A Neural Network Finite Element Trileaflet Heart Valve Model Incorporating Multi-Body Contact

The use of patient-specific computational modeling of cardiovascular diseases has become increasingly popular to improve patient standard of care. Most simulation approaches currently utilize the finite element method (FEM), which is very well established and succeeds in producing high-fidelity results. However, it remains too slow for use in clinical settings, especially when many-query solutions are required to determine optimal therapeutic approaches. As a step toward addressing these demands, we have developed a Neural Network Finite Element (NNFE) approach that greatly accelerates simulations of soft tissue organ function. While the NNFE method utilizes conventional FEM meshes to define the problem geometry, it leverages advancements in neural network architecture design in new GPU-based software tools to solve the governing hyperelastic material PDEs. The NNFE method has recently captured physical contact between a deformable body and a frictionless symmetry plane. In the present work, we extended the NNFE approach to simulate trileaflet heart valve closure as a critical step in moving toward patient-specific applications. Our approach addressed two critical aspects of heart valve simulations: the use of 3D solid leaflet models as opposed to shell-based leaflet models and multi-body contact between the leaflets. We verified the approach by comparing displacements of NNFE simulated closure of a single heart valve leaflet against a frictionless symmetry plane with an identical simulation in tIGAr, the open-source isogeometric analysis extension of FEniCS. The average nodal displacement error was 0.020 mm (0.47% of the maximum displacement). We further evaluated our implementation by varying leaflet collagen fiber directions to mimic physiologically accurate deformation modes. Results of the approach indicated that the observed leaflet deformation patterns agreed well with previous trileaflet simulations. Significant variations in stress were observed transmurally, underscoring the need for solid elements to model leaflet geometry. Computational speed improvements produced an approximately 100-fold speedup, with the NNFE simulations of single leaflet closure taking 0.28 s while its FE counterpart took 61 s. Full trileaflet valve models with multi-body contact simulations took approximately 5 s, whereas equivalent FEM simulations take several hours. Training the full trileaflet model took approximately 16 h and was trained over the full functional range of pressure, so that training was only required once for all subsequent simulations. We conclude that the NNFE method can be successfully used to perform rapid simulations of complex 3D soft organ systems, such as the trileaflet heart valve, that involve large deformations, 3D geometries, and multi-body contact. Moreover, the ability to perform post-trained simulations in dramatically shorter time periods underscores the promise of machine learning-based computational mechanics approaches in patient-specific predictive computational models.