Department of Biomedical Engineering, University of Arizona College of Engineering, Tucson, AZ, United States.
Department of Biomedical Engineering, University of Arizona College of Engineering, Tucson, AZ, United States; Department of Aerospace and Mechanical Engineering, University of Arizona College of Engineering, Tucson, AZ, United States.
Acta Biomater. 2023 Jan 1;155:400-409. doi: 10.1016/j.actbio.2022.11.024. Epub 2022 Nov 17.
Elasticity imaging is a technique that discovers the spatial distribution of mechanical properties of tissue using deformation and force measurements under various loading conditions. Given the complexity of this discovery, most existing methods approximate only one material parameter while assuming homogeneous distributions for the others. We employ physics-informed neural networks (PINN) in linear elasticity problems to discover the space-dependent distribution of both elastic modulus (E) and Poisson's ratio (ν) simultaneously, using strain data, normal stress boundary conditions, and the governing physics. We validated our model on three examples. First, we experimentally loaded hydrogel samples with embedded stiff inclusions, representing tumorous tissue, and compared the approximations against ground truth determined through tensile tests. Next, using data from finite element simulation of a rectangular domain containing a stiff circular inclusion, the PINN model accurately localized the inclusion and estimated both E and ν. We observed that in a heterogeneous domain, assuming a homogeneous ν distribution increases estimation error for stiffness as well as the area of the stiff inclusion, which could have clinical importance when determining size and stiffness of tumorous tissue. Finally, our model accurately captured spatial distribution of mechanical properties and the tissue interfaces on data from another computational model, simulating uniaxial loading of a rectangular hydrogel sample containing a human brain slice with distinct gray matter and white matter regions and complex geometrical features. This elasticity imaging implementation has the potential to be used in clinical imaging scenarios to reliably discover the spatial distribution of mechanical parameters and identify material interfaces such as tumors. STATEMENT OF SIGNIFICANCE: Our work is the first implementation of physics-informed neural networks to reconstruct both material parameters - Young's modulus and Poisson's ratio - and stress distributions for isotropic linear elastic materials by having deformation and force measurements. We comprehensively validate our model using experimental measurements and synthetic data generated using finite element modeling. Our method can be implemented in clinical elasticity imaging scenarios to improve diagnosis of tumors and for mechanical characterization of biomaterials and biological tissues in a minimally invasive manner.
弹性成像是一种利用变形和在各种加载条件下的力测量来发现组织力学特性的空间分布的技术。考虑到这一发现的复杂性，大多数现有的方法仅近似一个材料参数，而其他参数则假设为均匀分布。我们在线性弹性问题中使用基于物理的神经网络（PINN），使用应变数据、法向应力边界条件和控制物理来同时发现弹性模量 (E) 和泊松比 (ν) 的空间相关分布。我们在三个示例中验证了我们的模型。首先，我们通过实验对嵌入硬嵌体的水凝胶样本进行加载，代表肿瘤组织，并将近似值与通过拉伸试验确定的真实值进行比较。接下来，使用包含硬圆形嵌体的矩形域有限元模拟数据，PINN 模型准确地定位了嵌体并估计了 E 和 ν。我们观察到，在非均匀域中，假设均匀的 ν 分布会增加对刚度以及硬嵌体区域的估计误差，这在确定肿瘤组织的大小和刚度时可能具有临床意义。最后，我们的模型在另一个计算模型的数据上准确地捕捉了力学性质的空间分布和组织界面，该模型模拟了含有灰质和白质区域以及复杂几何特征的人脑切片的矩形水凝胶样本的单轴加载。这种弹性成像的实现有可能用于临床成像场景，以可靠地发现力学参数的空间分布并识别肿瘤等材料界面。
我们的工作是第一个实施基于物理的神经网络的工作，通过变形和力测量，重建各向同性线性弹性材料的材料参数 - 杨氏模量和泊松比 - 以及应力分布。我们使用实验测量和使用有限元建模生成的合成数据全面验证了我们的模型。我们的方法可以在临床弹性成像场景中实施，以改善肿瘤的诊断，并以微创的方式对生物材料和生物组织进行机械特性表征。
