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基于人体生物力学有限元模型的约束系统参数优化 被引量:4
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作者 裴永生 刘壮 张世哲 《汽车技术》 CSCD 北大核心 2022年第10期30-36,共7页
建立了人体胸部生物力学有限元模型,通过肋骨三点弯曲试验和胸部碰撞块冲击试验验证了模型的有效性。通过实车正面碰撞试验获取车身加速度,建立约束系统有限元模型,根据实车试验条件进行碰撞仿真,获取胸部压缩仿真曲线及心脏、肺部和肝... 建立了人体胸部生物力学有限元模型,通过肋骨三点弯曲试验和胸部碰撞块冲击试验验证了模型的有效性。通过实车正面碰撞试验获取车身加速度,建立约束系统有限元模型,根据实车试验条件进行碰撞仿真,获取胸部压缩仿真曲线及心脏、肺部和肝脏等胸腹部器官压力。针对乘员生物力学约束系统有限元模型,采用最优拉丁超立方试验设计方法采样,结合采样数据构建响应面近似模型,利用退火算法对汽车乘员约束系统进行了优化设计。优化后的仿真结果表明,正面碰撞中,乘员胸部压缩量减小,心脏、肺部和肝脏等胸腹部器官压力相对降低。 展开更多
关键词 生物力学有限元模型 约束系统 代理模型 优化设计
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人工颈椎间盘置换术后异位骨化三维有限元模型的建立与意义 被引量:3
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作者 李广州 刘浩 +3 位作者 杨毅 戎鑫 丁琛 陈华 《生物骨科材料与临床研究》 CAS 2019年第5期12-15,共4页
目的建立包含完整下颈椎(C3-C7)的C5/6节段人工颈椎间盘置换(cervical disc replacement,CDR)术后异位骨化(heterotopic ossification,HO)三维有限元模型,为CDR术后HO生物力学相关研究提供基础模型。方法将健康志愿者颈椎CT的DICOM格式... 目的建立包含完整下颈椎(C3-C7)的C5/6节段人工颈椎间盘置换(cervical disc replacement,CDR)术后异位骨化(heterotopic ossification,HO)三维有限元模型,为CDR术后HO生物力学相关研究提供基础模型。方法将健康志愿者颈椎CT的DICOM格式数据依次使用Mimics 16.0、Geomagic 12.0及Pro/Engineer 5.0软件构建包含C3-C7颈椎的C5/6节段CDR术后HO三维有限元模型,并观察HO对手术节段活动度和小关节压力的影响。结果本研究建立了CDR术后HO三维有限元模型,共包含394 198个单元和765 411个节点。运动加载结果显示HO发生后手术节段活动度有不同程度的下降,曲伸、侧弯及旋转活动较无HO模型减少分别20.6%、14.3%及11.3%;手术节段后方小关节应力在HO发生后在不同工况下有不同程度的下降,后伸、左侧弯、右侧弯、左旋转及旋转活动较无HO模型减少分别4.1%、3.7%、10.7%、26%及12.1%。结论本研究成功构建了包含C3-C7下颈椎的C5/6节段CDR术后HO三维有限元模型,为CDR术后HO的生物力学相关研究提供了基础模型。 展开更多
关键词 有限元生物力学 颈椎间盘置换 异位骨化
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外固定支架修复胫骨平台骨折的生物力学特点 被引量:20
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作者 尚红涛 王泉 +1 位作者 刘斌 刘伟 《中国组织工程研究》 CAS 北大核心 2016年第31期4651-4657,共7页
背景:目前有关胫骨平台骨折不同内固定方式的三维有限元模型研究较多,但是关于胫骨平台骨折外固定支架的三维有限元模型的少见报道。目的:采用三维有限元法分析外固定支架修复胫骨平台骨折的生物力学特点。方法:建立胫骨平台骨折锁定钢... 背景:目前有关胫骨平台骨折不同内固定方式的三维有限元模型研究较多,但是关于胫骨平台骨折外固定支架的三维有限元模型的少见报道。目的:采用三维有限元法分析外固定支架修复胫骨平台骨折的生物力学特点。方法:建立胫骨平台骨折锁定钢板固定模型和胫骨平台骨折外固定支架固定模型,采用三维有限元法分析胫骨平台骨折两种固定模型的应力分布以及位移情况。结果与结论:(1)胫骨平台骨折外固定支架固定模型组的平均位移值及最大位移值均小于胫骨平台骨折锁定钢板固定模型组,但差异无显著性意义(P>0.05);(2)胫骨平台骨折外固定支架固定模型组的X轴向位移值、Y轴向位移值均小于胫骨平台骨折锁定钢板固定模型组,但差异无显著性意义(P>0.05);(3)胫骨平台骨折锁定钢板固定的应力主要集中在螺钉和骨组织的交界处以及钢板和螺钉的交界处,最大应力值为173 MPa,明显大于胫骨平台骨折外固定支架固定模型的最大应力值86 MPa。胫骨平台骨折外固定支架固定的应力分布分散,未出现明显的应力集中情况,其中克氏钉夹具和克氏钉交界处、连接杆和螺钉的交界处的应力较其他部位的应力高,为临床上的力学薄弱环节;(4)结果表明,外固定支架固定胫骨平台骨折相对内固定而言,同样具有相似的稳定性和固定强度。 展开更多
关键词 胫骨 骨折 外固定器 有限元分析 生物力学 组织工程 骨科植入物 数字化骨科 胫骨平台骨折 外固定支架 锁定钢板 有限元分析 生物力学
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个性化全骨盆三维有限元建模及骶髂关节骨折脱位模拟 被引量:13
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作者 郑琦 廖胜辉 +3 位作者 石仕元 费骏 魏威 汪翼凡 《医用生物力学》 CAS CSCD 2008年第4期296-300,共5页
目的建立高度仿真的个性化的完整骨盆三维有限元模型,并在此基础上进行骶髂关节骨折脱位的模拟。方法从CT精确重建独立的左、右髋骨和骶骨实体模型,根据髋骨和骶骨的外形特征,利用专门的流线型生物力学有限元网格划分器生成规则的体网... 目的建立高度仿真的个性化的完整骨盆三维有限元模型,并在此基础上进行骶髂关节骨折脱位的模拟。方法从CT精确重建独立的左、右髋骨和骶骨实体模型,根据髋骨和骶骨的外形特征,利用专门的流线型生物力学有限元网格划分器生成规则的体网格模型,并进一步建立骶髂关节的终板、软骨、关节接触面,和骨盆上的主要韧带组织及耻骨间盘。在建立的完整模型上去掉一侧的骶髂关节韧带群进行骨折脱位模拟,并与正常的情况进行对比。结果建立了高精度的个性化全骨盆的三维有限元模型,包括左右髋骨和骶骨的皮质骨、松质骨,骶髂关节的终板、软骨和带摩擦的关节接触面,韧带包括骶髂骨间韧带、骶髂前韧带、骶髂后韧带、骶棘韧带、骶结节韧带、耻骨上韧带和耻骨弓状韧带,以及耻骨间盘。正常模型的加载模拟和骶髂关节骨折脱位模拟的预测结果均与文献试验生物力学结果相符合。结论利用专门的生物力学有限元建模工具能建立更复杂更精确的三维有限元模型,成为全骨盆生物力学分析研究的平台和基础。 展开更多
关键词 完整骨盆 生物力学有限元网格划分器 骶髂关节骨折 计算机辅助设计
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人工髋关节不同材料假体对骨界面的应力分布研究 被引量:26
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作者 林凤飞 郑明 +4 位作者 林朝晖 宋卫 林清坚 谢建荣 陈日齐 《中国矫形外科杂志》 CAS CSCD 北大核心 2008年第7期540-543,550,共5页
[目的]通过计算机三维有限元方法,了解在应力状态下不同材料的人工髋关节假体组合对骨界面的应力分布规律,从生物力学角度为人工髋关节的临床应用和设计制造提供有益的参考。[方法]采用三维有限元法对全髋置换前后进行单髋站立生物力学... [目的]通过计算机三维有限元方法,了解在应力状态下不同材料的人工髋关节假体组合对骨界面的应力分布规律,从生物力学角度为人工髋关节的临床应用和设计制造提供有益的参考。[方法]采用三维有限元法对全髋置换前后进行单髋站立生物力学测试,分析假体植入前后股骨和髋臼总体的应力模式和植入后各种组合的假体对骨界面的应力分布规律。[结果]1、各种假体置换后等效应力(vonMises)峰值均位于假体远端相应股骨区域,但应力峰值有所下降,以股骨距区下降最为明显,遮挡率最大,而以弹性模量较钛合金低的CFR/PSF作为柄的股骨的相应区域的遮挡率较低。2、各种组合的假体对股骨界面的应力从近端至远端均呈逐渐增高趋势,而对于相同的柄比较而言,不管是金属-金属、陶瓷-陶瓷、陶瓷-聚乙烯还是金属-聚乙烯组合,其相应界面应力值无明显差别(P>0.05),但以CFR/PSF作为柄对股骨相应界面存在较高的应力。3、置换前在髋臼顶穹部存在较高应力,并逐渐向周围递减;置换后应力主要集中在髋臼的周边区域,但从髋臼顶部→后下→前下呈逐渐递减趋势;而在相同区域的不同组合其界面应力值无明显差别(P>0.05)。[结论]1、各种假体植入后均在股骨距处形成较高的应力遮挡,而用弹性模量较低的CFR/PSF作为柄,其股骨相应区域的应力遮挡率较低,但股骨相应界面应力较大,而界面应力过大是产生假体微动主要因素。2、股骨界面从近端至远端呈逐渐增高趋势的应力规律符合该假体的设计原理;相同假体柄的不同组合其股骨和髋臼相应界面应力值无明显差别,实验表明力学因素并不是选择假体组合的主要标准。 展开更多
关键词 髋假体 应力/物理 生物力学/有限元
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Biomechanical evaluation of lumbosacral reconstruction after subtotal sacrectomy: A three-dimensional finite element analysis
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作者 Quan Li Longpo Zheng +1 位作者 Zhiyu Zhang Zhengdong Cai 《The Chinese-German Journal of Clinical Oncology》 CAS 2009年第11期638-641,共4页
Objective: The aim of this study was to investigate the biomechanical property of lumbosacral reconstruction after subtotal sacrectomy. Methods: Three three-dimensional finite element models of lumbosacral region we... Objective: The aim of this study was to investigate the biomechanical property of lumbosacral reconstruction after subtotal sacrectomy. Methods: Three three-dimensional finite element models of lumbosacral region were established: (1) An intact model (INT); (2) A defective model (DEF) on which subtotal sacrectomy was performed cephalad to the $1 foramina; (3) A reconstructed model (REC). These models were validated by compared with literature. Upright posture was stimulated under a compression load of 925N. A finite element analysis was performed to account for the displacement and stress on the models. The REC model was calculated twice, with the material property of reconstruction instrument set as titanium and stainless steel, respectively. Results: The displacements of anchor point on the L3 vertebrae in INT, DEF and REC model were 6.63 mm, 10.62 mm, 4.29 mm (titanium) and 3.86 mm (stainless steel), respectively. The stress distribution of the instrument in REC model showed excessively concentration on caudal spinal rod, which may cause rod failure between spine and ilia. The maximum von Mise stress of stainless steel instrument was higher than that of titanium instruments (992 MPa vs 655 MPa), and the value of stress of anchor point around sacroiliac joint in REC model were 26.4 MPa with titanium instruments and 23.9 MPa with stainless steel instruments. Conclusion: Lumbosacral reconstruction can significantly increase the stiffness of spino-pelvis of the patient who underwent subtotal sacrectomy. However, the rod between L5 and ilia is the weakest region of all the instruments. It is suggested that the bending of rod should be conducted carefully and smoothly to avoid significant stress concentration so as to reduce the risk of rod failure. And stainless steel instrument has higher maximum stress and significantly greater stress shielding effect than titanium instrument, which means stainless steel instruments are of higher risk of rod failure and less favorable for lumboiliac arthrodesis than titanium instruments. 展开更多
关键词 subtotal sacrectomy RECONSTRUCTION BIOMECHANICS finite element analysis
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Hipbone Biomechanical Finite Element Analysis and Clinical Study after the Resection of Ischiopubic Tumors
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作者 Ya-qi He Xue-lin Zhang +1 位作者 Bing-hang Tang Ang Yang 《Chinese Medical Sciences Journal》 CAS CSCD 2012年第3期153-160,共8页
Objective To investigate the changes of hipbone biomechanics after the resection of ischiopubic tumors and their relationships with the complications in the convalescent stage, and directing the postoperative pelvic r... Objective To investigate the changes of hipbone biomechanics after the resection of ischiopubic tumors and their relationships with the complications in the convalescent stage, and directing the postoperative pelvic reconstruction. Methods DICOM data were used to create an intact hipbone finite element model and postoperative model. The biomechanical indices on the same region in the two models under the same boundary condition were compared. The differences of displacement, stress, and strain of the two models were analyzed with statistical methods. Results The distribution areas of the hipbone nodes' displacement, stress, and strain were similar before and after the simulated operation. The sacroiliac joint nodes' displacement (P=0.040) and strain (P=0.000), and the acetabular roof nodes' stress (P=0.000) and strain (P=0.005) of two models had significant differences, respectively. But the sacroiliac joint nodes' stress (P=0.076) and the greater sciatic notch nodes' stress (P=0.825) and strain (P=0.506) did not have significant differences. Conclusions The resection of ischiopubic tumors mainly affect the biomechanical states of the homolateral sacroiliac joint and acetabular roof. The complications in the convalescent stage are due to the biomechanical changes of the sacroiliac joint and the acetabular roof and disappearances of the stabilization and connection functions of the pubic symphysis and superior ramus of pubis. 展开更多
关键词 HIPBONE BIOMECHANICS finite element analysis MODEL
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Stress analysis of three-dimensional finite element model of malunion calcaneus during gait
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作者 刘立峰 蔡锦方 梁进 《Journal of Medical Colleges of PLA(China)》 CAS 2004年第1期27-30,共4页
Objective: To analyze the stress distribution of calcaneus with posterior articular facet compressed after fracture and talus during gait. Methods: A wedge under the posterior articular was transected from a normal fi... Objective: To analyze the stress distribution of calcaneus with posterior articular facet compressed after fracture and talus during gait. Methods: A wedge under the posterior articular was transected from a normal finite element model of calcaneus and talus to simulate malformation of compression of the posterior facet after fracture of calcaneus. The model was used to simulate for three subphases of the stance during the gait(heel strike, midstance, push off) and calculate the finite element. The results were compared with normal situation. Results: The stress distribution within the bone in situation of malformation was obtained and regions of elevated stresses for three subphases were located. The results were significantly different from that of normal situation. Conclusion: The simulation of calcaneus and talus in malformation has important clinic implication and can provide an insight into the factors contributing to many clinic pathogenic changes after fracture of calcaneus. 展开更多
关键词 finite element CALCANEUS TALUS FRACTURE stress analysis
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A novel progress of leg tissue properties modeling based on biomechanics
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作者 王沫楠 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2009年第1期57-60,共4页
To describe strategies for addressing technical aspects of computational modeling of leg tissue with the finite element (FE) method, a patient's leg sample was selected and scanned by CT at the direction parallel t... To describe strategies for addressing technical aspects of computational modeling of leg tissue with the finite element (FE) method, a patient's leg sample was selected and scanned by CT at the direction parallel to the Frankfort Horizontal plane. A three-dimensional (3D) finite element model of the human leg was developed using the actual geometry of the leg skeleton and soft tissues, which were obtained from 3D reconstruction of CT images. All joints were defined as contact surfaces, which allow relative articulating movement. The major ligaments were simulated using tension-only truss elements by connecting the corresponding attachment points on the bone surfaces. The bony and ligamentous structures were embedded in a volume of soft tissues. The muscles were defined as non-linear viscoelastic material, and the skin, ligaments and tendons were defined as hyperelastic, while the bony structures were assumed to be linearly elastic. The muhilayer FEM model containing thighbone, tibia, fibula, kneecap, soft tissue was formed after meshing. Diverse forces were imposed on the FEM model. The results show that the multilayer FEM model can represent tissue deformation more accurately. 展开更多
关键词 virtual reality tissue properties model 3D reconstruction finite element method surgery simulation
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Cell Area and Strut Distribution Changes of Bent Coronary Stents:A Finite Element Analysis
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作者 ZHAO Yang WU Wei +1 位作者 YANG Da-zhi QI Min 《Chinese Journal of Biomedical Engineering(English Edition)》 2009年第1期40-46,共7页
Coronary stents are metal coils or mesh tubes delivered to blocked vessels through catheters, whic Recently, special drugs h are expanded by balloons to reopen and scaffold target vessels. are carried by stents (drug... Coronary stents are metal coils or mesh tubes delivered to blocked vessels through catheters, whic Recently, special drugs h are expanded by balloons to reopen and scaffold target vessels. are carried by stents (drug-eluting stents) to further reduce instent restenosis rate after stenting procedure. However, continual study on biomechanical characteristics of stents is necessary provide a more suitable drug loading for better interactions between stents and tissue, or to platform for drug-eluting stents. The purpose of this paper is to show how finite element methods can be used to study cell area and strut distribution changes of bent coronary stents. A same bending deformation was applied to two commercial coronary stent models by a rigid curved vessel. Results show that the stent design influenced the changes of cell area and strut distribution under bending situation. The stent with links had more cell area changes at outer curvature, and the stent with peak-peak ( 〉 〈 ) strut design could have strut contact and overlapping at inner curvature. In conclusion, this finite element method can be used to study and compare cell area and strut distribution changes of bent stents, and to provide a convenient tool for designers in testing and improving biomechanical characteristics of new stents. 展开更多
关键词 coronary stents biomechanical characteristics cell area tissue prolapse strut distribution finite element methods
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Three-dimensional finite element analysis of lumbar vertebra loaded by static stress and its biomechanical significance 被引量:9
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作者 苏佳灿 李卓东 +3 位作者 曹烈虎 禹宝庆 张春才 李明 《Chinese Journal of Traumatology》 CAS 2009年第3期153-156,共4页
Objective: To explore the mechanical behavior of lumbar spine loaded by stress and provide the mechanical basis for clinical analysis and judgement of lumbar spine fracture classification, mechanical distribution and... Objective: To explore the mechanical behavior of lumbar spine loaded by stress and provide the mechanical basis for clinical analysis and judgement of lumbar spine fracture classification, mechanical distribution and static stress. Methods: By means of computer simulation method, the constructed lumbar spine three-dimensional model was introduced into three-dimensional finite element analysis by software Ansys 7.0. The lumbar spine mechanical behavior in different parts of the stress loading were calculated. Impact load is 0-8000 N. The peak value was 8000 N. The loading time is 0-40 minutes. The values of the main stress, stress distribution and the lumbar spine unit displacement in the direction of main stress were analyzed. Results: The lumbar spine model was divided into a total of 121 239 nodes, 112 491 units. It could objectively reflect the true anatomy of lumbar spine and its biomechanical behavior and obtain the end-plate images under different stress. The stress distribution on the lumbar intervertebral disc (L3-L4) under the axial, lateral flexion and extension stress, and the displacement trace of the corresponding processus articularis were analyzed. Conclusion: It is helpful to analyze the stress distribution of lumbar spine and units displacement in static stress loading in the clinical research of lumbar spine injury and the distribution of internal stress. 展开更多
关键词 Lumbar vertebrae Models anatomical Stress mechanical
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Deformation and stress distribution of the human foot after plantar ligaments release:A cadaveric study and finite element analysis 被引量:8
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作者 LIANG Jun YANG YunFeng +2 位作者 YU GuangRong NIU WenXin WANG YuBin 《Science China(Life Sciences)》 SCIE CAS 2011年第3期267-271,共5页
The majority of foot deformities are related to arch collapse or instability,especially the longitudinal arch.Although the relationship between the plantar fascia and arch height has been previously investigated,the s... The majority of foot deformities are related to arch collapse or instability,especially the longitudinal arch.Although the relationship between the plantar fascia and arch height has been previously investigated,the stress distribution remains unclear.The aim of this study was to explore the role of the plantar ligaments in foot arch biomechanics.We constructed a geometrical detailed three-dimensional (3-D) finite element (FE) model of the human foot and ankle from computer tomography images.The model comprised the majority of joints in the foot as well as bone segments,major ligaments,and plantar soft tissue.Release of the plantar fascia and other ligaments was simulated to evaluate the corresponding biomechanical effects on load distribution of the bony and ligamentous structures.These intrinsic ligaments of the foot arch were sectioned to simulate different pathologic situations of injury to the plantar ligaments,and to explore bone segment displacement and stress distribution.The validity of the 3-D FE model was verified by comparing results with experimentally measured data via the displacement and von Mise stress of each bone segment.Plantar fascia release decreased arch height,but did not cause total collapse of the foot arch.The longitudinal foot arch was lost when all the four major plantar ligaments were sectioned simultaneously.Plantar fascia release was compromised by increased strain applied to the plantar ligaments and intensified stress in the midfoot and metatarsal bones.Load redistribution among the centralized metatarsal bones and focal stress relief at the calcaneal insertion were predicted.The 3-D FE model indicated that plantar fascia release may provide relief of focal stress and associated heel pain.However,these operative procedures may pose a risk to arch stability and clinically may produce dorsolateral midfoot pain.The initial strategy for treating plantar fasciitis should be non-operative. 展开更多
关键词 BIOMECHANICS finite element analysis foot arch LIGAMENT STRESS
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A finite element analysis of the stress distribution to the mandible from impact forces with various orientations of third molars 被引量:3
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作者 Yun-feng LIU Russell WANG +1 位作者 Dale A.BAUR Xian-feng JIANG 《Journal of Zhejiang University-Science B(Biomedicine & Biotechnology)》 SCIE CAS CSCD 2018年第1期38-48,共11页
Objective: To investigate the stress distribution to the mandible, with and without impacted third molars(IM3 s) at various orientations, resulting from a 2000-Newton impact force either from the anterior midline o... Objective: To investigate the stress distribution to the mandible, with and without impacted third molars(IM3 s) at various orientations, resulting from a 2000-Newton impact force either from the anterior midline or from the body of the mandible. Materials and methods: A 3 D mandibular virtual model from a healthy dentate patient was created and the mechanical properties of the mandible were categorized to 9 levels based on the Hounsfield unit measured from computed tomography(CT) images. Von Mises stress distributions to the mandibular angle and condylar areas from static impact forces(Load I-front blow and Load II left blow) were evaluated using finite element analysis(FEA). Six groups with IM3 were included: full horizontal bony, full vertical bony, full 450 mesioangular bony, partial horizontal bony, partial vertical, and partial 450 mesioangular bony impaction, and a baseline group with no third molars. Results: Von Mises stresses in the condyle and angle areas were higher for partially than for fully impacted third molars under both loading conditions, with partial horizontal IM3 showing the highest fracture risk. Stresses were higher on the contralateral than on the ipsilateral side. Under Load II, the angle area had the highest stress for various orientations of IM3 s. The condylar region had the highest stress when IM3 s were absent. Conclusions: High-impact forces are more likely to cause condylar rather than angular fracture when IM3 s are missing. The risk of mandibular fracture is higher for partially than fully impacted third molars, with the angulation of impaction having little effect on facture risk. 展开更多
关键词 Finite element analysis Third molar MANDIBLE Biomechanical simulation
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An in vitro and finite element study of load redistribution in the midfoot 被引量:8
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作者 NIU Wen Xin TANG Ting Ting +2 位作者 ZHANG Ming JIANG Cheng Hua FAN Yu Bo 《Science China(Life Sciences)》 SCIE CAS 2014年第12期1191-1196,共6页
A good knowledge of midfoot biomechanics is important in understanding the biomechanics of the entire foot,but it has never been investigated thoroughly in the literature.This study carried out in vitro experiments an... A good knowledge of midfoot biomechanics is important in understanding the biomechanics of the entire foot,but it has never been investigated thoroughly in the literature.This study carried out in vitro experiments and finite element analysis to investigate the midfoot biomechanics.A foot-ankle finite element model simulating the mid-stance phase of the normal gait was developed and the model validated in in vitro experimental tests.Experiments used seven in vitro samples of fresh human cadavers.The simulation found that the first principal stress peaks of all midfoot bones occurred at the navicular bone and that the tensile force of the spring ligament was greater than that of any other ligament.The experiments showed that the longitudinal strain acting on the medial cuneiform bone was-26.2±10.8μ-strain,and the navicular strain was-240.0±169.1μ-strain along the longitudinal direction and 65.1±25.8μ-strain along the transverse direction.The anatomical position and the spring ligament both result in higher shear stress in the navicular bone.The load from the ankle joint to five branches of the forefoot is redistributed among the cuneiforms and cuboid bones.Further studies on the mechanism of loading redistribution will be helpful in understanding the biomechanics of the entire foot. 展开更多
关键词 finite element analysis foot arch BIOMECHANICS cadaveric experiment MIDFOOT
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