Department of Mechanical Engineering, University of Texas at San Antonio, San Antonio, TX, 78249, USA.
Department of Management Science and Statistics, University of Texas at San Antonio, San Antonio, TX, 78249, USA.
J Mech Behav Biomed Mater. 2022 Jul;131:105254. doi: 10.1016/j.jmbbm.2022.105254. Epub 2022 May 4.
Trabecular bone is a random cellular solid with an interconnected network of plate-like and rod-like components. However, the structural randomness and complexity have hindered rigorous mathematical modeling of trabecular bone microarchitecture. Recent advancements in imaging processing techniques have enabled us to define the size, orientation, and spatial location of individual trabecular plates and rods in trabecular bone. Based on the essential information, this study proposed a probability-based approach to define the size, orientation, and spatial distributions of trabecular plates and rods for trabecular bone cubes (N = 547) acquired from six human cadaver proximal femurs. Using two groups of probability-based parameters, it was attempted to capture microarchitectural details, which could not be captured by the existing histomorphometric parameters, but crucial to the elastic properties of trabecular bone. The elastic properties of the trabecular bone cubes in three principal axes were estimated using microCT based finite element (FE) simulations. Based on the results of multivariate multiple regression modeling, the efficacy of the two groups of probability-based parameters in prediction of the elastic properties was verified in comparison with that of the existing histomorphometric parameters (BV/TV, Tb.Th, Tb.Sp, DA, EF.Med, and Conn.D). The results indicated that the regression models trained using the probability-based parameters had a comparable and even better accuracy (rMSE = 0.621 and 0.548) than that of the histomorphometric parameters (rMSE = 0.647). More importantly, the probability-based parameters could provide more insights into some unexplored microarchitectural features, such as individual trabecular size, orientation, and spatial distributions, which are also critical to the elastic properties of trabecular bone.
小梁骨是一种具有板状和杆状成分相互连接网络的随机多孔固体。然而，结构的随机性和复杂性阻碍了对小梁骨微观结构的严格数学建模。最近成像处理技术的进步使我们能够定义小梁骨中单个小梁板和小梁杆的大小、方向和空间位置。基于这些基本信息，本研究提出了一种基于概率的方法来定义小梁骨立方体（来自 6 个人体尸骸股骨近端）中小梁板和小梁杆的大小、方向和空间分布。使用两组基于概率的参数，尝试捕捉微观结构细节，这些细节无法通过现有的组织形态计量学参数来捕捉，但对小梁骨的弹性性质至关重要。使用基于微 CT 的有限元（FE）模拟估计小梁骨立方体在三个主轴上的弹性性质。基于多元多回归建模的结果，与现有的组织形态计量学参数（BV/TV、Tb.Th、Tb.Sp、DA、EF.Med 和 Conn.D）相比，验证了两组基于概率的参数在预测弹性性质方面的有效性。结果表明，使用基于概率的参数训练的回归模型具有相当甚至更好的准确性（rMSE=0.621 和 0.548），而不是现有的组织形态计量学参数（rMSE=0.647）。更重要的是，基于概率的参数可以提供更多关于一些未探索的微观结构特征的见解，例如单个小梁的大小、方向和空间分布，这些特征对小梁骨的弹性性质也至关重要。
