Self-Organized Pacemakers in a Coupled Reaction-Diffusion-Mechanics System

Panfilov, Alexander V.; Keldermann, R. H.; Nash, Martyn P.

doi:10.1103/physrevlett.95.258104

Cited by 99 publications

(170 citation statements)

References 12 publications

Supporting

Mentioning

161

Contrasting

Unclassified

Order By: Relevance

“…Note that the boundaries of the spatial domain are assumed electrically insulating and we will thus use Neumann boundary conditions in the numerical computations. Considering the Nash-Panfilov monodomain model [20,21,25], the ionic current term can be written as:…”

Section: A Governing Equationsmentioning

confidence: 99%

“…where g sac and e sac describe the conductance and reversal potential of the stretch-activated channels (following [20,21], we will set e sac = 1), while Θ denotes the standard Heaviside step function. This expression simply describes a linear increase of the current with the stretching and also assumes that no current is present when the sarcomere is compressed.…”

Section: A Governing Equationsmentioning

confidence: 99%

“…This phenomenon has been studied for a long time, both experimentally and theoretically (see for instance [7,[11][12][13][14][15][16][17][18][19][20][21][22]) and it is now well accepted that MEF can elicit spontaneous oscillatory behavior in muscle fibers. In the present work, we propose is a theoretical and numerical analysis of such oscillations.…”

Section: Introductionmentioning

confidence: 99%

“…Following [21], this function is assumed to be piecewise constant and equal to either ε 0 or ε 1 depending onV being respectively larger or smaller than a.…”

Section: A Governing Equationsmentioning

confidence: 99%

See 3 more Smart Citations

Temperature, geometry, and bifurcations in the numerical modeling of the cardiac mechano-electric feedback

Collet

Bragard

Dauby

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

This article characterizes the cardiac autonomous electrical activity induced by the mechanical deformations in the cardiac tissue through the mechano-electric feedback (MEF). A simplified and qualitative model is used to describe the system and we also account for temperature effects. The analysis emphasizes a very rich dynamics for the system, with periodic solutions, alternans, chaotic behaviors, etc. The possibility of self-sustained oscillations is analyzed in detail, particularly in terms of the values of important parameters such as the dimension of the system and the importance of the stretch-activated currents. It is also shown that high temperatures notably increase the parameters ranges for which self-sustained oscillations are observed and that several attractors can appear, depending on the location of the initial excitation of the system. Finally, the instability mechanisms by which the periodic solutions are destabilized have been studied by a Floquet analysis, which has revealed period-doubling phenomena and transient intermittencies.

show abstract

Section: A Governing Equationsmentioning

confidence: 99%

Section: A Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Following [21], this function is assumed to be piecewise constant and equal to either ε 0 or ε 1 depending onV being respectively larger or smaller than a.…”

Section: A Governing Equationsmentioning

confidence: 99%

See 2 more Smart Citations

Temperature, geometry, and bifurcations in the numerical modeling of the cardiac mechano-electric feedback

Collet

Bragard

Dauby

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

“…In the literature, there are already several studies on the impact of mechanical feedbacks on the bioelectrical activity, starting from the first ones by Nash and Panfilov [17,18]. However, to our knowledge, no previous works have investigated the effects of all previous mechanical influences in case of both healthy and eccentric hypertrophic fibers.…”

Section: Introductionmentioning

confidence: 99%

Computational modeling of the electromechanical response of a ventricular fiber affected by eccentric hypertrophy

Bianco

Franzone

Scacchi

et al. 2017

Communications in Applied and Industrial Mathematics

View full text Add to dashboard Cite

The aim of this work is to study the effects of eccentric hypertrophy on the electromechanics of a single myocardial ventricular fiber by means of a one-dimensional finite-element strongly-coupled model. The electrical current flow model is written in the reference configuration and it is characterized by two geometric feedbacks, i.e. the conduction and convection ones, and by the mechanoelectric feedback due to stretchactivated channels. First, the influence of such feedbacks is investigated for both a healthy and a hypertrophic fiber in case of isometric simulations. No relevant discrepancies are found when disregarding one or more feedbacks for both fibers. Then, all feedbacks are taken into account while studying the electromechanical responses of fibers. The results from isometric tests do not point out any notable difference between the healthy and hypertrophic fibers as regards the action potential duration and conduction velocity. The length-tension relationships show increased stretches and reduced peak values for tension instead. The tension-velocity relationships derived from afterloaded isotonic and quickrelease tests depict higher values of contraction velocity at smaller afterloads. Moreover, higher maximum shortenings are achieved during the isotonic contraction. In conclusion, our simulation results are innovative in predicting the electromechanical behavior of eccentric hypertrophic fibers.

show abstract

Computational modeling of cardiac electrophysiology: A novel finite element approach

Göktepe

Kuhl

2009

Numerical Meth Engineering

103

View full text Add to dashboard Cite

SUMMARYThe key objective of this work is the design of an unconditionally stable, robust, efficient, modular, and easily expandable finite element-based simulation tool for cardiac electrophysiology. In contrast to existing formulations, we propose a global-local split of the system of equations in which the global variable is the fast action potential that is introduced as a nodal degree of freedom, whereas the local variable is the slow recovery variable introduced as an internal variable on the integration point level. Cell-specific excitation characteristics are thus strictly local and only affect the constitutive level. We illustrate the modular character of the model in terms of the FitzHugh-Nagumo model for oscillatory pacemaker cells and the Aliev-Panfilov model for non-oscillatory ventricular muscle cells. We apply an implicit Euler backward finite difference scheme for the temporal discretization and a finite element scheme for the spatial discretization. The resulting non-linear system of equations is solved with an incremental iterative Newton-Raphson solution procedure. Since this framework only introduces one single scalar-valued variable on the node level, it is extremely efficient, remarkably stable, and highly robust. The features of the general framework will be demonstrated by selected benchmark problems for cardiac physiology and a two-dimensional patient-specific cardiac excitation problem.

show abstract

Self-Organized Pacemakers in a Coupled Reaction-Diffusion-Mechanics System

Cited by 99 publications

References 12 publications

Temperature, geometry, and bifurcations in the numerical modeling of the cardiac mechano-electric feedback

Temperature, geometry, and bifurcations in the numerical modeling of the cardiac mechano-electric feedback

Computational modeling of the electromechanical response of a ventricular fiber affected by eccentric hypertrophy

Computational modeling of cardiac electrophysiology: A novel finite element approach

Contact Info

Product

Resources

About