Identification of the Unloaded Heart Configuration Including External Interactions

Determining the unloaded, or reference, configuration of the heart is essential for developing patient-specific models that can accurately estimate in-vivo strains and stresses. Various strategies have been proposed to obtain this configuration, with inverse mechanics being a practical approach. The inverse mechanics method estimates the unloaded geometry from a deformed state and its known loads without the need for optimization procedures. However, for the resulting unloaded geometry to be physiologically meaningful, accurate boundary conditions are crucial. While spring boundary conditions are commonly applied to the epicardium to model interactions with surroundings, they do not account for the localized forces exerted by structures like the ribs and diaphragm. Since these external forces cannot be directly measured from medical images, we propose a novel approach that integrates them into the inverse mechanics formulation by penalizing large deformations. Using a series of test problems, we show this approach produces a reference configuration that closely matches the ground truth and improves circumferential strain estimations by an order of magnitude compared to standard inverse mechanics methods.