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1.
背景:由于骨盆具有复杂的结构,目前对于坐位骨盆的生物力学研究较少,有限元法日益成为骨盆生物力学研究的重要手段。目的:以有限元法研究成人正常静态坐位骨盆应力分布。方法:获取正常成年女性全骨盆CT扫描图像,利用CT数据通过Mimics10.0对图像数据进行重建,利用Geomagic,Proe5.0进行实体建模,输入ANSYS。再根据解剖部位建立骨盆主要韧带。对S1椎体上终板施加600N静载荷模拟坐位时骨盆受力环境,计算该加载方式下骨盆的应力、应变及位移的分布情况。结果与结论:垂直加载600N载荷于骶骨上表面时重力由骶骨经骶髂关节向下传递,到达坐骨结节。此时的坐骨结节处承受较大压应力。有限元模型在静载荷下的特征部位应力、应变值基本能够反应骨盆特有的力学结构特性,模型的准确性较高。计算结果与文献中报道的结果相近,建立的人体全骨盆三维有限元模型较客观地反映人体骨盆的解剖结构和力学特性,可作为骨盆生物力学研究的工具及满足临床研究的需要。  相似文献   

2.
骨盆环三维有限元模型的建立   总被引:3,自引:2,他引:1  
利用螺旋CT数据通过Mimics 12.0建立具有高度几何相似性的左、右骨盆、骶骨、股骨近端复合体的面模型,利用Abaqus 6.5进行实体建模.根据各单元CT值对有限元模型进行材料属性赋值,再根据解剖部位建立骨盆主要韧带.利用有限元分析软件Abaqus 6.5对S1椎体上终板施加600 N静载荷模拟站立位骨盆受力环境,计算特征部位位移、最大应变及von Mises应力.有限元模型在静载荷下的特征部位应力、应变值基本能够反应骨盆特有的力学结构特性,模型的准确性较高.在几何外形近似的情况下,特征材料赋值建模能够提高有限元模型的汁算准确性;在有限元计算时应通过更为接近生理状况下的边界及载荷条件进行模拟以提高结果的准确性.  相似文献   

3.
垂直载荷作用下骨盆的三维有限元分析   总被引:4,自引:1,他引:4  
背景:目前对骨盆的力学分析还处于极其粗糙阶段,而有限元法因其具有不受样本量限制,实验误差小,重复性好等优点,正日益成为骨盆生物力学研究的重要手段。 目的:建立正常骨盆的三维有限元模型,分析骨盆在垂直载荷作用下的应力/应变和位移分布。 设计、时间及地点:三维有限元分析,单一样本观察。于200703/09在南方医科大学生物力学实验室完成。 材料:健康成年男性志愿者1例进行PET—CT扫描,层厚1FfLrn,得N-维原始图像以DICOM格式输出。 方法:应用Mimics、Freeform、ANSYS等软件进行三维重建,并建立正常骨盆的有限元模型。模拟人体双腿直立位的生理姿势,对模型施加500N轴向载荷。具体方式为约束双侧靛臼,向骶骨椎体上表面垂直加压,压力均匀分布于各个结点。 主要观察指标:计算该加载方式下骨盆的应力、应变及位移的分布情况。 结果:垂直加载500N载荷于骶骨上表面时,应力经两侧骶骨翼、骶髂关节,斜向下方经过坐骨大切迹附近,髂骨中央弓状线,传导至两侧髋臼。骨盆前环即耻骨支和耻骨联合受力较小。应变集中在两侧骶髂关节,绝对值很小,前方的耻骨联合处应变极小,呵忽略不计。位移以骶骨背侧的骶正中嵴处最大。 结论:正常骨盆是一个非常稳定的力学结构。过大的垂直应力容易引起骶骨或骶髂关节受损导致骨盆的垂直稳定性下降;恢复骶骨至髋臼的连续性对应力传导非常重要。  相似文献   

4.
目的:对模仿站立及坐位两种状态对骨盆髋臼加载后进行三维有限元模型力学分析,观察相关力学参数变化。方法:①湿髋臼标本模型来源于解放军第二军医大学解剖学教研室。髋臼:对一具成年湿骨盆尸体标本行CT扫描成像得到每层横截面图像,提取边界坐标,利用有限元分析软件ANSYS5.6构建髋臼三维模型,并划分为121239个结点、112491个单元。同时将骶髂关节和耻骨联合部位锁定,模仿站立位对髋臼加载,力的方向按股骨颈力线方向,大小为400N(约80kg体质量一半)。分析加载后髋臼的三维力场分布。②骨盆模型:2004-08从自愿者中随机选取正常成年男性,然后行CT扫描。CT扫描范围从第3腰椎至坐骨结节,将扫描后图像用ANSYS5.6软件构建正常骨盆模型,并划分为356710个单元格。固定好正常骨盆模型的两侧坐骨结节,模仿坐位对骨盆加载,于腰椎上施加一竖直向下的力,大小为500N,方向与Z轴相反,通过有限元分析计算获取应力分布图像。结果:①髋臼三维有限元模型模仿站立位加载后在耻骨支、坐骨支、方区部、骶髂关节部、髋臼后壁部有较高应力出现,单元结构所受到的平均等效应力为(11.578~23.437)MPa。②骨盆三维有限元模型模仿坐位加载后在骶髂关节及坐骨结节部有较高应力出现,单元结构所受到的平均等效应力为(15.734~20.286)MPa。结论:实验结论提示,骨盆髋臼骨折的内固定应强调以满足术后早期卧床功能训练为目的的有效内固定,避免早期负重。  相似文献   

5.
许硕贵  佟大可  苏佳灿  张春才  蔡郑东  吴建国 《中国临床康复》2006,10(29):110-111,117,i0004
目的:对模仿站立及坐位两种状态对骨盆髋臼加载后进行三维有限元模型力学分析,观察相关力学参数变化。 方法:①湿髋臼标本模型来源于解放军第二军医大学解剖学教研室。髋臼:对一具成年湿骨盆尸体标本行CT扫描成像得到每层横截面图像,提取边界坐标,利用有限元分析软件ANSYS5.6构建髋臼三维模型,并划分为121 239个结点、112 491个单元。同时将骶髂关节和耻骨联合部位锁定,模仿站立位对髋臼加载,力的方向按股骨颈力线方向.大小为400N(约80kg体质量一半)。分析加载后髋臼的三维力场分布。②骨盆模型:2004-08从自愿者中随机选取正常成年男性,然后行CT扫描。CT扫描范围从第3腰椎至坐骨结节,将扫描后图像用ANSYS5.6软件构建正常骨盆模型,并划分为356 710个单元格。固定好正常骨盆模型的两侧坐骨结节,模仿坐位对骨盆加载,于腰椎上施加一竖直向下的力,大小为500N,方向与Z轴相反,通过有限元分析计算获取应力分布图像。 结果:①髋臼三维有限元模型模仿站立位加载后在耻骨支、坐骨支、方区部、骶髂关节部、髋臼后壁部有较高应力出现,单元结构所受到的平均等效应力为(11.578-23.437)MPa。②骨盆三维有限元模型模仿坐位加载后在骶髂关节及坐骨结节部有较高应力出现,单元结构所受到的平均等效应力为(15.734-20.286)MPa。 结论:实验结论提示,骨盆髋臼骨折的内固定应强调以满足术后早期卧床功能训练为目的的有效内固定,避免早期负重。  相似文献   

6.
目的:探讨骨盆受到静力载荷作用后的力学行为特征,为临床分析及判断骨盆力学分布、静载荷影响提供力学基础。方法:实验于2002-01/2004-04在第二军医大学长海医院骨科实验室和同济大学生命科学与技术学院生物力学实验室完成。采用计算机仿真模拟方法,将所构建骨盆三维实体模型导入三维有限元分析软件ANSYS7.0,分别计算单侧髂前上棘和单侧髂骨正后方静载荷作用下骨盆的力学行为表现,静载荷为8000N,分析主应力值、应力分布情况以及主应力方向上骨盆单元的位移。结果:单侧髂前上棘侧方加载下,应力沿着受力点与骶髂关节连线方向传导,没有应力沿着髋臼或者耻骨、坐骨传导;单侧髂骨后方静载荷加载时,应力沿着髂骨纵行方向、髂骨与骶髂关节部位连线方向、同侧耻骨上支传导。结论:分析静载荷作用下骨盆各部位应力分布以及骨盆各个单元在应力作用下的位移变化,有助于临床上进行骨盆损伤内固定力点的选择以及进一步明确骨盆内在应力值分布。  相似文献   

7.
静载荷作用下骨盆三维有限元分析及其生物力学意义   总被引:6,自引:1,他引:6  
目的:探讨骨盆受到静力载荷作用后的力学行为特征,为临床分析及判断骨盆力学分布、静载荷影响提供力学基础。方法:实验于2002—01/2004—04在第二军医大学长海医院骨科实验室和同济大学牛命科学与技术学院生物力学实验室完成采用计算机仿真模拟方法,将所构建骨盆三维实体模犁导入三维有限元分析软件ANSYS7.0,分别计算单侧髂前上棘和单侧髂骨正后方静载荷作用下骨盆的力学行为表现,静载荷为8000N,分析主直力值,应力分布情况以及主应力方向上骨盆单元的位移。结果:单侧髂前上棘侧方加载下,应力沿着受力点与骶髂关节连线方向传导,没有应力沿着髋臼或者耻骨、坐骨传导;单侧髂骨后方静载荷加载时.应力沿着髂骨纵行方向、髂骨与骶髂关节部位连线方向、同侧耻骨上支传导。结论:分析静载荷作用下骨盆各部位应力分布以及骨盆各个单元在应力作用下的位移变化.有助于临床上进行骨盆损伤内固定力点的选择。  相似文献   

8.
背景:有限元法能对复杂的结构、形态、载荷和材料力学性能进行应力分析比较,模拟的条件更接近正常,结果更加可信,已经是骨科生物力学研究中的重要手段.目的:以有限元分析方法建立骨盆骶髂关节(单侧)脱位模型,比较前路钉板内固定及骶髂关节拉力内固定治疗后的生物力学稳定性.方法:在正常骨盆三维有限元模型的基础上,截断骶髂关节问的骶髂前后韧带(包含骶髂骨间韧带)以及骶结节韧带和骶棘韧带等盆底韧带,造成骶髂关节脱位.分别在前路钉板内固定系统(共2块重建钢板6枚螺钉)及骶髂关节拉力螺钉内固定(2枚拉力螺钉)两种固定方法的模型上,加载后进行非线性有限元分析.计算该加载方式下的骨盆应力、应变及位移的分布情况.结果与结论:建立了高精度骨盆骶髂关节脱位两种内固定的三维有限元模型.通过应力应变云图分析与比较后发现,采用骶髂关节拉力螺钉内固定相对于前路钢板内固定移位的总位移小,应力分布均匀,无明显高度集中现象,固定强度更大,固定后的骨盆更稳定.利用有限元方法分析骨盆骶髂关节脱位两种内固定生物力学稳定性,具有较高真实性、精确度和可重复性,结果与其他生物力学实验结果相一致,能满足临床骨盆损伤研究的需要.  相似文献   

9.
背景:由于位置较深以及复杂的结构,目前对于骶髂关节的生物力学的了解并不全面,而对于该部位重建方式的生物力学研究则更少。目的:建立高位骶骨切除术后的骨盆有限元模型,并进行有效性验证,为骶髂关节重建方式的有限元评价提供平台。时间及地点:2008-01/03在解放军第二军医大学长海医院骨科实验室完成了三维有限元模型的建立与验证。材料:调取非腰椎、骨盆病变的成年男性骨盆CT扫描图像,扫描范围从下腰椎至坐骨结节,共有DICOM格式的CT图像132幅。方法:分别构建完整骨盆和经S1神经孔上缘水平施行骶骨次全切除术后的缺损骨盆的三维有限元模型。模拟Hugate等的生物力学实验情况,对完整骨盆模型施加3000N,对缺损骨盆模型施加1000N的垂直载荷进行计算,得到相应的位移和刚度,然后再与文献中的结果进行比较。主要观察指标:选择L5的最大下沉位移(U3)以及由此计算得到的刚度作为评价骶髂关节的稳定性的指标。结果:完整和缺损骨盆模型中L5的最大下沉位移分别为7.99mm和7.68mm,由此计算得到的刚度分别为375N/mm和130N/mm;文献中相应工况下的骨盆位移分别为(10.73±5.10)mm和(11.71±5.74)mm,刚度分别为(353±231)N/mm和(101±49)N/mm。结论:成功建立了保留骶髂关节活动的骶骨次全切除术后骨盆的有限元模型,计算结果与文献中报道的结果较好地吻合,可认为有效,能够用于各种骶髂关节重建方式的有限元评价。  相似文献   

10.
背景:对局部椎体或整个脊柱进行推拿手法的有限元分析具有一定的局限性。目的:通过建立腰-盆-髋有限元模型对腰部推拿手法进行相关生物力学分析。方法:利用螺旋CT数据通过Mimics10.01建立具有高度几何相似性的腰椎、骨盆和股骨近端复合体骨骼的面模型,利用geomagic9精修模型,在hypermesh10.0中划分网格,添加椎间盘和主要韧带。并对有限元模型各部件进行材料属性赋值。利用有限元分析软件模拟腰椎推拿手法三工况加载,计算特征部位位移、最大应变及应力。结果与结论:有限元模型在三工况载荷下的特征部位应力、应变值基本能够反映腰-盆-髋特有的力学结构特性,模型的仿真性较好。在近似的几何外形下,据生物力学资料报道的材料赋值建模保证了有限元模型计算的正确性;模拟接近生理状况下的边界及载荷条件进行计算可以确保结果的准确性。  相似文献   

11.
[Purpose] The purpose of this study was to compare joint angles between normal children and those with spastic diplegia using three-dimensional gait analysis. [Subjects and Methods] The study subjects were eight patients with spastic diplegia and eight normal children. Three-dimensional gait analysis was used for the survey. The measured gait variables were the joints of the lower extremity in the sagittal plane, frontal plane, and transverse planes and the maximum and minimum angles of their stance phase and swing phases. [Results] In the sagittal plane, the maximum angles of both the right and left pelvis and hip joint in the stance phase and swing phases were significantly greater for children with spastic diplegia than for normal children. In the stance phase of the right side of the hip joint, the maximum angles of the hip in the swing phase and the knee joint’s minimum angles in the stance phase differed significantly. In the transverse plane, there were a significant differences on the left side of the pelvis in the maximum angles in the swing and stance phases. There were also significant differences on the right side pelvis, in the maximum and minimum angles in the stance phase and minimum angles in the swing phase. [Conclusion] Children with spastic diplegia employ a different gait strategy and pattern from normal children.Key words: Spastic diplegia, Joint angle  相似文献   

12.
[Purpose] Limited studies exist on the impact of sustained work at a visual display terminal (VDT) on the position and motion of the pelvis and lumbar spine. We evaluated the changes in movement of the lumbar column and pelvis during VDT work. [Participants and Methods] We evaluated the sitting posture of 20 healthy adults while they performed VDT work. The effects of the sitting posture on lumbo-pelvic position and motion were captured using a three-dimensional accelerometer. Between-posture effects of VDT work were evaluated using an analysis of variance (ANOVA). A two-way ANOVA was used to assess the root mean square (RMS) values of the 80-min VDT work period for each posture. A one-way ANOVA was used to evaluate pre- and post-work changes in RMS values during the finger floor distance test (FFD). [Results] People in the dynamic sitting balance chair (DSBC)-based posture demonstrated significantly higher pelvic RMS values than those in reclining and upright sitting postures. The DSBC-based posture was also associated with significantly higher pre- and post-work lumbar and pelvic RMS values during the FFD than in the reclining and upright sitting postures. [Conclusion] The dynamic balance chair may be an effective method of establishing a pattern of spinal exercise during prolonged sitting.Key words: Dynamic sitting posture, Visual display terminal, Acceleration sensor  相似文献   

13.
背景:有限元法因其具有不受样本量限制,实验误差小,重复性好等优点而成为防滑倒生物力学研究的重要手段。目的:建立正常骨盆以及佩戴护具骨盆的三维有限元模型,分析滑倒过程中骨盆各部位的应力、应变和位移分布,验证护具的有效性。方法:以中国数字人原始资料应用Abaqus 6.51软件构建正常骨盆以及佩戴护具骨盆的三维有限元模型,固定约束地面刚体,对整个骨盆模型加载2 m/s的速度载荷,程序运算后观测骨盆模型佩戴护具前后的应力、应变及位移随时间的变化规律和分布云图。结果与结论:与未佩戴护具比较,佩戴护具时滑倒过程中骨盆与地面的接触力、骨盆与地面产生最大接触力时松质骨最大压缩应变、大转子以及股骨颈周围应变最大值、大转子和股骨颈附近的最大von-Mises应力值、大转子和股骨颈处的平均应力值等均明显减小。提示髋部保护支具对大转子具有保护作用,能有效降低人体滑倒时转子间骨折的发生率。  相似文献   

14.
OBJECTIVE: To develop a systematic methodology towards a realistic model, of the body/chair interaction as a tool to analyze sitting posture and the cushioning system influence on the pelvis/lower back stress development. BACKGROUND: The model concept comprises an integrative structure including both the pelvis girdle and the lower spine, as well as the surrounding soft tissues with their specific characteristic behavior during sitting. METHODS: In vivo measurements were performed, in order to obtain a set of contact moduli defining the behavior of the soft tissues under tension during the sitting down process. Additionally in vivo indentation of a metal ball into the same soft tissues during sitting were performed in order to obtain the characteristic moduli. A finite element model was also developed for the specific analyses. RESULTS: Validation of the model was achieved by comparing its results with in vivo measurements of contact stresses developed between the body and a stiff target seat area. Loading the model using two alternative cushioning materials lead to different sets of stresses within the model; as the stiffness of the seat decreased, the peak contact stresses, as well as the internal body stresses substantially decreased. RELEVANCE: Body/chair interaction model methodology may be a practical means to analyze and design structures and materials in order to achieve more comfort during work or leisure, as well as for geriatric or impaired subjects.  相似文献   

15.
背景:已有文献报道骶髂关节损伤及固定的生物力学研究,但多是在尸体标本或人工骨模型上模拟骶髂关节损伤。目的:利用三维有限元方法对骶髂关节脱位前路钢板内固定的垂直稳定性进行分析。方法:在完整骨盆三维有限元模型的基础上,建立一侧骶髂关节脱位后前路钢板内固定模型。对模型施加500N轴向载荷,经计算得到应力、应变及位移云图,并与完整骨盆的同一工况进行比较分析。结果与结论:在内固定系统处出现了应力集中现象,尤其以靠近骶髂关节的螺钉周围应力最大,远远大于完整骨盆同一工况下的最大应力。应变以健侧骶髂关节最大,内固定侧骶髂关节无应变。位移以损伤侧骶髂关节处最大,约为完整骨盆的2倍。提示前路钢板内固定治疗骶髂关节脱位,骨盆在垂直方向上稳定性较差,且钢板螺钉处出现了应力集中现象。  相似文献   

16.
BACKGROUNDWith the modernization of society and transportation in the last decades in China, the incidence of high-energy trauma increased sharply in China, including that of acetabular fractures.AIMTo establish different finite element models for acetabular posterior column fractures involving the quadrilateral area of the acetabulum.METHODSThe three-dimensional models of the normal and fractured pelvis and the five internal fixations were established using the computed tomography data of the pelvis of a living volunteer. After the vertebral body model was inserted in the way of origin matching and all cancellous bones were copied using the duplicated cancellous bone model as the subtractive entity, the Boolean operation was performed on the pelvis model to obtain the model of the complete pelvis cortical and cancellous bones.RESULTSIn the standing position, the maximum stress was 46.21 MPa. In the sitting position, the sacrum bore the simulated gravity load at the upper end. When comparing the five fixations, there were no significant differences in the stress mean values among groups (sitting: P = 0.9794; standing: P = 0.9741). In terms of displacement, the average displacement of the internal iliac plate group was smaller than that of the spring plate group (P = 0.002), and no differences were observed between the other pairs of groups (all P > 0.05). In the standing position, there were no significant differences in the mean value of displacement among the groups (P = 0.2985). It can be seen from the stress nephogram of the internal fixations in different positions that the stress of the internal fixation was mainly concentrated in the fracture segment.CONCLUSIONThere were no significant differences among the fixations for acetabular posterior column fractures involving the quadrilateral area of the acetabulum.  相似文献   

17.
基于CT及逆向工程软件构建正常人体骨盆三维有限元模型   总被引:1,自引:0,他引:1  
背景:骨盆是人体骨骼中形态及结构最复杂的部分,许多学者一直致力于其生物力学的研究。由于骨盆形状极其不规则,所附着肌肉及韧带解剖结构复杂,建立精确的包含主要肌肉及人韧带的骨盆有限元模型十分困难。 目的:建立正常成年人骨盆的三维有限元模型,为后续骨盆的生物力学分析提供数字模型。 方法:采集健康成年男性志愿者的骨盆CT数据,将DICOM格式的CT图像导入医学影像三维重建软件Mimics 10.0进行图像的分割及三维重建,将导出文件导入逆向工程软件Geomagic studio 11中对图像进行曲面化处理,建立曲面模型,使其更加光顺,将生成的曲面模型导入有限元分析软件Ansys 14.0中进行有限元网格划分。 结果与结论:建立了正常成年人骨盆的三维有限元模型,总单元数为818294个,总节点数为149290个。课题基于健康成年男性志愿者的骨盆 CT 图像建立骨盆有限元模型,所得的模型精确度高、逼真、具有良好的解剖及几何相似性,可为下一步骨盆的生物力学分析提供基础。  相似文献   

18.
背景:目前关于骨盆生物力学有限元分析主要是针对正常和外伤后的骨盆,缺乏对EnnekingⅡ区的恶性肿瘤切除、组配式人工半骨盆假体重建骨盆环缺损后骨盆生物力学模型进行三维有限元分析。目的:观察正常骨盆及半骨盆切除、组配式人工半骨盆假体置换后患者站立体位下应力分布。方法:采用CT薄层扫描采集1例半骨盆切除、组配式人工半骨盆假体置换后17个月患者的骨盆原始数字影像和通信标准数据,将数据导入Mimics8.1软件建立三维实体模型,再将实体模型导入Abaqus6.7-1分析软件,分别以正常骨盆及组配式人工半骨盆假体置换后的骨盆,建立三维有限元模型,并分别对双脚站立、患侧单脚站立两种静力状态下进行生物力学加载并对结果进行分析。结果与结论:在正常骨盆及组配式人工半骨盆假体置换后骨盆2种有限元模型中,不同站立体位相同载荷下健侧骨盆应力值接近;患侧组配式半骨盆假体不同站立体位时应力最大值均出现在髋臼杯上方CS脊柱内固定器与髋臼杯连接部内侧,所受最大应力均远低于其疲劳强度;组配式半骨盆假体重建后骨盆站立位时应力的分布规律与正常骨盆基本一致。说明:①组配式人工半骨盆假体置换对健侧骨盆影响较小。②站立体位下组配式人工半骨盆假体安全性好。③组配式人工半骨盆假体重建后的骨盆符合人体正常生物力学规律,具有良好的生物力学相容性基础。  相似文献   

19.
OBJECTIVE: To develop a new sitting spinal model and an optimal driver's seat by using review of the literature of seated positions of the head. spine, pelvis, and lower extremities. DATA SELECTION: Searches included MEDLINE for scientific journals, engineering standards, and textbooks. Key terms included sitting ergonomics, sitting posture, spine model, seat design, sitting lordosis, sitting electromyography, seated vibration, and sitting and biomechanics. DATA SYNTHESIS: In part I, papers were selected if (1) they contained a first occurrence of a sitting topic, (2) were reviews of the literature, (3) corrected errors in previous studies, or (4) had improved study designs compared with previous papers. In part II, we separated information pertaining to sitting dynamics and drivers of automobiles from part 1. RESULTS: Sitting causes the pelvis to rotate backward and causes reduction in lumbar lordosis, trunk-thigh angle, and knee angle and an increase in muscle effort and disc pressure. Seated posture is affected by seat-back angle, seat-bottom angle and foam density, height above floor, and presence of armrests. CONCLUSION: The configuration of the spine, postural position, and weight transfer is different in the 3 types of sitting: anterior, middle, and posterior. Lumbar lordosis is affected by the trunk-thigh angle and the knee angle. Subjects in seats with backrest inclinations of 110 to 130 degrees, with concomitant lumbar support, have the lowest disc pressures and lowest electromyography recordings from spinal muscles. A seat-bottom posterior inclination of 5 degrees and armrests can further reduce lumbar disc pressures and electromyography readings while seated. To reduce forward translated head postures, a seat-back inclination of 110 degrees is preferable over higher inclinations. Work objects, such as video monitors, are optimum at eye level. Forward-tilting, seat-bottom inclines can increase lordosis, but subjects give high comfort ratings to adjustable chairs, which allow changes in position.  相似文献   

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