Mizrahi J, Silva M J, Keaveny T M, Edwards W T, Hayes W C
Department of Orthopaedic Surgery, Charles A. Dana Research Institute, Beth Israel Hospital, Boston, Massachusetts.
Spine (Phila Pa 1976). 1993 Oct 15;18(14):2088-96. doi: 10.1097/00007632-199310001-00028.
A finite-element model of an isolated elderly human L3 vertebral body was developed to study how material properties and loading conditions influence end-plate and cortical-shell displacements and stresses. The model consisted of an idealized geometric representation of an isolated vertebral body, with a 1-mm-thick end plate and cortical shell. For uniform compression, large tensile stresses occurred all around the cortical shell just below the end plate as a result of bending of the cortical shell as it supported the end plate. Large tensile bending stresses also developed in the inferior surface of the end plate. Equal reductions in both trabecular and cortical bone moduli increased displacements but did not affect peak stresses. A 50% reduction in trabecular bone modulus alone increased peak stresses in the end plate by 74%. Elimination of the cortical shell reduced peak stresses in the end plate by approximately 20%. For nonuniform, anteriorly eccentric compression, peak stresses everywhere changed by less than 11% but moved to the anterior aspect. When material properties were adjusted to represent osteoporosis with disproportionate reductions in trabecular (50% decrease) and cortical (25% decrease) bone moduli, anterior compression increased peak stresses by up to 250% compared to uniform compression. If fractures are initiated in regions of large tensile stresses, the results from this relatively simple model may explain how central end-plate and transverse fractures initiate from uniform compression of the end plate. Furthermore, for anterior compression, disproportionate modulus reductions in trabecular and cortical bone may substantially increase end plate and cortical shell stresses, suggesting a cause of age-related spine fractures.
建立了一个孤立的老年人体L3椎体的有限元模型，以研究材料特性和加载条件如何影响终板和皮质骨壳的位移及应力。该模型由一个孤立椎体的理想化几何表示组成，有一个1毫米厚的终板和皮质骨壳。对于均匀压缩，由于皮质骨壳在支撑终板时发生弯曲，终板下方的皮质骨壳周围会出现较大的拉应力。终板下表面也会产生较大的拉伸弯曲应力。小梁骨和皮质骨模量同等程度降低会增加位移，但不影响峰值应力。仅小梁骨模量降低50%会使终板的峰值应力增加74%。去除皮质骨壳会使终板的峰值应力降低约20%。对于非均匀的前侧偏心压缩，各处的峰值应力变化小于11%，但会移至前侧。当调整材料特性以代表骨质疏松症，小梁骨模量（降低50%）和皮质骨模量（降低25%）不成比例地降低时，与均匀压缩相比，前侧压缩会使峰值应力增加高达250%。如果骨折始于大拉应力区域，这个相对简单的模型结果可能解释了终板中央骨折和横向骨折如何由终板的均匀压缩引发。此外，对于前侧压缩，小梁骨和皮质骨模量不成比例地降低可能会大幅增加终板和皮质骨壳的应力，这表明了与年龄相关的脊柱骨折的一个原因。
