几何与材料参数逆向辨识的全可微框架及其在软组织无应力构型确定中的应用
Fully differentiable framework for inverse identification of geometry and material parameters with application to determining stress-free configuration of soft tissues
- Purdue University（普渡大学）
- Columbia University（哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对软组织图像反映承载状态而非无应力状态的问题，提出全可微逆向有限元框架，联合重建无应力几何并估计超弹性参数，实验验证其鲁棒性和准确性，适用于个性化建模等。
AI中文摘要：
软组织医学图像通常描绘的是承载状态而非真实的无载荷（无应力）状态，这可能使生物力学模拟和逆向材料辨识产生偏差。本文提出了一种基于梯度的逆向有限元框架，该框架可从两个或多个观测到的变形构型中联合重建有效的无载荷参考几何，并估计超弹性材料参数。该公式完全可微，利用端到端的精确梯度实现几何与本构参数的统一同步优化。目标函数结合了节点位置失配项与基于变形梯度的失配项，从而在大变形条件下增强了鲁棒性。基准研究量化了载荷多样性和观测次数的影响，并展示了对较差材料初始化的敏感性降低。最后，应用于基于MRI的乳腺模型，展示了从多个重力加载状态下准确恢复无载荷构型和本构参数的能力。该框架为逆向生物力学提供了一种统一且可扩展的工具，在个性化建模、弹性成像和手术规划中具有潜在应用价值。
英文摘要：
Medical images of soft tissues typically depict loaded configurations rather than true unloaded (stress-free) states, which can bias biomechanical simulations and inverse material identification. A gradient-based inverse finite element framework is presented that jointly reconstructs an effective unloaded reference geometry and estimates hyperelastic material parameters from two or more observed deformed configurations. The formulation is fully differentiable and leverages exact end-to-end gradients to enable unified, simultaneous optimization of geometry and constitutive parameters. The objective function combines a nodal-position misfit with a deformation-gradient-based mismatch term, improving robustness under large deformations. Benchmark studies quantify the influence of loading diversity and observation count and demonstrate reduced sensitivity to poor material initialization. Finally, application to an MRI-derived breast model shows accurate recovery of the unloaded configuration and constitutive parameters from multiple gravity-loaded states. The framework provides a unified and scalable tool for inverse biomechanics with potential applications in personalized modeling, elastography, and surgical planning.
