Integrated Heart—Coupling multiscale and multiphysics models for the simulation of the cardiac function

Quarteroni, Alfio; Lassila, Toni; Rossi, Simone; Ruiz–Baier, Ricardo

doi:10.1016/j.cma.2016.05.031

Cited by 207 publications

(224 citation statements)

References 260 publications

(347 reference statements)

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“…Interesting, but rather complex descriptions based on active strains and thermodynamics have been proposed for instance in [26][27][28][29]. Here we will instead consider the active stress approach, which amounts to simply assume that the stress tensor can be expressed as a linear superposition of an elastic contribution S M N elastic , describing the passive properties of cardiac tissue, and an active part S M N active , resulting from the contractile behavior of the muscle:…”

Section: A Governing Equationsmentioning

confidence: 99%

“…(27)- (33). In the following these equations will be solved numerically and the behavior of the solutions as function of important parameters will be analyzed in detail.…”

Section: B 1-d Model and Global Couplingmentioning

confidence: 99%

“…For the temporal integration of Eq. (27) we have used the explicit Runge-Kutta method. In particular we have used the fifth order Cash-Karp Runge-Kutta method [41].…”

Section: Numerical Techniquesmentioning

confidence: 99%

“…For the initial condition of Eq. (27), an external current, i app , is applied locally on a small region, which has a 5 × ∆X extension, and during a time interval of 5 ms. The amplitude of the imposed stimulation current is set to i app = 0.06 ms −1 .…”

Section: Numerical Techniquesmentioning

confidence: 99%

“…The Laplacian is discretized using a standard second-order central difference scheme and the spatial average (denoted by an over-bar) in Eqs. (27)- (33) is computed using the Simpson's rule [40]. For the temporal integration of Eq.…”

Section: Numerical Techniquesmentioning

confidence: 99%

See 4 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

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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.

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Section: A Governing Equationsmentioning

confidence: 99%

“…(27)- (33). In the following these equations will be solved numerically and the behavior of the solutions as function of important parameters will be analyzed in detail.…”

Section: B 1-d Model and Global Couplingmentioning

confidence: 99%

“…For the temporal integration of Eq. (27) we have used the explicit Runge-Kutta method. In particular we have used the fifth order Cash-Karp Runge-Kutta method [41].…”

Section: Numerical Techniquesmentioning

confidence: 99%

Section: Numerical Techniquesmentioning

confidence: 99%

Section: Numerical Techniquesmentioning

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

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Mechanical Characterization of hiPSC‐Derived Cardiac Tissues for Quality Control

et al. 2018

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Heart disease is one of the leading death causes in developed countries. To facilitate heart rehabilitation, engineered cardiac implantation has emerged as a promising alternative to organ transplantation. Currently there is no quantitative standard to ensure the safety and functionality of the engineered cardiac tissues intended for clinical uses. In anticipation of the clinical application of the engineered cardiac tissues to heart disease patients, a suite of methods is assembled to evaluate the mechanical characteristics critical to cardiac functions, including contractility, viscoelasticity, and dynamic stress distribution. As a proof of concept, 3D bioprinted cardiac tissues derived from human induced pluripotent stem cells are tested. First, the engineered cardiac tissues labeled with particles are recorded and tracked to determine spatially and temporally variable contraction forces. Viscoelastic properties are measured using magnetic tweezers. The results are used to compute 3D force and stress distribution over the engineered tissue by finite element method. In summary, a framework is developed to assess clinical‐grade engineered cardiac tissues and determine the appropriate value ranges suitable for implantation. The results relating contractility, intrinsic mechanical properties, and stress distribution in the engineered tissue, can also inform better design for future fabrication of engineered tissues.

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Numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network

Landajuela

Vergara

Gerbi

et al. 2018

Numer Methods Biomed Eng

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In this work, we consider the numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network. The mathematical model couples the 3D elastodynamics and bidomain equations for the electrophysiology in the myocardium with the 1D monodomain equation in the Purkinje network. For the numerical solution of the coupled problem, we consider a fixed-point iterative algorithm that enables a partitioned solution of the myocardium and Purkinje network problems. Different levels of myocardium-Purkinje network splitting are considered and analyzed. The results are compared with those obtained using standard strategies proposed in the literature to trigger the electrical activation. Finally, we present a numerical study that, although performed in an idealized computational domain, features all the physiological issues that characterize a heartbeat simulation, including the initiation of the signal in the Purkinje network and the systolic and diastolic phases.

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Integrated Heart—Coupling multiscale and multiphysics models for the simulation of the cardiac function

Cited by 207 publications

References 260 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

Mechanical Characterization of hiPSC‐Derived Cardiac Tissues for Quality Control

Numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network

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