人体足踝系统建模与相关力学问题研究
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摘要
在我国,特别是近些年,随着经济的不断发展和人民生活水平的不断提高,人们对于如何更好地提高自身生命质量的要求更加强烈。人体生物力学研究正是从力学的角度来研究人体的生物学相关理论和运动机理,从而为临床医学和康复医学的发展提供有力的理论指导和帮助。本研究所的“中国力学虚拟人”项目是国家自然科学基金2006年批准立项的重点项目(30530230),其研究目标是建立一个中国标准的人体的“骨骼-肌肉-韧带”生物力学系统,进行人体局部和整体的静力学、运动学和动力学研究,从而解决医学上出现的相关生物力学问题。
本论文的研究内容是“中国力学虚拟人”项目中的子课题之一:人体足踝骨肌系统建模与相关力学问题研究;同时本课题也是我所与复旦大学附属华山医院足踝外科、英国Salford大学人类功能康复研究中心(CRHPR)建立的国际合作项目,并得到了英国皇家学会(UK Royal Society)的项目支持(Grant: IPJ/2006/R3)。
力学解剖结构上,足踝部不仅包括26块骨骼,而且骨骼结构与错综复杂的韧带、跖腱膜、肌肉肌腱等软组织形成了稳定的关节结构和足弓结构;在功能上,足踝起到支撑承重、吸收震荡、传递运动和杠杆平衡等作用,是人类直立行走的基本保证。然而现实生活和临床医疗中,足踝的生物力学研究未得到应有的重视,目前随着人们对足踝认识的不断深入,其重要性也逐渐显现出来。在人体生物力学研究领域中,足部生物力学研究正是随着足外科的发展在近些年内渐渐兴起,主要由于以下几方面因素:首先,从临床角度来说,随着各种足部疾病发病率不断上升,如糖尿病并发症糖尿病足、 外翻足、老年跟痛足等,医学工作者迫切地需要知道这些足部病理现象的原因和科学的治疗方法;再者,从市场角度来说,各种功能鞋、矫形器和运动鞋有着很大的消费市场,患者与消费者往往要求这类鞋具、支具有特殊功能、穿着舒适并具有保护作用;最后,从技术角度来说,各种测量技术和计算机软硬件的快速发展为足部生物力学研究提供了必要条件,包括运动捕捉系统、压力平台、鞋内压力传感器、超声波测量、CT和MRI三维扫描技术、各种逆向工程反求软件以及有限元分析软件等等。本论文正是基于以上背景进行人体足踝系统的建模仿真和相关实验测量的研究,主要内容包括以下几个方面:
(1)基于健康人体的足踝三维MRI扫描数据,建立了三种常见姿态(背屈状态、平衡站立姿态和后跟提起姿态)下足踝三维几何实体模型与有限元模型,这三组模型中均包含了足部全部骨骼以及组成踝关节的胫骨和腓骨末端部分、韧带和跖腱膜、关节软骨和外部软组织结构等的详细几何信息,数据完整、解剖相似性高,并对这三种姿态的几何与有限元模型中的数据信息进行了模块化的处理和管理,模型中建立的各模块化组织结构可独立使用,且二次改建的可行性高。
(2)为了给足踝模型仿真分析提供必要的依据和信息,我们以健康的足踝为研究对象,对行走、站立和跳跃状态下的足踝受力状态进行了测量与分析。其中,以每分钟行走的步数这一频域指标作为基本参数,测量了不同步速行走时站立相中足底反力情况,通过统计分析和回归分析量化了步态中的一些关注的力学参数值,以及它们与步速、体重和身高的关系;此外还测量了四条浅层足外在肌(胫骨前肌、腓骨长肌、比目鱼肌和腓肠肌)在不同运动状态(正常步行、跳跃状态以及双足平衡站立时重心前移情况)下表面肌电信号,从而定性地研究和分析了它们在这些运动过程中肌力发力情况。
(3)以平衡站立姿态下的足踝有限元模型为例,对模型进行了详细的论证和验证工作。针对模型中的几何结构的简化和假设、单元选择、关节接触问题处理、材料属性确定等内容进行了详细的分析比较和论证,解决了一些关键性的技术问题;此外还设计了活体实验验证方案,将足底反力、足底压力分布和足部垂直压缩变形这三项指标同步采集,用以比较足踝有限元模型预测的相应结果,从而验证了足踝模型的有效性和正确性。此足踝模型的活体验证方案将当前几种常用的足踝研究测量方法有效的结合在一起,对人体没有任何伤害性。同时基于以上被验证的模型,开发了一个人体足踝模型仿真软件,整个软件由几何模型、有限元模型、原始数据、相关参数与基本算例五部分组成,将以上建立的足踝几何模型和有限元模型整体模型、各骨骼的独立模型以不同的数据格式提供给用户,为研究人员和医学工作者提供一个足踝模型仿真分析平台;同时附上了原始MRI扫描数据、足踝模型中的相关参数和一个典型站立姿态下的算例介绍;此足踝模型软件正在注册中,属于国内外足踝有限元仿真的首个软件。
(4)对行走步态中的三个典型姿态(后跟着地、站立中相与后跟离地)进行了准静态有限元模拟,仿真计算中考虑了不同姿态下足踝外在肌的肌力作用;仿真结果与实验测量结果(足底压力和足底反力)一致性高,同时结果量化了这三个姿态下足踝内外部组织结构的受力信息,包括骨组织上的应力应变分布和软组织受力状态的变化等,这为全面认识行走步态中足踝内部的受力情况提供了重要的参考。
(5)采用此足踝有限元模型研究和分析了足踝结构中两个基础力学问题:一是分别模拟了站立载荷下跖腱膜、弹簧韧带、足底长韧带和短韧带独立释放后的情况,与健康状态下同样站立载荷时的模型预测结果进行了多方面的比较,量化了它们在维持足弓静态稳定性中所起的相对力学作用;二是通过模拟站立位下足底载荷分布变化情况,定量地分析了跖骨的应力应变的分布变化情况,从而增加对跖骨生物力学的认识,并据此对 外翻矫形手术方案的要求提出理论支持。
(6)对健康年青测试者、健康年长测试者和II型糖尿病患者三组人群进行正常行走步态下足底压力分布测量和统计分析;同时通过改建前面建立的足踝有限元模型,分别对以上三组人群足底软组织受力状态进行了计算仿真,分析了足底软组织层属性改变对足踝内部的受力影响。通过测量与仿真,对不同测量人群的足底软组织的外部受力情况和内部受力状态进行了比较,得到了正常人和糖尿病患者足部受力的差异,为预防糖尿病患者发生足部溃疡提供有用的力学信息。
总之,本文以足踝三维有限元建模和分析为中心,同时将实验测量与临床问题结合起来。文中建立的三种典型姿态下足踝肌骨系统的三维几何和有限元模块化的模型,为人体足踝系统生物力学研究提供了一个分析平台,可以应用于足踝基础生物力学研究,也可以结合临床医学和康复医学中一些具体足踝部问题进行模型二次改建后进行相关的力学仿真分析;本文还针对足踝生物力学的一些基本问题进行了实验测量研究与相应的有限元仿真,量化了足踝的内外部力学信息,为足踝的临床和康复生物力学的发展提供了重要的力学依据。
In our country, particularly in recent years, with the continuous economic development and the rising of the living standards, people have more intense demands on how to really improve their quality of life. Biomechanical study of the human body from a mechanical point of view is to study human biology-related theoretical knowledge and motion mechanism, thus provides strong theoretical guidance and help for the development of clinical medicine and rehabilitation medicine. Our Institute's "Chinese Mechanical Virtual Human" project is the National Natural Science Foundation key project which was approved in 2006 (No. 30.53023), whose research goal is to establish a Chinese standard biomechanical system of the human body, including "bones - muscles - ligament", for partial and whole body statics and kinematics, as well as the dynamics studies, so as to solve the medical problems related to biomechanics.
The research in this dissertation is an sub-project of the key project "Chinese Mechanical Virtual Human": the human foot-ankle musculoskeletal system modeling and related mechanical research. At the same time, it is also an international collaborative project of our institute with the orthopedics department, Fudan University affiliated Huashan Hospital, and England Rehabilitation Centre for Rehabilitation & Human Performance Research (CRHPR), Salford University, while supported by the British Royal Society (UK Royal Society) (Grant: IPJ/2006/R3).
Human foot-ankle not only includes 26 bones, but also the complex structures of ligaments, plantar aponeurosis, muscle and tendon, joint capsules joints and the stable arch structure; From a functional point of view, the foot-ankle complex is a supporting and load-bearing structure to absorb shock and transfer movement. However, in real life and medical care, the ankle biomechanics system was not paid enough attention. With the current continuous understanding of the foot-ankle, its importance gradually displayed. In the human biomechanics field, the foot-ankle biomechanics research is rising in recent years with the development of foot and ankle surgery, mainly due to the following factors: Firstly, from a clinical point of view, with a rising incidence variety of foot diseases, such as the complications of diabetes foot, hallux valgus feet, foot pain and so on, medical researchers are eager to know the causes of foot pathology; Secondly, from a market perspective, the various functions shoes, orthoses and sport shoes have a large consumer market, patients and consumers tend to demand such shoes or fixers which is comfort, having a special function and playing a protective role; Finally, from a technical point of view, a variety of measurement techniques and computer hardware and software provide the necessary conditions for the rapid development of foot biomechanics study, including motion capture system, the pressure platform, the plantar pressure sensors, ultrasonic measurement, three-dimensional CT and MRI scanning technologies, various anti-seeking software and finite element analysis softwares and so on. The research was carried out based on the above background, and the specific research content included the following:
(1) Based on the three-dimensional MRI scan images of ankle of one healthy subject, three-dimensional geometric solid models and finite element models under three typical postures (heel-striking, mid-stance and heel-lift) were established. These physical models include detailed geometric information in the foot: all of the foot bones and the distal segments of the tibia and fibula and fibula, ligaments and plantar aponeurosis, joint cartilages and external soft tissue structures, which have high data integrity, high anatomical similarity and revisability. All data of these geometrical and finite element models were proceeded and managed in modular style. The modular structure can be used independently, and feasible for secondary alteration.
(2) With healthy young people as research subjects, plantar reaction forces were measured under different walking rhythms (beat per minute). Using this kind of frequency-domain parameter, statistical analysis and regression analysis were used to quantify some of the basic mechanical parameters values and their relationships with walking rhythms, body weight and height. Surface EMGs of four extrinsic muscles (tibialis anterior, peroneus longus, soleus and gastrocnemius) under different states of motion (normal walking, jumping conditions and balanced standing with an anterior shift of CoP) were measured to research their muscle strengths in the course of these movements. These experiments provided the necessary basis and information for the simulation of the foot-ankle model.
(3) Aiming at the finite element model under static standing posture, a detailed verification and validation work for the model were carried out. Here, a number of key technical issues, such as major simplifications of the model and assumptions, element selections, joint contact problem handling, material properties and so on were determined by a detailed analysis and comparison; An in vivo validation test was designed to synchronously record foot reaction force, plantar pressure distribution and vertical deformation. These measured results were used to compare to the corresponding model predictions, in order to validate the effectiveness and correctness of the model. This in vivo model validation method combined several commonly used measurement methods effectively, and was unharmful to human body. Meanwhile, based on the validated foot model, we developed a software of the human foot&ankle model which included five parts: geometric model, finite element model, the original data, the relevant parameters and calculation case; all established geometric model and finite element model of the whole model as well as individual skeletal part of the model were provided to the user with different data formats, in this way provide a foot&ankle simulation analysis platform to users for research or medical workers. Currently, this software is the first case at home and abroad.
(4) The quasi-static finite element simulation analysis of foot&ankle under three typical postures ( heel-striking, mid-stance and heel off) was carried out for the first time and the external muscle forces were taken into account; FE simulated results (plantar pressure and foot reaction force) were compared with the experimental measurement results and it was found basically the same. The internal mechanics information under the three postures were quantified, including stress/strain in bony structure and tensions in some soft tissues. All these mechanics information were in the first report of domestic and foreign, and provided an important reference for the comprehensive understanding of gait in force within the foot-ankle.
(5) Two basic mechanical issues in the foot were studied using the validated finite element model in mid-stance. First, for the standing neutral posture, individual releases of plantar aponeurosis, spring ligament, plantar long and short ligaments ligaments, were simulated respectively and model predictions were compared to the model prediction results under the health status of the same standing. These comparisons in several aspects were used to quantify their importance in maintaining stability in the foot arch. Second, under the standing load, model predicted detailed changes of metatarsal stress/strain distributions caused by the plantar load redistribution, and thereby this quantitative analysis increased our understanding of metatarsal biomechanics and also provided academic support for some requests in orthopedic surgery for hallux valgus program.
(6) Cooperated with the Orthopedic Surgery, Shanghai Huashan Hospital, we carried out gait plantar pressure distribution measurement with a normal walking speed. The study goal was to compare the difference of plantar pressure distribution between normal foot and diabetic foot. Meanwhile, finite element model was used to simulate normal young foot, normal elderly foot and diabetic foot respectively and investigated effects of the different mechanical properties of plantar soft tissue layers on the internal biomechanics of the foot-ankle. A comprehensive comparison of the normal foot and diabetic foot from two aspects of external plantar pressure distribution and internal mechanical status provided the mechanical information for the prevention of diabetic patients with foot ulcers.
In a word, three-dimensional modular geometry and finite element models of the human foot-ankle musculoskeletal system were established under three typical postures, as a research platform it can be widely used in basic foot mechanics research. For the specific problems in medicine and rehabilitation medicine, the above foot models can be reconstructed to do related mechanical simulation analysis. At the same time this paper has researched several foot and ankle biomechanical problems via experimental measurement and finite element analysis, and quantified the internal and external mechanics information of the foot-ankle, which provided important knowledge for the development of clinic and rehabilitation.
本论文的研究内容是“中国力学虚拟人”项目中的子课题之一:人体足踝骨肌系统建模与相关力学问题研究;同时本课题也是我所与复旦大学附属华山医院足踝外科、英国Salford大学人类功能康复研究中心(CRHPR)建立的国际合作项目,并得到了英国皇家学会(UK Royal Society)的项目支持(Grant: IPJ/2006/R3)。
力学解剖结构上,足踝部不仅包括26块骨骼,而且骨骼结构与错综复杂的韧带、跖腱膜、肌肉肌腱等软组织形成了稳定的关节结构和足弓结构;在功能上,足踝起到支撑承重、吸收震荡、传递运动和杠杆平衡等作用,是人类直立行走的基本保证。然而现实生活和临床医疗中,足踝的生物力学研究未得到应有的重视,目前随着人们对足踝认识的不断深入,其重要性也逐渐显现出来。在人体生物力学研究领域中,足部生物力学研究正是随着足外科的发展在近些年内渐渐兴起,主要由于以下几方面因素:首先,从临床角度来说,随着各种足部疾病发病率不断上升,如糖尿病并发症糖尿病足、 外翻足、老年跟痛足等,医学工作者迫切地需要知道这些足部病理现象的原因和科学的治疗方法;再者,从市场角度来说,各种功能鞋、矫形器和运动鞋有着很大的消费市场,患者与消费者往往要求这类鞋具、支具有特殊功能、穿着舒适并具有保护作用;最后,从技术角度来说,各种测量技术和计算机软硬件的快速发展为足部生物力学研究提供了必要条件,包括运动捕捉系统、压力平台、鞋内压力传感器、超声波测量、CT和MRI三维扫描技术、各种逆向工程反求软件以及有限元分析软件等等。本论文正是基于以上背景进行人体足踝系统的建模仿真和相关实验测量的研究,主要内容包括以下几个方面:
(1)基于健康人体的足踝三维MRI扫描数据,建立了三种常见姿态(背屈状态、平衡站立姿态和后跟提起姿态)下足踝三维几何实体模型与有限元模型,这三组模型中均包含了足部全部骨骼以及组成踝关节的胫骨和腓骨末端部分、韧带和跖腱膜、关节软骨和外部软组织结构等的详细几何信息,数据完整、解剖相似性高,并对这三种姿态的几何与有限元模型中的数据信息进行了模块化的处理和管理,模型中建立的各模块化组织结构可独立使用,且二次改建的可行性高。
(2)为了给足踝模型仿真分析提供必要的依据和信息,我们以健康的足踝为研究对象,对行走、站立和跳跃状态下的足踝受力状态进行了测量与分析。其中,以每分钟行走的步数这一频域指标作为基本参数,测量了不同步速行走时站立相中足底反力情况,通过统计分析和回归分析量化了步态中的一些关注的力学参数值,以及它们与步速、体重和身高的关系;此外还测量了四条浅层足外在肌(胫骨前肌、腓骨长肌、比目鱼肌和腓肠肌)在不同运动状态(正常步行、跳跃状态以及双足平衡站立时重心前移情况)下表面肌电信号,从而定性地研究和分析了它们在这些运动过程中肌力发力情况。
(3)以平衡站立姿态下的足踝有限元模型为例,对模型进行了详细的论证和验证工作。针对模型中的几何结构的简化和假设、单元选择、关节接触问题处理、材料属性确定等内容进行了详细的分析比较和论证,解决了一些关键性的技术问题;此外还设计了活体实验验证方案,将足底反力、足底压力分布和足部垂直压缩变形这三项指标同步采集,用以比较足踝有限元模型预测的相应结果,从而验证了足踝模型的有效性和正确性。此足踝模型的活体验证方案将当前几种常用的足踝研究测量方法有效的结合在一起,对人体没有任何伤害性。同时基于以上被验证的模型,开发了一个人体足踝模型仿真软件,整个软件由几何模型、有限元模型、原始数据、相关参数与基本算例五部分组成,将以上建立的足踝几何模型和有限元模型整体模型、各骨骼的独立模型以不同的数据格式提供给用户,为研究人员和医学工作者提供一个足踝模型仿真分析平台;同时附上了原始MRI扫描数据、足踝模型中的相关参数和一个典型站立姿态下的算例介绍;此足踝模型软件正在注册中,属于国内外足踝有限元仿真的首个软件。
(4)对行走步态中的三个典型姿态(后跟着地、站立中相与后跟离地)进行了准静态有限元模拟,仿真计算中考虑了不同姿态下足踝外在肌的肌力作用;仿真结果与实验测量结果(足底压力和足底反力)一致性高,同时结果量化了这三个姿态下足踝内外部组织结构的受力信息,包括骨组织上的应力应变分布和软组织受力状态的变化等,这为全面认识行走步态中足踝内部的受力情况提供了重要的参考。
(5)采用此足踝有限元模型研究和分析了足踝结构中两个基础力学问题:一是分别模拟了站立载荷下跖腱膜、弹簧韧带、足底长韧带和短韧带独立释放后的情况,与健康状态下同样站立载荷时的模型预测结果进行了多方面的比较,量化了它们在维持足弓静态稳定性中所起的相对力学作用;二是通过模拟站立位下足底载荷分布变化情况,定量地分析了跖骨的应力应变的分布变化情况,从而增加对跖骨生物力学的认识,并据此对 外翻矫形手术方案的要求提出理论支持。
(6)对健康年青测试者、健康年长测试者和II型糖尿病患者三组人群进行正常行走步态下足底压力分布测量和统计分析;同时通过改建前面建立的足踝有限元模型,分别对以上三组人群足底软组织受力状态进行了计算仿真,分析了足底软组织层属性改变对足踝内部的受力影响。通过测量与仿真,对不同测量人群的足底软组织的外部受力情况和内部受力状态进行了比较,得到了正常人和糖尿病患者足部受力的差异,为预防糖尿病患者发生足部溃疡提供有用的力学信息。
总之,本文以足踝三维有限元建模和分析为中心,同时将实验测量与临床问题结合起来。文中建立的三种典型姿态下足踝肌骨系统的三维几何和有限元模块化的模型,为人体足踝系统生物力学研究提供了一个分析平台,可以应用于足踝基础生物力学研究,也可以结合临床医学和康复医学中一些具体足踝部问题进行模型二次改建后进行相关的力学仿真分析;本文还针对足踝生物力学的一些基本问题进行了实验测量研究与相应的有限元仿真,量化了足踝的内外部力学信息,为足踝的临床和康复生物力学的发展提供了重要的力学依据。
In our country, particularly in recent years, with the continuous economic development and the rising of the living standards, people have more intense demands on how to really improve their quality of life. Biomechanical study of the human body from a mechanical point of view is to study human biology-related theoretical knowledge and motion mechanism, thus provides strong theoretical guidance and help for the development of clinical medicine and rehabilitation medicine. Our Institute's "Chinese Mechanical Virtual Human" project is the National Natural Science Foundation key project which was approved in 2006 (No. 30.53023), whose research goal is to establish a Chinese standard biomechanical system of the human body, including "bones - muscles - ligament", for partial and whole body statics and kinematics, as well as the dynamics studies, so as to solve the medical problems related to biomechanics.
The research in this dissertation is an sub-project of the key project "Chinese Mechanical Virtual Human": the human foot-ankle musculoskeletal system modeling and related mechanical research. At the same time, it is also an international collaborative project of our institute with the orthopedics department, Fudan University affiliated Huashan Hospital, and England Rehabilitation Centre for Rehabilitation & Human Performance Research (CRHPR), Salford University, while supported by the British Royal Society (UK Royal Society) (Grant: IPJ/2006/R3).
Human foot-ankle not only includes 26 bones, but also the complex structures of ligaments, plantar aponeurosis, muscle and tendon, joint capsules joints and the stable arch structure; From a functional point of view, the foot-ankle complex is a supporting and load-bearing structure to absorb shock and transfer movement. However, in real life and medical care, the ankle biomechanics system was not paid enough attention. With the current continuous understanding of the foot-ankle, its importance gradually displayed. In the human biomechanics field, the foot-ankle biomechanics research is rising in recent years with the development of foot and ankle surgery, mainly due to the following factors: Firstly, from a clinical point of view, with a rising incidence variety of foot diseases, such as the complications of diabetes foot, hallux valgus feet, foot pain and so on, medical researchers are eager to know the causes of foot pathology; Secondly, from a market perspective, the various functions shoes, orthoses and sport shoes have a large consumer market, patients and consumers tend to demand such shoes or fixers which is comfort, having a special function and playing a protective role; Finally, from a technical point of view, a variety of measurement techniques and computer hardware and software provide the necessary conditions for the rapid development of foot biomechanics study, including motion capture system, the pressure platform, the plantar pressure sensors, ultrasonic measurement, three-dimensional CT and MRI scanning technologies, various anti-seeking software and finite element analysis softwares and so on. The research was carried out based on the above background, and the specific research content included the following:
(1) Based on the three-dimensional MRI scan images of ankle of one healthy subject, three-dimensional geometric solid models and finite element models under three typical postures (heel-striking, mid-stance and heel-lift) were established. These physical models include detailed geometric information in the foot: all of the foot bones and the distal segments of the tibia and fibula and fibula, ligaments and plantar aponeurosis, joint cartilages and external soft tissue structures, which have high data integrity, high anatomical similarity and revisability. All data of these geometrical and finite element models were proceeded and managed in modular style. The modular structure can be used independently, and feasible for secondary alteration.
(2) With healthy young people as research subjects, plantar reaction forces were measured under different walking rhythms (beat per minute). Using this kind of frequency-domain parameter, statistical analysis and regression analysis were used to quantify some of the basic mechanical parameters values and their relationships with walking rhythms, body weight and height. Surface EMGs of four extrinsic muscles (tibialis anterior, peroneus longus, soleus and gastrocnemius) under different states of motion (normal walking, jumping conditions and balanced standing with an anterior shift of CoP) were measured to research their muscle strengths in the course of these movements. These experiments provided the necessary basis and information for the simulation of the foot-ankle model.
(3) Aiming at the finite element model under static standing posture, a detailed verification and validation work for the model were carried out. Here, a number of key technical issues, such as major simplifications of the model and assumptions, element selections, joint contact problem handling, material properties and so on were determined by a detailed analysis and comparison; An in vivo validation test was designed to synchronously record foot reaction force, plantar pressure distribution and vertical deformation. These measured results were used to compare to the corresponding model predictions, in order to validate the effectiveness and correctness of the model. This in vivo model validation method combined several commonly used measurement methods effectively, and was unharmful to human body. Meanwhile, based on the validated foot model, we developed a software of the human foot&ankle model which included five parts: geometric model, finite element model, the original data, the relevant parameters and calculation case; all established geometric model and finite element model of the whole model as well as individual skeletal part of the model were provided to the user with different data formats, in this way provide a foot&ankle simulation analysis platform to users for research or medical workers. Currently, this software is the first case at home and abroad.
(4) The quasi-static finite element simulation analysis of foot&ankle under three typical postures ( heel-striking, mid-stance and heel off) was carried out for the first time and the external muscle forces were taken into account; FE simulated results (plantar pressure and foot reaction force) were compared with the experimental measurement results and it was found basically the same. The internal mechanics information under the three postures were quantified, including stress/strain in bony structure and tensions in some soft tissues. All these mechanics information were in the first report of domestic and foreign, and provided an important reference for the comprehensive understanding of gait in force within the foot-ankle.
(5) Two basic mechanical issues in the foot were studied using the validated finite element model in mid-stance. First, for the standing neutral posture, individual releases of plantar aponeurosis, spring ligament, plantar long and short ligaments ligaments, were simulated respectively and model predictions were compared to the model prediction results under the health status of the same standing. These comparisons in several aspects were used to quantify their importance in maintaining stability in the foot arch. Second, under the standing load, model predicted detailed changes of metatarsal stress/strain distributions caused by the plantar load redistribution, and thereby this quantitative analysis increased our understanding of metatarsal biomechanics and also provided academic support for some requests in orthopedic surgery for hallux valgus program.
(6) Cooperated with the Orthopedic Surgery, Shanghai Huashan Hospital, we carried out gait plantar pressure distribution measurement with a normal walking speed. The study goal was to compare the difference of plantar pressure distribution between normal foot and diabetic foot. Meanwhile, finite element model was used to simulate normal young foot, normal elderly foot and diabetic foot respectively and investigated effects of the different mechanical properties of plantar soft tissue layers on the internal biomechanics of the foot-ankle. A comprehensive comparison of the normal foot and diabetic foot from two aspects of external plantar pressure distribution and internal mechanical status provided the mechanical information for the prevention of diabetic patients with foot ulcers.
In a word, three-dimensional modular geometry and finite element models of the human foot-ankle musculoskeletal system were established under three typical postures, as a research platform it can be widely used in basic foot mechanics research. For the specific problems in medicine and rehabilitation medicine, the above foot models can be reconstructed to do related mechanical simulation analysis. At the same time this paper has researched several foot and ankle biomechanical problems via experimental measurement and finite element analysis, and quantified the internal and external mechanics information of the foot-ankle, which provided important knowledge for the development of clinic and rehabilitation.
引文
[1]王成焘.中国力学虚拟人,医用生物力学, 2006, 21(3), 172-178.
[2]张发惠,郑和平.足外科临床解剖学,合肥,安徽科学技术出版社, 2004.
[3]董骧,樊瑜波,张明.人体足部生物力学的研究,生物医学工程学杂志, 2002, 19(1), 148-153.
[4] Chu T. M., Reddy N. P., Padovan J. Three-dimensional finite element stress analysis of the polypropylene, ankle-foot orthosis: static analysis, Med Eng Phys, 1995, 17(5), 372-379.
[5] Jacob S., Patil M. K. Stress analysis in three-dimensional foot models of normal and diabetic neuropathy, Front Med Biol Eng, 1999, 9(3), 211-227.
[6] Gefen A., Megido-Ravid M., Itzchak Y., etc. Biomechanical analysis of the three-dimensional foot structure during gait: a basic tool for clinical applications, J Biomech Eng, 2000, 122(6), 630-639.
[7] Gefen A. Stress analysis of the standing foot following surgical plantar fascia release, J Biomech, 2002, 35(5), 629-637.
[8] Chen W. P., Tang F. T., Ju C. W. Stress distribution of the foot during mid-stance to push-off in barefoot gait: a 3-D finite element analysis, Clin Biomech (Bristol, Avon), 2001, 16(7), 614-620.
[9] Chen W. P., Ju C. W., Tang F. T. Effects of total contact insoles on the plantar stress redistribution: a finite element analysis, Clin Biomech (Bristol, Avon), 2003, 18(6), S17-S24.
[10] Ledoux W., Camacho D., Ching R., etc. 2000, The development and validation of a computational foot and ankle model, Proceedings of the 22nd Annual EMBS International ConferenceChicago IL, p. 2899-2902.
[11] Cheung J. T., Zhang M., An K. N. Effects of plantar fascia stiffness on the biomechanical responses of the ankle-foot complex, Clin Biomech (Bristol, Avon), 2004, 19(8), 839-846.
[12] Cheung J. T., Zhang M. A 3-dimensional finite element model of the human foot and ankle for insole design, Arch Phys Med Rehabil, 2005, 86(2), 353-358.
[13] Cheung J. T., Zhang M., Leung A. K., etc. Three-dimensional finite element analysis of the foot during standing--a material sensitivity study, J Biomech, 2005, 38(5), 1045-1054.
[14] Cheung J. T., Zhang M., An K. N. Effect of Achilles tendon loading on plantar fascia tension in the standing foot, Clin Biomech (Bristol, Avon), 2006, 21(2), 194-203.
[15] Wu L. Nonlinear finite element analysis for musculoskeletal biomechanics of medial and lateral plantar longitudinal arch of Virtual Chinese Human after plantar ligamentous structure failures, Clin Biomech (Bristol, Avon), 2007, 22(2), 221-229.
[16] Wu L., Zhong S., Zheng R., etc. Clinical significance of musculoskeletal finite element model of the second and the fifth foot ray with metatarsal cavities and calcaneal sinus, Surg Radiol Anat, 2007, 29(7), 561-567.
[17]杨云峰,俞光荣,牛文鑫等.人体足主要骨-韧带结构三维有限元模型的建立及分析,中国运动医学杂志, 2007, 26(5), 542-546+551.
[18]毛宾尧.现代踝足外科学的发展和现状,现代实用医学, 2007, 19(7), 513-514+517.
[19]毛宾尧.我国踝足外科的发展和现状,中国矫形外科杂志, 2007, 15(14), 1079-1080.
[20]秦泗河.我国足踝外科的现状与发展的思考,中国矫形外科杂志, 2007, 15(5), 327.
[21]温建民.我国足踝外科的再思考,中国矫形外科杂志, 2007, 15(7), 560.
[22]俞光荣,赵宏谋.足踝外科的演进,中国矫形外科杂志, 2009, 17(22), 1681-1684.
[23]李保文,毛宾尧,刘明廷等.距下关节的稳定及活动范围,滨州医学院学报, 1994, 17(2), 151-152.
[24]毛宾尧,刘明廷,杨星光等.距跟关节的内稳定和不稳,中国矫形外科杂志, 1996, 3(3), 233-234.
[25]杨星光,毛宾尧,刘明廷等.距下关节运动的探讨,中国矫形外科杂志, 1996, 3(4), 312-313.
[26]俞光荣,杨云峰,张凯等.距下关节、踝关节对后足运动影响的实验研究,中华骨科杂志, 2005, 25(4), 236-239.
[27]周军杰,俞光荣,曹成福等.距下关节在成人足三维运动中的力学研究,中国临床解剖学杂志, 2006, 24(6), 695-697.
[28]陈大伟,李兵,俞光荣.第1跖趾关节相关生物力学研究进展,中国临床解剖学杂志, 2009, 27(3), 366-368.
[29]俞光荣.跟骨骨折的手术治疗,国外医学(骨科学分册), 2001, 22(4), 226-229.
[30]俞光荣.跟骨骨折临床研究若干问题,同济大学学报(医学版), 2005, 26(1), 1-4.
[31]俞光荣,梅炯,朱辉等.伴有跟骰关节损伤的跟骨骨折,中华骨科杂志, 2004, 24(1), 18-21.
[32]张凯,俞光荣,施向挺等.距跟骨间韧带的应用解剖,同济大学学报(医学版), 2005, 26(2), 80-82.
[33]陈雁西,俞光荣. F-Scan足底压力步态分析仪临床应用现状,国外医学(骨科学分册), 2005, 26(3), 187-189+192.
[34]王劲松,王令军,王婷等.不同步速下人体步态规律的测量与研究,传感器与微系统, 2008, 27(9), 43-45+49.
[35] Bohannon R.W., Andrews A.W., Thomas M.W. Walking speed: reference values and correlates for older adults, J Orthop Sports Phys Ther, 1996, 24, 86-90.
[36] Chiu M. C., Wang M. J. The effect of gait speed and gender on perceived exertion, muscle activity, joint motion of lower extremity, ground reaction force and heart rate during normal walking, Gait Posture, 2007, 25(3), 385-392.
[37] Crowe A., Samson M.M., Hoitsma M.J., etc. The influence of walking speed on parameters of gait symmetry determined from ground reaction forces, Hum Mov Sci, 1996, 15(3), 347-367.
[38] Hamill J, McNiven S. Reliability of selected ground reaction force parameters during walking, Hum Mov Sci, 1990, 9, 117-131.
[39] Nilsson J., Thorstensson A. Ground reaction forces at different speeds of human walking and running., Acta Physiol Scand, 1989, 136(2), 217-227.
[40] Stansfield B. W., Hillman S. J., Hazlewood M. E., etc. Normalisation of gait data in children, Gait Posture, 2003, 17(1), 81-87.
[41] Stansfield B. W., Hillman S. J., Hazlewood M. E., etc. Regression analysis of gait parameters with speed in normal children walking at self-selected speeds, Gait Posture, 2006, 23(3), 288-294.
[42] White R., Agouris I., Selbie R. D., etc. The variability of force platform data in normal and cerebral palsy gait, Clin Biomech (Bristol, Avon), 1999, 14(3), 185-192.
[43] Bojsen-Moller F. Calcaneocuboid joint and stability of the longitudinal arch of the foot at high and low gear push off, J Anat, 1979, 129(Pt 1), 165-176.
[44] Kitaoka H. B., Ahn T. K., Luo Z. P., etc. Stability of the arch of the foot, Foot Ankle Int, 1997, 18(10), 644-648.
[45]燕晓宇,俞光荣.获得性扁平足的基础研究进展,中国矫形外科杂志, 2004, 12(21), 114-116.
[46]燕晓宇,俞光荣.正常足弓的维持及临床意义,中国临床解剖学杂志, 2005, 23(2), 219-221.
[47]陈雁西,俞光荣,丁祖泉等.跟骰关节融合对距舟关节三维运动度影响的实验研究,中国修复重建外科杂志, 2007, 21(3), 255-258.
[48]陈雁西,俞光荣,丁祖泉等.跟骰关节融合对足部运动影响的实验研究,中国矫形外科杂志, 2006, 14(12), 915-917+961.
[49]陈雁西,俞光荣,梅炯.扁平足外科治疗研究进展,国外医学(骨科学分册), 2003, 24(6), 374-376.
[50]黄四平,俞光荣.第1跖楔关节与(足母)外翻关系的研究进展,中国矫形外科杂志, 2006, 14(17), 1320-1322.
[51]李山珠,俞光荣,梅炯等.跟骨骨折的手术与康复,现代康复, 2001, 5(14), 74-75.
[52]毛宾尧.跟痛症,中国医刊, 2005, 40(11), 8-10.
[53]杨云峰,俞光荣,梅炯等.距下关节融合对后足运动的影响,上海医学, 2004, 27(2), 98-100.
[54]俞光荣,陈雁西.糖尿病足的外科治疗,中国实用内科杂志, 2007, 27(7), 497-499.
[55]朱辉,李兵,俞光荣等.经皮克氏针治疗第2、3、4跖骨干、跖骨颈骨折,临床骨科杂志, 2009, 12(6), 649-650.
[56]朱辉,俞光荣,梅炯等.跟骨骨折内固定的生物力学研究,现代康复, 2001, 5(1), 32-33.
[57]王旭,陶凯,马昕等.第一跖列负重变化对(足母)趾形态影响的有限元分析,复旦学报(医学版), 2006, 33(2), 167-170.
[58] Tao K., Wang C. T., Dong-mei W., etc. 2005, Primary analysis of the first ray using a 3-dimension finite element foot model, Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings, p. 2946-2949.
[59] Crary J. L., Hollis J. M., Manoli A., 2nd. The effect of plantar fascia release on strain in the spring and long plantar ligaments, Foot Ankle Int, 2003, 24(3), 245-250.
[60] Cheung J. T., An K. N., Zhang M. Consequences of partial and total plantar fascia release: a finite element study, Foot Ankle Int, 2006, 27(2), 125-132.
[61] Kitaoka H. B., Luo Z. P., An K. N. Effect of plantar fasciotomy on stability of arch of foot, Clin Orthop Relat Res, 1997, (344), 307-312.
[62] Murphy G. A., Pneumaticos S. G., Kamaric E., etc. Biomechanical consequences of sequential plantar fascia release, Foot Ankle Int, 1998, 19(3), 149-152.
[63] Sharkey N. A., Ferris L., Smith T. S., etc. Strain and loading of the second metatarsal during heel-lift, J Bone Joint Surg Am, 1995, 77(7), 1050-1057.
[64] Donahue S. W., Sharkey N. A. Strains in the metatarsals during the stance phase of gait: implications for stress fractures, J Bone Joint Surg Am, 1999, 81(9), 1236-1244.
[65] Jacob S., Patil K. M., Braak L. H., etc. 1995, A three dimensional two arch model of a normal foot for stress analysis, Proceeding of the First Regional Conference - Ieee Engineering in Medicine & Biology Society and 14th Conference of the Biomedical Engineering Society of India, p. 275-276.
[66] Camacho D. L., Ledoux W. R., Rohr E. S., etc. A three-dimensional, anatomically detailed foot model: a foundation for a finite element simulation and means of quantifying foot-bone position, J Rehabil Res Dev, 2002, 39(3), 401-410.
[67] Bandak F. A., Tannous R. E., Toridis T. On the development of an osseo-ligamentous finite elementmodel of the human ankle joint, Int J Solids Struct, 2001, 38(10-13), 1681-1697.
[68] Yu J., Cheung J. T., Fan Y., etc. Development of a finite element model of female foot for high-heeled shoe design, Clin Biomech (Bristol, Avon), 2008, 23 Suppl 1, 31-38.
[69]陶凯,王冬梅,王成焘等.韧带和跖腱膜在足部有限元分析中的力学作用,生物医学工程学杂志, 2008, 25(2), 336-340.
[70] Erdemir A., Saucerman J. J., Lemmon D., etc. Local plantar pressure relief in therapeutic footwear: design guidelines from finite element models, J Biomech, 2005, 38(9), 1798-1806.
[71] Lemmon D., Shiang T. Y., Hashmi A., etc. The effect of insoles in therapeutic footwear--A finite element approach, J Biomech, 1997, 30(6), 615-620.
[72] Dai X. Q., Li Y., Zhang M., etc. Effect of sock on biomechanical responses of foot during walking, Clin Biomech (Bristol, Avon), 2006, 21(3), 314-321.
[73]燕晓宇,俞光荣,丁祖泉等.距舟关节的三维运动度及其临床意义,中国临床解剖学杂志, 2007, 25(6), 693-695.
[74]杨云峰,俞光荣,梅炯等.距下关节三维运动测量方法学比较,中国运动医学杂志, 2005, 24(2), 191-194+198.
[75] Giakas G, Baltzopoulos V. Time and frequency domain analysis of ground reaction forces during walking: An investigation of variability and symmetry, Gait Posture, 1997, 5(3), 189-197.
[76] Kerrigan D. C., Todd M. K., Della Croce U., etc. Biomechanical gait alterations independent of speed in the healthy elderly: evidence for specific limiting impairments., Arch Phys Med Rehabil, 1998, 79(3), 317-322.
[77] Stergiou N., Giakas G., Byrne J. B., etc. Frequency domain characteristics of ground reaction forces during walking of young and elderly females, Clin Biomech (Bristol, Avon), 2002, 17(8), 615-617.
[78] Winter D.A., Patla A.E., Frank J.S., etc. Biomec hanical walking pattern changes in the fit and healthy elderly, Phys Ther, 1990, 75, 15-21.
[79] ScanIP_FE_CAD_Tutorials, Exeter, Simpleware LTD, Innovation Centre, 2006.
[80] Viceconti M., Olsen S., Nolte L. P., etc. Extracting clinically relevant data from finite element simulations, Clin Biomech (Bristol, Avon), 2005, 20(5), 451-454.
[81] Brekelmans W. A., Poort H. W., Slooff T. J. A new method to analyse the mechanical behaviour of skeletal parts, Acta Orthop Scand, 1972, 43(5), 301-317.
[82]王正义等.足踝外科学,北京,人民卫生出版社, 2006.
[83] Heim M., Siev-Ner Y., Nadvorna H., etc. Metatarsal-phalangeal sesamoid bones, Current Orthopaedics, 1997, 11(4), 267-270.
[84]何毓珏.髌股关节三维解剖形态建模及其性能研究, [博士学位论文],上海,上海交通大学, 2005.
[85] Interactive Foot and Ankle II, Primal Picture Limited, UK,
[86] Mkandawire C., Ledoux W. R., Sangeorzan B. J., etc. Foot and ankle ligament morphometry, J Rehabil Res Dev, 2005, 42(6), 809-820.
[87]毛宾尧.人工踝关节外科学,北京,人民军医出版社, 2005.
[88] Erdemir A., Hamel A. J., Fauth A. R., etc. Dynamic loading of the plantar aponeurosis in walking, J Bone Joint Surg Am, 2004, 86-A(3), 546-552.
[89] Fukashiro S., Komi P. V., Jarvinen M., etc. In vivo Achilles tendon loading during jumping in humans, Eur J Appl Physiol Occup Physiol, 1995, 71(5), 453-458.
[90] Lichtwark G. A., Wilson A. M. In vivo mechanical properties of the human Achilles tendon during one-legged hopping, J Exp Biol, 2005, 208(Pt 24), 4715-4725.
[91] Hsu C. C., Tsai W. C., Chen C. P., etc. Effects of aging on the plantar soft tissue properties under the metatarsal heads at different impact velocities, Ultrasound Med Biol, 2005, 31(10), 1423-1429.
[92] Hsu T. C., Wang C. L., Tsai W. C., etc. Comparison of the mechanical properties of the heel pad between young and elderly adults, Arch Phys Med Rehabil, 1998, 79(9), 1101-1104.
[93] Zheng Y. P., Choi Y. K., Wong K., etc. Biomechanical assessment of plantar foot tissue in diabetic patients using an ultrasound indentation system, Ultrasound Med Biol, 2000, 26(3), 451-456.
[94] Gefen A., Megido-Ravid M., Azariah M., etc. Integration of plantar soft tissue stiffness measurements in routine MRI of the diabetic foot, Clin Biomech (Bristol, Avon), 2001, 16(10), 921-925.
[95] Ledoux W. R., Blevins J. J. The compressive material properties of the plantar soft tissue, J Biomech, 2007, 40(13), 2975-2981.
[96] Chao E. Y., Laughman R. K., Schneider E., etc. Normative data of knee joint motion and ground reaction forces in adult level walking, J Biomech, 1983, 16(3), 219-233.
[97] Giakas G, Baltzopoulos V, Dangerfield P, etc. Comparison of gait patterns between healthy and scoliotic patients using time and frequency domain analysis of ground reaction forces, Spine, 1996, 21(19), 2235-2242.
[98] DA Winter. Biomechanics and motion control of human movement Wiley, 2004.
[99] An K. N., Berglund L., Cooney W. P., etc. Direct in vivo tendon force measurement system, J Biomech, 1990, 23(12), 1269-1271.
[100] Komi P. V. Relevance of in vivo force measurements to human biomechanics, J Biomech, 1990, 23 Suppl 1, 23-34.
[101] Schuind F., Garcia-Elias M., Cooney W. P., etc. Flexor tendon forces: In vivo measurements, J Hand Surg Am, 1992, 17(2), 291-298.
[102] Reilly P., Bull M. J., Amis M. M., etc. A novel technique for the quantification of tendon forces: Application to the subscapularis tendon, Trans Orthop Res Soc, 2003, (28), 180.
[103] Finni T., Komi P. V., Lukkariniemi J. Achilles tendon loading during walking: application of a novel optic fiber technique, Eur J Appl Physiol Occup Physiol, 1998, 77(3), 289-291.
[104] Finni T., Komi P. V., Lepola V. In vivo human triceps surae and quadriceps femoris muscle function in a squat jump and counter movement jump, Eur J Appl Physiol, 2000, 83(4 -5), 416-426.
[105] Fleming B. C., Beynnon B. D. In vivo measurement of ligament/tendon strains and forces: a review, Ann Biomed Eng, 2004, 32(3), 318-328.
[106]丁海曙,容观澳,王广志.人体运动信息检测与处理,北京,中国宇航出版社, 1992.
[107] Vaughan C.L., Davis B.L. , O'Connor J.C. . 1999, "Dynamics of Human Gait," Kiboho Publishers.
[108] Crowninshield R.D. . A physiologically based criterion for muscle force predictions on locomotion, Bull Hosp Jt Dis Orthop Inst, 1983, 43(2), 164-170.
[109] Dietz V., Zijlstra W., Prokop T., etc. Leg muscle activation during gait in Parkinson's disease: adaptation and interlimb coordination, Electroencephalogr Clin Neurophysiol, 1995, 97(6), 408-415.
[110]王成焘.人体生物摩擦学,北京,科学出版社, 2008.
[111] Sharkey N. A., Hamel A. J. A dynamic cadaver model of the stance phase of gait: performance characteristics and kinetic validation, Clin Biomech (Bristol, Avon), 1998, 13(6), 420-433.
[112] Oreskes N., Shrader-Frechette K., Belitz K. Verification, Validation, and Confirmation of Numerical Models in the Earth Sciences, Science, 1994, 263(5147), 641-646.
[113] Babuska I., Oden J. T. Verification and validation in computational engineering and science: basic concepts, Comput Methods Appl Mech Eng, 2004, 193(36-38), 4057-4066.
[114] Trucano T., Post D. Guest Editors' Introduction: Verification and Validation in Computational Science and Engineering, Comput Sci Eng, 2004, 6(5), 8-9.
[115] Zienkiewiz O.C., Taylor K.L. The finite element method, Butterworth Heinemann., 2000.
[116]朱伯芳.有限单元法原理和应用,北京,中国水利电力出版社, 1998.
[117] Zienkiewicz O.C., Zhu J.Z. A simple error estimator and adaptive procedure for practical engineering analysis, Int J Numer Meth Eng, 1987, 24(2), 337-357.
[118] Dar F. H., Meakin J. R., Aspden R. M. Statistical methods in finite element analysis, J Biomech, 2002, 35(9), 1155-1161.
[119] Dennis K. J., McKinney S. Sesamoids and accessory bones of the foot, Clin Podiatr Med Surg, 1990, 7(4), 717-723.
[120]王旭,顾湘杰.足横弓与NFEA7外翻关系的研究进展,中国矫形外科杂志, 2000, 7(4), 387-389.
[121] Biedert R., Hintermann B. Stress fractures of the medial great toe sesamoids in athletes, Foot Ankle Int, 2003, 24(2), 137-141.
[122] Siegler S., Block J., Schneck C. D. The mechanical characteristics of the collateral ligaments of the human ankle joint, Foot Ankle, 1988, 8(5), 234-242.
[123] Wright D. G., Rennels D. C. A Study of the Elastic Properties of Plantar Fascia, J Bone Joint Surg Am, 1964, 46, 482-492.
[124] ANSYS 9.0. The general-purpose finite element software. Documentation.,
[125] Moaveni S. . Finite element analysis: Theory and application with ANSYS., New Jersey, USA, Pearson Education, Inc., 2003.
[126]王勖成.有限单元法,北京,清华大学出版社, 2003.
[127] Duvaut G. , Lions J. L. Inequalities in mechanics and physics New York, Springer-Verlag, 1976.
[128] Simo J.C., Laursen T.A. An Augmented Lagrangian Treatment of Contact Problems Involving Friction, Comput Struct, 1992, 42(1), 97-116.
[129] Krishnan R., Kopacz M., Ateshian G. A. Experimental verification of the role of interstitial fluid pressurization in cartilage lubrication, J Orthop Res, 2004, 22(3), 565-570.
[130] Zhang M., Mak A. F. In vivo friction properties of human skin, Prosthet Orthot Int, 1999, 23(2), 135-141.
[131] Aerts P., Ker R. F., De Clercq D., etc. The mechanical properties of the human heel pad: a paradox resolved, J Biomech, 1995, 28(11), 1299-1308.
[132] Miller-Young J. E., Duncan N. A., Baroud G. Material properties of the human calcaneal fat pad in compression: experiment and theory, J Biomech, 2002, 35(12), 1523-1531.
[133] Athanasiou K. A., Liu G. T., Lavery L. A., etc. Biomechanical topography of human articular cartilage in the first metatarsophalangeal joint, Clin Orthop Relat Res, 1998, (348), 269-281.
[134] Gefen A., Megido-Ravid M., Itzchak Y. In vivo biomechanical behavior of the human heel pad during the stance phase of gait, J Biomech, 2001, 34(12), 1661-1665.
[135] Rome K., Webb P., Unsworth A., etc. Heel pad stiffness in runners with plantar heel pain, ClinBiomech (Bristol, Avon), 2001, 16(10), 901-905.
[136] Cavanagh P. R. Plantar soft tissue thickness during ground contact in walking, J Biomech, 1999, 32(6), 623-628.
[137] Cristofolini L., Viceconti M., Cappello A., etc. Mechanical validation of whole bone composite femur models, J Biomech, 1996, 29(4), 525-535.
[138] "F-Scan User Mannual."
[139] "http://en.wikipedia.org/wiki/Flat_feet."
[140] Huang C. K., Kitaoka H. B., An K. N., etc. Biomechanical evaluation of longitudinal arch stability, Foot Ankle, 1993, 14(6), 353-357.
[141] Kitaoka H. B., Luo Z. P., An K. N. Mechanical behavior of the foot and ankle after plantar fascia release in the unstable foot, Foot Ankle Int, 1997, 18(1), 8-15.
[142]杨云峰.人体足纵弓静力性内在维持结构的生物力学研究, [博士学位论文],上海,同济大学, 2007.
[143] Anderson R.B., Foster M.D. Operative treatment of subcalcaneal pain, Foot Ankle, 1989, 9(6), 317-323.
[144] Daly P.J., Kitaoka H.B. Plantar fasciotomy for intactable plantar fasciitis: clinical results and biomechanical evaluation, Foot Ankle, 1992, 13(4), 188-195.
[145] Davies M.S., Weiss G.A., Saxby T.S. Plantar fasciitis: how successful is surgical intervention?, Foot Ankle Int, 1999, 20(12), 803-807.
[146] Viladot A, Viladot A. Stress fractures in the foot, Foot Ankle Surg, 1998, 4(1), 3-11.
[147] Hopton B. P., Harris N. J. Fractures of the Foot and Ankle, Surgery (Oxford), 2003, 21(9), 236-240.
[148] Menz H. B., Morris M. E. Clinical determinants of plantar forces and pressures during walking in older people, Gait Posture, 2006, 24(2), 229-236.
[149] Hsiang S. M., Chang C. C. The effect of gait speed and load carrying on the reliability of ground reaction forces, Safety Science, 2002, 40(7-8), 639-657.
[150] Donahue S. W., Sharkey N. A., Modanlou K. A., etc. Bone strain and microcracks at stress fracture sites in human metatarsals, Bone, 2000, 27(6), 827-833.
[151] Simkin A.Structural analysis of the human foot in standing posture, [Dissertation], Tel Aviv, Israel, Tel Aviv University, 1982.
[152] Reilly D. T., Burstein A. H. The elastic and ultimate properties of compact bone tissue, J Biomech, 1975, 8(6), 393-405.
[153] Burstein A. H., Reilly D. T., Martens M. Aging of bone tissue: mechanical properties, J Bone Joint Surg Am, 1976, 58(1), 82-86.
[154] Muscolo L., Migues A., Slullitel G., etc. Stress fracture nonunion at the base of the second metatarsal in a ballet dancer - A case report, American Journal of Sports Medicine, 2004, 32(6), 1535-1537.
[155] Morris G., Nix K., Goldman F. D. Fracture of the second metatarsal base - An overlooked cause of chronic midfoot pain, J Am Podiatr Med Assoc, 2003, 93(1), 6-10.
[156] Bayraktar H.H., Morgan E.F., Niebur G.L., etc. Comparison of the elastic and yield properties of human femeoral trabecular and cortial bone tissue, J Biomech, 2004, 37, 27-35.
[157]王旭.足三维有限元建模第一跖列与拇外翻关系的临床与生物力学研究, [博士学位论文],上海,复旦大学, 2005.
[158] Mann R. A., Coughlin M. J. Hallux valgus--etiology, anatomy, treatment and surgical considerations, Clin Orthop Relat Res, 1981, (157), 31-41.
[159] MeGlamry E.D. (著),鲁英(译).拇趾外翻及相关畸形,北京,中国医药科技出版社, 1996.
[160]方朝晖.糖尿病家庭调养,上海,上海中医药大学出版社, 2006.
[161]俞光荣,陈雁西.糖尿病足的骨科治疗,中华医学杂志, 2007, 87(26), 1806-1807.
[162] Kwon O. Y., Mueller M. J. Walking patterns used to reduce forefoot plantar pressures in people with diabetic neuropathies, Phys Ther, 2001, 81(2), 828-835.
[163]王永慧.糖尿病患者足底压力改变与足溃疡的关系,国外医学(内分泌学分册), 2004, 24(5), 324-326.
[164] Pham H., Harkless L. B., Armstrong D. G., etc. Screening techniques to identify people at high risk for diabetic foot ulceration - A prospective multicenter trial, Diabetes Care, 2000, 23(5), 606-611.
[165] Boulton A. J. M., Gries F. A., Jervell J. A. Guidelines for the diagnosis and outpatient management of diabetic peripheral neuropathy (Reprinted from Diabet Med, vol 15, pg 508-514, 1998), Diabetes Reviews, 1999, 7(4), 237-244.
[166]毛宾尧,贾学文,郑菲蓉等.行走和站立时足底应力分布研究,中国矫形外科杂志, 2002, 10(12), 68-70.
[167]王明鑫,俞光荣.正常人足底压力分析的研究进展,中国矫形外科杂志, 2006, 14(22), 1722-1724.
[168]王明鑫,俞光荣,陈雁西等.正常中国成年人足底压力分析,中国矫形外科杂志, 2008, 16(9), 687-690.
[169]刘新成,陈雁西,俞光荣等.糖尿病伴足趾畸形的三维动态足底压力分析,中国骨与关节外科, 2009, 2(6), 488-493.
[170] McLellan K., Petrofsky J. S., Bains G., etc. The effects of skin moisture and subcutaneous fat thickness on the ability of the skin to dissipate heat in young and old subjects, with and without diabetes, at three environmental room temperatures, Med Eng Phys, 2009, 31(2), 165-172.
[171] Charanya G., Patil K. M. , Thomas V.J., etc. Standing foot pressure image analysis for variations in foot sole soft tissue properties and levels of diabetic neuropathy, ITBM-RBM, 2004, 25(1), 23-33.
[172] Olefsky J.M. Pathogenesis of insulin resistance and hyperglycemia in non-insulin-dependent diabetes mellitus, Am J Med, 1985, 79(3), 1-7.
[173] Milczarczyk A., Franek E. Osteoporosis and bone fractures in patients with diabetes mellitus, Diabetologia Doswiadczalna i Kliniczna, 2008, 8(2), 63-67.
[2]张发惠,郑和平.足外科临床解剖学,合肥,安徽科学技术出版社, 2004.
[3]董骧,樊瑜波,张明.人体足部生物力学的研究,生物医学工程学杂志, 2002, 19(1), 148-153.
[4] Chu T. M., Reddy N. P., Padovan J. Three-dimensional finite element stress analysis of the polypropylene, ankle-foot orthosis: static analysis, Med Eng Phys, 1995, 17(5), 372-379.
[5] Jacob S., Patil M. K. Stress analysis in three-dimensional foot models of normal and diabetic neuropathy, Front Med Biol Eng, 1999, 9(3), 211-227.
[6] Gefen A., Megido-Ravid M., Itzchak Y., etc. Biomechanical analysis of the three-dimensional foot structure during gait: a basic tool for clinical applications, J Biomech Eng, 2000, 122(6), 630-639.
[7] Gefen A. Stress analysis of the standing foot following surgical plantar fascia release, J Biomech, 2002, 35(5), 629-637.
[8] Chen W. P., Tang F. T., Ju C. W. Stress distribution of the foot during mid-stance to push-off in barefoot gait: a 3-D finite element analysis, Clin Biomech (Bristol, Avon), 2001, 16(7), 614-620.
[9] Chen W. P., Ju C. W., Tang F. T. Effects of total contact insoles on the plantar stress redistribution: a finite element analysis, Clin Biomech (Bristol, Avon), 2003, 18(6), S17-S24.
[10] Ledoux W., Camacho D., Ching R., etc. 2000, The development and validation of a computational foot and ankle model, Proceedings of the 22nd Annual EMBS International ConferenceChicago IL, p. 2899-2902.
[11] Cheung J. T., Zhang M., An K. N. Effects of plantar fascia stiffness on the biomechanical responses of the ankle-foot complex, Clin Biomech (Bristol, Avon), 2004, 19(8), 839-846.
[12] Cheung J. T., Zhang M. A 3-dimensional finite element model of the human foot and ankle for insole design, Arch Phys Med Rehabil, 2005, 86(2), 353-358.
[13] Cheung J. T., Zhang M., Leung A. K., etc. Three-dimensional finite element analysis of the foot during standing--a material sensitivity study, J Biomech, 2005, 38(5), 1045-1054.
[14] Cheung J. T., Zhang M., An K. N. Effect of Achilles tendon loading on plantar fascia tension in the standing foot, Clin Biomech (Bristol, Avon), 2006, 21(2), 194-203.
[15] Wu L. Nonlinear finite element analysis for musculoskeletal biomechanics of medial and lateral plantar longitudinal arch of Virtual Chinese Human after plantar ligamentous structure failures, Clin Biomech (Bristol, Avon), 2007, 22(2), 221-229.
[16] Wu L., Zhong S., Zheng R., etc. Clinical significance of musculoskeletal finite element model of the second and the fifth foot ray with metatarsal cavities and calcaneal sinus, Surg Radiol Anat, 2007, 29(7), 561-567.
[17]杨云峰,俞光荣,牛文鑫等.人体足主要骨-韧带结构三维有限元模型的建立及分析,中国运动医学杂志, 2007, 26(5), 542-546+551.
[18]毛宾尧.现代踝足外科学的发展和现状,现代实用医学, 2007, 19(7), 513-514+517.
[19]毛宾尧.我国踝足外科的发展和现状,中国矫形外科杂志, 2007, 15(14), 1079-1080.
[20]秦泗河.我国足踝外科的现状与发展的思考,中国矫形外科杂志, 2007, 15(5), 327.
[21]温建民.我国足踝外科的再思考,中国矫形外科杂志, 2007, 15(7), 560.
[22]俞光荣,赵宏谋.足踝外科的演进,中国矫形外科杂志, 2009, 17(22), 1681-1684.
[23]李保文,毛宾尧,刘明廷等.距下关节的稳定及活动范围,滨州医学院学报, 1994, 17(2), 151-152.
[24]毛宾尧,刘明廷,杨星光等.距跟关节的内稳定和不稳,中国矫形外科杂志, 1996, 3(3), 233-234.
[25]杨星光,毛宾尧,刘明廷等.距下关节运动的探讨,中国矫形外科杂志, 1996, 3(4), 312-313.
[26]俞光荣,杨云峰,张凯等.距下关节、踝关节对后足运动影响的实验研究,中华骨科杂志, 2005, 25(4), 236-239.
[27]周军杰,俞光荣,曹成福等.距下关节在成人足三维运动中的力学研究,中国临床解剖学杂志, 2006, 24(6), 695-697.
[28]陈大伟,李兵,俞光荣.第1跖趾关节相关生物力学研究进展,中国临床解剖学杂志, 2009, 27(3), 366-368.
[29]俞光荣.跟骨骨折的手术治疗,国外医学(骨科学分册), 2001, 22(4), 226-229.
[30]俞光荣.跟骨骨折临床研究若干问题,同济大学学报(医学版), 2005, 26(1), 1-4.
[31]俞光荣,梅炯,朱辉等.伴有跟骰关节损伤的跟骨骨折,中华骨科杂志, 2004, 24(1), 18-21.
[32]张凯,俞光荣,施向挺等.距跟骨间韧带的应用解剖,同济大学学报(医学版), 2005, 26(2), 80-82.
[33]陈雁西,俞光荣. F-Scan足底压力步态分析仪临床应用现状,国外医学(骨科学分册), 2005, 26(3), 187-189+192.
[34]王劲松,王令军,王婷等.不同步速下人体步态规律的测量与研究,传感器与微系统, 2008, 27(9), 43-45+49.
[35] Bohannon R.W., Andrews A.W., Thomas M.W. Walking speed: reference values and correlates for older adults, J Orthop Sports Phys Ther, 1996, 24, 86-90.
[36] Chiu M. C., Wang M. J. The effect of gait speed and gender on perceived exertion, muscle activity, joint motion of lower extremity, ground reaction force and heart rate during normal walking, Gait Posture, 2007, 25(3), 385-392.
[37] Crowe A., Samson M.M., Hoitsma M.J., etc. The influence of walking speed on parameters of gait symmetry determined from ground reaction forces, Hum Mov Sci, 1996, 15(3), 347-367.
[38] Hamill J, McNiven S. Reliability of selected ground reaction force parameters during walking, Hum Mov Sci, 1990, 9, 117-131.
[39] Nilsson J., Thorstensson A. Ground reaction forces at different speeds of human walking and running., Acta Physiol Scand, 1989, 136(2), 217-227.
[40] Stansfield B. W., Hillman S. J., Hazlewood M. E., etc. Normalisation of gait data in children, Gait Posture, 2003, 17(1), 81-87.
[41] Stansfield B. W., Hillman S. J., Hazlewood M. E., etc. Regression analysis of gait parameters with speed in normal children walking at self-selected speeds, Gait Posture, 2006, 23(3), 288-294.
[42] White R., Agouris I., Selbie R. D., etc. The variability of force platform data in normal and cerebral palsy gait, Clin Biomech (Bristol, Avon), 1999, 14(3), 185-192.
[43] Bojsen-Moller F. Calcaneocuboid joint and stability of the longitudinal arch of the foot at high and low gear push off, J Anat, 1979, 129(Pt 1), 165-176.
[44] Kitaoka H. B., Ahn T. K., Luo Z. P., etc. Stability of the arch of the foot, Foot Ankle Int, 1997, 18(10), 644-648.
[45]燕晓宇,俞光荣.获得性扁平足的基础研究进展,中国矫形外科杂志, 2004, 12(21), 114-116.
[46]燕晓宇,俞光荣.正常足弓的维持及临床意义,中国临床解剖学杂志, 2005, 23(2), 219-221.
[47]陈雁西,俞光荣,丁祖泉等.跟骰关节融合对距舟关节三维运动度影响的实验研究,中国修复重建外科杂志, 2007, 21(3), 255-258.
[48]陈雁西,俞光荣,丁祖泉等.跟骰关节融合对足部运动影响的实验研究,中国矫形外科杂志, 2006, 14(12), 915-917+961.
[49]陈雁西,俞光荣,梅炯.扁平足外科治疗研究进展,国外医学(骨科学分册), 2003, 24(6), 374-376.
[50]黄四平,俞光荣.第1跖楔关节与(足母)外翻关系的研究进展,中国矫形外科杂志, 2006, 14(17), 1320-1322.
[51]李山珠,俞光荣,梅炯等.跟骨骨折的手术与康复,现代康复, 2001, 5(14), 74-75.
[52]毛宾尧.跟痛症,中国医刊, 2005, 40(11), 8-10.
[53]杨云峰,俞光荣,梅炯等.距下关节融合对后足运动的影响,上海医学, 2004, 27(2), 98-100.
[54]俞光荣,陈雁西.糖尿病足的外科治疗,中国实用内科杂志, 2007, 27(7), 497-499.
[55]朱辉,李兵,俞光荣等.经皮克氏针治疗第2、3、4跖骨干、跖骨颈骨折,临床骨科杂志, 2009, 12(6), 649-650.
[56]朱辉,俞光荣,梅炯等.跟骨骨折内固定的生物力学研究,现代康复, 2001, 5(1), 32-33.
[57]王旭,陶凯,马昕等.第一跖列负重变化对(足母)趾形态影响的有限元分析,复旦学报(医学版), 2006, 33(2), 167-170.
[58] Tao K., Wang C. T., Dong-mei W., etc. 2005, Primary analysis of the first ray using a 3-dimension finite element foot model, Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings, p. 2946-2949.
[59] Crary J. L., Hollis J. M., Manoli A., 2nd. The effect of plantar fascia release on strain in the spring and long plantar ligaments, Foot Ankle Int, 2003, 24(3), 245-250.
[60] Cheung J. T., An K. N., Zhang M. Consequences of partial and total plantar fascia release: a finite element study, Foot Ankle Int, 2006, 27(2), 125-132.
[61] Kitaoka H. B., Luo Z. P., An K. N. Effect of plantar fasciotomy on stability of arch of foot, Clin Orthop Relat Res, 1997, (344), 307-312.
[62] Murphy G. A., Pneumaticos S. G., Kamaric E., etc. Biomechanical consequences of sequential plantar fascia release, Foot Ankle Int, 1998, 19(3), 149-152.
[63] Sharkey N. A., Ferris L., Smith T. S., etc. Strain and loading of the second metatarsal during heel-lift, J Bone Joint Surg Am, 1995, 77(7), 1050-1057.
[64] Donahue S. W., Sharkey N. A. Strains in the metatarsals during the stance phase of gait: implications for stress fractures, J Bone Joint Surg Am, 1999, 81(9), 1236-1244.
[65] Jacob S., Patil K. M., Braak L. H., etc. 1995, A three dimensional two arch model of a normal foot for stress analysis, Proceeding of the First Regional Conference - Ieee Engineering in Medicine & Biology Society and 14th Conference of the Biomedical Engineering Society of India, p. 275-276.
[66] Camacho D. L., Ledoux W. R., Rohr E. S., etc. A three-dimensional, anatomically detailed foot model: a foundation for a finite element simulation and means of quantifying foot-bone position, J Rehabil Res Dev, 2002, 39(3), 401-410.
[67] Bandak F. A., Tannous R. E., Toridis T. On the development of an osseo-ligamentous finite elementmodel of the human ankle joint, Int J Solids Struct, 2001, 38(10-13), 1681-1697.
[68] Yu J., Cheung J. T., Fan Y., etc. Development of a finite element model of female foot for high-heeled shoe design, Clin Biomech (Bristol, Avon), 2008, 23 Suppl 1, 31-38.
[69]陶凯,王冬梅,王成焘等.韧带和跖腱膜在足部有限元分析中的力学作用,生物医学工程学杂志, 2008, 25(2), 336-340.
[70] Erdemir A., Saucerman J. J., Lemmon D., etc. Local plantar pressure relief in therapeutic footwear: design guidelines from finite element models, J Biomech, 2005, 38(9), 1798-1806.
[71] Lemmon D., Shiang T. Y., Hashmi A., etc. The effect of insoles in therapeutic footwear--A finite element approach, J Biomech, 1997, 30(6), 615-620.
[72] Dai X. Q., Li Y., Zhang M., etc. Effect of sock on biomechanical responses of foot during walking, Clin Biomech (Bristol, Avon), 2006, 21(3), 314-321.
[73]燕晓宇,俞光荣,丁祖泉等.距舟关节的三维运动度及其临床意义,中国临床解剖学杂志, 2007, 25(6), 693-695.
[74]杨云峰,俞光荣,梅炯等.距下关节三维运动测量方法学比较,中国运动医学杂志, 2005, 24(2), 191-194+198.
[75] Giakas G, Baltzopoulos V. Time and frequency domain analysis of ground reaction forces during walking: An investigation of variability and symmetry, Gait Posture, 1997, 5(3), 189-197.
[76] Kerrigan D. C., Todd M. K., Della Croce U., etc. Biomechanical gait alterations independent of speed in the healthy elderly: evidence for specific limiting impairments., Arch Phys Med Rehabil, 1998, 79(3), 317-322.
[77] Stergiou N., Giakas G., Byrne J. B., etc. Frequency domain characteristics of ground reaction forces during walking of young and elderly females, Clin Biomech (Bristol, Avon), 2002, 17(8), 615-617.
[78] Winter D.A., Patla A.E., Frank J.S., etc. Biomec hanical walking pattern changes in the fit and healthy elderly, Phys Ther, 1990, 75, 15-21.
[79] ScanIP_FE_CAD_Tutorials, Exeter, Simpleware LTD, Innovation Centre, 2006.
[80] Viceconti M., Olsen S., Nolte L. P., etc. Extracting clinically relevant data from finite element simulations, Clin Biomech (Bristol, Avon), 2005, 20(5), 451-454.
[81] Brekelmans W. A., Poort H. W., Slooff T. J. A new method to analyse the mechanical behaviour of skeletal parts, Acta Orthop Scand, 1972, 43(5), 301-317.
[82]王正义等.足踝外科学,北京,人民卫生出版社, 2006.
[83] Heim M., Siev-Ner Y., Nadvorna H., etc. Metatarsal-phalangeal sesamoid bones, Current Orthopaedics, 1997, 11(4), 267-270.
[84]何毓珏.髌股关节三维解剖形态建模及其性能研究, [博士学位论文],上海,上海交通大学, 2005.
[85] Interactive Foot and Ankle II, Primal Picture Limited, UK,
[86] Mkandawire C., Ledoux W. R., Sangeorzan B. J., etc. Foot and ankle ligament morphometry, J Rehabil Res Dev, 2005, 42(6), 809-820.
[87]毛宾尧.人工踝关节外科学,北京,人民军医出版社, 2005.
[88] Erdemir A., Hamel A. J., Fauth A. R., etc. Dynamic loading of the plantar aponeurosis in walking, J Bone Joint Surg Am, 2004, 86-A(3), 546-552.
[89] Fukashiro S., Komi P. V., Jarvinen M., etc. In vivo Achilles tendon loading during jumping in humans, Eur J Appl Physiol Occup Physiol, 1995, 71(5), 453-458.
[90] Lichtwark G. A., Wilson A. M. In vivo mechanical properties of the human Achilles tendon during one-legged hopping, J Exp Biol, 2005, 208(Pt 24), 4715-4725.
[91] Hsu C. C., Tsai W. C., Chen C. P., etc. Effects of aging on the plantar soft tissue properties under the metatarsal heads at different impact velocities, Ultrasound Med Biol, 2005, 31(10), 1423-1429.
[92] Hsu T. C., Wang C. L., Tsai W. C., etc. Comparison of the mechanical properties of the heel pad between young and elderly adults, Arch Phys Med Rehabil, 1998, 79(9), 1101-1104.
[93] Zheng Y. P., Choi Y. K., Wong K., etc. Biomechanical assessment of plantar foot tissue in diabetic patients using an ultrasound indentation system, Ultrasound Med Biol, 2000, 26(3), 451-456.
[94] Gefen A., Megido-Ravid M., Azariah M., etc. Integration of plantar soft tissue stiffness measurements in routine MRI of the diabetic foot, Clin Biomech (Bristol, Avon), 2001, 16(10), 921-925.
[95] Ledoux W. R., Blevins J. J. The compressive material properties of the plantar soft tissue, J Biomech, 2007, 40(13), 2975-2981.
[96] Chao E. Y., Laughman R. K., Schneider E., etc. Normative data of knee joint motion and ground reaction forces in adult level walking, J Biomech, 1983, 16(3), 219-233.
[97] Giakas G, Baltzopoulos V, Dangerfield P, etc. Comparison of gait patterns between healthy and scoliotic patients using time and frequency domain analysis of ground reaction forces, Spine, 1996, 21(19), 2235-2242.
[98] DA Winter. Biomechanics and motion control of human movement Wiley, 2004.
[99] An K. N., Berglund L., Cooney W. P., etc. Direct in vivo tendon force measurement system, J Biomech, 1990, 23(12), 1269-1271.
[100] Komi P. V. Relevance of in vivo force measurements to human biomechanics, J Biomech, 1990, 23 Suppl 1, 23-34.
[101] Schuind F., Garcia-Elias M., Cooney W. P., etc. Flexor tendon forces: In vivo measurements, J Hand Surg Am, 1992, 17(2), 291-298.
[102] Reilly P., Bull M. J., Amis M. M., etc. A novel technique for the quantification of tendon forces: Application to the subscapularis tendon, Trans Orthop Res Soc, 2003, (28), 180.
[103] Finni T., Komi P. V., Lukkariniemi J. Achilles tendon loading during walking: application of a novel optic fiber technique, Eur J Appl Physiol Occup Physiol, 1998, 77(3), 289-291.
[104] Finni T., Komi P. V., Lepola V. In vivo human triceps surae and quadriceps femoris muscle function in a squat jump and counter movement jump, Eur J Appl Physiol, 2000, 83(4 -5), 416-426.
[105] Fleming B. C., Beynnon B. D. In vivo measurement of ligament/tendon strains and forces: a review, Ann Biomed Eng, 2004, 32(3), 318-328.
[106]丁海曙,容观澳,王广志.人体运动信息检测与处理,北京,中国宇航出版社, 1992.
[107] Vaughan C.L., Davis B.L. , O'Connor J.C. . 1999, "Dynamics of Human Gait," Kiboho Publishers.
[108] Crowninshield R.D. . A physiologically based criterion for muscle force predictions on locomotion, Bull Hosp Jt Dis Orthop Inst, 1983, 43(2), 164-170.
[109] Dietz V., Zijlstra W., Prokop T., etc. Leg muscle activation during gait in Parkinson's disease: adaptation and interlimb coordination, Electroencephalogr Clin Neurophysiol, 1995, 97(6), 408-415.
[110]王成焘.人体生物摩擦学,北京,科学出版社, 2008.
[111] Sharkey N. A., Hamel A. J. A dynamic cadaver model of the stance phase of gait: performance characteristics and kinetic validation, Clin Biomech (Bristol, Avon), 1998, 13(6), 420-433.
[112] Oreskes N., Shrader-Frechette K., Belitz K. Verification, Validation, and Confirmation of Numerical Models in the Earth Sciences, Science, 1994, 263(5147), 641-646.
[113] Babuska I., Oden J. T. Verification and validation in computational engineering and science: basic concepts, Comput Methods Appl Mech Eng, 2004, 193(36-38), 4057-4066.
[114] Trucano T., Post D. Guest Editors' Introduction: Verification and Validation in Computational Science and Engineering, Comput Sci Eng, 2004, 6(5), 8-9.
[115] Zienkiewiz O.C., Taylor K.L. The finite element method, Butterworth Heinemann., 2000.
[116]朱伯芳.有限单元法原理和应用,北京,中国水利电力出版社, 1998.
[117] Zienkiewicz O.C., Zhu J.Z. A simple error estimator and adaptive procedure for practical engineering analysis, Int J Numer Meth Eng, 1987, 24(2), 337-357.
[118] Dar F. H., Meakin J. R., Aspden R. M. Statistical methods in finite element analysis, J Biomech, 2002, 35(9), 1155-1161.
[119] Dennis K. J., McKinney S. Sesamoids and accessory bones of the foot, Clin Podiatr Med Surg, 1990, 7(4), 717-723.
[120]王旭,顾湘杰.足横弓与NFEA7外翻关系的研究进展,中国矫形外科杂志, 2000, 7(4), 387-389.
[121] Biedert R., Hintermann B. Stress fractures of the medial great toe sesamoids in athletes, Foot Ankle Int, 2003, 24(2), 137-141.
[122] Siegler S., Block J., Schneck C. D. The mechanical characteristics of the collateral ligaments of the human ankle joint, Foot Ankle, 1988, 8(5), 234-242.
[123] Wright D. G., Rennels D. C. A Study of the Elastic Properties of Plantar Fascia, J Bone Joint Surg Am, 1964, 46, 482-492.
[124] ANSYS 9.0. The general-purpose finite element software. Documentation.,
[125] Moaveni S. . Finite element analysis: Theory and application with ANSYS., New Jersey, USA, Pearson Education, Inc., 2003.
[126]王勖成.有限单元法,北京,清华大学出版社, 2003.
[127] Duvaut G. , Lions J. L. Inequalities in mechanics and physics New York, Springer-Verlag, 1976.
[128] Simo J.C., Laursen T.A. An Augmented Lagrangian Treatment of Contact Problems Involving Friction, Comput Struct, 1992, 42(1), 97-116.
[129] Krishnan R., Kopacz M., Ateshian G. A. Experimental verification of the role of interstitial fluid pressurization in cartilage lubrication, J Orthop Res, 2004, 22(3), 565-570.
[130] Zhang M., Mak A. F. In vivo friction properties of human skin, Prosthet Orthot Int, 1999, 23(2), 135-141.
[131] Aerts P., Ker R. F., De Clercq D., etc. The mechanical properties of the human heel pad: a paradox resolved, J Biomech, 1995, 28(11), 1299-1308.
[132] Miller-Young J. E., Duncan N. A., Baroud G. Material properties of the human calcaneal fat pad in compression: experiment and theory, J Biomech, 2002, 35(12), 1523-1531.
[133] Athanasiou K. A., Liu G. T., Lavery L. A., etc. Biomechanical topography of human articular cartilage in the first metatarsophalangeal joint, Clin Orthop Relat Res, 1998, (348), 269-281.
[134] Gefen A., Megido-Ravid M., Itzchak Y. In vivo biomechanical behavior of the human heel pad during the stance phase of gait, J Biomech, 2001, 34(12), 1661-1665.
[135] Rome K., Webb P., Unsworth A., etc. Heel pad stiffness in runners with plantar heel pain, ClinBiomech (Bristol, Avon), 2001, 16(10), 901-905.
[136] Cavanagh P. R. Plantar soft tissue thickness during ground contact in walking, J Biomech, 1999, 32(6), 623-628.
[137] Cristofolini L., Viceconti M., Cappello A., etc. Mechanical validation of whole bone composite femur models, J Biomech, 1996, 29(4), 525-535.
[138] "F-Scan User Mannual."
[139] "http://en.wikipedia.org/wiki/Flat_feet."
[140] Huang C. K., Kitaoka H. B., An K. N., etc. Biomechanical evaluation of longitudinal arch stability, Foot Ankle, 1993, 14(6), 353-357.
[141] Kitaoka H. B., Luo Z. P., An K. N. Mechanical behavior of the foot and ankle after plantar fascia release in the unstable foot, Foot Ankle Int, 1997, 18(1), 8-15.
[142]杨云峰.人体足纵弓静力性内在维持结构的生物力学研究, [博士学位论文],上海,同济大学, 2007.
[143] Anderson R.B., Foster M.D. Operative treatment of subcalcaneal pain, Foot Ankle, 1989, 9(6), 317-323.
[144] Daly P.J., Kitaoka H.B. Plantar fasciotomy for intactable plantar fasciitis: clinical results and biomechanical evaluation, Foot Ankle, 1992, 13(4), 188-195.
[145] Davies M.S., Weiss G.A., Saxby T.S. Plantar fasciitis: how successful is surgical intervention?, Foot Ankle Int, 1999, 20(12), 803-807.
[146] Viladot A, Viladot A. Stress fractures in the foot, Foot Ankle Surg, 1998, 4(1), 3-11.
[147] Hopton B. P., Harris N. J. Fractures of the Foot and Ankle, Surgery (Oxford), 2003, 21(9), 236-240.
[148] Menz H. B., Morris M. E. Clinical determinants of plantar forces and pressures during walking in older people, Gait Posture, 2006, 24(2), 229-236.
[149] Hsiang S. M., Chang C. C. The effect of gait speed and load carrying on the reliability of ground reaction forces, Safety Science, 2002, 40(7-8), 639-657.
[150] Donahue S. W., Sharkey N. A., Modanlou K. A., etc. Bone strain and microcracks at stress fracture sites in human metatarsals, Bone, 2000, 27(6), 827-833.
[151] Simkin A.Structural analysis of the human foot in standing posture, [Dissertation], Tel Aviv, Israel, Tel Aviv University, 1982.
[152] Reilly D. T., Burstein A. H. The elastic and ultimate properties of compact bone tissue, J Biomech, 1975, 8(6), 393-405.
[153] Burstein A. H., Reilly D. T., Martens M. Aging of bone tissue: mechanical properties, J Bone Joint Surg Am, 1976, 58(1), 82-86.
[154] Muscolo L., Migues A., Slullitel G., etc. Stress fracture nonunion at the base of the second metatarsal in a ballet dancer - A case report, American Journal of Sports Medicine, 2004, 32(6), 1535-1537.
[155] Morris G., Nix K., Goldman F. D. Fracture of the second metatarsal base - An overlooked cause of chronic midfoot pain, J Am Podiatr Med Assoc, 2003, 93(1), 6-10.
[156] Bayraktar H.H., Morgan E.F., Niebur G.L., etc. Comparison of the elastic and yield properties of human femeoral trabecular and cortial bone tissue, J Biomech, 2004, 37, 27-35.
[157]王旭.足三维有限元建模第一跖列与拇外翻关系的临床与生物力学研究, [博士学位论文],上海,复旦大学, 2005.
[158] Mann R. A., Coughlin M. J. Hallux valgus--etiology, anatomy, treatment and surgical considerations, Clin Orthop Relat Res, 1981, (157), 31-41.
[159] MeGlamry E.D. (著),鲁英(译).拇趾外翻及相关畸形,北京,中国医药科技出版社, 1996.
[160]方朝晖.糖尿病家庭调养,上海,上海中医药大学出版社, 2006.
[161]俞光荣,陈雁西.糖尿病足的骨科治疗,中华医学杂志, 2007, 87(26), 1806-1807.
[162] Kwon O. Y., Mueller M. J. Walking patterns used to reduce forefoot plantar pressures in people with diabetic neuropathies, Phys Ther, 2001, 81(2), 828-835.
[163]王永慧.糖尿病患者足底压力改变与足溃疡的关系,国外医学(内分泌学分册), 2004, 24(5), 324-326.
[164] Pham H., Harkless L. B., Armstrong D. G., etc. Screening techniques to identify people at high risk for diabetic foot ulceration - A prospective multicenter trial, Diabetes Care, 2000, 23(5), 606-611.
[165] Boulton A. J. M., Gries F. A., Jervell J. A. Guidelines for the diagnosis and outpatient management of diabetic peripheral neuropathy (Reprinted from Diabet Med, vol 15, pg 508-514, 1998), Diabetes Reviews, 1999, 7(4), 237-244.
[166]毛宾尧,贾学文,郑菲蓉等.行走和站立时足底应力分布研究,中国矫形外科杂志, 2002, 10(12), 68-70.
[167]王明鑫,俞光荣.正常人足底压力分析的研究进展,中国矫形外科杂志, 2006, 14(22), 1722-1724.
[168]王明鑫,俞光荣,陈雁西等.正常中国成年人足底压力分析,中国矫形外科杂志, 2008, 16(9), 687-690.
[169]刘新成,陈雁西,俞光荣等.糖尿病伴足趾畸形的三维动态足底压力分析,中国骨与关节外科, 2009, 2(6), 488-493.
[170] McLellan K., Petrofsky J. S., Bains G., etc. The effects of skin moisture and subcutaneous fat thickness on the ability of the skin to dissipate heat in young and old subjects, with and without diabetes, at three environmental room temperatures, Med Eng Phys, 2009, 31(2), 165-172.
[171] Charanya G., Patil K. M. , Thomas V.J., etc. Standing foot pressure image analysis for variations in foot sole soft tissue properties and levels of diabetic neuropathy, ITBM-RBM, 2004, 25(1), 23-33.
[172] Olefsky J.M. Pathogenesis of insulin resistance and hyperglycemia in non-insulin-dependent diabetes mellitus, Am J Med, 1985, 79(3), 1-7.
[173] Milczarczyk A., Franek E. Osteoporosis and bone fractures in patients with diabetes mellitus, Diabetologia Doswiadczalna i Kliniczna, 2008, 8(2), 63-67.