Evaluating constrained and unconstrained mixture frameworks for predicting engineered heart tissue mechanics

Engineered heart tissues (EHTs) provide a controlled platform for studying cardiac tissue mechanics under both healthy and diseased conditions. The use of imaging techniques enables the detailed characterization of tissue structure and function, allowing for the measurement of EHT changes in response to diverse stimuli. Increasingly, computational models are being built and used to help synthesize and contextualize this detailed information to understand the mechanobiology of EHTs. Many of these approaches consider a constrained mixture approach, which homogenizes the kinematic response of EHTs based on a density-weighted sum of the strain energies of the different mechanical constituents. However, the challenge when considering the mechanobiology of EHTs is whether this assumption of shared kinematics holds and its influence on the predicted mechanical response of EHTs. To explore this phenomenon, we extended our EHT modeling framework (based on constrained mixture) to consider EHTs as an UNConstrained Mixture (UN-CM), where the kinematics of fibers and cells are given by separate independent variables which are constrained at explicit cell-matrix adhesions. Predictions from both frameworks were evaluated across a range of idealized and tissue-specific models, with variations in averaged regional mechanical quantities (strain, strain rate, and stress) ranging up to 40% depending on the regions, assumptions about adhesions, and the conditions of the tests. Consistently, strain rate between models showed the greatest variance across all tests considered. These results highlight the benefits of the CM approach, the flexibility of the UN-CM approach, and the divergence of both approaches when considering local mechanics in EHTs. Statement of Significance Biomechanical computational models can augment observations from engineered heart tissue (EHT) platforms. Most existing models rely on a constrained mixture (CM) framework, in which myofibrils and extracellular matrix fibers are assumed to deform together. However, microscale experiments show that fibers can deform independently of cells, except at discrete adhesion sites. To capture this behavior, we developed an unconstrained mixture (UN-CM) framework and compared it with the CM approach across a series of test cases. Although both models produce similar predictions on average, we identified localized differences, with strain rate emerging as the most divergent variable. These findings help contextualize results from computational EHT models and provide a new framework for studying diseases that impair the cell's ability to form adhesions.