level to the level of the whole organ. In order to construct this type of model, a researcher needs to collect a wide range of information from books and journal articles on various aspects of biology, physiology, electrophysiology, numerical mathematics and computer programming. The aim of this methodological article is to survey recent developments in integrative modelling of electrical activity in the ventricles of the heart, and to provide a practical guide to the resources and tools that are available for work in this exciting and challenging area.
The paper presents the results of laboratory experiments on electromagnetic emissions excitation (the electric component of electromagnetic fields) by rock samples due to different forms of ...mechanical stress applications. It was shown that samples generate electric impulses with different spectra when the impact action, gradual loading or dynamic friction is applied. It was ascertained that level and spectral compositions of signals, generated by rock samples, change with an increasing number of hits. It was found that strong electromagnetic signals, generated while rock samples were fracturing, were accompanied by repetitive weak but perceptible variations in the electric field intensity in short frequency ranges.
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