Institute for Biomechanics, ETH Zürich, Zürich, Switzerland.
Med Eng Phys. 2011 Oct;33(8):993-1000. doi: 10.1016/j.medengphy.2011.03.012. Epub 2011 Apr 30.
The smallest functional unit of cancellous bone is the single trabecula. To investigate its influence at the macroscopic level, a mechanical characterization is required. The aim of this work is to present a new procedure for measuring the elastic behavior of a single trabecula, assumed as an isotropic material, by means of a bending protocol. Our experimental setup permits the measurement of the bending force and deflection of a single trabecula within the natural network. The exact geometry of the trabecula is attained by using a laser scanning microscopy of the labeled sample and subsequently using it as the input for FE simulation. The results between the FE analysis and experimental data are compared in order to determine an isotropic elastic modulus of the trabecula. The system uncertainty has been estimated using the propagation of uncertainty method based on the analytical bending function for a fixed beam. Variables are force, deflection, radius and length and their relative uncertainties. It results in a total uncertainty of 13%, dominated by the influence of radius uncertainty, which is related to the exact determination of the real geometry of the trabecula. The system has been subsequently validated using samples with known geometry and elastic modulus. Finally, the proposed new method consists of sample preparation, a newly designed sample positioning system, an experimental bending test on a single trabecula within the trabecular network, labeling of the bone with a fluorescent marker, 3D imaging of the trabecula and FE analysis of the bending test.
松质骨的最小功能单位是单个小梁。为了研究其在宏观水平上的影响，需要进行力学特性表征。本工作的目的是提出一种新的方法，通过弯曲实验来测量单个小梁（假设为各向同性材料）的弹性行为。我们的实验装置允许在天然网络内测量单个小梁的弯曲力和挠度。通过对标记样本进行激光扫描显微镜测量，获得小梁的确切几何形状，并随后将其用作有限元模拟的输入。将有限元分析和实验数据之间的结果进行比较，以确定小梁的各向同性弹性模量。使用基于固定梁的解析弯曲函数的不确定度传播方法来估计系统不确定度。变量为力、挠度、半径和长度及其相对不确定度。结果表明，系统不确定度为 13%，主要由半径不确定度的影响决定，这与小梁真实几何形状的精确确定有关。该系统随后使用具有已知几何形状和弹性模量的样本进行了验证。最后，提出的新方法包括样品制备、新设计的样品定位系统、在小梁网络内对单个小梁进行弯曲实验、用荧光标记物标记骨骼、小梁的 3D 成像和弯曲实验的有限元分析。
