We now consider the anisotropic monodomain electromechanical problem 2. Orientation of muscle fibers for a slab, an idealized left ventricle, and a biventricular geometry. In that model, w is a vector of dimensionless ion-channel gating vari- ables, and the total ionic current density Iion. A 2D slab of tissue In order to validate our mechanical numerical scheme following [31] , we perform one time-step iteration, so that all potential fields are known constant quantities acting as initial conditions. As discussed in, for example, [38] for the simulation of arteries, this setting may be regarded as an elastic resistance of the tissues surrounding the myocardium, being proportional to the displacement. A stretching in the X1 -direction is assumed, along with a compression in the X2 -direction.

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Regarding ventricular twist and torsion, previous studies [35] suggest that a compressible model is able to better reproduce the experimental data.

calcolo scientifico quarteroni pdf

Remarks on rate constitutive equations for finite deformations. As present limitations in our treatment, we have neglected several aspects in the modeling of the heart function, such as an accurate anatomi- cal representation of the fiber directions, a model for the blood circulation, Starling effects, quareroni more involved model for the passive mechanical properties of the medium, and ionic-scale electromechan- ics intracellular calcium handling and cross-bridge formation.

The deformation of the tissue is modeled assum- ing a quasi-steady elasticity framework, in which we suppose that a multiplicative decomposition between the active and passive mechanical response is introduced at the deformation level.

Secondly, other finite element discretiza- tions and more sophisticated preconditioning algorithms are sought, such as the monodomain-based block-triangular preconditioning proposed in [7] or structured algebraic multigrid preconditioners in the spirit of [8].

As in the 1D simulations, it is observed that the propagation of the electrical wave induces contraction of the tissue. Similar decompositions have been proposed in the context of scientivico elastoplasticity quarteronni and growth modeling [18].


Paola Gervasio – Unibs – DICATAM –

From the modeling point of view, we stress that a deeper understanding of the electromechan- ical coupling is still needed and open to discussion. The system can’t perform the operation now.

Their extension to the case of a deforming domain is postponed to Section 2. The Jacobian J describes the volume map of infinitesimal reference elements onto the corresponding current elements.

calcolo scientifico quarteroni pdf

Next, when evolving in time, as initial guess, we take the deformation at the previous time step. With this choice of parameters, the traveling waves produced have positive speed. Computational Cardiology ; For the pure electric problem, a linear convergence is obtained for the electrical potential.

His current research involves computational fluid dynamics, modelling and simulation of haemodynamics, numerical analysis of domain decomposition methods with application to multi-physics problems. In this work, we follow a simplified approach and, as an intermediate step, propose to account for the anisotropic behavior of the fibers only by assigning direction-specific active deformation fields in the active part of the decomposition.

Detailed expressions for physiologically rele- vant boundary conditions are provided in [22], and a deep discussion on some mathematical and numerical implications of choosing appropriate boundary conditions is presented in [39].

Finite element and finite volume-element simulation of pseudo-ECGs and cardiac scientjfico. Test on a truncated ellipsoid Now we prf the behavior of the electromechanical coupled model on a idealized left ventricle of height 10 cm, discretized using 29, nodes formingtetrahedra.

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We now consider the anisotropic monodomain electromechanical problem 2. The associated tetrahedral mesh consists of vertices and 30, elements. Action potential curve top and phase portrait bottom for the Rogers—McCulloch model in the adimensional left and dimensionalized right setting, starting from the initial states A D.

Several experiments have been quafteroni to obtain a qualitative comparison between the behav- iors of the incompressible and nearly compressible formulations.


Annals of Biomedical Engineering ; The undeformed geometry is represented by a cloud of points. We point out that if the chosen strain energy function has desirable stability properties such as polyconvexity scuentifico coercivity, as discussed in, e. In addition, by changing from a Eulerian to a Lagrangian configuration, the bidomain or monodomain equations modeling the evolution of the electrical propagation exhibit a nonlinear diffusion term.

(PDF) An active strain electromechanical model for cardiac tissue | Alfio Quarteroni –

Figure 10 examines the scaling of the solver for the Luo—Rudy bidomain electromechanical model on a refined ellipsoid 39, vertices at time instant t D 60 ms when the physics of the coupled problem is already clearly noticeable. The membrane model used is quarterlni rescaled Rogers—McCulloch 2. Already at t D 10 ms, one observes a displacement of the apex induced by the initial impulse, followed by an overall con- traction of the myocardium with an increased intensity in the zones czlcolo the wave of electrical excitation assumes high values.

Journal of Biomechanics ; The problem in its weak form reads as follows. Active deformation function D l a measure of the active strain in the direction of the fibers depending on the transmembrane potential leftaction potential curve and active deformation func- tion during a period of ms for the Rogers—McCulloch and Luo—Rudy I models quwrteroni and right, respectively.

Here, Iion and Hwhen taken as calcloo 2. For the orientation of the cardiac fibers, we employ an analytical description given in, for example, [6] Figure 8.