Cardiovascular mathematics · 2006-bio-9
Biophysics and Biomechanics · ICM 2006: Cardiovascular mathematics
Inferred from the community field; finer classification has not been reviewed.
Problem statement
Construct and validate an anatomically based mathematical and computational model of whole-heart function that self-consistently couples cardiac electrical excitation and wave propagation, biochemical activation, finite-deformation mechanics of the myocardium, and the ventricular blood flow responsible for ejection. Couple this heart model bidirectionally to a one-dimensional network model of the systemic circulation, so that cardiac electrical activity determines myocardial activation and circulatory input while arterial pressure pulses feed back into cardiac electromechanics. Formulate mathematically consistent interface conditions and a stable, efficient numerical method that resolves the different spatial and temporal scales of the coupled electrical, mechanical, biochemical, and fluid subsystems, and determine whether the resulting global model is well posed and reproduces physiological heart function.
Lean 4
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Remaining questions in this record
Remaining questions recorded by the source
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Question 1
Construct and validate a stable, bidirectionally coupled model in which an anatomically based three-dimensional biventricular or four-chamber cardiac electromechanics model is coupled to a closed-loop global one-dimensional blood-flow model of the systemic and pulmonary circulation, including arterial and venous networks, so that arterial pulse-wave propagation determines cardiac afterload, venous return determines cardiac preload, and the changes in cardiac-chamber volumes are consistent with the vascular flow rates.
Source reference: Federica Caforio, Christoph M. Augustin, Jordi Alastruey, Matthias A. F. Gsell, and Gernot Plank, “A coupling strategy for a first 3D–1D model of the cardiovascular system to study the effects of pulse wave propagation on cardiac function,” Computational Mechanics 70 (2022), 703–722, Section 6.3 (“Limitations”), DOI: https://doi.org/10.1007/s00466-022-02206-6; arXiv:2111.05683, https://arxiv.org/abs/2111.05683.
Question 2
Establish well-posedness, including existence, uniqueness, and continuous dependence on the data, for a fully coupled nonlinear cardiac electro-mechano-fluid system in which a reaction-diffusion model of cardiac electrophysiology drives biochemical active-force generation in anisotropic, finite-deformation myocardial mechanics, while the deforming myocardium interacts bidirectionally, through kinematic and dynamic interface conditions, with incompressible Navier-Stokes blood flow in moving heart chambers.
Source reference: Alfio Quarteroni, Toni Lassila, Simone Rossi, and Ricardo Ruiz-Baier, “Integrated Heart—Coupling multiscale and multiphysics models for the simulation of the cardiac function,” Computer Methods in Applied Mechanics and Engineering 314 (2017), 345–407, Sections 4 and 7, DOI: https://doi.org/10.1016/j.cma.2016.05.031.
Progress & source assessment
Source-reported assessment from the ICM catalogue snapshot. This is not an independent review by Frontier Science.
The problem is unresolved. No located work constructs and validates one anatomically based whole-heart model having all of the stated couplings, a one-dimensional systemic-circulation network, a stable multiscale solver, and a well-posedness result for the resulting global system. The strongest papers solve different, non-interchangeable parts of this task; their results therefore do not combine into a resolution.
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“Integrated Heart—Coupling multiscale and multiphysics models for the simulation of the cardiac function,” Alfio Quarteroni, Toni Lassila, Simone Rossi, and Ricardo Ruiz-Baier, Computer Methods in Applied Mechanics and Engineering 314 (2017), 345–407. DOI: 10.1016/j.cma.2016.05.031. This work integrates electrophysiology, subcellular activation, tissue mechanics, and ventricular fluid mechanics at prototype level and surveys existence theory for the separate subsystems. It reports rigorous solvability only for restricted electrophysiology, linearized electromechanics, and simplified fluid–structure models, explains that nonlinear electro-mechano-fluid solvability requires new techniques, and concludes that integration across all salient scales remains beyond reach.
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“Fully coupled fluid-electro-mechanical model of the human heart for supercomputers,” Alfonso Santiago, Jazmin Aguado-Sierra, Miguel Zavala-Ake, Ruben Doste-Beltran, Samuel Gomez, Ruth Aris, Juan C. Cajas, Eva Casoni, and Mariano Vazquez, International Journal for Numerical Methods in Biomedical Engineering 34(12) (2018), e3140. DOI: 10.1002/cnm.3140. This gives a bidirectionally coupled whole-heart electrophysiology–mechanics–fluid simulation. It is major partial progress on the core multiphysics coupling, but it neither supplies the required 1D systemic network nor proves well-posedness of the full physiological system.
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“A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart,” Michele Bucelli, Alberto Zingaro, Pasquale Claudio Africa, Ivan Fumagalli, Luca Dede', and Alfio Quarteroni, International Journal for Numerical Methods in Biomedical Engineering 39(3) (2023), e3678. DOI: 10.1002/cnm.3678; arXiv: 2208.05551. This couples 3D electrophysiology, active-force generation, nonlinear mechanics, and blood flow through fluid–structure interaction, with a closed-loop 0D circulation model, and obtains physiological-range indicators. It treats only the left heart, leaves the left atrium passive, uses prescribed reduced valve kinematics, and expressly describes itself as a step toward an integrated whole-heart model.
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“A coupling strategy for a first 3D–1D model of the cardiovascular system to study the effects of pulse wave propagation on cardiac function,” Federica Caforio, Christoph M. Augustin, Jordi Alastruey, Matthias A. F. Gsell, and Gernot Plank, Computational Mechanics 70 (2022), 703–722. DOI: 10.1007/s00466-022-02206-6; arXiv: 2111.05683. This constructs and numerically validates a stable bidirectional coupling of a 3D left-ventricular electromechanics model to a 1D network of 116 systemic arteries. It does not model intracardiac fluid–structure interaction, the other chambers, or a closed-loop global 1D circulation; the paper identifies the latter extensions as future work.
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“An electromechanics-driven fluid dynamics model for the simulation of the whole human heart,” Alberto Zingaro, Michele Bucelli, Roberto Piersanti, Francesco Regazzoni, Luca Dede', and Alfio Quarteroni, Journal of Computational Physics 504 (2024), 112885. DOI: 10.1016/j.jcp.2024.112885; arXiv: 2301.02148. This reaches four-chamber electromechanics, active-force generation, whole-heart blood flow with reduced valves and transition-to-turbulence modeling, and a closed-loop circulation, with simulated biomarkers in physiological ranges. However, its circulation is 0D, and its electromechanical displacement is a unidirectional input to the fluid solver: the authors explicitly state that there is no dynamic fluid-to-structure feedback and propose bidirectional blood–myocardium and blood–valve FSI as further development.
Thus, realistic simulations now cover nearly every requested ingredient in important special-purpose frameworks, but the exact global 3D multiphysics–1D circulation construction, its full bidirectional coupling, and its mathematical well-posedness and comprehensive physiological validation remain open.
Recorded progress
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