A Unified Modular Framework for Implicit 3D-0D Coupling in Cardiovascular Finite Element Simulations*

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, also known as a lumped-parameter network or 0-dimensional (0D) fluid model, to represent blood flow throughout the cardiovascular system. In this work, we present a modular framework for implicitly coupling 3-dimensional (3D) finite element simulations of fluid or solid mechanics to 0D fluid models of blood circulation. The coupling 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 couples 3D blood flow models to 0D circulation models (3D fluid - 0D fluid). Here, we extend it to couple 3D cardiac tissue mechanics models to 0D circulation models (3D structure - 0D fluid), showing that both mathematical problems can be solved within a unified coupling scheme. We also provide a new derivation inspired by the Approximate Newton Method, which explains how the proposed numerical scheme combines the stability of monolithic approaches with the modularity and flexibility of partitioned approaches. The effectiveness, temporal convergence, and computational cost of the algorithm are assessed through several examples relevant to the cardiovascular modeling community.