Department of Applied Physics, University of Eastern Finland, Kuopio, Finland.
Department of Applied Physics, University of Eastern Finland, Kuopio, Finland.
J Biomech. 2021 Jan 4;114:110141. doi: 10.1016/j.jbiomech.2020.110141. Epub 2020 Nov 22.
Computational models of the knee joint are useful for evaluating stresses and strains within the joint tissues. However, the outcome of those models is sensitive to the material model and material properties chosen for ligaments, the collagen reinforced tissues connecting bone to bone. The purpose of this study was to investigate different compositionally motivated material models and further to develop a model that can accurately reproduce experimentally measured stress-relaxation data of bovine anterior cruciate ligament (ACL). Tensile testing samples were extracted from ACLs of bovine knee joints (N = 10) and subjected to a three-step stress-relaxation test at the toe region. Data from the experiments was averaged and one average finite element model was generated to replicate the experiment. Poroelastic and different fibril-reinforced poro(visco)elastic material models were applied, and their material parameters were optimized to reproduce the experimental force-time response. Material models with only fluid flow mediated relaxation were not able to capture the stress-relaxation behavior (R = 0.806, 0.803 and 0.938). The inclusion of the viscoelasticity of the fibrillar network improved the model prediction (R = 0.978 and 0.976), but the complex stress-relaxation behavior was best captured by a poroelastic model with a nonlinear two-relaxation-time strain-recruited viscoelastic fibrillar network (R = 0.997). The results suggest that in order to replicate the multi-step stress-relaxation behavior of ACL in tension, the fibrillar network formulation should include the complex nonlinear viscoelastic phenomena.
膝关节的计算模型可用于评估关节组织内的应力和应变。然而，这些模型的结果对用于连接骨骼的韧带（胶原增强组织）的材料模型和材料特性很敏感。本研究的目的是研究不同组成性的材料模型，并进一步开发一种能够准确再现牛前交叉韧带（ACL）实验测量的应力松弛数据的模型。从牛膝关节的 ACL 中提取拉伸测试样本（N = 10），并在前跟区域进行三步应力松弛测试。对实验数据进行平均，并生成一个平均有限元模型以复制实验。应用了多孔弹性和不同纤维增强多孔（粘弹）弹性材料模型，并优化了它们的材料参数以再现实验的力-时响应。仅通过流体流动介导松弛的材料模型无法捕捉到应力松弛行为（R = 0.806、0.803 和 0.938）。纤维网络粘弹性的包含提高了模型预测（R = 0.978 和 0.976），但通过具有非线性双松弛时间应变募集粘弹性纤维网络的多孔弹性模型可以最佳地捕捉复杂的应力松弛行为（R = 0.997）。结果表明，为了复制 ACL 在拉伸中的多步应力松弛行为，纤维网络配方应包括复杂的非线性粘弹性现象。
