  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.
