A HOMOGENIZATION SAMPLING PROCEDURE FOR CALCULATING TRABECULAR BONE EFFECTIVE STIFFNESS AND TISSUE-LEVEL STRESS
A HOMOGENIZATION SAMPLING PROCEDURE FOR CALCULATING TRABECULAR BONE EFFECTIVE STIFFNESS AND TISSUE-LEVEL STRESS
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DOI：
10.1016/0021-9290(94)90019-1
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发表时间：
1994-04-01
影响因子：
2.4
通讯作者：
KIKUCHI, N
中科院分区：
文献类型：
--
作者：
HOLLISTER, SJ;BRENNAN, JM;KIKUCHI, N
介绍了一种均匀化抽样程序，该程序允许基于骨小梁结构的精确模型计算有效骨小梁刚度和个体骨小梁水平应力。53个小梁骨标本的三维数字化图像的分辨率为50微米，每个体素直接转换成三维有限元网格，使每个体素的8节点等参砖元素。针对8000个单元的大网格，编写了逐单元预处理共轭梯度法（EBEPCG）程序，求解局部均匀化有限元方程。预测的有效刚度测量与实验结果相关良好（R2 > 0.73）。预测的有效刚度往往低估了实验值。有效刚度估计值的平均绝对误差范围为31%至38%之间的抽样程序相比，范围为49%至150%的回归拟合体积分数的平方。骨小梁水平应力的范围为-200和+300倍，预测通过分析骨小梁作为一个连续体。组织的拉伸和压缩应力都是由连续的压缩应力引起的。小梁水平应变能密度（SED）范围为0和100倍的连续SED值的两个小梁标本。总之，均匀化取样程序一致地预测了骨小梁结构对有效刚度的影响。它还可以提供骨小梁组织应力和应变估计的任意全球负载的整个骨骼。组织应力和应变表现出较大的变化相比，相应的连续水平的数量。
A homogenization sampling procedure is introduced which allows computation of effective trabecular bone stiffness and individual trabecula level stress based on precise models of trabecular bone architecture. Three-dimensional digitized images of 53 trabecular bone specimens with a resolution of 50 mum per voxel were directly converted into three-dimensional finite element meshes by making each voxel an 8-node isoparametric brick element. Owing to the large mesh of 8000 elements, an element-by-element preconditioned conjugate gradient (EBEPCG) program was written to solve the local homogenization finite element equations. Predicted effective stiffness measures correlated well with experimental results (R2 > 0.73). The predicted effective stiffnesses tended to under estimate the experimental values. Average absolute errors in effective stiffness estimates ranged between 31 and 38% for the sampling procedure compared to a range 49-150% for a regression fit to volume fraction squared. Trabecula level stress ranged between - 200 and + 300 times that predicted by analyzing trabecular bone as a continuum. Both tensile and compressive tissue stresses were engendered by a continuum compressive stress. Trabecula level strain energy density (SED) ranged between 0 and 100 times the continuum SED value for two trabecular specimens. In conclusion, the homogenization sampling procedure consistently predicted the influence of trabecular bone architecture on effective stiffness. It can also provide trabecular tissue stress and strain estimates for arbitrary global loading of whole bones. Tissue stresses and strains showed large variations compared to corresponding continuum level quantities.