Simulating patterns of excitation, repolarization and action potential duration with cardiac Bidomain and Monodomain models

Franzone, Piero Colli; Pavarino, Luca F.; Taccardi, Bruno

doi:10.1016/j.mbs.2005.04.003

Cited by 142 publications

(131 citation statements)

References 48 publications

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“…Therefore, even if we considered the total derivative of a generic concentration c (18) Dc Dt = ∂c ∂t + grad c · V, the second term would be negligible as the diffusive flow has already been removed. Now, it is well known that the Bidomain model in a one-dimensional fiber is equivalent to the Monodomain one (see [27,28]), which, for constant intra-and extracellular conductivity coefficients σ i,e f along the fiber, is given by (19) c m ∂v…”

Section: The Electrophysiological Modelmentioning

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

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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.

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Section: The Electrophysiological Modelmentioning

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

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“…For better clarity, the condition number and CPU times are also plotted in Figure 5. The scaled speedup, defined as speedup(procs) = time (8) time(procs)…”

Section: Test 3: Weak Scaling On Ellipsoidal Domains Structured Meshmentioning

confidence: 99%

“…Table 4 reports the average condition number, extreme eigenvalues, PCG iterations count and CPU time per time step. The speedup, defined with respect to the 8 processors run as speedup(procs) := T time (8) T…”

Section: Test 4: Strong Scaling On a Slab Domain Unstructured Meshmentioning

confidence: 99%

“…Alternatively, most previous works have considered IMEX time discretizations and/or operator splitting schemes, where the reaction and diffusion terms are treated separately, see e.g. [4,6,8,14,20,22,28,35,38,45,47,[53][54][55]. The advantage of IMEX and operator splitting schemes is that they only require the solution of a linear system for the parabolic and elliptic PDEs at each time step.…”

Section: Introductionmentioning

confidence: 99%

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A comparison of coupled and uncoupled solvers for the cardiac Bidomain model

2013

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Abstract. The aim of this work is to compare a new uncoupled solver for the cardiac Bidomain model with a usual coupled solver. The Bidomain model describes the bioelectric activity of the cardiac tissue and consists of a system of a non-linear parabolic reaction-diffusion partial differential equation (PDE) and an elliptic linear PDE. This system models at macroscopic level the evolution of the transmembrane and extracellular electric potentials of the anisotropic cardiac tissue. The evolution equation is coupled through the non-linear reaction term with a stiff system of ordinary differential equations (ODEs), the so-called membrane model, describing the ionic currents through the cellular membrane. A novel uncoupled solver for the Bidomain system is here introduced, based on solving twice the parabolic PDE and once the elliptic PDE at each time step, and it is compared with a usual coupled solver. Three-dimensional numerical tests have been performed in order to show that the proposed uncoupled method has the same accuracy of the coupled strategy. Parallel numerical tests on structured meshes have also shown that the uncoupled technique is as scalable as the coupled one. Moreover, the conjugate gradient method preconditioned by Multilevel Hybrid Schwarz preconditioners converges faster for the linear systems deriving from the uncoupled method than from the coupled one. Finally, in all parallel numerical tests considered, the uncoupled technique proposed is always about two or three times faster than the coupled approach.Mathematics Subject Classification. 65N55, 65M55, 65F10, 92C30.

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“…This simpler model requires less computational effort than (2.4), and even though the assumption of equal anisotropy ratios is very strong and generally unrealistic, (2.8) is adequate for a qualitative investigation of repolarization sequences and the distribution of patterns of durations of the action potential [29]. We assume that the functions M e , M i , I ion , and H are sufficiently smooth so that the following definitions of weak solutions make sense.…”

Section: The Macroscopic Bidomain and Monodomain Modelsmentioning

confidence: 99%

A multiresolution space‐time adaptive scheme for the bidomain model in electrocardiology

Bendahmane¹,

Bürger²,

Ruiz–Baier³

2009

Numerical Methods Partial

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The bidomain model of electrical activity of myocardial tissue consists of a possibly degenerate parabolic PDE coupled with an elliptic PDE for the transmembrane and extracellular potentials, respectively. This system of two scalar PDEs is supplemented by a time-dependent ODE modeling the evolution of the gating variable. In the simpler subcase of the monodomain model, the elliptic PDE reduces to an algebraic equation. Since typical solutions of the bidomain and monodomain models exhibit wavefronts with steep gradients, we propose a finite volume scheme enriched by a fully adaptive multiresolution method, whose basic purpose is to concentrate computational effort on zones of strong variation of the solution. Time adaptivity is achieved by two alternative devices, namely locally varying time stepping and a Runge-Kutta-Fehlberg-type adaptive time integration. A series of numerical examples demonstrates that these methods are efficient and sufficiently accurate to simulate the electrical activity in myocardial tissue with affordable effort. In addition, the optimal choice of the threshold for discarding nonsignificant information in the multiresolution representation of the solution is addressed, and the numerical efficiency and accuracy of the method is measured in terms of CPU time speed-up, memory compression, and errors in different norms.

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Simulating patterns of excitation, repolarization and action potential duration with cardiac Bidomain and Monodomain models

Cited by 142 publications

References 48 publications

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

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

A comparison of coupled and uncoupled solvers for the cardiac Bidomain model

A multiresolution space‐time adaptive scheme for the bidomain model in electrocardiology

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