Cell-specific mathematical models of cardiac electrophysiology

Author(s):  
Ross Johnstone ◽  
Rémi Bardenet ◽  
Teun de Boer ◽  
David Gavaghan ◽  
Mark Davies ◽  
...  
2002 ◽  
Vol 5 (4) ◽  
pp. 215-239 ◽  
Author(s):  
G.T. Lines ◽  
M.L. Buist ◽  
P. Grottum ◽  
A.J. Pullan ◽  
J. Sundnes ◽  
...  

Author(s):  
Martin Fink ◽  
Wayne R Giles ◽  
Denis Noble

Repolarization of the action potential (AP) in cardiac muscle is a major determinant of refractoriness and excitability, and can also strongly modulate excitation–contraction coupling. In clinical cardiac electrophysiology, the Q-T interval, and hence action potential duration, is both an essential marker of normal function and an indicator of risk for arrhythmic events. It is now well known that the termination of the plateau phase of the AP and the repolarization waveform involve a complex interaction of transmembrane ionic currents. These include a slowly inactivating Na + current, inactivating Ca 2+ current, the decline of an electrogenic current due to Na + /Ca 2+ exchange and activation of three or four different K + currents. At present, many of the quantitative aspects of this important physiological and pathophysiological process remain incompletely understood. Recently, three mathematical models of the membrane AP in human ventricle myocyte have been developed and made available on the Internet. In this study, we have implemented these models for the purpose of comparing the K + currents, which are responsible for terminating the plateau phase of the AP and generating its repolarization. In this paper, our emphasis is on the two highly nonlinear inwardly rectifying potassium currents, and . A more general goal is to obtain improved understanding of the ionic mechanisms, which underlie all-or-none repolarization and the parameter denoted ‘repolarization reserve’ in the human ventricle. Further, insights into these fundamental variables can be expected to provide a more rational basis for clinical assessment of the Q-T and Q-T C intervals, and hence provide insights into some of the very substantial efforts in safety pharmacology, which are based on these parameters.


Author(s):  
S. Linge ◽  
J. Sundnes ◽  
M. Hanslien ◽  
G.T. Lines ◽  
A. Tveito

Knowledge of cardiac electrophysiology is efficiently formulated in terms of mathematical models. However, most of these models are very complex and thus defeat direct mathematical reasoning founded on classical and analytical considerations. This is particularly so for the celebrated bidomain model that was developed almost 40 years ago for the concurrent analysis of extra- and intracellular electrical activity. Numerical simulations based on this model represent an indispensable tool for studying electrophysiology. However, complex mathematical models, steep gradients in the solutions and complicated geometries lead to extremely challenging computational problems. The greatest achievement in scientific computing over the past 50 years has been to enable the solving of linear systems of algebraic equations that arise from discretizations of partial differential equations in an optimal manner, i.e. such that the central processing unit (CPU) effort increases linearly with the number of computational nodes. Over the past decade, such optimal methods have been introduced in the simulation of electrophysiology. This development, together with the development of affordable parallel computers, has enabled the solution of the bidomain model combined with accurate cellular models, on geometries resembling a human heart. However, in spite of recent progress, the full potential of modern computational methods has yet to be exploited for the solution of the bidomain model. This paper reviews the development of numerical methods for solving the bidomain model. However, the field is huge and we thus restrict our focus to developments that have been made since the year 2000.


2007 ◽  
Vol 292 (1) ◽  
pp. H43-H55 ◽  
Author(s):  
Elizabeth M. Cherry ◽  
Flavio H. Fenton

The extensive development of detailed mathematical models of cardiac myocyte electrophysiology in recent years has led to a proliferation of models, including many that model the same animal species and specific region of the heart and thus would be expected to have similar properties. In this paper we review and compare two recently developed mathematical models of the electrophysiology of canine ventricular myocytes. To clarify their similarities and differences, we also present studies using them in a range of preparations from single cells to two-dimensional tissue. The models are compared with each other and with new and previously published experimental results in terms of a number of their properties, including action potential morphologies; transmembrane currents during normal heart rates and during alternans; alternans onsets, magnitudes, and cessations; and reentry dynamics of spiral waves. Action potential applets and spiral wave movies for the two canine ventricular models are available online as supplemental material. We find a number of differences between the models, including their rate dependence, alternans dynamics, and reentry stability, and a number of differences compared with experiments. Differences between models of the same species and region of the heart are not unique to these canine models. Similar differences can be found in the behavior of two models of human ventricular myocytes and of human atrial myocytes. We provide several possible explanations for the differences observed in models of the same species and region of the heart and discuss the implications for the applicability of models in addressing questions of mechanism in cardiac electrophysiology.


2019 ◽  
Author(s):  
Alexander Meduna ◽  
Petr Horacek ◽  
Martin Tomko
Keyword(s):  

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