Micro-CT月骨矢状面有限元模型建立及应力分析

doi:10.3969/j.issn.2095-4344.2017.27.021

中国组织工程研究 ›› 2017, Vol. 21 ›› Issue (27): 4385-4390.doi: 10.3969/j.issn.2095-4344.2017.27.021

• 骨与关节图像与影像 bone and joint imaging • 上一篇下一篇

Micro-CT月骨矢状面有限元模型建立及应力分析

杜传超^1，2，熊革¹，任爽³，荣起国⁴，张衡²

¹北京积水潭医院手外科，北京市 100035；²清华大学第一附属医院，北京市 100016；³北京大学工学院生物力学实验室，北京市 100871；⁴北京大学工学院，北京市 100871

出版日期:2017-09-28 发布日期:2017-10-24
通讯作者: 熊革，教授，北京积水潭医院手外科，北京市 100035 荣起国，教授，北京大学工学院，北京市 100871
作者简介:杜传超，男，1985年生，汉族，2014年7月北京大学医学部第四临床医学院暨北京积水潭医院毕业，硕士，医师。
基金资助:
国家临床重点专科建设项目-手外科[财社(2010)305号]；北京市卫生系统高层次卫生技术人才培养计划(2009-3-17)

Construction of a finite element model based on lunate sagittal Micro-CT images and its stress analysis

Du Chuan-chao^{1, 2}, Xiong Ge¹, Ren Shuang³, Rong Qi-guo⁴, Zhang Heng²

¹Department of Hand Surgery, Beijing Jishuitan Hospital, Beijing 100035, China; ²the First Hospital of Tsinghua University, Beijing 100016, China; ³Biomechanical Laboratory of College of Engineering, Peking University, Beijing 100871, China; ⁴College of Engineering, Peking University, Beijing 100871, China

Online:2017-09-28 Published:2017-10-24
Contact: Xiong Ge, Professor, Department of Hand Surgery, Beijing Jishuitan Hospital, Beijing 100035, China; Rong Qi-guo, Professor, College of Engineering, Peking University, Beijing 100871, China
About author:Du Chuan-chao, Master, Physician, Department of Hand Surgery, Beijing Jishuitan Hospital, Beijing 100035, China; the First Hospital of Tsinghua University, Beijing 100016, China
Supported by:
the National Clinical Key Construction Project-Hand Surgery, No. (2010)305; the High-Level Health Technology Talent Training Program of Beijing Health System, No. 2009-3-17

摘要/Abstract

摘要：

文章快速阅读：

文题释义：

Micro-CT：也称为显微 CT，是基于螺旋CT断层扫描三维重建技术而研发的，其成像原理和普通X线成像原理大致相同，区别是采用微焦点X线球管技术，将图像的分辨率提高到微米级别。

有限元分析：是利用数学近似的方法对真实连续的物理系统(几何和载荷工况)进行分析、设计和建模的一种高效数值计算方法，将无限未知的真实物理系统分成简单而又相互作用的元素，即单元，就可以用有限数量的未知量去逼近无限未知量的真实系统。

摘要

背景：腕关节生物力学机制复杂，过去的研究多着眼于腕骨间应力的传导，但对腕骨内部骨小梁的应力分布及形变特点研究极少。

目的：建立人月骨矢状面的二维有限元模型，并探讨在月骨矢状面上施加轴向应力时应力的分布规律及形变特点。

方法：运用Micro-CT扫描离体的正常人月骨标本，将处理后的矢状面图像导入有限元分析软件，建立起月骨矢状面的二维有限元模型。在二维有限元模型上均匀地选取9个兴趣区，计算每个兴趣区的第一主应力、第三主应力及节点等效应力、平面剪切力及纵向位移，比较其大小和方向，并生成月骨矢状面二维有限元模型的形变图、各应力及位移云图。

结果与结论：①人月骨矢状面的二维有限元模型分析：月骨矢状面近端兴趣区所受的应力大于远端兴趣区所受的应力；月骨矢状面掌侧兴趣区所受的应力大于背侧兴趣区所受的应力；月骨矢状面近端和远端的掌、背侧兴趣区所受的应力分别大于对应的月骨中间兴趣区所受的应力；月骨矢状面远端兴趣区被压向近端，近端中间区域的兴趣区被压向远端，而近端掌侧和背侧兴趣区的纵向位移方向随着腕关节姿势的不同而不同；屈腕位和背伸位时各兴趣区的应力和位移明显增加。此外，实验还发现应力集中区域是平面剪切力方向发生变化及轴向位移方向发生变化的主要区域。②结果证实：月骨矢状面在施加轴向应力时，其应力分布具有一定的规律，在月骨矢状面近端的掌、背侧及远端的掌、背侧形成4个应力集中区。而且，腕关节的姿势可以明显地影响月骨矢状面上所受的应力大小和分布。

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
orcid: 0000-0002-7893-8846(Du Chuan-chao)

关键词: 骨科植入物, 数字化骨科, 骨关节图像与影像, 月骨, 腕关节, 腕关节位置, 关节接触面, Micro-CT, 二维有限元模型, 有限元分析, 应力分布, 轴向位移, 形变, 应力集中区

Abstract:

BACKGROUND: Biomechanical mechanisms are complex, and previous studiers focus on the stress conduction in the carpus. However, the stress distribution and characteristics of trabecula in the carpus are rarely reported.

OBJECTIVE: To investigate the stress distribution and deformation characteristics of the normal lunate through a two-dimensional sagittal finite element model.

METHODS: A normal cadaveric lunate sample was scanned with Micro-CT and the central sagittal image was chosen for further finite element analysis (FEA). The chosen image was processed and imported into the finite element analysis software (Ansys 14.0). A two-dimensional sagittal finite element model of the lunate bone was established. Axial pressure was applied to the model with the wrist held in different positions, and nine regions of interests (ROIs) were identified, for which stress and displacement nephograms were created. These included the first principal stress (S1, the maximum stress in a principal plane), the third principal stress (S3, the minimal stress in a principal plane), shear stress (SXY, the component of stress coplanar with a material cross section), von Mises stress (SEQV, yielding begins when the elastic energy of distortion reaches a critical value) and displacement of each ROI (UY, displacement on the vertical plane of the lunate) which were calculated and compared.

RESULTS AND CONCLUSION: (1) The stresses on ROIs located in the proximal and volar cortices of the lunate bone were much higher than those in the distal and dorsal cortices. At the proximal lunate, S1 was less than S3; however at the distal lunate, S1 was greater than S3. The ROIs of the distal and proximal ends of the lunate bone received much higher stress than the ROIs of the middle part. As for axial trabecular displacement, both distal and proximal ROIs were compressed by axial pressure. However, the dorsal and the volar parts of the proximal lunate moved in different directions at different wrist postures. Besides, the stress values and magnitudes of displacement were elevated in wrist flexion and extension compared to neutral position. Furthermore, the stress concentration zones (the proximal volar ROI, the proximal dorsal ROI, the distal volar ROI, and the distal dorsal ROI) had different directions of shear stress and displacement in different wrist postures. (2) These results suggest that when stress is loaded on a normal lunate model, four stress concentration zones, the proximal volar ROI, the proximal dorsal ROI, the distal volar ROI, and the distal dorsal ROI are found. The wrist postures can significantly affect the value and distribution of axial stress on the sagittal lunate.

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

Key words: Tissue Engineering, Wrist Joint, Fracture, Bone

中图分类号:

R318

杜传超，熊革，任爽，荣起国，张衡. Micro-CT月骨矢状面有限元模型建立及应力分析[J]. 中国组织工程研究, 2017, 21(27): 4385-4390.

Du Chuan-chao, Xiong Ge, Ren Shuang, Rong Qi-guo, Zhang Heng. Construction of a finite element model based on lunate sagittal Micro-CT images and its stress analysis[J]. Chinese Journal of Tissue Engineering Research, 2017, 21(27): 4385-4390.

图/表（结果） 3

Stress and displacement nephogram

Deformation, the stress nephograms and displacement contours were created using a post-processing module of the Ansys14.0 software. The nephograms showed the distribution features of the parameters in neutral wrist position (Figure 4).

Column diagrams of stresses and displacements at each ROI

Although the nephograms could show the feature of the parameters in one positions, the regularities of stress distribution and displacement of the same ROI in different wrist posture were of more significance. Bar charts of stresses (MPa) and displacements (mm) at each ROI of the FE model in different wrist positions were established (Figure 5) to analyze the variation of the parameter alone with the different postures of wrist.

Each ROI shared more S1 stress (tensile stress) in flexion or extension than that in neutral wrist, in addition, zone 1, 2, 3 and 9 (volar ROIs) got more S1 stressed in extension than those in the flexion, while zone 4, 5, 6, 7 and 8 (dorsal ROIs) got more stressed in flexion. As to S3 (compressive stress), the proximal ROIs got more compressed than the distal ROIs without obvious influence by wrist postures. For the SXY (shear stress), zone 1, 2 and 4 (volar ROIs) shared more shear stress in extension than those in flexion, but the conditions for the zone 3 (volar ROIs) was just the opposite. Besides, the directions of SXY were greatly influenced by the wrist postures. Directions of UY were also different with the change of wrist postures. However, SEQV was little affected by the wrist postures.

In brief, the ROIs on the volar side shared more stress than those on the dorsal side, but the displacements of the ROIs on the volar side are much less. Besides, the directions of SXY on the volar and dorsal side are different (Figure 6).

参考文献

[1] Kinney JH, Johnson QC, Nichols MC, et al. X-ray micro-tomography X at SSRL. Environ Sci Technol. 1989; 60(7):2471-2474.

[2] Neldam CA, Pinholt EM. Synchrotron μCT imaging of bone, titanium implants and bone substitutes-a systematic review of the literature. J Craniomaxillofac Surg. 2014;42(6): 801-805.

[3] Ritman EL. Current status of developments and applications of Micro-CT. Annu Rev Biomed Eng. 2011; 13(1): 531-552.

[4] Ledoux P, Lamblin D, Wuilbaut A, et al. A finite-element analysis of Kienbock’s disease. J Hand Surg Eur Vol. 2008; 33(3):286-291.

[5] Mayfield JK. Mechanism of carpal injuries. Clin Orthop Relat Res. 1980;149(1):45-54.

[6] Xiao ZR, Xaiong G, Tao JF, et al. Microstructure study of normal lunates with microCT. Zhonghua Shouwaike Zazhi. 2015;31(6):455-459.

[7] Bonzar M, Firrell JC, Hainer M, et al. Kienbock disease and negative ulnar variance. J Bone Joint Surg Am. 1998;80(8): 1154-1157.

[8] Watson HK, Guidera PM. Aetiology of Kienbock’s disease. J Hand Surg Br. 1997;22(1):5-7.

[9] Low SC, Bain GI, Findlay DM, et al. External and internal bone micro-architecture in normal and Kienbock’s the lunates: a whole-bone micro-computed tomography study. J Orthop Res. 2014;32(6):826-833.

[10] Han KJ, Kim JY, Chung NS, et al. Trabecular microstructure of the human the lunate in Kienbock’s disease. J Hand Surg Br. 2012;37(4):336-341.

[11] Jaecques SV, Van OH, Muraru L, et al. Individualised, micro CT-based finite element modelling as a tool for biomechanical analysis related to tissue engineering of bone. Biomaterials. 2004;25(9):1683-1696.

[12] Majima M, Horii E, Matsuki H, et al. Load transmission through the wrist in the extended position. J Hand Surg Am. 2008;33(2):182-188.

[13] Luo YH, Lin YW. The blood supply of lunar bone and its clinical significance. Zhongguo Linchuang Jiepouxue Zazhi. 1990;14(3):151-152.

[14] Anderson DD, Daniel TE. A contact-coupled finite element analysis of the radiocarpal joint. Semin Arthroplasty. 1995; 6(1):30-36.

[15] Gaisne E, Dap F, Bour C, et al. Arthrodesis of the wrist in manual workers. Apropos of 36 cases. Rev Chir Orthop Reparatrice Appar Mot. 1990;77(8):537-544.

[16] Schuind F, Eslami S, Ledoux P. Kienbock’s disease. J Bone Joint Surg Br. 2008;90(2):133-139.

[17] Pappas ND, Lee DH. Perilunate injuries. Am J Orthop. 2015; 44(9):E300.

[18] Imhof H, Sulzbacher I, Grampp S, et al. Subchondral bone and cartilage disease: a rediscovered functional unit. Invest Radiol. 2000;35(10):581-588.

[19] Low SC, Bain GI, Findlay DM, et al. External and internal bone micro-architecture in normal and Kienbock’s the lunates: a whole-bone micro-computed tomography study. J Orthop Res. 2014;32(6):826-833.

[20] Dempster DW, Compston JE, Drezner MK, et al. Standardized nomenclature, symbols, and units for bone histomorphometry: a 2012 update of the report of the ASBMR Histomorphometry Nomenclature Committee. J Bone Miner Res. 2013;28(1):2-17.

[21] Schiltenwolf M, Martini AK, Eversheim S, et al. Significance of intraosseous pressure for pathogenesis of Kienbock’s disease. Handchir Mikrochir Plast Chir. 1996;28(4): 215-219.

[22] Watson HK, Guidera PM. Aetiology of Kienbock’s disease. J Hand Surg Br. 1997;22(1):5-7.

[23] Hashizume H, Asahara H, Nishida K, et al. Histopathology of Kienbock’s disease: correlation with magnetic resonance and other imaging techniques. J Hand Surg Br. 1996;21(1): 89-93.

[24] AssoulineDY, Chang C, Greenspan A, et al. Pathogenesis and natural history of osteonecrosis. Semin Arthritis Rheum. 2002;32(2):94-124.

[25] Klas T, Per A, Karl-Goran T. Lipid extracted bank bone: bone conductive and mechanical properties. Clin Orthop Related Res. 1995;311(1):232-246.

引言

Micro-CT is defined by structural CT image analysis down to the level of the micron^[1]. Some properties of bone microstructure (such as, trabecular bone area, trabecular bone thickness, trabecular spacing and trabecular bone number) can be quantitatively analyzed using relevant parameters obtained through associated software. Additionally, the two-dimensional (2D) or three-dimensional (3D) structures of trabecular bone can be reconstructed based on its Micro-CT images. If these data are combined with a finite element model of stress distribution and deformation, the properties of trabecular bone may be investigated^[2]. The finite element analysis (FEA) method has already been widely used to study various microstructures and mechanical properties of the diseased bones^[3-4].

Lunate injury is commonly seen because of its central location in the wrist joint and huge stresses it bears during stress conduction^[5]. Xiao, et al. analyzed the trabecular microstructures and nutrient foramina of normal lunates with Micro-CT, and found the volar and dorsal distal ends have lower subchondral bone plate intensity than those of the distal central part^[6]. While few papers adress the mechanisms of stress conduction through lunate. Kienbock’s disease (KD), aseptic lunate osteonecrosis, results in serious disturbance of wrist joint function, due to end-stage bony deformation, instability and wrist joint arthritis. Previous researches on the pathogenesis of KD have focused on abnormal anatomical factors which increase forces across the lunate such as ulna-negative variance, excessive radial tilt angleand deformation of the lunate’s gross spatial structure^[8-9].

Although Han compared the micro-structure differences between the normal and KD lunates, the mechanical analysis FEA for lunate has not yet been reparted^[10], which may uncover the microstructure mechanical reason for KD. So we established a sagittal 2D FEA model based on the Micro-CT data images of a normal lunate, and analyzed the microstructure and mechanical properties of the normal lunate under axial stress,to investigate the stress distribution and deformation characteristics.

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

材料方法

Design

Biomechanic research of the lunate microstructure based on FEA model experiment of single lunate sample.

Time and setting

From December 2013 to March 2014, the experiment was performed at the Trauma Orthopaedic Institute of Beijing Jishuitan Hospital and State Key Biomechanical Laboratory of Peking University.

Materials

A normal fresh frozen right lunate was obtained from a healthy cadaver (36 years old, male, right upper extremity amputated for destructive injury, Bone Bank of Beijing Jishuitan Hospital, Beijing). The sample was scanned by Micro-CT (Skyscan1172, Belgium) at room temperature.

To determine the vector and scale of stress and deformation under different physiological loading positions, a right wrist of a healthy volunteer (male, 29 years old, Beijing) was scanned with a spiral CT (TOSHIBA/Aquili, Japan) in neutral, flexion and extension positions (flexion 62° and extension 71°, the largest angle of activity during work). Geomagic-studio (a reverse engineering software) and Materialism’s interactive medical image control system (Mimics 10.01, 64bit, Materialise Inc., USA) were used.

Methods

Loading positions and directions

The spiral CT images of the right wrist of the healthy volunteer were stored as DICOM format and imported into Mimics 10.01 software for 3D reconstruction. The capitolunate angle was measured in the sagittal section. The different wrist positions for the 3D model were neutral, flexion (62°) and extension (71°). The contact surfaces of the capitolunate and radiolunate joints were inspected and only the central sagittal lunate section was found to exhibit a high contact area. The precise contact surfaces were chosen as loading positions (Figure 1A). In addition, the direction of load was co-ordinated by application of X, Y and Z-axes (Figure 1B). The same processes were performed in three wrist positions, and the anatomic features of joint were measured (Table 1).

The lunate scanned with Micro-CT

After reduction and compression, the original images of lunate from the Micro-CT were converted into the 3D images. The central sagittal section was extracted with Data Viewer 1.4.1.0 software (Sky Scan, Kontich, Belgium). The chosen image was then converted into a readable format for further finite element analysis.

Establishing a sagittal 2D FEA model

Derived from Capitolunate Angle (proximal parts of lunate constrained), radiolunate and capitolunate contact surfaces, loading positions and directions on the sagittal lunate finite element model in different wrist positions were determined (Figure 2).

In the finite element model, both cortical and cancellous bone were assumed to have isotropic homogeneity and continuous linear elastic properties with an elasticity modulus set at 10 000 MPa and Poisson’s ratio 0.2. A combination of manual and computerized methods was used, and the 2D FEA image model was divided into 4 862 units and 6 428 nodes. Nine regions of interest (ROIs) were chosen, and each region contains 11 units (Figure 3). Under different loading conditions (load position, direction and size, 0.1 MPa), a finite element analysis was conducted^[11]. S1 (the first main stress, the maximum stress in a principal plane), S3 (the third main stress, the minimal stress in a principal plane), SEQV (von Mises stress, yielding begins when the elastic energy of distortion reaches a critical value), SXY (XY shear stress, the component of stress coplanar with a material cross section) and UY (Y axial displacement, displacement on the vertical plane of the lunate) for each unit were calculated with Ansys 14.0 software.

The procession of experimental data

The distribution nephograms and bar charts were used to document and analyze different stresses and their distributions.

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

讨论

Although there are some researches about the stress transmission through wrist and force distributions among the wrist bones^[12], the stress distribution in the lunate is still unrevealed, which may contribute to the understanding of the lunate diseases, such as KD. Our research found that the stress transmitted in the lunate changed with different wrist postures, and the stress concentration points were also determined. The tension of the ligaments around the lunate changed with different wrist postures, thus influencing the stress distribution and displacement of the lunate. In flexion, the volar ligaments are flabby while the dorsal ligaments are relatively tight, which would inflict a greater load on dorsal part of the lunate. Furthermore, the force bearing point of the lunate moved volarly in wrist flexion. It also made the stress increased when wrist flexed. In dorsal flexion, the situation was reversed, and there was more stress on the volar part of the lunate.

It was reported that the main arteries of the lunate located on the volar side, and would be compressed by the volar ligaments in tension, thus reducing the blood supply to the lunate bone^[13]. Therefore, the volar part of the lunate bone may be vulnerable to be vascular insufficiency in wrist extension^[14]. So KD is commonly seen in those doing heavy labour who have to extend or flex their wrists^[15-17].

In our study, we found a high consistency between the clinically common broken points of the lunate and stress concentration regions. Among stress concentration regions, the zone 3 and 6 are apt to be injured, because of the single layer of the cortical bone in these two zones and different directions of SXY and UY in different wrist positions. The zone 1 is also easy to be injured because it shares more SXY than zone 3 and 4 in extension, and also because it is the transitional zone from transverse cortical plate to longitudinal bone trabecula in the sagittal plane. However, the central part of the distal sagittal lunate bone consists of multi layers of cortical plates which are intercalated with the trabecula perpendicular to them and thus has very high strength and rigidity^[18]. Below the central part, there are some trabecula extended from the distal to the proximal, which is in favor of stress dispersion and maintenance of the lunate height. These trabecula would be lost and broken in the late stages of KD^[19]. Zone 1 and 8 are vulnerable to be injured, because they are the stress concentrated ROIs, the junctional zone between transverse trabecula and longitudinal trabecula, and suffered more stress in extension^[20]. The dorsal ROIs are easier to be injured in volar flexion at which they share more stress; on the contrary, the volar ROIs are easier to be injured in dorsal flexion. Schiltenwolf et al. came to the consistent conclusion as our finding through measuring the pressures in the lunate bone in different wrist postures^[21]. The regularity of stress distribution is consistent to the structure characteristic that there is more trabecula on the volar lunate bone than the dorsal lunate bone, which fully embodies the basic theory that structures are always consistent with their functions.

With Micro-CT images, the structures at micron level of bonelunate can be firstly investigated as well as their mechanic properties. We provide a new way for studying the failure process of trabecula and may be used to test the well-known theory that stress concentration causes fractures of a few trabecula, and then the capillaries in the fracture site are compressed when bone healing, so newly formed bone become necrosis secondary to reduction of blood supply or fragile to be broken again^[21-22]. Histologically, the trabecula become thickened, collapsed, flattened, density increased, fatty changes, trabecula space and anisotropy reduced, which are consistent with the pathological appearance of vascular bone necrosis^[23-24]. In the future, we intend to further explore lunates at different stages of KD. Honestly, there are several limitations in our study. Firstly, the 3D finite element model of the lunate bone is impossible to be created by personal computers, because the vast information in those images is impossible to be reconstructed. Therefore, a 2D finite element model of the sagittal lunate bone was created rather than a 3D one which is the real structure of trabecula. Secondly, both the cortical bone and trabecula were assumed as isotropic homogeneity and continuous linear elastic material without considering the differences among trabecula^[25]. Additionally, the mechanical model of the lunate bone was simplified in order to simulate the complicated mechanical environment of the lunate bone, which obviously cannot fully reflect the real physical situation around the lunette joints.

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

Micro-CT月骨矢状面有限元模型建立及应力分析

Construction of a finite element model based on lunate sagittal Micro-CT images and its stress analysis

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表（结果） 3

参考文献

相关文章 15

引言

材料方法

讨论

文章快阅

延伸阅读

编辑推荐

Metrics

本文评价

[1]	魏国强, 李云峰, 王一, 牛晓芬, 车丽芳, 王海燕, 李志军, 史国鹏, 白灵, 莫凯, 张晨晨, 许阳阳, 李筱贺. 非均匀材料股骨在不同负荷情况下的生物力学分析[J]. 中国组织工程研究, 2022, 26(9): 1318-1322.
[2]	吕倩忆, 陈芯仪, 郑慧娥, 何灏龙, 李棋龙, 陈楚淘, 田浩梅. 不同角度肘按法对正常人腰椎椎体及后部结构的应力和位移分析[J]. 中国组织工程研究, 2022, 26(9): 1346-1350.
[3]	张玉芳, 吕蒙, 梅钊. 青少年脊柱侧弯全脊柱生物力学模型的构建及验证[J]. 中国组织工程研究, 2022, 26(9): 1351-1356.
[4]	张吉超, 董跃福, 牟志芳, 张震, 李冰言, 徐祥钧, 李佳意, 任梦, 董万鹏. 骨关节炎患者在不同步态角度下膝关节内部生物力学变化的有限元分析[J]. 中国组织工程研究, 2022, 26(9): 1357-1361.
[5]	马超, 王飞, 刘晓民, 王子昀, 许奎, 杨文东, 冯伟. 应用体表地形图量化腰椎间盘突出症腰型客观化指标：下腰曲线弹性固定转折点的三维成角[J]. 中国组织工程研究, 2022, 26(6): 924-928.
[6]	李桂军, 方晓辉, 孔维峰, 袁晓庆, 金荣忠, 杨俊. 微型钢板联合超强缝线弹性固定治疗拇外翻畸形的有限元分析[J]. 中国组织工程研究, 2022, 26(6): 938-942.
[7]	温明韬, 梁学振, 李嘉程, 许波, 李刚 . 两种方式固定Sanders Ⅱ型跟骨骨折后的力学稳定性[J]. 中国组织工程研究, 2022, 26(6): 838-842.
[8]	王海龙, 李龙, 买合木提·亚库甫, 陈洪涛, 刘旭, 伊力哈木·托合提. 髋臼假体在Lewinnek 安全区内应力分布的有限元分析[J]. 中国组织工程研究, 2022, 26(6): 843-847.
[9]	魏兵, 常山. 脊柱骨折矢状面不同角度置钉方式的有限元分析[J]. 中国组织工程研究, 2022, 26(6): 864-869.
[10]	袁景, 孙效虎, 陈慧, 乔永杰, 王立新. 成人继发性膝外翻畸形股骨远端的数字化测量与分析[J]. 中国组织工程研究, 2022, 26(6): 881-885.
[11]	张建国, 陈晨, 胡凤玲, 黄道宇, 宋亮. 三维有限元分析牙种植体孔隙结构设计及生物力学性能[J]. 中国组织工程研究, 2022, 26(4): 585-590.
[12]	白布加甫·叶力思, 热娜古丽·买合木提, 艾孜买提江·赛依提, 王俊祥, 尼加提·吐尔逊. 上颌中切牙联冠种植修复体在不同咬合方式中的应力分析[J]. 中国组织工程研究, 2022, 26(4): 567-572.
[13]	王璨, 顾卫平, 蒋煜彬, 朱琳, 陈岗. 不同种植设计对下颌无牙颌应力影响的有限元分析[J]. 中国组织工程研究, 2022, 26(4): 573-578.
[14]	林博颖, 沈茂. 内镜下腰椎椎间融合：单侧椎弓根螺钉联合对侧椎板关节突螺钉固定的生物力学稳定性[J]. 中国组织工程研究, 2022, 26(3): 329-333.
[15]	李凯, 刘振东, 李小磊, 王静成. 后外侧入路全髋关节置换后假体反复性脱位的危险因素[J]. 中国组织工程研究, 2022, 26(3): 354-358.