Goel V K, Ramirez S A, Kong W, Gilbertson L G
Iowa Spine Research Center, Department of Biomedical Engineering, College of Engineering, University of Iowa, Iowa City 52242, USA.
J Biomech Eng. 1995 Aug;117(3):266-71. doi: 10.1115/1.2794180.
Bone remodeling theory based on strain energy density (SED) as the feedback control variable was used in conjunction with the finite element method to analyze the shape of the vertebral bodies within the ligamentous motion segment. The remodeling theory was once again applied to the altered two motion segments model to predict the Young's modulus distribution of the cancellous bone within the vertebral bodies. A three-dimensional finite element model of the two motion segments ligamentous lumbar spine (L3-5) was developed. Bone remodeling response (external as well as internal) of the motion segments to a uniaxial compressive load of 424.7 N was studied. The external shape of the converged model matched the normal shape of a vertebral body. The internal remodeling resulted in regional cancellous bone Young's moduli (or bone density) distributions similar to those reported in the literature; posterocentral regions of the vertebrae were predicted to have greater values of the elastic modulus than that of the outer regions. The results of the present study suggest that vertebral body assumes an adequate/optimum structure in terms of both its shape and its elastic moduli distribution within the cancellous region in response to the applied load. Extensions of the present model and its clinically relevant applications are discussed.
基于应变能密度（SED）作为反馈控制变量的骨重塑理论与有限元方法相结合，用于分析韧带运动节段内椎体的形状。该重塑理论再次应用于改变后的双运动节段模型，以预测椎体内松质骨的杨氏模量分布。建立了双运动节段韧带腰椎（L3 - 5）的三维有限元模型。研究了运动节段对424.7 N单轴压缩载荷的骨重塑反应（外部和内部）。收敛模型的外部形状与椎体的正常形状相符。内部重塑导致区域松质骨杨氏模量（或骨密度）分布与文献报道相似；预计椎体后中央区域的弹性模量值高于外部区域。本研究结果表明，椎体在形状及其松质骨区域内的弹性模量分布方面，会根据施加的载荷呈现出适当/最佳的结构。讨论了本模型的扩展及其临床相关应用。
