Wu Wensi, Daneker Mitchell, Turner Kevin T, Jolley Matthew A, Lu Lu
Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, PA 19104.
Division of Cardiology, Children's Hospital of Philadelphia, Philadelphia, PA 19104.
ArXiv. 2024 Jul 18:arXiv:2402.10741v3.
The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying full-field heterogeneous elastic properties of soft materials using traditional engineering approaches is fundamentally challenging due to difficulties in estimating local stress fields. Recently, there has been a growing interest in using data-driven models to learn full-field mechanical responses such as displacement and strain from experimental or synthetic data. However, research studies on inferring full-field elastic properties of materials, a more challenging problem, are scarce, particularly for large deformation, hyperelastic materials. Here, we propose a physics-informed machine learning approach to identify the elasticity map in nonlinear, large deformation hyperelastic materials. We evaluate the prediction accuracies and computational efficiency of physics-informed neural networks (PINNs) by inferring the heterogeneous elasticity maps across three materials with structural complexity that closely resemble real tissue patterns, such as brain tissue and tricuspid valve tissue. We further applied our improved architecture to three additional examples of breast cancer tissue and extended our analysis to three hyperelastic constitutive models: Neo-Hookean, Mooney Rivlin, and Gent. Our selected network architecture consistently produced highly accurate estimations of heterogeneous elasticity maps, even when there was up to 10% noise present in the training data.
生物组织的非均匀微观力学特性在不同的医学和工程领域具有深远影响。然而，使用传统工程方法识别软材料的全场非均匀弹性特性从根本上来说具有挑战性，因为估计局部应力场存在困难。最近，人们越来越关注使用数据驱动模型从实验或合成数据中学习全场力学响应，如位移和应变。然而，关于推断材料全场弹性特性这一更具挑战性问题的研究却很少，特别是对于大变形的超弹性材料。在此，我们提出一种基于物理知识的机器学习方法来识别非线性、大变形超弹性材料中的弹性图谱。我们通过推断三种具有与真实组织模式（如脑组织和三尖瓣组织）紧密相似结构复杂性的材料的非均匀弹性图谱，评估了基于物理知识的神经网络（PINNs）的预测准确性和计算效率。我们进一步将改进后的架构应用于乳腺癌组织的另外三个示例，并将分析扩展到三种超弹性本构模型：新胡克模型、穆尼 - 里夫林模型和根特模型。我们所选的网络架构始终能对非均匀弹性图谱产生高度准确的估计，即使训练数据中存在高达10%的噪声。
