基于不同应变判定准则模拟皮质骨断裂的准确性

文题释义：基于等效应变断裂模拟：即在大鼠股骨皮质骨断裂模拟过程中，应用皮质骨有限元模型在外部载荷作用下所产生的等效应变数值，与皮质骨组织的失效应变进行对比，当等效应变数值大于皮质骨组织失效应变时，有限元模型内的单元便发生失效，直至失效单元达到一定数量，模型便发生整体失效，此过程为基于等效应变的断裂模拟。 基于主应变断裂模拟：即在大鼠股骨皮质骨断裂模拟过程中，应用皮质骨有限元模型在外部载荷作用下所产生的主应变数值，与皮质骨组织的失效应变进行对比，当主应变数值大于皮质骨组织失效应变时，有限元模型内的单元便发生失效，直至失效单元达到一定数量，模型便发生整体失效，此过程为基于主应变的断裂模拟。 背景：由于意外碰撞等外力因素所产生的皮质骨裂纹是引起骨折的重要原因之一，要防止此类骨折发生，首先需弄清不同载荷作用下皮质骨裂纹的产生与扩展机制。由于实验分析对样本具有破坏性，难以同时了解骨结构在断裂前后的内部力学状态，找到一种能够准确模拟皮质骨从裂纹产生、扩展，直至断裂过程的有限元方法就显得尤为重要。当前模拟方法主要应用主应变或等效应变判定模型单元力学状态，继而进行断裂模拟，却鲜有关于这2种应变进行模拟准确性的探究。 目的：验证应用主应变与等效应变进行皮质骨断裂模拟的准确程度。 方法：结合实验与仿真分析，应用主应变与等效应变进行皮质骨断裂模拟，将仿真与实验结果进行对比，确定应用哪种应变进行模拟更加准确。 结果与结论：①应用主应变模拟的皮质骨断裂时间要明显晚于应用等效应变；②通过与实验对比发现，相比主应变，应用等效应变进行仿真所得结果与实验值更为接近；③因此，应用等效应变进行皮质骨断裂模拟相对更加准确。 ORCID: 0000-0003-0313-1359(王伟军) 中国组织工程研究杂志出版内容重点：人工关节；骨植入物；脊柱；骨折；内固定；数字化骨科；组织工程     

不同失效模式下皮质骨结构临界能量释放率预测

背景:临界能量释放率是结构在破坏过程中可测得的一个全局断裂力学参数,即使针对同一结构,在不同失效模式下其数值也可能存在差异。目的:提出一种方法预测皮质骨结构在不同失效模式下的临界能量释放率。方法:针对大鼠股骨皮质骨结构进行三点弯曲与轴向压缩实验以及相应断裂仿真。通过对有限元模型赋予不同临界能量释放率进行断裂模拟,并将每次模拟所得载荷-位移曲线与实验数据进行比较,当仿真与实验所得断裂参数差异小于5%时,即代表拟合成功,以此反演预测皮质骨结构在不同失效模式下的临界能量释放率。结果与结论:①结果显示大鼠股骨皮质骨结构在三点弯曲载荷下主要发生拉伸破坏,该失效模式下所预测临界能量释放率为0.16N/mm;②在轴向压缩载荷下主要发生剪切破坏,所预测临界能量释放率为0.12N/mm,这说明同一皮质骨结构在不同失效模式下的临界能量释放率存在差异;③此文通过对结构力学性能与损伤机制进行综合分析,揭示了不同失效模式下皮质骨结构临界能量释放率存在差异的原因,为能量释放率测量以及准确的皮质骨断裂模拟提供理论依据。     

皮质骨中骨单元应力集中效应的有限元分析

目的建立包含骨单元的皮质骨三维实体模型,通过有限元分析验证骨单元的应力集中效应,并对应力集中位置进行疲劳仿真和预测。方法利用Pro/E wildfire 5.0和ANSYS 12.0软件建立包含骨单元的皮质骨三维实体模型,在不同轴向压缩载荷条件下计算分析皮质骨中局部应力和应变分布情况;选取关键位置进行疲劳仿真,预测不同疲劳载荷强度下骨组织的疲劳状态。结果轴向压缩载荷作用下,骨单元附近会出现明显的应力集中效应,随着压缩载荷的增加,模型内部病理性局部应变的比例逐渐增大;关键位置的疲劳仿真结果证明了骨组织生理强度运动时的低疲劳风险,也预测了高强度运动或训练时骨组织疲劳骨折的高风险。结论成功建立了包含骨单元的皮质骨三维实体模型,验证了骨单元的应力集中效应,预测了高强度运动训练条件下骨组织的疲劳损伤位置和风险,实验结果可为部队新兵或中长跑运动员运动训练计划的制定以及运动疲劳损伤的预防提供参考。     

基于表观压缩实验与有限元分析相结合的骨微观力学性能参数预测方法的研究

骨表观力学性能参数常被用来评定骨质量,而微观力学性能参数由于难以测得尚未被广泛应用。为从微观水平评判骨质量,本研究提出一种骨微观力学性能参数的预测方法。该方法以大鼠股骨皮质骨为研究对象,预测其在微观水平的失效应变。首先依据扫描影像建立大鼠股骨皮质骨有限元模型,然后以表观压缩实验为研究依据,模仿实验条件,模拟皮质骨有限元模型在压缩载荷作用下的断裂过程,并通过与实验所测表观应力-应变曲线进行对比、反演,预测出大鼠股骨皮质骨在微观水平的失效应变。分析结果显示四只7月龄大鼠股骨皮质骨的微观失效应变数值处于4.53%~4.75%之间。经验证,本方法能够准确预测出骨结构在微观水平的力学性能参数。     

循环加载下关节软骨的棘轮应变及理论预测

目的获得不同加载条件下关节软骨的棘轮应变,建立预测棘轮应变的理论模型,并对软骨的棘轮应变进行预测。方法将猪股骨远端滑车部的新鲜关节软骨作为研究对象,采用非接触式数字图像技术,测试循环压缩载荷下关节软骨的棘轮应变;建立预测棘轮应变的理论模型,对不同应力幅值和加载率下软骨的棘轮应变进行预测,并比较预测结果与实验结果。结果随循环圈数的增加,软骨的棘轮应变先快速增长然后趋于稳定;定加载率下,软骨的棘轮应变随应力幅值的增大而增大;定应力幅值下,棘轮应变随加载率的增大而减小。实验结果与建立的理论模型预测结果吻合良好。结论关节软骨的棘轮应变与应力幅值成正比,与加载率成反比。建立的理论模型可以预测软骨的棘轮行为,同时为组织工程软骨的构造提供指导。     

兔脊柱节段压缩的生物力学研究

目的通过进行动物脊柱的轴向压缩实验,探究脊柱损伤的病理机制,为脊柱损伤的治疗、预防和研究提供参考。方法通过轴向压缩实验对兔脊柱节段进行生物力学研究,同时利用数字图像相关(digital image correlation,DIC)技术记录压缩过程并进行应变分析。结果沿脊柱从上向下,节段的极限载荷和承载能力均不断增加;相对应的单椎体的平均极限载荷明显大于节段;椎间盘在水平和竖直方向的应变明显大于上下椎体。结论在脊柱承受压应力的过程中,应重点考虑椎间盘的承载能力,脊柱节段的损伤主要表现为椎间盘异常。研究结果有助于脊柱压缩性骨折的预防和治疗,以及相关治疗器械和辅助器械的设计。     

兔单椎轴向动态冲击的实验研究

目的通过对兔单椎进行动态冲击破坏试验,并与静态压缩实验进行对比,研究椎体轴向冲击的损伤机制。方法通过落锤动态冲击实验装置,利用示波器和高速摄影获得力传感器的电压波形图和椎体冲击的详细过程。结果胸、腰椎平均静态载荷分别为910、947 N,平均动态载荷分别为1 196、1 026 N;胸、腰椎平均动荷系数分别为1.37和1.08。静载条件下,胸、腰椎平均等效应力为15.28、12.51 MPa;动载条件下,胸、腰椎平均等效应力20.03、13.56 MPa。动态冲击过程中,纵向、横向平均应变分别为-0.3和-0.005(压缩);动载条件下,椎骨的破坏能量从0 J一直增大到4.4 J。结论在动、静态实验条件下,同一椎体动态载荷大于静态载荷;胸椎平均动荷系数大于腰椎;胸椎应力大于腰椎;椎体受到轴向冲击力时纵向应变大于横向应变;椎体能量增长呈现先缓慢后快速的过程。研究结果可以为临床人脊柱椎体损伤的预防和康复提供指导意见。     

压缩力学性质:青年与老年尸体肋骨的比较

对正常国人青年和老年新鲜尸体肋骨进行压缩实验,确定老年尸体肋骨和青年尸体肋骨是否具有不同的压缩力学性质.实验标本取自4具正常国人男性新鲜尸体,年龄分别为25、28、72、76岁,由白求恩医科大学解剖教研室提供.人死亡后1 h内解剖取出死者肋骨标本,将标本沿纵向切成长40 mm的试样,每组各20个.实验环境温度为(36.5±1)℃,以5 mm/min的实验速度进行压缩试验,试样破坏后,计算机自动输出实验结果.结果表明:青年组肋骨最大载荷、最大位移、最大应力、最大应变均显著大于老年组(P＜0.05).肋骨压缩实验断口多数为斜断口,少数为横断口.宏观观察青年组肋骨骨皮质较厚,老年组肋骨皮质较薄,呈现出老年骨质疏松的表现形式.青年组肋骨和老年组肋骨具有不同的压缩力学特性,老年组试样由于骨质疏松导致压缩力学特性发生改变.     

矩形微缺损关节软骨在压缩载荷损伤演化的数值分析

目的 研究软骨在压缩载荷作用下的损伤扩展行为和演变机制。方法 采用有限元方法建立微缺损的纤维增强多孔弹性的软骨模型,对压缩载荷作用下损伤演化过程进行模拟和参数研究,获得不同损伤扩展阶段软骨基体和纤维的应力、应变分布规律。结果 软骨损伤表层和损伤前沿的应变随压缩量的增大而显著增大,两者呈明显的正相关性;在软骨演化过程中同时存在向深层和左右两侧扩展的趋势;软骨中的裂纹和损伤优先沿着纤维切线方向延伸,随着损伤的加剧,软骨横向扩展度明显快于纵向扩展速度。结论 软骨损伤演化过程与纤维的分布有着密切的关系,基质和纤维的损伤相互促进,骨演化速度和程度在不同层区和不同阶段存在变化。研究结果可为软骨创伤性退变的预测及修复提供定性的参考,为临床解释损伤退变病理现象和治疗提供理论依据。     

侧向冲击载荷作用下股骨-骨盆复合体的生物力学响应

目的利用三维有限元分析方法研究股骨-骨盆复合体在人体侧向摔倒时冲击载荷作用下的生物力学行为特性。方法基于中国力学虚拟人模型库建立股骨-骨盆-软组织复合体的三维有限元模型,包括皮质骨、松质骨和软组织;同时,构建一个刚体平面仿真地面。约束地面刚体,对整个股骨-骨盆-软组织复合体模型施加侧向2 m/s的速度载荷,整个仿真分析时间设定为20 ms。通过三维有限元分析计算获得股骨-骨盆侧摔冲击过程中应力应变变化特性。结果在13 ms时,股骨大转子处软组织与地面的接触力达到最大值7 656 N,对应的骨盆软组织上的最大等效应力值为2.64 MPa。冲击过程中,耻骨联合处骨皮质上等效应力出现极大值,为142.64 MPa,接近其屈服强度;股骨颈和大转子处应力水平较高,股骨颈处皮质骨上的最大等效应力值为76.49 MPa;股骨颈处松质骨上的最大等效应力值为8.44 MPa,最大压缩应变值为0.94%;股骨大转子处松质骨上的最大等效应力值为8.50 MPa,最大压缩应变值为0.93%。结论人体股骨-骨盆复合体在侧摔减速冲击载荷作用下股骨颈、大转子及耻骨联合处易出现骨折。     

Fracture characterization of human cortical bone under mode II loading using the end-notched flexure test

Fracture characterization of human cortical bone under mode II loading was analyzed using a miniaturized version of the end-notched flexure test. A data reduction scheme based on crack equivalent concept was employed to overcome uncertainties on crack length monitoring during the test. The crack tip shear displacement was experimentally measured using digital image correlation technique to determine the cohesive law that mimics bone fracture behavior under mode II loading. The developed procedure was validated by finite element analysis using cohesive zone modeling considering a trapezoidal with bilinear softening relationship. Experimental load-displacement curves, resistance curves and crack tip shear displacement versus applied displacement were used to validate the numerical procedure. The excellent agreement observed between the numerical and experimental results reveals the appropriateness of the proposed test and procedure to characterize human cortical bone fracture under mode II loading. The proposed methodology can be viewed as a novel valuable tool to be used in parametric and methodical clinical studies regarding features (e.g., age, diseases, drugs) influencing bone shear fracture under mode II loading.     

Advancing the deer calcaneus model for bone adaptation studies: ex vivo strains obtained after transecting the tension members suggest an unrecognized important role for shear strains

Sheep and deer calcanei are finding increased use as models for studies of bone adaptation, including advancing understanding of how the strain (deformation) environment influences the ontogenetic emergence of biomechanically relevant structural and material variations in cortical and trabecular bone. These artiodactyl calcanei seem ideal for these analyses because they function like simply loaded short‐cantilevered beams with net compression and tension strains on the dorsal and plantar cortices, respectively. However, this habitual strain distribution requires more rigorous validation because it has been shown by limited in vivo and ex vivo strain measurements obtained during controlled ambulation (typically walking and trotting). The conception that these calcanei are relatively simply and habitually loaded ‘tension/compression bones’ could be invalid if infrequent, though biologically relevant, loads substantially change the location of the neutral axis (NA) that separates ‘compression’ and ‘tension’ regions. The effect on calcaneus strains of the tension members (plantar ligament and flexor tendon) is also not well understood and measuring strains after transecting them could reveal that they significantly modulate the strain distribution. We tested the hypothesis that the NA location previously described during simulated on‐axis loads of deer calcanei would exhibit limited variations even when load perturbations are unusual (e.g. off‐axis loads) or extreme (e.g. after transection of the tension members). We also examined regional differences in the predominance of the three strain modes (tension, compression, and shear) in these various load conditions in dorsal, plantar, medial, and lateral cortices. In addition to considering principal strains (tension and compression) and maximum shear strains, we also considered material‐axis (M‐A) shear strains. M‐A shear strains are those that are aligned along the long axis of the bone and are considered to have greater biomechanical relevance than maximum shear strains because failure theories of composite materials and bone are often based on stresses or strains in the principal material directions. We used the same load apparatus from our prior study of mule deer calcanei. Results showed that although the NA rotated up to 8° medially and 15° laterally during these off‐axis loads, it did not shift dramatically until after transection of all tension members. When comparing results based on maximum shear strain data vs. M‐A shear strain data, the dominant strain mode changed only in the plantar cortex – as expected (in accordance with our a priori view) it was tension when M‐A shear strains were considered (shear : tension = 0.2) but changed to dominant shear when maximum shear strain data were considered (shear : tension = 1.3). This difference leads to different conclusions and speculations regarding which specific strain modes and magnitudes most strongly influence the emergence of the marked mineralization and histomorphological differences in the dorsal vs. plantar cortices. Consequently, our prior simplification of the deer calcaneus model as a simply loaded ‘tension/compression bone’ (i.e. plantar/dorsal) might be incorrect. In vivo and in finite element analyses are needed to determine whether describing it as a ‘shear‐tension/compression’ bone is more accurate. Addressing this question will help to advance the artiodactyl calcaneus as an experimental model for bone adaptation studies.     

Finite element prediction of surface strain and fracture strength at the distal radius

To better understand the mechanisms underlying distal radius fracture we have developed finite element models to predict radius bone strain and fracture strength under loading conditions simulating a fall. This study compares experimental surface strains and fracture loads of the distal radius with specimen-specific finite element models to validate our model-generating algorithm. Five cadaveric forearms were instrumented with strain gage rosettes, loaded non-destructively to 300 N, and subsequently loaded until failure. Finite element models were created from computed tomography data; three separate density-elasticity relationships were examined. Fracture strength was predicted for three specimens that failed at the distal radius using six different failure theories. The density-elasticity relationship providing the strongest agreement between measured and predicted strains had a correlation of r=0.90 and a root mean squared error 13% of the highest measured strain. Mean absolute percent error (11.6%) between measured and predicted fracture loads was minimized with Coulomb-Mohr failure theory and a tensile-compressive strength ratio of 0.5. These results suggest that our modeling method is a suitable candidate for the in vivo assessment of distal radius bone strain and fracture strength under fall type loading configurations.     

步态周期下髋臼生物力学特征

目的 研究正常步态周期下髋臼周围区域应力分布规律,并进一步探究髋臼各柱的生物力线和骨皮质厚薄形态分布。方法 通过人体逆向动力学分析获取人体步态周期8个典型阶段的肌肉及髋关节载荷,应用三维重建技术构建髋关节三维模型,以所得载荷作为加载边界条件进行有限元分析及拓扑优化。结果 步态周期支撑相下髋关节载荷较大,中柱应变能占总应变能55%～69%,髋臼顶部应力较大;摆动相下髋关节载荷减小,中柱应变能所占百分比减小。髋关节不同的运动角度影响肌肉力,进而影响髋关节上应力分布规律。所获得髋臼各柱的生物力线分布与解剖学所提出的生物力线及骨小梁排布基本吻合,与拓扑优化结果中骨皮质较厚区域相对应。结论 通过数值模拟方法可以确定髋臼各柱的生物力线和骨皮质厚薄形态分布,为骨折治疗内固定装置的合理放置提供理论指导。     

The effect of strain rate on fracture toughness of human cortical bone: a finite element study

Evaluating the mechanical response of bone under high loading rates is crucial to understanding fractures in traumatic accidents or falls. In the current study, a computational approach based on cohesive finite element modeling was employed to evaluate the effect of strain rate on fracture toughness of human cortical bone. Two-dimensional compact tension specimen models were simulated to evaluate the change in initiation and propagation fracture toughness with increasing strain rate (range: 0.08–18 s⁻¹). In addition, the effect of porosity in combination with strain rate was assessed using three-dimensional models of micro-computed tomography-based compact tension specimens. The simulation results showed that bone’s resistance against the propagation of a crack decreased sharply with increase in strain rates up to 1 s⁻¹ and attained an almost constant value for strain rates larger than 1 s⁻¹. On the other hand, initiation fracture toughness exhibited a more gradual decrease throughout the strain rates. There was a significant positive correlation between the experimentally measured number of microcracks and the fracture toughness found in the simulations. Furthermore, the simulation results showed that the amount of porosity did not affect the way initiation fracture toughness decreased with increasing strain rates, whereas it exacerbated the same strain rate effect when propagation fracture toughness was considered. These results suggest that strain rates associated with falls lead to a dramatic reduction in bone’s resistance against crack propagation. The compromised fracture resistance of bone at loads exceeding normal activities indicates a sharp reduction and/or absence of toughening mechanisms in bone during high strain conditions associated with traumatic fracture.     

不同力学激励对骨重建数值模拟的影响

目的研究采用应变能密度、等效应力、等效应变3种不同力学激励对骨重建数值模拟结果的影响。方法建立股骨近端的二维有限元模型,基于力学稳态理论的重建控制方程并结合有限元法,分别用3种不同力学激励模拟股骨近端的内部结构及密度分布,并与CT数据计算得到的骨密度值进行定量分析比较。结果 3种力学激励模拟得到的重建结果均能反映出股骨近端的主要特征结构,但采用等效应力作为激励时得到的股骨密度曲线图的趋势和数值都与CT图像数据更为一致。结论在骨重建力学调控机制中,应力可能起主导作用。准确预测和模拟骨重建过程将对矫形外科、骨伤治疗、人工假体的优化和个体化设计等临床实践提供理论依据。     

Finite Element Analysis of the Multiple Drilling Technique for Early Osteonecrosis of the Femoral Head

We used finite element (FE) method to investigate the effect of the drilling number and entry location of holes used in the multiple drilling technique on the stress and strain state in femur. Different three-dimensional FE models of a human hip joint with or without multiple drilling were fabricated using computed tomographic images obtained from the hip joint of a cadaver. The analysis technique was evaluated in a compression test using the cadaver specimen and FE analysis for the test using an FE model of the specimen. Von Mises stresses, principal stresses, and principal strains in the cancellous and cortical bone were calculated by using the different models, and changes in these values in relation to drilling number and entry hole locations were evaluated. Calculated peak values were much smaller than the yield strength, tensile strength, and yield strain of the cancellous and cortical bone for all cases of multiple drilling. Our results support that the multiple drilling technique for osteonecrosis of the femoral head is a stable operation technique.     

侧向冲击载荷作用下髋护具对股骨-骨盆复合体生物力学响应的影响

目的利用三维有限元法研究髋部护具对人体股骨-骨盆复合体在侧向冲击载荷作用下生物力学响应的影响。方法基于中国力学虚拟人模型库建立股骨-骨盆-软组织复合体的三维有限元模型,包括皮质骨、松质骨和软组织,并在此基础上建立髋部护具和股骨-骨盆-软组织复合体系统的三维有限元模型;同时,在两个模型中构建刚体平面仿真地面。约束地面刚体,对两个模型均施加侧向2 m/s的速度载荷,整个仿真分析时间设定为20 ms。通过三维有限元分析计算获得两模型受侧向冲击载荷过程中应力、应变变化特性,对比分析髋部护具对股骨-骨盆复合体生物力学响应的影响。结果髋部护具使股骨-骨盆复合体在侧向冲击载荷作用下的应力峰值出现时间提前4 ms以上,且应力应变水平出现大幅度降低;皮质骨上的应力峰值降低67.88%以上,松质骨上的峰值应力下降69.34%以上,松质骨上的压缩主应变峰值降低可达63%。结论在侧向冲击载荷作用下,髋部护具对股骨-骨盆复合体具有良好的保护作用,能够有效预防骨折的发生或降低骨折风险。