Lowet G, Dayuan X, Van der Perre G
Division of Biomechanics and Engineering Design, K.U. Leuven, Heverlee, Belgium.
J Biomech. 1996 Aug;29(8):1003-10. doi: 10.1016/0021-9290(96)00002-4.
Two finite element models of a fractured tibia with healing callus were developed. In the first model, the callus was modelled at the middle of the diaphysis, while in the second one the callus was located at two-thirds of the length, distal from the knee. From these two models the static torsional stiffness as well as the resonant frequencies and mode shapes of the first four vibration modes were calculated for a series of increasing values of Young's modulus of the callus. Two situations were considered. In the first situation, the geometry of the callus was kept constant, while in the second, the dimensions of the callus were reduced while its Young's modulus was increased. The resonant frequencies were found to increase with increasing stiffness of the callus. The single bending modes were found to be more sensitive when the callus was at the middle of the diaphysis, whereas the double bending modes were more sensitive when the callus was situated distally. Mode shapes were similar to those for the intact tibia when the stiffness of the callus was 5% of the stiffness of the intact bone or higher. A basically linear relation was found between the torsional stiffness and the resonant frequencies. A theoretical relation between resonant frequencies and torsional stiffness was evaluated and found to be valid if the Young's modulus of the callus was equal to or greater than 5% of the Young's modulus of the intact bone. The present results support the quantitative interpretation of vibration analysis measurements for the assessment of tibial fracture healing.
建立了两个带有愈合骨痂的胫骨骨折有限元模型。在第一个模型中，骨痂建模于骨干中部，而在第二个模型中，骨痂位于距膝关节远端三分之二处。从这两个模型中，针对骨痂杨氏模量的一系列递增数值，计算了静态扭转刚度以及前四种振动模式的共振频率和振型。考虑了两种情况。在第一种情况下，骨痂的几何形状保持不变，而在第二种情况下，骨痂尺寸减小，同时其杨氏模量增加。发现共振频率随骨痂刚度的增加而增加。当骨痂位于骨干中部时，单弯曲模式更敏感，而当骨痂位于远端时，双弯曲模式更敏感。当骨痂刚度为完整骨刚度的5%或更高时，振型与完整胫骨的振型相似。发现扭转刚度与共振频率之间存在基本的线性关系。评估了共振频率与扭转刚度之间的理论关系，发现当骨痂的杨氏模量等于或大于完整骨杨氏模量的5%时该关系有效。目前的结果支持对振动分析测量进行定量解释以评估胫骨骨折愈合情况。
