Isogeometric finite element‐based simulation of the aortic heart valve: Integration of neural network structural material model and structural tensor fiber architecture representations

Abstract

The functional complexity of native and replacement aortic heart valves (AVs) is well known, incorporating such physical phenomenons as time‐varying non‐linear anisotropic soft tissue mechanical behavior, geometric non‐linearity, complex multi‐surface time varying contact, and fluid–structure interactions to name a few. It is thus clear that computational simulations are critical in understanding AV function and for the rational basis for design of their replacements. However, such approaches continued to be limited by ad‐hoc approaches for incorporating tissue fibrous structure, high‐fidelity material models, and valve geometry. To this end, we developed an integrated tri‐leaflet valve pipeline built upon an isogeometric analysis framework. A high‐order structural tensor (HOST)‐based method was developed for efficient storage and mapping the two‐dimensional fiber structural data onto the valvular 3D geometry. We then developed a neural network (NN) material model that learned the responses of a detailed meso‐structural model for exogenously cross‐linked planar soft tissues. The NN material model not only reproduced the full anisotropic mechanical responses but also demonstrated a considerable efficiency improvement, as it was trained over a range of realizable fibrous structures. Results of parametric simulations were then performed, as well as population‐based bicuspid AV fiber structure, that demonstrated the efficiency and robustness of the present approach. In summary, the present approach that integrates HOST and NN material model provides an efficient computational analysis framework with increased physical and functional realism for the simulation of native and replacement tri‐leaflet heart valves.

Study of Biomechanics of the Heart Valve Leaflet Apparatus Using Numerical Simulation Method

“…On the one hand, one can find in the literature the description of a sufficient number of high-level approaches to an in silico study of the leaflet apparatus of the heart valve bioprostheses, and many of them are modeling, among other things, sophisticated multidisciplinary interactions (multiphysics) as well. The most explicit of these studies reproduce the liquid–solid body processes with a complex description of materials [ 24 , 25 ], detailed selection of boundary conditions, and imitation of a multicomponent liquid, such as blood [ 5 , 26 ], but their results in the majority of cases are not compared with the results of the bench tests or do not deliberately reproduce important effects observed in the in vitro experiment in the modeling process [ 27 , 28 ]. At the same time, the researchers in their works make the conclusions on the interrelation between the leaflet geometry and hydrodynamics [ 2 , 29 ], the leaflet form and cooptation zone size [ 7 ], i.e.…”

The Potential of Deep Learning to Advance Clinical Applications of Computational Biomechanics

“…To analyze the effect of the microstructure on the fatigue of bioprosthetic heart valves, Zhang et al [70] where p is the pressure, ρ is the fluid density, and µ is the fluid viscosity.…”

Integrating mechanism-based modeling with biomedical imaging to build practical digital twins for clinical oncology

“…Furthermore, HeartFlow Planner allows physicians to interactively explore different intervention scenarios, virtually modifying each identified stenosis to see the potential impact on blood flow. Nevertheless, there are more challenges in cardiac modeling attracting great interest, including, for example, the incorporation of models and data across multiple spatial and temporal scales [3,[59][60][61][62][63], as well as more complete analyses of cardiac electrophysiology, mechanics, and hemodynamics [9,60,[64][65][66]. Additionally, there are several efforts to develop open-source software environments [60,67,68] to make cutting-edge cardiovascular modeling techniques (e.g., image analysis, mesh generation, numerical solvers, and visualization) accessible to a wide audience, including researchers, clinicians, and students.…”

“…Moreover, Zhang et al utilized a neural network representation of a complex structural constitutive model accounting for detailed tissue features to efficiently calculate the mechanical response of heart valves [63].…”

“…Furthermore, a robust digital twin implementation requires the provision of accurate real-time predictive feedback, which further increases the expensive computational cost. To overcome this limitation, the hybrid AI-mechanistic approaches constructed as neural networks encoding mechanism-based models are promising to facilitate rapid (and accurate) model evaluations (see Section IV.B) [63,87,196,237,238]. Importantly, the challenging demand on the computational cost can be met by properly using high-performance computing techniques involving parallelization to solve, select, or average the models in the digital twin, while accounting for data uncertainties, model inadequacies, and new data availability.…”