A modular framework for implicit 3D–0D coupling in cardiac mechanics

• Published in: Computer methods in applied mechanics and engineering Vol. 421; p. 116764
• Main Authors: Brown, Aaron L., Salvador, Matteo, Shi, Lei, Pfaller, Martin R., Hu, Zinan, Harold, Kaitlin E., Hsiai, Tzung, Vedula, Vijay, Marsden, Alison L.
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier B.V 01-03-2024
• Subjects: 3D–0D coupling; Approximate Newton Method; Cardiac mechanics; Cardiovascular modeling; Multi-domain modeling; 3D–0D coupling; Approximate Newton Method; Multi-domain modeling; Cardiovascular modeling; Cardiac mechanics; multi-domain modeling; 3D-0D coupling; cardiac mechanics
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2024.116764

In numerical simulations of cardiac mechanics, coupling the heart to a model of the circulatory system is essential for capturing physiological cardiac behavior. A popular and efficient technique is to use an electrical circuit analogy, known as a lumped parameter network or zero-dimensional (0D) fluid model, to represent blood flow throughout the cardiovascular system. Due to the strong physical interaction between the heart and the blood circulation, developing accurate and efficient numerical coupling methods remains an active area of research. In this work, we present a modular framework for implicitly coupling three-dimensional (3D) finite element simulations of cardiac mechanics to 0D models of blood circulation. The framework is modular in that the circulation model can be modified independently of the 3D finite element solver, and vice versa. The numerical scheme builds upon a previous work that combines 3D blood flow models with 0D circulation models (3D fluid–0D fluid). Here, we extend it to couple 3D cardiac tissue mechanics models with 0D circulation models (3D structure–0D fluid), showing that both mathematical problems can be solved within a unified coupling scheme. The effectiveness, temporal convergence, and computational cost of the algorithm are assessed through multiple examples relevant to the cardiovascular modeling community. Importantly, in an idealized left ventricle example, we show that the coupled model yields physiological pressure–volume loops and naturally recapitulates the isovolumic contraction and relaxation phases of the cardiac cycle without any additional numerical techniques. Furthermore, we provide a new derivation of the scheme inspired by the Approximate Newton Method of Chan (1985), explaining how the proposed numerical scheme combines the stability of monolithic approaches with the modularity and flexibility of partitioned approaches.
•Coupling between 3D cardiac mechanics and 0D lumped-parameter circulation model.•Method combines advantages of monolithic and partitioned approaches.•Coupled left ventricle example recapitulates isovolumic cardiac phases.•Generalization of previous algorithm developed for 3D blood flow simulations.•Approximate Newton Method of Chan (1985) used to derive the coupling scheme.