Dynamic characteristics of the lumbosacral vertebrae based on three-dimensional finite element models

doi:10.3969/j.issn.2095-4344.2017.15.017

Abstract

Abstract:

BACKGROUND: Inherent modal analysis and harmonic response analysis on the human normal lumbosacral vertebrae have been reported, but there is a lack of comparative research on their modal analysis results before and after pedicle screw fixation.

OBJECTIVE: To explore the dynamic characteristics of human lumbosacral vertebrae using three-dimensional finite element method.

METHODS: Finite element model of lumbosacral vertebrae (L₁-S₁) before and after pedicle screw fixation was developed and validated based on CT images, and the modal analysis and harmonic response analysis were then conducted.

RESULTS AND CONCLUSION: (1) Representative nodes were selected at the spinous process segments of L₁, L₃ and L₅, and numbered as A, B, and C, respectively. (2) The maximum displacement of each node in Y and Z directions of lumbosacral vertebral model after internal fixation was significantly decreased compared with those of the normal lumbosacral vertebral model, suggesting that screw fixation system plays a protective role in lumbosacral vertebrae, and reduces its amplitude under external load, thus diminishing its sensitivity to external load. (3) The lumbosacral vertebral modal analysis can provide basis for further study on dynamic analysis, and the parameters such as natural frequency, modal shape and vibration amplitude of the lumbar spine have been determined.

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: Lumbar Vertebrae, Internal Fixators, Biomechanics, Finite Element Analysis, Kinetics, Tissue Engineering

CLC Number:

R318

Wu Xiao-dan, Zhang Shun-xin, Fan Shun-cheng, Li Ye, Jia Shao-wei, Xie Jun-de, Han Li . Dynamic characteristics of the lumbosacral vertebrae based on three-dimensional finite element models [J]. Chinese Journal of Tissue Engineering Research, 2017, 21(15): 2388-2394.

Figures/Tables 2

一些研究表明人体严重的振动响应均在30 Hz以下，对于腰骶椎模态分析结果前三阶模态具有实际意义，图2，3分别为正常腰骶椎、内固定后腰骶椎的前3阶模态振型。图中的振型变化大小只是一个相对值，反映在某一频率下的振动情况，并不反映实际振动位移变化。通过观察变形动画，调节位移放大比例，可以观察每一阶模态腰骶椎变形情况。由模态振型描述可知，低阶振型比较简单，叠加现象不明显，但对腰骶椎整体结构动态特性影响较大。随着频率的增加，振型越来越复杂。通过分析各阶振型，可知正常腰骶椎及内固定后腰骶椎的一阶振型均表现为整体的前后俯仰振动，L1后部结构棘突处振动最大；二阶振型均表现为整体向左弯曲振动，L1后部结构变形较大；三阶振型均表现垂向拉伸振动，L1后部变形最大；第4-10阶振型则表现为相对复杂的振动。由上可知，前3阶的最大振动均发生在L1椎体后部，表明L1椎体后部对外界振动较敏感，而且高阶振型比低阶振型复杂，这与实际的脊柱生物力学理论知识相符合。由模态分析得到的腰骶椎结构每一阶的固有频率和振型对避免腰骶椎与外界环境发生共振具有重要意义。 2.2 稳态动力学分析对腰骶椎结构进行稳态动力学分析是腰骶椎结构受到谐波激励下的稳态响应，通过稳态动力学分析，可以了解简谐载荷对人体腰骶椎结构的影响。将激励力为10 N垂直施加在L1上表面，约束骶椎下表面的全部自由度使其固定，以模拟人体上身振动对腰骶椎的影响。并根据模态分析结果选取频率范围为0-5 Hz。根据腰椎解剖结构特点分别在正常腰骶椎模型和内固定后腰骶椎模型的腰椎L1，L3，L5节段棘突处选取代表性节点，节点编号分别为A，B，C，通过计算，获得选取节点X，Y，Z 三个方向的振动幅值随频率变化情况，如图4-6所示。图中横坐标为简谐载荷的频率，单位为Hz，纵坐标表示节点的振动幅值，单位为mm。图4-6分别为两种不同腰骶椎模型的腰椎L1，L3，L5棘突处节点A，B，C位移对频率的响应曲线，比较各个模型的腰椎棘突处3个节点A，B，C在各个方向上的位移最大峰值，可知节点A处位移最大峰值最大，节点B处位移最大峰值次之，节点C处位移最大峰值最小。表明腰骶椎模型的位移峰值从上往下逐渐减小。由图可知内固定后腰骶椎模型的节点A，B，C在X方向上的位移最大峰值比正常腰骶椎模型位移最大峰值都要稍微增大，但在Y，Z方向上位移最大峰值比正常腰骶椎模型位移最大峰值均明显减小。表明螺钉内固定系统对腰骶椎部分起到了保护作用，使得固定后的腰骶椎在受到外界激励时振幅减小；正常腰骶椎模型在1.0-2.0 Hz频率范围内各节点X，Y，Z方向位移均出现峰值，表明该腰骶椎结构对1.0-2.0 Hz频率范围比较敏感，这分别与模态分析得到的第一阶振型的前后俯仰模态固有频率1.33 Hz和第二阶振型的侧向俯仰模态固有频率1.65 Hz相近；内固定后腰骶椎模型在1.0-2.0 Hz频率范围内各节点X，Y，Z方向位移均出现峰值，表明该腰骶椎结构对1.0-2.0 Hz频率范围比较敏感，这分别与模态分析得到的第一阶振型的前后俯仰模态固有频率1.57 Hz和第二阶振型的侧向俯仰模态固有频率1.86 Hz相近；表明这两种腰骶椎结构在这些频率范围内容易产生共振，为避免发生共振，应尽量使人们所处环境的外界振动频率远离腰骶椎固有频率。"

References

[1] Li XF, Liu ZD, Dai LY, et al. Dynamic response of the idiopathic scoliotic spine to axial cyclic loads. Spine. 2011; 36(7): 521-528.

[2] Guo LX, Teo EC, Lee KK, et al. Vibration characteristics of the human spine under axial cyclic loads: effect of frequency and damping. Spine. 2005;30(6): 631-637.

[3] Kong WZ,Goel VK. Ability of the finite element models to predict response of the human spine to sinusoidal vertical vibration. Spine. 2003;28(28): 1961-1967.

[4] Seidel H, Blüthner R, Hinz B. Application of finite-element models to predict forces acting on the lumbar spine during whole-body vibration. Clin Biomech. 2001;16Suppl 1(16 Suppl 1): S57-S63.

[5] Kasra M, Shirazi-Adl A, Drouin G. Dynamics of human lumbar intervertebral joints. Experimental and finite-element investigations. Spine. 1992;17(1): 93-102.

[6] 黄凯,刘展亮,刘少喻,等. 腰椎单侧与双侧椎弓根螺钉固定的生物力学对比性研究[J]. 中华临床医师杂志:电子版, 2015(22): 4143-4147.

[7] 郝剑,姚进,朴哲,等. 腰椎坚强固定后邻近节段的有限元法生物力学分析[J]. 中国中西医结合外科杂志,2016,22(5):475-478.

[8] Zhu R, Yu Y, Zeng ZL, et al. A Review of the Static Loads Applying on the Finite Element Models of the Lumbar Spine. J Med Imaging Health Informat. 2015.

[9] Zafarparandeh I. Application of Finite Element Method in the human Spine Biomechanics. 2016.

[10] Zhang Z, Yang L I, Liao Z, et al. Research Progress and Prospect of Applications of Finite Element Method in Lumbar Spine Biomechanics. J Biomed Eng. 2016.

[11] 王端阳,奚春阳,杨辉,等. 有限元分析法在腰椎生物力学研究中的应用及新进展[J]. 现代生物医学进展, 2015,15(9): 1794- 1797.

[12] Zulkiflil A, Ariffinl AK, Rahman MM. Probabilistic finite element analysis of vertebrae of the lumbar spine under hyperextension loading. Int J Autom Mech Eng. 2011;3(1): 256-264.

[13] Kavitha A, Sudhir G, Ranjani T S, et al. Implant Analysis on the Lumbar-Sacrum Vertebrae Using Finite Element Method. Springer Singapore, 2017.

[14] Wang DY, Chun-Yang XI, Yang H, et al. New Progress and Application of Finite Element Analysis Technology in Lumbar Spine Biomechanics. Prog Mod Biomed. 2015.

[15] Alonso-Rasgado MT, Martinez-Lozada FM, Bailey CG, et al. The effects of L4-L5 Fusion on the Adjacent Segments in Lumbar Spine: Finite Element Analysis. Int J Stroke. 2015; 10(2):269-274.

[16] Li K, Zhang J, Jiang J, et al. Lumbar spinal finite element analysis in a gravity environment. in Eighth International Conference on Digital Image Processing. 2016.

[17] 韩硕. 有限元分析在腰椎间盘生物力学中的应用研究[D]. 河北医科大学, 2016.

[18] 曹丽君.正常及退变下腰椎在不同工况下三维有限元力学分析[D].河北医科大学, 2015.

[19] 张伟,宫赫.振动载荷作用下人体腰椎多孔弹性有限元分析[C]//北京力学会学术年会. 2015.

[20] 张振军,李阳,廖振华,等. 有限元法在腰椎生物力学应用中的研究进展和展望[J]. 生物医学工程学杂志, 2016,(6): 1196-1202.

[21] 秦计生, 王昱, 彭雄奇, 等. 全腰椎三维有限元模型的建立及其有效性验证[J]. 医用生物力学, 2013, 28(3):321-325.

[22] 黄菊英,李海云,吴浩. 腰椎间盘突出症力学特征的仿真计算方法[J]. 医用生物力学, 2012, 27(1): 4630-4631.

[23] 苏晋,赵文志,陈秉智,等. 建立全腰椎有限元接触模型[J]. 医用生物力学, 2010, 25(3): 200-205.

[24] 牛文鑫.人体振动生物力学响应的数学模型研究进展[J]. 2008.

[25] 马亮,郭卫春.成年人腰椎-骨盆的三维有限元模型的建立及验证[J]. 生物医学工程与临床, 2016,(3): 229-235.

[26] 魏峰. 基于CT图像的人体腰椎有限元模型构建与力学分析[D].南京理工大学, 2015.

[27] 陈为坚,段扬,林周胜,等. 基于三维有限元法的腰椎动态稳定系统建立及生物力学行为初步分析[J]. 广东医学, 2015,36(10): 1497-1500.

[28] 冯杰荣,殷海东,陈伟,等. T(12)椎体前缘不同压缩状态下相邻椎体终板应力的有限元分析[J]. 中国组织工程研究,2016,20(22): 3263-3271.

[29] Pawlikowski M, Domański J, Suchocki C. Advanced finite element analysis of L4–L5 implanted spine segment. Cont Mech Ther. 2015;27(4): 571-582.

[30] 吕永强,彭春政. 负重屈伸运动对腰椎受力的有限元分析[J]. 沈阳体育学院学报, 2016, 35(2): 92-97.

[31] 陶勇,吴云乐,宗少晖,等. 基于有限元分析腰椎内固定的生物力学特征[J]. 中国组织工程研究, 2016, 20(13): 1932-1938.

[32] 胡迎春,赵舒婷,余兵浩. 人体腰椎模拟植入椎弓根螺钉的有限元分析[J]. 广西科技大学学报, 2014, 25(3): 10-13.

[33] 任伟.基于人体腰椎有限元分析的乘坐舒适性研究[D].东北大学, 2010.

[34] 申成刚. 基于人体腰椎动力学特性分析的高速列车座椅舒适性研究[D].东北大学, 2011.

[35] 项嫔, 都承斐, 赵美雅, 等.全腰椎有限元模态分析[J]. 医用生物力学, 2014, 29(2): 154-160.

[36] Kurutz M,Oroszváry L. Finite element analysis of weightbath hydrotraction treatment of degenerated lumbar spine segments in elastic phase. J Biomech. 2010;43(3): 433-441.

[37] Chen CS, Chen WJ, Cheng CK, et al. Failure analysis of broken pedicle screws on spinal instrumentation. Med Eng Phys. 2005;27(6): 487-496.

[38] 肖振平. 腰椎动态—非动态椎弓根钉内固定系统的有限元分析及初步临床应用[D].南华大学,2012.

[39] Zhang QH,Teo EC. Finite element application in implant research for treatment of lumbar degenerative disc disease. Med Eng Phys. 2008;30(10): 1246-1256.

[40] 黄宇峰,潘福敏,赵卫东,等. 关于腰椎三维有限元模型的建模及有效性验证[J]. 生物骨科材料与临床研究, 2015,12(5):16-19.

[41] 董凡,侯筱魁.小关节在腰椎结构刚度中的作用[J]. 中华外科杂志,1993,31(7): 417-420.

[42] Heth J, Hitchon P, Goel V, et al. A biomechanical comparison between anterior and transverse interbody fusion cages. Spine. 2001;26(12): e261-e267.

[43] Yamamoto I, Panjabi M, Crisco T, et al. Three-dimensional movements of the whole lumbar spine. Spine. 1989;14(11): 1256-1260.