A deep learning application to approximate the geometric orifice and coaptation areas of the polymeric heart valves under time - varying transvalvular pressure

Synergistic Integration of Deep Neural Networks and Finite Element Method with Applications of Nonlinear Large Deformation Biomechanics

Patient-specific finite element analysis (FEA) holds great promise in advancing the prognosis of cardiovascular diseases by providing detailed biomechanical insights such as high-fidelity stress and deformation on a patient-specific basis. Albeit feasible, FEA that incorporates three-dimensional, complex patient-specific geometry can be time-consuming and unsuitable for time-sensitive clinical applications. To mitigate this challenge, machine learning (ML) models, e.g., deep neural networks (DNNs), have been increasingly utilized as potential alternatives to finite element method (FEM) for biomechanical analysis. So far, efforts have been made in two main directions: (1) learning the input-to-output mapping of traditional FEM solvers and replacing FEM with data-driven ML surrogate models; (2) solving equilibrium equations using physics-informed loss functions of neural networks. While these two existing strategies have shown improved performance in terms of speed or scalability, ML models have not yet provided practical advantages over traditional FEM due to generalization issues. This has led us to the question: instead of abandoning or replacing the traditional FEM framework that can reliably solve biomechanical problems, can we integrate FEM and DNNs to enhance performance? In this study, we propose a synergistic integration of DNNs and FEM to overcome their individual limitations. Using biomechanical analysis of the human aorta as the test bed, we demonstrated two novel integrative strategies in forward and inverse problems. For the forward problem, we developed DNNs with state-of-the-art architectures to predict a nodal displacement field, and this initial DNN solution was then updated by a FEM-based refinement process, yielding a fast and accurate computing framework. For the inverse problem of heterogeneous material parameter identification, our method employs DNN as a regularizer of the spatial distribution of material parameters, aiding the optimizer in locating the optimal solution. In our demonstrative examples, despite that the DNN-only forward models yielded small displacement errors in most test cases; stress errors were considerably large, and for some test cases, the peak stress errors were greater than 50%. Our DNN-FEM integration eliminated these non-negligible errors in DNN-only models and was magnitudes faster than the FEM-only approach. Additionally, compared to FEM-only inverse method with errors greater than 50%, our DNN-FEM inverse approach significantly improved the parameter identification accuracy and reduced the errors to less than 1%.

Perfect prosthetic heart valve: generative design with machine learning, modeling, and optimization

Majority of modern techniques for creating and optimizing the geometry of medical devices are based on a combination of computer-aided designs and the utility of the finite element method This approach, however, is limited by the number of geometries that can be investigated and by the time required for design optimization. To address this issue, we propose a generative design approach that combines machine learning (ML) methods and optimization algorithms. We evaluate eight different machine learning methods, including decision tree-based and boosting algorithms, neural networks, and ensembles. For optimal design, we investigate six state-of-the-art optimization algorithms, including Random Search, Tree-structured Parzen Estimator, CMA-ES-based algorithm, Nondominated Sorting Genetic Algorithm, Multiobjective Tree-structured Parzen Estimator, and Quasi-Monte Carlo Algorithm. In our study, we apply the proposed approach to study the generative design of a prosthetic heart valve (PHV). The design constraints of the prosthetic heart valve, including spatial requirements, materials, and manufacturing methods, are used as inputs, and the proposed approach produces a final design and a corresponding score to determine if the design is effective. Extensive testing leads to the conclusion that utilizing a combination of ensemble methods in conjunction with a Tree-structured Parzen Estimator or a Nondominated Sorting Genetic Algorithm is the most effective method in generating new designs with a relatively low error rate. Specifically, the Mean Absolute Percentage Error was found to be 11.8% and 10.2% for lumen and peak stress prediction respectively. Furthermore, it was observed that both optimization techniques result in design scores of approximately 95%. From both a scientific and applied perspective, this approach aims to select the most efficient geometry with given input parameters, which can then be prototyped and used for subsequent in vitro experiments. By proposing this approach, we believe it will replace or complement CAD-FEM-based modeling, thereby accelerating the design process and finding better designs within given constraints. The repository, which contains the essential components of the study, including curated source code, dataset, and trained models, is publicly available at https://github.com/ViacheslavDanilov/generative_design.

Analysis of the Effect of Thickness on the Performance of Polymeric Heart Valves

Polymeric heart valves (PHVs) are a promising and more affordable alternative to mechanical heart valves (MHVs) and bioprosthetic heart valves (BHVs). Materials with good durability and biocompatibility used for PHVs have always been the research focus in the field of prosthetic heart valves for many years, and leaflet thickness is a major design parameter for PHVs. The study aims to discuss the relationship between material properties and valve thickness, provided that the basic functions of PHVs are qualified. The fluid-structure interaction (FSI) approach was employed to obtain a more reliable solution of the effective orifice area (EOA), regurgitant fraction (RF), and stress and strain distribution of the valves with different thicknesses under three materials: Carbothane PC-3585A, xSIBS and SIBS-CNTs. This study demonstrates that the smaller elastic modulus of Carbothane PC-3585A allowed for a thicker valve (>0.3 mm) to be produced, while for materials with an elastic modulus higher than that of xSIBS (2.8 MPa), a thickness less than 0.2 mm would be a good attempt to meet the RF standard. What is more, when the elastic modulus is higher than 23.9 MPa, the thickness of the PHV is recommended to be 0.l-0.15 mm. Reducing the RF is one of the directions of PHV optimization in the future. Reducing the thickness and improving other design parameters are reliable means to reduce the RF for materials with high and low elastic modulus, respectively.

Multiscale model for blood flow after a bileaflet artificial aortic valve implantation

Cardiovascular diseases are the leading cause of mortality in the world, mainly due to atherosclerosis and its consequences. The article presents the numerical model of the blood flow through artificial aortic valve. The overset mesh approach was applied to simulate the valve leaflets motion and to realize the moving mesh, in the aortic arch and the main branches of cardiovascular system. To capture the cardiac system's response and the effect of vessel compliance on the outlet pressure, the lumped parameter model has been also included within the solution procedure. Three different turbulence modeling approaches were used and compared - the laminar, k-ϵ and k-ω model. The simulation results were also compared with the model excluding the moving valve geometry and the importance of the lumped parameter model for the outlet boundary condition was analyzed. Proposed numerical model and protocol was found as suitable for performing the virtual operations on the real patient vasculature geometry. The time-efficient turbulence model and overall solving procedure allows to support the clinicians in making decisions about the patient treatment and to predict the results of the future surgery.

Synergistic Integration of Deep Neural Networks and Finite Element Method with Applications for Biomechanical Analysis of Human Aorta

Motivation: Patient-specific finite element analysis (FEA) has the potential to aid in the prognosis of cardiovascular diseases by providing accurate stress and deformation analysis in various scenarios. It is known that patient-specific FEA is time-consuming and unsuitable for time-sensitive clinical applications. To mitigate this challenge, machine learning (ML) techniques, including deep neural networks (DNNs), have been developed to construct fast FEA surrogates. However, due to the data-driven nature of these ML models, they may not generalize well on new data, leading to unacceptable errors.

Methods

We propose a synergistic integration of DNNs and finite element method (FEM) to overcome each other’s limitations. We demonstrated this novel integrative strategy in forward and inverse problems. For the forward problem, we developed DNNs using state-of-the-art architectures, and DNN outputs were then refined by FEM to ensure accuracy. For the inverse problem of heterogeneous material parameter identification, our method employs a DNN as regularization for the inverse analysis process to avoid erroneous material parameter distribution.

Results

We tested our methods on biomechanical analysis of the human aorta. For the forward problem, the DNN-only models yielded acceptable stress errors in majority of test cases; yet, for some test cases that could be out of the training distribution (OOD), the peak stress errors were larger than 50%. The DNN-FEM integration eliminated the large errors for these OOD cases. Moreover, the DNN-FEM integration was magnitudes faster than the FEM-only approach. For the inverse problem, the FEM-only inverse method led to errors larger than 50%, and our DNN-FEM integration significantly improved performance on the inverse problem with errors less than 1%.