股骨近端结构形态对其强度影响的生物力学数值仿真研究
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摘要
股骨作为支撑上半身体重、连接躯干与下半身、完成行走步态的最重要骨骼，其发生骨折的几率是相当大的，尤其是在患有骨质疏松症的老龄人群中。在医疗条件飞速发展的今天，人们已经不满足于单纯地提高医疗技术来治疗骨折。更多人开始寻找影响骨折风险的因素，制定预防措施来阻止可能会发生的骨折。能够影响骨折风险最重要的因素是骨结构的力学性能及其形态特征。然而在体骨骼的力学性能无法通过力学实验测试得到。逆向工程技术和非线性有限元分析技术恰好可以解决这个问题。对此，本研究建立了一套新的方法测量股骨近端三维形态参数，然后对股骨近端进行有限元分析模拟骨的损伤过程。对股骨近端三维形态参数和预测的骨强度进行统计分析，研究三维形态参数对股骨近端强度的影响。另外，本研究借助Micro-CT影像技术和显微有限元方法，对股骨头内部松质骨的力学性能进行预测，在细观水平上研究股骨近端骨折的发生机制。本研究主要可以分为以下三个部分：
第一部分建立了股骨近端三维形态参数的测量方法。应用此方法测量了50名66-75岁健康男性的股骨近端三维形态参数，并且分析了形态参数之间的内在联系，以及年龄对形态参数的影响。首先利用逆向工程软件MIMICS根据QCT影像重建出股骨近端三维模型。然后在快速成型制造软件MAGICS中对股骨近端模型进行旋转与平移来统一体位。在统一体位后的股骨模型上进行切割获取模型的特征点坐标，导入我们自行研发的股骨近端三维形态参数测量程序中进行计算，得出8个股骨近端三维形态参数，分别是股骨头直径（HD）、股骨头的高（HH）、偏心距（OFF）、颈干角（NSA）、股骨头中心到大转子顶点高度差（TRH）、股骨干的厚度（TOF）、股骨颈直径（ND）、股骨颈的长（NL）。随机选取5例样本制造出实体模型进行手工测量三维形态参数，并与计算机辅助测量的参数进行配对T检验以验证我们制定的算法的可靠性。将三维模型投影到冠状面上模拟X射线平片并且测量股骨近端平面形态参数。对两种形态参数进行配对T检验分析两种测量方法的差异。将测量的三维形态参数按年龄段划分为两个组（66-70岁为A组，71-75岁为B组），分析股骨近端形态参数随着年龄增长的变化趋势。结果显示：（1）手工测量方法和计算机辅助测量方法之间没有显著性差异，说明我们制定的股骨近端三维形态参数测量方法是可靠的。（2）ND、NSA、TRH三个参数在平面和三维两种测量方式下表现出显著差异，说明平面参数的误差较大。（3）除TOF外，BMD与其他形态参数均不显著相关，说明单独依靠BMD预测骨折风险是不准确的。（4）HD、ND、NL在两个年龄段之间具有显著性差异。
第二部分在测量过形态参数的股骨模型中随机选取14例（A组7例，B组7例）进行有限元分析预测其强度。复杂的骨材料属性以及屈服和断裂准则在UMAT子程序中编写代码来实现。由于骨是一种非均匀的拉、压不对称材料，因此在每个载荷增量加载之前需要判断每个单元的拉、压状态及损伤程度，并赋予对应的屈服准则和断裂准则。在股骨头的顶端建立简易压头模型保证载荷能够均匀施加在股骨头表面。在压头顶端施加竖直向下5mm位移边界条件进行计算。结果显示预测的股骨近端损伤过程与实验数据是吻合的。股骨近端强度与股骨近端三维形态参数中的TRH、NSA、TOF显著相关（P<0.05）。A组受试者股骨近端强度与B组受试者股骨近端强度未显示出显著性差异。
第三部分在细观水平上借助Micro-CT影像技术和显微有限元分析技术预测股骨近端骨折患者的股骨头内部松质骨强度，以及分析骨小梁三维形态特征对松质骨力学性能的影响。选取7例股骨近端骨折患者进行全髋关节置换术后取下的股骨头作为实验样本，进行micro-CT扫描并重建出股骨头模型。将每个股骨头模型依照骨小梁的主要生长方向及区域特征划分为3个区域12个子区域。在每个子区域提取出一个125mm3的立方体骨块。测量骨块的骨小梁形态参数，包括骨小梁分离度（Tb.Sp）、骨小梁厚度（Tb.Th）、骨体积分数（BV/TV）、骨表面积密度（BS/BV）、结构模型指数（SMI）、各向异性度（DA）。对不同区域的骨小梁形态参数进行二独立样本非参数检验，分析骨小梁形态参数的区域差异。对每一个骨块分别沿三个正交方向模拟压缩工况进行有限元分析。计算每个骨块沿三个正交方向的表观弹性模量和骨块内部平均应力。结果显示骨块沿主要受力方向表现出的力学性能显著优于其他两个非主要受力方向，两个非主要受力方向的力学性能没有显著性差异。松质骨沿主要受力方向计算出的力学参数显示出显著的区域差异性，其中外侧区域的力学参数显著高于中间区域和内侧区域。
本研究改进了股骨近端形态参数的测量方法和股骨近端的损伤算法，在宏观和细观两方面阐述了结构形态特征对骨强度的影响作用。为临床工作者尽早发现骨折风险，预防骨折的发生提供更为直观的依据。
Femur, as the most important bone of bearing the weight of upper body andforming gait process, is susceptible to fracture, especially for theelderly people with serious osteoporosis. With the rapid development ofmedical standards, people are not satisfied with curing the fracture onlydepending on the improvement of medical technology. More and more peoplestarted to investigate the factors which can affect the fracture risk andspecified precautions to prevent fractures. Mechanical properties andmorphological features of bones are two most important factors that affectthe fracture risk. However, in vivo mechanical experiments for livingskeleton could not be performed by mechanical test machine. This problemcan be solved by incorporating reverse engineering technology withnon-linear finite element analysis technology. Accordingly, in this studya suite of new measurement of3D proximal femoral morphological parameterswas established and the damage processes of proximal femurs were simulatedwith finite element analysis. Statistical analyses were performed on theproximal femoral morphological parameters and femoral strengths toanalyze the effect of3D morphological parameters on proximal femoralstrengths. In addition, mechanical properties of trabecular bone insidethe femoral heads were investigated by combining micro-CT imagingtechnology with micro-finite element method. The fracture mechanism ofproximal femur was studied at the tissue level. This study was mainlycomposed of three sections:
In section one, the method of measuring3D proximal femoral morphologicalparameters was established.51healthy elderly males with the age rangeof66-75were measured with this method, and the effects of age on themorphological parameters were analyzed. First,3D proximal femoral models were reconstructed from QCT images using reverse engineering softwareMIMICS. Models were performed a series of translation and rotation tounify the positions in rapid prototype software MAGICS. Coordinates offeature points were obtained from the surface and interior of the models.
In section two, finite element analyses were performed on14randomlyselected proximal femoral models (7samples from group A and7samplesfrom group B) to predict the proximal femoral strength. Complex bonematerial properties, yield criterion and fracture criterion were compiledin UMAT subroutines. As bone was a kind of inhomogeneous and asymmetricalmaterial in tension and compression, at the beginning of each loadincrement, the corresponding yield criterion and fracture criterion weregiven to each element after judging the damage degree and tension orcompression status. A simple load cap was established to make sure thatthe load could be applied to the surface of femoral head uniformly.5mmvertically downward displacement was exerted on the top of the cap.Results revealed that the predicted damage process of proximal femur wasconsistent with experimental data. The predicted strength of proximalfemur significantly related to the morphological parameters TRH, NSA andTOF (P<0.05). There were no statistical difference in strengths betweengroup A and group B.
In section three, the strength of cancellous bone inside femoral headsfrom proximal femoral fracture patients were analyzed using micro-CTimaging technology in combination with micro-finite element analysis atthe tissue level, as well as the effects of3D trabecular morphologicalfeatures on the trabecular mechanical properties.7femoral heads fromproximal femoral fracture patients were performed micro-CT scanning toreconstruct the femoral head models. Every femoral head models weredivided into3regions and12sub-regions according to the trabecularorientations. One125mm3trabecular cube was extracted from eachsub-region.6trabecular morphological parameters were measured on each cube including trabecular separation (Tb.Sp), trabecular thickness(Tb.Th), bone volume friction (BV/TV), specific area density (BS/BV),structural model index (SMI) and degree of anisotropy (DA). Twoindependent samples tests were performed on trabecular morphologicalparameters from different regions to analyze regional differences oftrabecular morphological parameters. Finite element analyses wereperformed on each cube along three orthogonal directions, respectively.The apparent Young’s modulus and average von Mises stress were calculatedon each cube along three orthogonal directions. The results showed thatthe mechanical properties along the principal loading direction were muchbetter than the other two non-principal loading directions. There was nosignificant difference between two non-major loading directions. Therewere significant differences in mechanical parameters of cancellous bonealong the principle loading direction between regions. The mechanicalparameters in the lateral region were significantly different from middleregion and medial region.
This study improved the measurement of proximal femoral morphologicalparameters and proximal femoral damage algorithm. The effects ofmorphological features on bone strength were elaborated at macro and mesolevels, which provided more evidence for clinicians to prevent fractures.
第一部分建立了股骨近端三维形态参数的测量方法。应用此方法测量了50名66-75岁健康男性的股骨近端三维形态参数，并且分析了形态参数之间的内在联系，以及年龄对形态参数的影响。首先利用逆向工程软件MIMICS根据QCT影像重建出股骨近端三维模型。然后在快速成型制造软件MAGICS中对股骨近端模型进行旋转与平移来统一体位。在统一体位后的股骨模型上进行切割获取模型的特征点坐标，导入我们自行研发的股骨近端三维形态参数测量程序中进行计算，得出8个股骨近端三维形态参数，分别是股骨头直径（HD）、股骨头的高（HH）、偏心距（OFF）、颈干角（NSA）、股骨头中心到大转子顶点高度差（TRH）、股骨干的厚度（TOF）、股骨颈直径（ND）、股骨颈的长（NL）。随机选取5例样本制造出实体模型进行手工测量三维形态参数，并与计算机辅助测量的参数进行配对T检验以验证我们制定的算法的可靠性。将三维模型投影到冠状面上模拟X射线平片并且测量股骨近端平面形态参数。对两种形态参数进行配对T检验分析两种测量方法的差异。将测量的三维形态参数按年龄段划分为两个组（66-70岁为A组，71-75岁为B组），分析股骨近端形态参数随着年龄增长的变化趋势。结果显示：（1）手工测量方法和计算机辅助测量方法之间没有显著性差异，说明我们制定的股骨近端三维形态参数测量方法是可靠的。（2）ND、NSA、TRH三个参数在平面和三维两种测量方式下表现出显著差异，说明平面参数的误差较大。（3）除TOF外，BMD与其他形态参数均不显著相关，说明单独依靠BMD预测骨折风险是不准确的。（4）HD、ND、NL在两个年龄段之间具有显著性差异。
第二部分在测量过形态参数的股骨模型中随机选取14例（A组7例，B组7例）进行有限元分析预测其强度。复杂的骨材料属性以及屈服和断裂准则在UMAT子程序中编写代码来实现。由于骨是一种非均匀的拉、压不对称材料，因此在每个载荷增量加载之前需要判断每个单元的拉、压状态及损伤程度，并赋予对应的屈服准则和断裂准则。在股骨头的顶端建立简易压头模型保证载荷能够均匀施加在股骨头表面。在压头顶端施加竖直向下5mm位移边界条件进行计算。结果显示预测的股骨近端损伤过程与实验数据是吻合的。股骨近端强度与股骨近端三维形态参数中的TRH、NSA、TOF显著相关（P<0.05）。A组受试者股骨近端强度与B组受试者股骨近端强度未显示出显著性差异。
第三部分在细观水平上借助Micro-CT影像技术和显微有限元分析技术预测股骨近端骨折患者的股骨头内部松质骨强度，以及分析骨小梁三维形态特征对松质骨力学性能的影响。选取7例股骨近端骨折患者进行全髋关节置换术后取下的股骨头作为实验样本，进行micro-CT扫描并重建出股骨头模型。将每个股骨头模型依照骨小梁的主要生长方向及区域特征划分为3个区域12个子区域。在每个子区域提取出一个125mm3的立方体骨块。测量骨块的骨小梁形态参数，包括骨小梁分离度（Tb.Sp）、骨小梁厚度（Tb.Th）、骨体积分数（BV/TV）、骨表面积密度（BS/BV）、结构模型指数（SMI）、各向异性度（DA）。对不同区域的骨小梁形态参数进行二独立样本非参数检验，分析骨小梁形态参数的区域差异。对每一个骨块分别沿三个正交方向模拟压缩工况进行有限元分析。计算每个骨块沿三个正交方向的表观弹性模量和骨块内部平均应力。结果显示骨块沿主要受力方向表现出的力学性能显著优于其他两个非主要受力方向，两个非主要受力方向的力学性能没有显著性差异。松质骨沿主要受力方向计算出的力学参数显示出显著的区域差异性，其中外侧区域的力学参数显著高于中间区域和内侧区域。
本研究改进了股骨近端形态参数的测量方法和股骨近端的损伤算法，在宏观和细观两方面阐述了结构形态特征对骨强度的影响作用。为临床工作者尽早发现骨折风险，预防骨折的发生提供更为直观的依据。
Femur, as the most important bone of bearing the weight of upper body andforming gait process, is susceptible to fracture, especially for theelderly people with serious osteoporosis. With the rapid development ofmedical standards, people are not satisfied with curing the fracture onlydepending on the improvement of medical technology. More and more peoplestarted to investigate the factors which can affect the fracture risk andspecified precautions to prevent fractures. Mechanical properties andmorphological features of bones are two most important factors that affectthe fracture risk. However, in vivo mechanical experiments for livingskeleton could not be performed by mechanical test machine. This problemcan be solved by incorporating reverse engineering technology withnon-linear finite element analysis technology. Accordingly, in this studya suite of new measurement of3D proximal femoral morphological parameterswas established and the damage processes of proximal femurs were simulatedwith finite element analysis. Statistical analyses were performed on theproximal femoral morphological parameters and femoral strengths toanalyze the effect of3D morphological parameters on proximal femoralstrengths. In addition, mechanical properties of trabecular bone insidethe femoral heads were investigated by combining micro-CT imagingtechnology with micro-finite element method. The fracture mechanism ofproximal femur was studied at the tissue level. This study was mainlycomposed of three sections:
In section one, the method of measuring3D proximal femoral morphologicalparameters was established.51healthy elderly males with the age rangeof66-75were measured with this method, and the effects of age on themorphological parameters were analyzed. First,3D proximal femoral models were reconstructed from QCT images using reverse engineering softwareMIMICS. Models were performed a series of translation and rotation tounify the positions in rapid prototype software MAGICS. Coordinates offeature points were obtained from the surface and interior of the models.
In section two, finite element analyses were performed on14randomlyselected proximal femoral models (7samples from group A and7samplesfrom group B) to predict the proximal femoral strength. Complex bonematerial properties, yield criterion and fracture criterion were compiledin UMAT subroutines. As bone was a kind of inhomogeneous and asymmetricalmaterial in tension and compression, at the beginning of each loadincrement, the corresponding yield criterion and fracture criterion weregiven to each element after judging the damage degree and tension orcompression status. A simple load cap was established to make sure thatthe load could be applied to the surface of femoral head uniformly.5mmvertically downward displacement was exerted on the top of the cap.Results revealed that the predicted damage process of proximal femur wasconsistent with experimental data. The predicted strength of proximalfemur significantly related to the morphological parameters TRH, NSA andTOF (P<0.05). There were no statistical difference in strengths betweengroup A and group B.
In section three, the strength of cancellous bone inside femoral headsfrom proximal femoral fracture patients were analyzed using micro-CTimaging technology in combination with micro-finite element analysis atthe tissue level, as well as the effects of3D trabecular morphologicalfeatures on the trabecular mechanical properties.7femoral heads fromproximal femoral fracture patients were performed micro-CT scanning toreconstruct the femoral head models. Every femoral head models weredivided into3regions and12sub-regions according to the trabecularorientations. One125mm3trabecular cube was extracted from eachsub-region.6trabecular morphological parameters were measured on each cube including trabecular separation (Tb.Sp), trabecular thickness(Tb.Th), bone volume friction (BV/TV), specific area density (BS/BV),structural model index (SMI) and degree of anisotropy (DA). Twoindependent samples tests were performed on trabecular morphologicalparameters from different regions to analyze regional differences oftrabecular morphological parameters. Finite element analyses wereperformed on each cube along three orthogonal directions, respectively.The apparent Young’s modulus and average von Mises stress were calculatedon each cube along three orthogonal directions. The results showed thatthe mechanical properties along the principal loading direction were muchbetter than the other two non-principal loading directions. There was nosignificant difference between two non-major loading directions. Therewere significant differences in mechanical parameters of cancellous bonealong the principle loading direction between regions. The mechanicalparameters in the lateral region were significantly different from middleregion and medial region.
This study improved the measurement of proximal femoral morphologicalparameters and proximal femoral damage algorithm. The effects ofmorphological features on bone strength were elaborated at macro and mesolevels, which provided more evidence for clinicians to prevent fractures.
引文
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