An Integrated DNN-FEA Approach for Inverse Identification of Passive, Heterogeneous Material Parameters of Left Ventricular Myocardium

Zhuofan Li¹, Daniel H. Pak², James S. Duncan², Liang Liang³, Minliang Liu^1,*
1 Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA
2 Department of Biomedical Engineering, Yale University, New Haven, CT 06520, USA
3 Department of Computer Science, University of Miami, Coral Gables, FL 33146, USA
* Corresponding Author: Minliang Liu. Email: email
(This article belongs to the Special Issue: Machine Learning Based Computational Mechanics)

Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2025.073757

Received 25 September 2025; Accepted 29 December 2025; Published online 14 January 2026

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Abstract

Patient-specific finite element analysis (FEA) is a promising tool for noninvasive quantification of cardiac and vascular structural mechanics in vivo. However, inverse material property identification using FEA, which requires iteratively solving nonlinear hyperelasticity problems, is computationally expensive which limits the ability to provide timely patient-specific insights to clinicians. In this study, we present an inverse material parameter identification strategy that integrates deep neural networks (DNNs) with FEA, namely inverse DNN-FEA. In this framework, a DNN encodes the spatial distribution of material parameters and effectively regularizes the inverse solution, which aims to reduce susceptibility to local optima that often arise in heterogeneous nonlinear hyperelastic problems. Consequently, inverse DNN-FEA enables identification of material parameters at the element level. For validation, we applied DNN-FEA to identify four spatially varying passive Holzapfel-Ogden material parameters of the left ventricular myocardium in synthetic benchmark cases with a clinically-derived geometry. To evaluate the benefit of DNN integration, a baseline FEA-only solver implemented in PyTorch was used for comparison. Results demonstrated that DNN-FEA achieved substantially lower average errors in parameter identification compared to FEA (case 1, DNN-FEA: 0.37%~2.15% vs. FEA: 2.64%~12.91%). The results also demonstrate that the same DNN architecture is capable of identifying a different spatial material property distribution (case 2, DNN-FEA: 0.03%~0.60% vs. FEA: 0.93%~16.25%). These findings suggest that DNN-FEA provides an accurate framework for inverse identification of heterogeneous myocardial material properties. This approach may facilitate future applications in patient-specific modeling based on in vivo clinical imaging and could be extended to other biomechanical simulation problems.