Luan Shengzhi, Morgan Elise F
Department of Mechanical Engineering, Boston University, Boston, MA 02215, USA; Center for Multiscale and Translational Mechanobiology, Boston University, Boston, MA 02215, USA.
Department of Mechanical Engineering, Boston University, Boston, MA 02215, USA; Center for Multiscale and Translational Mechanobiology, Boston University, Boston, MA 02215, USA; Department of Biomedical Engineering, Boston University, Boston, MA 02215, USA.
J Mech Behav Biomed Mater. 2025 Mar;163:106888. doi: 10.1016/j.jmbbm.2025.106888. Epub 2025 Jan 10.
Despite the broad agreement that bone stiffness is heavily dependent on the underlying bone density, there is no consensus on a unified relationship that applies to both cancellous and cortical compartments. Bone from the two compartments is generally assessed separately, and few mechanical test data are available for samples from the transitional regions between them. In this study, we present a data-driven framework integrating experimental testing and numerical modeling of the human lumbar vertebra through an energy balance criterion, to develop a unified density-modulus relationship across the entire vertebral body, without the necessity of differentiation between trabecular and cortical regions. A dataset of 25 spinal segments harvested from fresh-frozen human spines consisting of L1 vertebrae with adjacent intervertebral disks and neighboring T12 and L2 endplates was examined through a systematic process. Each specimen was subjected to axial compression using a custom-designed radiolucent device, and the deformation at multiple points during the ramp was quantified using digital volume correlation applied to the time-lapse series of microcomputed tomography images acquired during loading. A finite element model of each specimen was constructed from quantitative computed tomography images, with the experimental displacement fields imposed to replicate the observed deformation. The optimal density-modulus relationship, both in exponential and polynomial forms, was then determined by using data-driven techniques to match the numerical strain energy with the experimental external work. The resulting relationships effectively recovered bone tissue modulus at the microscale. Subsequently, the unified relationships were applied to investigate the vertebral structure-property correlations at the macroscale: as expected, compressive stiffness exhibited a moderate correlation with bone mineral density, whereas bending stiffness was revealed to correlate strongly with bone mineral content. These findings support the accuracy of the developed density-modulus relationships for the vertebral body and indicate the potential of the proposed framework to extend to other properties of interest such as vertebral strength and toughness.
尽管人们普遍认为骨刚度在很大程度上取决于潜在的骨密度，但对于适用于松质骨和皮质骨部分的统一关系尚无共识。通常分别评估来自这两个部分的骨，并且来自它们之间过渡区域样本的力学测试数据很少。在本研究中，我们提出了一个数据驱动的框架，通过能量平衡准则整合人体腰椎的实验测试和数值建模，以建立整个椎体的统一密度-模量关系，而无需区分小梁骨和皮质骨区域。通过一个系统的过程检查了从新鲜冷冻人体脊柱采集的25个脊柱节段的数据集，该数据集由带有相邻椎间盘以及相邻T12和L2终板的L1椎体组成。每个标本使用定制设计的射线可透过装置进行轴向压缩，并使用数字体积相关技术对加载过程中采集的微计算机断层扫描图像的延时序列应用，来量化斜坡加载期间多个点的变形。根据定量计算机断层扫描图像构建每个标本的有限元模型，并施加实验位移场以复制观察到的变形。然后通过使用数据驱动技术使数值应变能与实验外力功相匹配，确定指数和多项式形式的最佳密度-模量关系。所得关系有效地恢复了微观尺度下的骨组织模量。随后，将统一关系应用于研究宏观尺度下的椎体结构-性能相关性：正如预期的那样，压缩刚度与骨矿物质密度呈中等相关性，而弯曲刚度与骨矿物质含量呈强相关性。这些发现支持了所建立的椎体密度-模量关系的准确性，并表明了所提出框架扩展到其他感兴趣特性（如椎体强度和韧性）的潜力。
