Department of Anatomy and Biomechanics, Karl Landsteiner University of Health Sciences, Austria; Institute of Lightweight Design and Structural Biomechanics, Vienna University of Technology, Austria.
Department of Anatomy and Biomechanics, Karl Landsteiner University of Health Sciences, Austria; Institute of Lightweight Design and Structural Biomechanics, Vienna University of Technology, Austria.
J Mech Behav Biomed Mater. 2024 Feb;150:106259. doi: 10.1016/j.jmbbm.2023.106259. Epub 2023 Nov 18.
The response of bone tissue to mechanical load is complex and includes plastic hardening, viscosity and damage. The quantification of these effects plays a mayor role in bone research and in biomechanical clinical trials as to better understand related diseases. In this study, the damage growth in individual wet human trabeculae subjected to cyclic overloading is quantified by inverse rheological modeling. Therefore, an already published rheological material model, that includes linear elasticity, plasticity and viscosity is extended by a damage law. The model is utilized in an optimization process to identify the corresponding material parameters and damage growth in single human trabeculae under tensile load. Results show that the damage model is leading to a better fit of the test data with an average root-mean-square-error (RMSE) of 2.52 MPa compared to the non-damage model with a RMSE of 3.03 MPa. Although this improvement is not significant, the damage model qualitatively better represents the data as it accounts for the visible stiffness reduction along the load history. It returns realistic stiffness values of 11.92 GPa for the instantaneous modulus and 5.73 GPa for the long term modulus of wet trabecular human bone. Further, the growth of damage in the tissue along the load history is substantial, with values above 0.8 close to failure. The relative loss of stiffness per cycle is in good agreement with comparable literature. Inverse rheological modeling proves to be a valuable tool for quantifying complex constitutive behavior from a single mechanical measurement. The evolution of damage in the tissue can be identified continuously over the load history and separated from other effects.
骨组织对机械载荷的响应是复杂的，包括塑性硬化、粘性和损伤。这些效应的量化在骨研究和生物力学临床试验中起着重要作用，可以更好地理解相关疾病。在这项研究中，通过反流变学建模来量化个体湿人小梁在周期性过载下的损伤增长。因此，扩展了已经发表的流变材料模型，该模型包括线性弹性、塑性和粘性，并增加了损伤定律。该模型用于优化过程中，以确定在拉伸载荷下单个人类小梁的相应材料参数和损伤增长。结果表明，损伤模型导致与测试数据的拟合更好，平均均方根误差（RMSE）为 2.52 MPa，而非损伤模型的 RMSE 为 3.03 MPa。尽管这种改进并不显著，但损伤模型定性上更好地表示了数据，因为它考虑了载荷历史中可见的刚度降低。它返回了湿人小梁骨的瞬时模量为 11.92 GPa 和长期模量为 5.73 GPa 的现实刚度值。此外，组织中损伤沿着载荷历史的增长是实质性的，接近失效时的数值大于 0.8。每个循环的刚度相对损失与可比文献非常吻合。反流变学建模被证明是从单个机械测量中定量复杂本构行为的有用工具。可以在载荷历史上连续识别组织中的损伤演变，并将其与其他效应分开。
