人体足部运动的有限元建模及其生物力学功能耦合分析
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摘要
人体足部运动生物力学研究在足部疾病治疗、体育竞技运动保护、康复与矫形器材设计、假肢的计算机辅助设计与制造、机器人足部精细设计及工程仿生、军事仿生等方面具有重要的科学意义与应用价值。本文基于人体运动生物力学试验测试、足部医学图像、逆向工程技术、有限元方法、生物耦合理论以及可拓方法对人体足部运动及其生物力学功能进行了建模研究与理论分析。
论文中自行设计、制作了人体足部红外反光标记系统,可用于多种运动状态下足部运动的试验研究与测试；基于足部医学图像和运动生物力学试验,创新性地提出了人体足部生物力学研究领域的首个纯动态二维足部有限元模型,借助该模型可对人体常速行走运动中的运动特征参数、足部各区域应力进行较好的仿真预测,并可进行相关足部临床病症的辅助分析；通过多次仿真筛选测试计算,提出了基于Slipring连接单元的肌肉建模方法；构建了基于解剖学的精细三维人体足部骨骼-肌肉系统有限元模型,为首次集成多条韧带(85)和多条足部外在肌肉组(12)的足部有限元模型。该模型可对足底压力、骨骼应力等参数进行合理预测与评估；结合生物耦合理论,从系统、整体角度对步态周期运动中的足部减震、储能功能,足部肌-腱、骨骼系统进行了理论分析,并借助可拓方法建立了两者的耦合可拓模型,对耦合信息进行形式化表达,为进一步相关工程仿生与军事仿生研究与应用提供了智力支持。
The human foot is an immensely complex structure comprising numerous bones, muscles, ligaments and synovial joints, playing very important role in lots of human sports and activities. Biomechanical functions and characteristics of the human foot are research hotspots in foot biomechanics, and are also the solid biological data base of bionic engineering. Meantime, it is of great significance in science and its application for many related fields, such as foot diseases therapy, sports protection, rehabilitation and orthopedic instruments design, computer aid design and manufacture of artificial limb, fine design of humanoid robot's foot, etc.
Combined with experimental test, foot medical images, inverse engineering technique, finite element method, biological coupling theory and extenics, human foot finite element modeling and biomechanical function coupling analysis during locomotion were conducted in this dissertation. In the dissertation, based on the multiple rigid-body model of human lower limb and foot, a novel infrared reflective tracking marker system was designed. The marker system had been used successfully in multi-locomotion test, such as walking, running, turning etc., to study the human foot biomechanics combined with stereophotogrammetry motion capture system and technique; A 2-dimensional subject-specific dynamic finite element model of the human foot complex was proposed based on individualized medical imaging data and the loading conditions derived from gait measurements on the same subject. With the help of this model, main parameter estimation of human normal walking and foot plantar stress distribution can be got successfully, and the model can also be used for analyzing some related foot diseases; Foot muscle modeling method based on Slipring connector element was proposed through running multiple simulations. On the basis of medical images and anatomy, a 3-dimenstional human foot musculoskeletal finite element model comprising 29 bones,85 ligaments,12 muscle groups and foot plantar was established. To our knowledge, it is the most complicated foot musculoskeletal finite element model in foot biomechanics research field. The 3-dimensional foot model can predict the stress distribution of foot plantar and bony structure effectively in gait simulation; finally, systematic coupling analysis of specific foot biomechanical functions (vibration and energy absorption, foot musculoskeletal functional system) was carried out based on biological coupling theory. And the corresponding extension models of these two biological coupling systems were established by Extenics method, to describe coupling information in formalization. This kind of illustration of biological coupling system can be useful to build a biological functional knowledge base and manage data, and can also be recognized as the basis of the combination of bionic engineering and an intelligent computer processing technique. The detailed research work and conclusions obtained of the dissertation are as follows:
1. Human foot medical images were collected with the aid of medical imaging technique and instrument. Foot medical imaging data is the foundation of foot finite element modeling work (2-dimensional,3-dimensional). Two different kinds of foot medical images were collected, they are CT images (with interval 1.5mm,157 images in total) and MR images (with interval 2mm,104 images in total), respectively.
2. The lower limb of 13 segments human multiple rigid-body model was adopted, furthermore, the foot segment of the lower limb was redefined into five segments, they are hind foot, mid-foot, medial fore-foot, lateral fore-foot and phalanx, respectively. The new model was introduced by kinetic description method. According to the model and specific foot measurement requirements, a novel infrared reflective tracking marker system was designed. The marker system was consisted of 53 reflective markers in total, including 32 technical markers and 21 anatomical landmarks, and was used to track the motion the motion of pelvis, femur, shank and foot segments. The system had been used successfully in multi-locomotion experimental test, such as walking, running, jumping, turning, etc., to study the human foot biomechanics.
3. Measurement platform comprising 12 infrared camera motion analysis system,6 force plates array and 1 metre-long pressure plate, was built to study foot biomechanics during locomotion. Based on the measurement platform and tracking marker system, the 3-dimensional human motion experiments of 7 subjects were successfully conducted. Each subject had been measured for six kinds of state of motion. They are slow walking/running, normal walking/running and fast walking/running, respectively. Conclusions were drawn from measurement results:in the state of walking, whatever slow speed, normal speed or fast speed, the ground reaction force of the same subject has two main components; they are the force componets along O-X and O-Y direction, respectively; under these three different walking conditions, for the same subject, the similar development trend of right ankle joint force and torque were found; the ankle joint force components (along O-X and O-Y direction) and the ankle joint torque in sagittal plane play very important role during human locomotion; by the comparison among these three walking conditions, it is also found that there is no big difference in the ankle joint force components (along O-X and O-Y direction) and the ankle joint torque in sagittal plane between slow walking and normal walking condition, whereas, the magnitude of ankle joint force components and torque increased during fast walking. The similar conclusions were also derived from running experimental test.
4. A 2-dimensional subject-specific dynamic finite element model of the human foot complex was proposed based on individualized medical imaging data and the loading conditions derived from gait measurements. Normal walking gait simulation was conducted by the help of the proposed 2-dimensional model. Through the comparison of ground reaction force (GRF), the trajectory of center of pressure (COP), foot rotation angle (FRA) and foot plantar stress distribution between simulation results and measurement, it is showed the simulation results all are agreed well with the measurement. Material sensitivity analysis was carried out to study the biomechanical effects of soft tissue stiffening (+5%,+10%) and softening (-5%,-10%) on above FE calculated results. It is showed that there is no significant effect on GRF, GRA and COP trajectory whatever stiffening or softening the soft tissue, besides plantar stress distribution. With the increase of soft tissue stiffness, the maximum von Mises stress on foot model increased as well, and the magnitude of stress decreased along with the soft tissue softening. Slow release effect of stress was proposed on the basis of material sensitivity analysis results. That is, in the stance phase, due to the decrease of soft tissue stiffness, the flexibility and adaptability of the whole foot plantar were reinforced. Therefore, under the same loading condition, it is easy to deform to absorb more energy or work done by external forces, furthermore, abate the strength of interaction forces between foot-ground contact to make the human foot avoiding possible danger and damage caused by high stress. At the same time, the conclusion may give a help to explain tissue breakdown syndrome of diabetic feet.
5. By use of commercial software (Mimics, Solidworks, Geomagic and Rhinocreos), a 3-dimenstional human foot skeletal model comprising 29 bones and foot plantar was established. Then, combined with foot ligaments anatomy,85 ligaments including plantar fascia were constructed by the help of truss elements; Foot muscle modeling method based on Slipring connector element was proposed through running multiple simulations. Finally, based on the foot skeletal-ligament model,12 muscle groups were integrated into the 3-dimensional foot model by using slipring connector elements and mid-reference points. To our knowledge, it is the most complicated foot musculoskeletal finite element model in foot biomechanics research field. Mid-stance phase during locomotion was simulated by the model. Through the analysis of simulation results of foot plantar stress distribution, bony structure stress, ligaments and plantar fascia, it is showed the proposed 3-dimensional foot model worked effectively in gait simulation. And it may be used in some foot related fields, such as foot diseases therapy, sports protection, computer aid design and manufacture of artificial limb, etc.
6. Based on biological coupling theory, systematic coupling analysis of specific foot biomechanical function (vibration and energy absorption) was carried out by combining finite element method and experimental measurement results. The corresponding coupling mechanism is the following:1) Reticular fiber structure and fat cells material are coupling elements of foot pad vibration and energy absorption functional coupling system; these two coupling elements are connected with each other by cross-link coupling way; during locomotion, the foot pad energy absorption function was implemented with fully equipoise parallel pattern.2) Foot arc structure and plantar fascia are coupling elements of foot arc vibration and energy absorption functional coupling system; these two coupling elements are connected with each other by immovable coupling way; the corresponding biological function was implemented with compound non-fully equipoise parallel pattern.3) The vibration and energy absorption biomechanical function of whole foot was coupling result of foot pad coupling system and foot arc coupling system. These two coupling system are the basic elements, and connected each other by up-down orientation coupling way; during locomotion, the whole foot vibration and energy absorption function was implemented with combined non-fully equipoise parallel pattern.
7. Based on biological coupling theory, systematic coupling analysis of foot musculoskeletal functional system was carried out. Dynamic coupling conception was proposed, and the corresponding basic element, coupling way and implement pattern of biological function were also discussed. The conclusion is the following:the implementation of foot functional motion was dynamic coupling result of foot muscle-tendon and foot bony structure system. Foot muscle-tendon is an active coupling system; muscle and tendon are the basic elements of the system and connected with each other by closely overlapping coupling way; the active coupling system implemented the function of generating and transferring muscle force with non-fully equipoise parallel pattern. Whilst, foot bony structure is a passive coupling system; foot bones and ligaments are basic elements of the system and connected each other with immovable coupling way; the passive coupling system receive acting muscle force from muscle-tendon active coupling system with second-level combined non-fully equipoise parallel pattern, and generate corresponding foot action. Therefore, muscle-tendon active coupling system and foot bony structure passive coupling system are connected with each other with dynamic dominance coupling way; the specific foot functional motion or action during locomotion was implemented with combined non-fully equipoise parallel pattern.
8. An extension model of biological coupling system was proposed based on basic element theory of Extenics. By use of the model, the coupling analysis information of foot biomechanical function (part 7) were all described in formalization, so as to facilitate building biological function knowledge base, data management and bionic engineering general design.
Human foot biomechanics study is one of the research fronts of biomechanics field, which is related to human anatomy, human physiology, mathematics, mechanics, kinematics, and biomedical engineering, etc. and therefore, it is a highly comprehensive topic. This dissertation mainly focused on human foot finite element modeling and biomechanical function coupling analysis during locomotion. Specific-subject based finite element foot models were proposed, supply an innovative and more proper method for dynamic foot finite element modeling during locomotion, and facilitate the further study of dynamic response of foot musculoskeletal system and tissue mechanics.
论文中自行设计、制作了人体足部红外反光标记系统,可用于多种运动状态下足部运动的试验研究与测试；基于足部医学图像和运动生物力学试验,创新性地提出了人体足部生物力学研究领域的首个纯动态二维足部有限元模型,借助该模型可对人体常速行走运动中的运动特征参数、足部各区域应力进行较好的仿真预测,并可进行相关足部临床病症的辅助分析；通过多次仿真筛选测试计算,提出了基于Slipring连接单元的肌肉建模方法；构建了基于解剖学的精细三维人体足部骨骼-肌肉系统有限元模型,为首次集成多条韧带(85)和多条足部外在肌肉组(12)的足部有限元模型。该模型可对足底压力、骨骼应力等参数进行合理预测与评估；结合生物耦合理论,从系统、整体角度对步态周期运动中的足部减震、储能功能,足部肌-腱、骨骼系统进行了理论分析,并借助可拓方法建立了两者的耦合可拓模型,对耦合信息进行形式化表达,为进一步相关工程仿生与军事仿生研究与应用提供了智力支持。
The human foot is an immensely complex structure comprising numerous bones, muscles, ligaments and synovial joints, playing very important role in lots of human sports and activities. Biomechanical functions and characteristics of the human foot are research hotspots in foot biomechanics, and are also the solid biological data base of bionic engineering. Meantime, it is of great significance in science and its application for many related fields, such as foot diseases therapy, sports protection, rehabilitation and orthopedic instruments design, computer aid design and manufacture of artificial limb, fine design of humanoid robot's foot, etc.
Combined with experimental test, foot medical images, inverse engineering technique, finite element method, biological coupling theory and extenics, human foot finite element modeling and biomechanical function coupling analysis during locomotion were conducted in this dissertation. In the dissertation, based on the multiple rigid-body model of human lower limb and foot, a novel infrared reflective tracking marker system was designed. The marker system had been used successfully in multi-locomotion test, such as walking, running, turning etc., to study the human foot biomechanics combined with stereophotogrammetry motion capture system and technique; A 2-dimensional subject-specific dynamic finite element model of the human foot complex was proposed based on individualized medical imaging data and the loading conditions derived from gait measurements on the same subject. With the help of this model, main parameter estimation of human normal walking and foot plantar stress distribution can be got successfully, and the model can also be used for analyzing some related foot diseases; Foot muscle modeling method based on Slipring connector element was proposed through running multiple simulations. On the basis of medical images and anatomy, a 3-dimenstional human foot musculoskeletal finite element model comprising 29 bones,85 ligaments,12 muscle groups and foot plantar was established. To our knowledge, it is the most complicated foot musculoskeletal finite element model in foot biomechanics research field. The 3-dimensional foot model can predict the stress distribution of foot plantar and bony structure effectively in gait simulation; finally, systematic coupling analysis of specific foot biomechanical functions (vibration and energy absorption, foot musculoskeletal functional system) was carried out based on biological coupling theory. And the corresponding extension models of these two biological coupling systems were established by Extenics method, to describe coupling information in formalization. This kind of illustration of biological coupling system can be useful to build a biological functional knowledge base and manage data, and can also be recognized as the basis of the combination of bionic engineering and an intelligent computer processing technique. The detailed research work and conclusions obtained of the dissertation are as follows:
1. Human foot medical images were collected with the aid of medical imaging technique and instrument. Foot medical imaging data is the foundation of foot finite element modeling work (2-dimensional,3-dimensional). Two different kinds of foot medical images were collected, they are CT images (with interval 1.5mm,157 images in total) and MR images (with interval 2mm,104 images in total), respectively.
2. The lower limb of 13 segments human multiple rigid-body model was adopted, furthermore, the foot segment of the lower limb was redefined into five segments, they are hind foot, mid-foot, medial fore-foot, lateral fore-foot and phalanx, respectively. The new model was introduced by kinetic description method. According to the model and specific foot measurement requirements, a novel infrared reflective tracking marker system was designed. The marker system was consisted of 53 reflective markers in total, including 32 technical markers and 21 anatomical landmarks, and was used to track the motion the motion of pelvis, femur, shank and foot segments. The system had been used successfully in multi-locomotion experimental test, such as walking, running, jumping, turning, etc., to study the human foot biomechanics.
3. Measurement platform comprising 12 infrared camera motion analysis system,6 force plates array and 1 metre-long pressure plate, was built to study foot biomechanics during locomotion. Based on the measurement platform and tracking marker system, the 3-dimensional human motion experiments of 7 subjects were successfully conducted. Each subject had been measured for six kinds of state of motion. They are slow walking/running, normal walking/running and fast walking/running, respectively. Conclusions were drawn from measurement results:in the state of walking, whatever slow speed, normal speed or fast speed, the ground reaction force of the same subject has two main components; they are the force componets along O-X and O-Y direction, respectively; under these three different walking conditions, for the same subject, the similar development trend of right ankle joint force and torque were found; the ankle joint force components (along O-X and O-Y direction) and the ankle joint torque in sagittal plane play very important role during human locomotion; by the comparison among these three walking conditions, it is also found that there is no big difference in the ankle joint force components (along O-X and O-Y direction) and the ankle joint torque in sagittal plane between slow walking and normal walking condition, whereas, the magnitude of ankle joint force components and torque increased during fast walking. The similar conclusions were also derived from running experimental test.
4. A 2-dimensional subject-specific dynamic finite element model of the human foot complex was proposed based on individualized medical imaging data and the loading conditions derived from gait measurements. Normal walking gait simulation was conducted by the help of the proposed 2-dimensional model. Through the comparison of ground reaction force (GRF), the trajectory of center of pressure (COP), foot rotation angle (FRA) and foot plantar stress distribution between simulation results and measurement, it is showed the simulation results all are agreed well with the measurement. Material sensitivity analysis was carried out to study the biomechanical effects of soft tissue stiffening (+5%,+10%) and softening (-5%,-10%) on above FE calculated results. It is showed that there is no significant effect on GRF, GRA and COP trajectory whatever stiffening or softening the soft tissue, besides plantar stress distribution. With the increase of soft tissue stiffness, the maximum von Mises stress on foot model increased as well, and the magnitude of stress decreased along with the soft tissue softening. Slow release effect of stress was proposed on the basis of material sensitivity analysis results. That is, in the stance phase, due to the decrease of soft tissue stiffness, the flexibility and adaptability of the whole foot plantar were reinforced. Therefore, under the same loading condition, it is easy to deform to absorb more energy or work done by external forces, furthermore, abate the strength of interaction forces between foot-ground contact to make the human foot avoiding possible danger and damage caused by high stress. At the same time, the conclusion may give a help to explain tissue breakdown syndrome of diabetic feet.
5. By use of commercial software (Mimics, Solidworks, Geomagic and Rhinocreos), a 3-dimenstional human foot skeletal model comprising 29 bones and foot plantar was established. Then, combined with foot ligaments anatomy,85 ligaments including plantar fascia were constructed by the help of truss elements; Foot muscle modeling method based on Slipring connector element was proposed through running multiple simulations. Finally, based on the foot skeletal-ligament model,12 muscle groups were integrated into the 3-dimensional foot model by using slipring connector elements and mid-reference points. To our knowledge, it is the most complicated foot musculoskeletal finite element model in foot biomechanics research field. Mid-stance phase during locomotion was simulated by the model. Through the analysis of simulation results of foot plantar stress distribution, bony structure stress, ligaments and plantar fascia, it is showed the proposed 3-dimensional foot model worked effectively in gait simulation. And it may be used in some foot related fields, such as foot diseases therapy, sports protection, computer aid design and manufacture of artificial limb, etc.
6. Based on biological coupling theory, systematic coupling analysis of specific foot biomechanical function (vibration and energy absorption) was carried out by combining finite element method and experimental measurement results. The corresponding coupling mechanism is the following:1) Reticular fiber structure and fat cells material are coupling elements of foot pad vibration and energy absorption functional coupling system; these two coupling elements are connected with each other by cross-link coupling way; during locomotion, the foot pad energy absorption function was implemented with fully equipoise parallel pattern.2) Foot arc structure and plantar fascia are coupling elements of foot arc vibration and energy absorption functional coupling system; these two coupling elements are connected with each other by immovable coupling way; the corresponding biological function was implemented with compound non-fully equipoise parallel pattern.3) The vibration and energy absorption biomechanical function of whole foot was coupling result of foot pad coupling system and foot arc coupling system. These two coupling system are the basic elements, and connected each other by up-down orientation coupling way; during locomotion, the whole foot vibration and energy absorption function was implemented with combined non-fully equipoise parallel pattern.
7. Based on biological coupling theory, systematic coupling analysis of foot musculoskeletal functional system was carried out. Dynamic coupling conception was proposed, and the corresponding basic element, coupling way and implement pattern of biological function were also discussed. The conclusion is the following:the implementation of foot functional motion was dynamic coupling result of foot muscle-tendon and foot bony structure system. Foot muscle-tendon is an active coupling system; muscle and tendon are the basic elements of the system and connected with each other by closely overlapping coupling way; the active coupling system implemented the function of generating and transferring muscle force with non-fully equipoise parallel pattern. Whilst, foot bony structure is a passive coupling system; foot bones and ligaments are basic elements of the system and connected each other with immovable coupling way; the passive coupling system receive acting muscle force from muscle-tendon active coupling system with second-level combined non-fully equipoise parallel pattern, and generate corresponding foot action. Therefore, muscle-tendon active coupling system and foot bony structure passive coupling system are connected with each other with dynamic dominance coupling way; the specific foot functional motion or action during locomotion was implemented with combined non-fully equipoise parallel pattern.
8. An extension model of biological coupling system was proposed based on basic element theory of Extenics. By use of the model, the coupling analysis information of foot biomechanical function (part 7) were all described in formalization, so as to facilitate building biological function knowledge base, data management and bionic engineering general design.
Human foot biomechanics study is one of the research fronts of biomechanics field, which is related to human anatomy, human physiology, mathematics, mechanics, kinematics, and biomedical engineering, etc. and therefore, it is a highly comprehensive topic. This dissertation mainly focused on human foot finite element modeling and biomechanical function coupling analysis during locomotion. Specific-subject based finite element foot models were proposed, supply an innovative and more proper method for dynamic foot finite element modeling during locomotion, and facilitate the further study of dynamic response of foot musculoskeletal system and tissue mechanics.
引文
1. Lei Ren, David Howard, Luquan Ren, Chris Nester, Limei Tian. A phase-dependent hypothesis for locomotor functions of human foot complex [J]. Journal of bionic Engineering,2008,5(3),175-180.
2. Zhihui Qian, Lei Ren, Luquan Ren, John Huchinson. A Dynamic finite element analysis of the human foot complex During Level Walking[J]. Journal of Biomechanics. (In review)
3. 陈宝兴.祝贺我国足病的研究与治疗[J].中华骨科杂志,1994,11(12),707.
4. http://baike.baidu.com/view/62803.htm
5. 陈秉聪.车辆行走机构形态学及仿生减粘脱土理论[M].第1版.北京：机械工业出版社,2001.
6. Cavanagh P.R., Ulbrecht J.S., Caputo G.M. Biomechanical aspects of diabetic foot disease:aetiology, treatment, and prevention [J]. Diabetic medicine,1996,13(1), s17-22.
7. Weng-Pin Chen, Fuk-Tan Tang, Chia-Wei Ju. stress distribution of the foot during mid-stance to push off in bare foot gait, a 3d finite element analysis[J]. Clinical biomechanics,2001,16(7),614-620.
8. Balmaseda M.T., Koozekanani S.H., Fathhi M.T., Gordon C., Dreyfuss P.H., Tanbonliong EC. Ground reaction forces, center of pressure, and duration of stance with and without an ankle-foot orthosis[J]. Arch Phys Med Rehabil,1988,69(12):1009-1012.
9. Lundeen S., Lundquist K., Cornwall M.W., et al. Plantar pressures during level walking compared with other ambulatory activities[J]. Foot & Ankle Int,1994,15(6):324-328.
10. Alexander I.J., Chao E.Y.S., Johnson K.A. The assessment of dynamic foot to ground contact forces and plantar pressure distribution:a review of the evolution of current techniques and clinical applications[J]. Foot & ankle,1990,11(3),152-167.
11. Brown M., Rudicel S., Esquenazi A. Measurement of dynamic pressures at the shoe-foot interface during normal walkingwith various foot orthosis using the FSCAN system[J]. Foot Ankle Int, 1996,17(3):152-156.
12. Rosenbaum D., Bauer G., Augat P.. Calcaneal fractures cause a lateral load shift in chopart joint contact stress and plantar pressure pattern in vitro[J]. Journal of biomechanics, 1996,29(1):1435-1443.
13. Parenteau C.S., Viano D.C., Petit PY. Biomechanical properties of human cadaveric ankle-subtalar joints in quasi-static loading[J]. Journal of biomechanical engineering,1998,120(1):105-111.
14. Stahelin T., Nigg B.M., Stefanyshyn D.J., van den Bogert A.J., Kim S.J. A method to determine bone movement in the ankle joint complex in vitro[J]. Journal of biomechanics,1997,30(5),513-516.
15. Jacob H.A.C, Zollinger H. Biomechanics of the foot-forces in the fore-foot during walking and their clinical relevance[J]. Orthopade,1992,21(1):75-80.
16.林师诚.正常人体足部之三维动态有限元素分析[D].中原大学.
17.王立平,李建设.足底压力测量技术的发展现状与应用研究[J].浙江体育科学,2004,26(1),40-43.
18.林建宏.足底软组织与鞋内垫力学性质对足压分布影响之有限元分析[D].中原大学.
19. Hutton W.C., Drabble G.E. An apparatus to give the distribution of vertical load under the foot[J].
Rheumatology & physical medicine,1972,11(6),313-31
20.李建设,王立平.足底压力测量技术在生物力学研究中的应用于进展[J].北京体育大学学报,2005,28(2),191-193.
21.张潇,卢世璧.人体足底压力的测量与分析[J].医用生物力学,1994,9(2),108-115.
22. Henry A.P.J., Waugh W. The use of footprints in assessing the results of operations for hallux valgus[J]. Journal of bone joint surgery,1975,57(4),478-481.
23.李慧,张欣,陈翔,李毅.足底压力分布测量系统的设计[J].西安工程科技学院学报,2006,20(1),36-40.
24.韦启航,陆文莲,傅祖芸,卢世璧.人体步态分析系统—足底压力测量系统的研制[J].中国生物医学工程学报,2000,19(1),32-40.
25.戴尅戎,徐乃明,汤荣光,高玉兰.S9-1型步态分析系统的研制和平地行走时足-地接触能力的三维分析[J].生物力学,1986,1(1),24.
26.高琴,姜寿山,魏忠义,张欣.携式人体足底压力分布测量系统的研制[J].中国国际毛纺织会议暨WTO羊毛论坛论文集,2006,77-80,中国,西安.
27.王军,徐新智,张伟,刘金祥.足底压力动态图像分析系统与临床应用[J].中国临床康复,2002,6(6),802-803.
28.袁刚,张木勋,张建华.足底压力分布测量系统及临床应用[J].中国康复,2003,18(1),22-25.
29.金观昌,张军,张建中,孙超.一种新型足底压力分布测量系统及其应用[J].生物医学工程学杂志,2005,22(1),133-136.
30. Cavanagh P.R., Rodgers M.M., Iiboshi A. Pressure distribution under sysmptom-free feet during barefoot standing[J]. Foot & Ankle,1987,7(5),262-276.
31. Groundy M., Blackburn T.P.A., McLeish R.D., Smidt L. An investigation of the centers of pressure under the foot while walking[J]. Journal of bone and joint surgery,1975,57(1),98-103.
32. Hessert M.J., Vyas M., Leach L., Hu K., Lipsitz, L.A., Novak V. Foot pressure distribution during walking in young and old adults[J]. BMC Geriatrics,2005,5:8
33. Meyring S., Diehl R.R., Milani T.L., Hennig E.M., Berlit P Dynamic plantar pressure distribution measurement in hemiparetic patients[J]. Clinical biomechanics,1997,12(1),60-65.
34.王兰美,郭业民,潘志国.人体足底压力分布研究与应用[J].机械制造与研究,2005,34(1),35-38.
35.汤荣光.正常人足底静态和动态压力分布的测定[J].中国生物医学工程学报,1994,13(2),175-177.
36.袁刚,张木勋,王中琴,张建华.正常人足底压力分布及其影响因素分析[J].中华物理医学与康复杂志,2004,26(3),156-159.
37.王明鑫,俞光荣,陈雁西,杨云峰,黄四平,胡孙君.正常中国成年人足底压力分析[J].中国矫形外科杂志,2008,1 6(9),687-690.
38. Siegler S., Chen J., Schneck C.D. The three-dimensional kinematics and flexibility characteristics of the human ankle and subtalar joints-part Ⅰ:kinematics[J]. Journal of biomechanical engineering, 1988,110(4):364-73.
39. Ker R.F., Bennett, M.B., Bibby, S.R., Kester, R.C., Alexander, R.M. The spring in the arch of the human foot[J]. Nature,1987.325,147-149.
40. Sammarco G.J., Burstein A.H., Frankel V.H. Biomechanics of the ankle:a kinematic study[J]. Orthop Clin North Am,1973,4(1),75-96.
41. Arndt A., Wolf P., Liu A., Nester C., Stacoff A., Jones R., Lundgren P., Lundberg A. Intrinsic foot kinematics measured in vivo during the stance phase of slow running. Journal of biomechanics,2007, 40(12),2672-2678.
42. Nester C., Jones R.K., Liu A., Howard D., Lunderg A., Arndt A., Lundgren P., Stacoff A., Wolf P. Foot kinematics during walking measured using bone and surface mounted markers[J]. Journal of biomechanics,2007,40(15),3412-3423.
43.董骧,樊瑜波,张明.人体足部生物力学的研究[J].生物医学工程,2002,19(1),148-153.
44. De Cock A., Vanrenterghem., Willems T., Witvrouw E., De Clercq D. The trajectory of the center of pressure during barefoot running as a potential measure for foot function[J]. Gait & Posture,2008, 27(4),669-675.
45. Carrier, D.R., Heglund, N.C., Earls, K.D. Variable gearing during locomotion in the human musculoskeletal system[J]. Science,1994,265(5172),651-653.
46. Scott, S.H., Winter, D.A. Biomechanical model of the human foot:Kinematics and kinetics during the stance phase of walking[J]. Journal of Biomechanics,1993,26 (9),1091-1104.
47. Gilchrist L. A., Winter D. A. A two-part, viscoelastic foot model for use in gait simulations[J]. journal of biomechanics,1996,29(6),795-798.
48. Nester, C.J., Liu, A.M., Ward, E., Howard, D., Cocheba, J., Derrick, T., Paterson, P. In vitro study of foot kinematics using a dynamic walking cadaver model[J]. Journal of Biomechanics 2007,40(9), 1927-1937.
49. Ren Lei, Howard David, Ren Luquan, Nester Chris, Tian Limei. A generic analytical foot rollover model for predicting translational ankle kinematics in gait simulation studies[J]. journal of biomechanics,2009. (In Press)
50. Yettram A.L., Camilleri N.N. The force acting on the human calcaneus[J]. Journal of biomedical engineering,1993,15(1),46-50.
51. Cavanagh P.R., Shiang T.Y. Approaches to finite element analysis of the foot-shoe interface in diabetic patients[J]. Journal of biomechanics.1993,26(3),323-323.
52. Chu T.M., Reddy N.P., Padovan J. Three dimensional finite element stress analysis of the polypropylene, ankle-foot orthosis:static analysis[J]. Medical engineering & physics,1995,17(5), 372-379.
53. Patil K.M., Braak L.H., Huson A. Analysis of stresses in two-dimensional models of normal and neuropathic feet[J]. Medical & biologicall engineering & computing,1996,34(4),280-284.
54. Jacob, S., Patil, K.M., Braak, L.H., Huson, A. Stresses in a 3-D two arch model of a normal human foot[J]. Mechanics Research Communications,1996,23(4),387-393.
55. Jacob, S., Patil, K.M. Three-dimensional foot modeling and analysis of stresses in normal and early stage Hansen's disease with muscle paralysis[J]. Journal of Rehabilitation Research & Development, 1999,36(3),252-263.
56. Lemmon D., Shiang T.Y., Hashmi A. Ulbrecht J.S., Cavanagh P.R. The effect of insoles in therapeutic footwear:a finite element approach[J]. Journal of biomechanics,1997,30(6),615-620.
57. Gefen A.,, Megido-Ravid M., Itzchak Y., Arcan M. Biomechanical analysis of the three-dimensional foot structure during gait:a basic tool for clinical applications[J]. Journal of biomechanics,2000,122 (6),630-639.
58. Gefen A. Stress analysis of the standing foot following surgical plantar fascia release[J]. Journal of Biomechanics,2002,35 (5),629-637.
59. Gefen A. Plantar soft tissue loading under the medial metatarsals in the standing diabetic foot[J]. Medical engineering & physics,2003,25 (6),491-499.
60. Bandak F.A., Tannous R.E., Toridis T. On the development of an osseo-ligamentous finite element model of the human ankle joint[J]. International journal of solids and structures,2001,38 (10-13),1681-1697.
61. 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[J]. Clinical biomechanics,2001,16(7),614-620.
62. Cheung J.T., Zhang M., An K.N. Effects of plantar fascia stiffness on the biomechanical responses of the ankle-foot complex[J]. Clinical biomechanics,2004,19 (8),839-846.
63. Cheung J.T., Zhang M., Leung A.K., Fan Y.B. Three-dimensional finite element analysis of the foot during standing--a material sensitivity study[J]. Journal of biomechanics,2005,38 (5),1045-1054.
64. Cheung J.T., Zhang M. Parametric design of pressure-relieving foot orthosis using statistics-based finite element method[J]. Medical engineering & physics,2008,30 (3),269-277.
65. Garcia-Aznar J.M., Bayod J., Rosas A., Larrainzar R., Garcia-Bogalo R., Doblare M., Llanos L.F. Load transfer mechanism for different metatarsal geometries:a finite element study[J]. Journal of biomechanical engineering,2009,131 (2),1-7.
66. Cheng HY.K., Lin C.L., Wang H.W., Chou S.W. Finite element analysis of plantar fascia under stretch-The relative contribution of windlass mechanism and Achilles tendon force[J]. Journal of biomechanics,2008,41 (9),1937-1944.
67. Wu L.J. Nonlinear finite element analysis for musculoskeletal biomechanics of medial and lateral plantar longitudinal arch of Virtual Chinese Human after plantar ligamentous structure failures[J]. Clinical biomechanics,2007,22 (2),221-229.
68. Dai X.Q., Li Y., Zhang M., Cheung J.T. Effect of sock on biomechanical responses of foot during walking[J]. Clinical biomechanics,2006,21 (3),314-321.
69. Halloran J.P., Erdemir A.,van den Bogert A.J. Adaptive surrogate modeling for efficient coupling of musculoskeletal control and tissue deformation models[J].Journal of biomechanical engineering-transactions of the ASME,2009,131 (1),011014.
70. Alberto Garcia-Gonzalez, Javier Bayod, Juan Carlos Prados-Frutos, Marta Losa-Iglesias, Kevin T. Jules, Ricardo Becerro de Bengoa-Vallejo and Manuel Doblare. Finite-element simulation of flexor digitorum longus or flexor digitorum brevis tendon transfer for the treatment of claw toe deformity [J]. Journal of biomechanics,2009,42 (11),1697-1704.
71.屈钧利,韩江水.工程结构的有限元方法[M].第1版.西安：西北工业大学出版社,2004.
72.曾攀(译著).工程中的有限元方法[M].第3版.北京：清华大学出版社,2006.
73.刘怀横.结构及弹性力学有限元方法[M].第1版.西安：西北工业大学出版社,2007.
74.田杰,林珠,杭洽时,等.x线头颅侧位定位片硬组织形态二维有限元分析模型的建立[J].实用口腔
医学杂志,1999,15(2),129-31.
75.田杰,林珠,杭洽时,等.X线头颅侧位定位片硬组织形态三维有限元分析模型的建立[J].实 用口腔医学杂志,1999,15(2),135-6.
76.周学军,赵志河,赵美英,等.包括下颌骨的颞下颌关节三维有限元模型的建立[J].实用口腔医学杂志,2000,16(1),17-19.
77.苏友新,许书亮,陈日齐,等.用枕不当与颈椎病发病相关性的动态平面有限元分析[J].中国中医骨伤科杂志,1999,7(6),9-12.
78. Yongxiang Lu. Significance and progress of bionics[J].Journal of bionics engineering,2004,1(1),1-3.
79.张美超,钟世镇.国内生物力学中有限元的应用研究进展[J].解剖科学进展,2003,9(1),53-56.
80. Ren L.Q., Liang Y.H. Biological Couplings:Classification and Characteristic Rules[J]. Sci China Ser E-Tech Sci,2009,52(10):2791-2800.
81. Barthlott W., Neinhuis C. Purity of the sacred lotus or escape from contamination in biological surfaces[J]. Planta,1997,202 (1),1-8.
82. Barthlott W, Neinhuis C., Boil D. The lotus-effect:Non-adhesive biological and biomimetic technical surfaces[J]. Proceeding of the 1st International Industrial Conference, Bionik2004, Hannover, Germany,2004,211-214.
83. Xuefeng Gao, Lei Jiang. Biophysics:Water-repellent legs of water striders[J]. Nature,2004,432 (7013),36.
84.任露泉,尚广瑞,杨晓东.禽羽结构及羽表脂质对其润湿性能的影响[J].吉林大学学报(工学版),2007,36(2),213-218.
85.高峰,黄河,任露泉.新疆岩蜥三元耦合耐冲蚀磨损特性及其仿生试验[J].吉林大学学报(工学版),2008,38(3),586-590.
86. Yan Zhang, Changhai Zhou, Luquan Ren. Biology Coupling Characteristics on Soil-engaging Components of Mole Crickets [J]. Journal of Bionic Engineering,2008,5(Supl.),164-171.
87.孙少明,任露泉,徐成宇.长耳鸮皮肤和覆羽耦合吸声降噪特性研究.噪声与振动控制,2008,3,119-123.
88.任露泉,梁云虹.生物耦元及其耦联模式[J].吉林大学学报(工学版),2009,39(06),1504-1511.
89.田捷.医学影像处理与分析[M].第1版.北京：电子工业出版社,2003.
90. Herbert Hatze. The complete optimization of a human motion[J]. Mathematical Biosciences,1976, 28(1-2),99-135.
91. Vaugham C. L., Davis B. L.,O'Connor J. C. Dynamics of human gait[M].The 2nd edition. Illinois:Human Kinetics Publishers, Champaign,1992.
92. Lei Ren, Richard K. J., David H. Whole body inverse dynamics over a complete gait cycle based only on measured kinematics[J]. Journal of biomechanics,2008,41(12),2750-2759.
93.赵国如.基于多刚体逆向运动学原理的人体运动测试技术及运动耦合特性研究[D].吉林大学,2009.
94. Wu G., Cavanagh P. R. ISB recommendations for standardization in the reporting data[J]. Journal of Biomechanics,1995,28(10):1257-1261.
95. Appozzo A., Catani F., Croce U. D., Leardini A.. Position and orientation of bones during movement: anatomical frame definition and determination[J]. Clinical Biomechanics,1995,10(4):171-178.
96. Cappozzo A., Della Croce U; Leardini A,. Chiarid L. Human movement analysis using stereophotogrammetry-Part 1:theoretical background[J]. Gait & Posture,2005,21(2),186-196.
97. Jenkyn T.R., Nicol A.C. A multi-segment kinematic model of the foot with a novel definition of forefoot motion for use in clinical gait analysis during walking[J].Journal of biomechanics,2007, 40(14),3271-3278.
98.石亦平,周玉蓉.ABAQUS有限元分析实例详解[M].第1版.北京：机械工业出版社,2006.
99.张洪武,关振群,李云鹏,顾元宪.有限元分析与CAE技术基础[M].第1版.北京：清华大学出版社,2004.
100.王勖成.有限单元法[M].第1版.北京：清华大学出版社,2003.
101.钱志辉.仿生耦合功能表面应力-应变关系研究[D].吉林大学,2007.
102.庄茁等著.ABAQUS非线性有限元实例[M].第1版.北京：科学技术出版社,2005.
103.孙林松,王德信,谢能刚.接触问题有限元分析方法综述[J].水利水电科技进展,2001,21(3),18-20.
104. Hicks J.H. The mechanics of the foot Ⅱ. The plantar aponeurosis and the arch[J]. Journal of Anatomy, 1954,88,25-30.
105. Cheng HY.K., Lin C.L., Wang H.W., Chou S.W. Finite element analysis of plantar fascia under stretch-The relative contribution of windlass mechanism and Achilles tendon force[J]. Journal of Biomechanics,2008,41 (9),1937-1944.
106. Miller-Young, J.E., Duncan, N.A., Baroud, G..Material properties of the human calcaneal fat pad in compression:experiment and theory[J]. Journal of Biomechanics,2002,35(12),1523-1531.
107.钱志辉,任露泉,田丽梅,孙少明.仿生耦合功能表面应力-应变本构关系[J].吉林大学学报(工学版),2008,38(5),1105-1109.
108. Boulton A.J. The diabetic foot:a global review[J]. Diabetes Metab Res Rev,2000,16(suppl),S2-S5.
109.王爱红,许樟荣.足底压力缓解与糖尿病溃疡的防治[J].中华糖尿病杂志,2005,13(6),478-480.
110. Lavery L.A., Armstrong D.G., Wunderlich R.P., et al. Predictive value of foot pressure assessment as part of a population-based diabetes disease management program[J]. Diabetes Care,2003,26(4), 1069-1073.
111. Freberg R.G, Lavery L.A., Pham H., et al. Role of neuropathy and high foot pressue in diabetic foot ulceration[J]. Diabetes Care,1998,21(10),1714-1719.
112. Pataky Z., Golay A., Faravel L., et al. The impact of callosities on the magnitude and duration of plantar pressure in patients with diabetes mellitus. A callus may cause 18,600 kilograms of excess plantar pressure per day[J]. Diabetes Metab,2002,28 (5),356-361.
113.张发惠,郑和平.足外科临床解剖学[M].第1版.合肥：安徽科学技术出版社,2003.
114.吴永强.精通UG NX5+Imageware逆向工程设计[M].第1版.北京：电子工业出版社,2008.
115.金涛,童永光.逆向工程技术[M].第1版.北京：机械工业出版社,2003.
116.杨加,吴祈耀,田捷,杨骅.几种图像分割算法在CT图像分割上的实现和比较[J].北京理工大学学报,2000,20(6),720-723.
117.李久权,王平,王永强.CT图像分割集中算法[J].微计算机信息(测控自动化),2006,22(2-1),240-242.
118. MIMICS user's manual, version10.0,2006.Materialise Company, Haasrode, Leuven, Belgium.
119. Dicom sample image sets, Osirix. http://pubimage.hcuge.ch:8080/.
120.郭松青.基于CT图像建立人体足部骨骼[D].合肥工业大学,2006.
121.铁瑛.中国力学虚拟人颅骨系统研究及其在颌面骨缺损修复中的应用[D].上海交通大学,2006.
122. Hirokawa S., Tsuruno R.Three-dimensional deformation and stress distribution in an analytical/computational model of the anterior cruciate ligament[J]. Journal of biomechanics, 2000,33(9),1069-1077.
123. Song Y., Debski J.K., Musahl V., Thomas M., L.-Y.Woo S. A three-dimensional finite element model of the human anterior cruciate ligament:a computational analysis with experimental validation[J]. Journal of biomechanics,2004,37(3),383-390.
124.王海鹏,容可,钟砚林,王友,谢叻.膝关节周围韧带三维有限元模型的建立[J].上海交通大学学报,2008,28(4),367-370.
125.胡岩君.基于MR、CT影像下膝关节及交叉韧带重建可视化的初步应用研究[D].第一军医大学,2007.
126. Hsu Y.C., Gung Y.W., Shih S.L., Feng C.H., Wei S.H., Yu C.H., Chen C.S. Using an optimization approach to design an insole for lowering plantar fascia stress-a finite element study[J].Journal of biomedical engineering,2008,36(8),1345-1352.
127.陶凯,王冬梅,王成焘,王旭.韧带和跖腱膜在足部有限元分析中的力学作用[J].生物医学工程学杂志,2008,25(2),336-340.
128. David A.Winter. Biomechanics and motor control of human movement[M].The 4th edition. Canada, John wiley and Sons,2009.
129.郑秀媛,贾书慧,高云峰.现代运动生物力学[M].第1版.北京：国防工业出版社,2002.
130. Seireg A., Arvikar R.J. A m athematical model for evaluation of forces in lower extremeties of the musculo-skeletal system Journal of biomechanics,1973,6(3),313-326.
131. Hoek van Dijke G.A.,Snijders C.J.,Stoeckart R.,etal.A biomechanical model on muscle forces in the transfer of spinal load to the pelvis and legs. Journal of biomechanics,1999,32 (9),927-933.
132. Anderson F.C., Pandy M.G A dynamic optimization solution for vertical jumping in three dimensions[J].Computer methods in biomechanics and biomedical engineering,1999,2(3),201-231.
133.王炜,秦现生.仿肌肉驱动器及其在仿生机器人中的应用[J].微特电机,2009,6,56-60.
134. Cho, K.J., Asada, H. Architecture design of a multiaxis cellular actuator array using segmented binary control of shape memory alloy[J].IEEE transactions of robotics,2006,22(4),831-842.
135. Folgheraiter, M., Gini, G. Human-like hierarchical reflex control for an artificial hand[C].Proceedings of the IEEE-RAS International Conference on Humanoid Robots, Waseda University, Tokyo, Giappone, novembre 2001.
136.高峰,李建军,魏鹏绪,刘舒佳.人工肌肉的研究进展及其在康复医学中的应用[J].中国康复理论与实践,2008,14(12),1146-1148.
137.徐力,郭巧,陈海英.人体下肢肌力分布的仿真模型及参数影响研究[J].计算机仿真,2006,23(1).283-287.
138.余慧杰.具有生理学特性的高精度人体肌肉疲劳建模及其在手臂屈曲运动中的应用研究[D].复旦大学,2008.
139. Jensen R.H., Davy D.T. An investigation of muscle lines of action about the hip:A centroid line approach vs the straight line approach[J].Journal of biomechanics,1975,8(2),103-110.
140. ABAQUS user's manual, version6.8-1,2008. Simulia, Providence, U.S.A.
141.张明,张德文,余嘉,樊瑜波.足部三维有限元建模方法及其生物力学应用[J].医用生物力学,2007,22(4),339-344.
142. Rodgers M.M. Dynamic foot biomechanics [J].Journal of Orthopaedic and Sports Physical Therapy, 1995,21(6),306-316.
143. Hughes J., Clark P., Linge K., Klenerman L. A comparison of two sstudies of the pressure distribution under the feet of normal subjects using different equipments[J]. Foot & Ankle,1993, 14(9),514-519.
144. Margareta N., Victor H.F. Basic biomechanics of the musculoskeletal system[M].The 3rd editon.
145.邝适存,郭霞.泽著：肌肉骨骼系统基础生物力学[M].第一版,北京,人民卫生出版社,2008.
146.郑秀媛.现代运动生物力学[M].第一版.北京：国防工业出版社,2002.
147. Ren L.Q., Liang Y.H. Biological Couplings:function, characteristics and implementation mode[J]. Sci China Ser E-Tech Sci,2010,53 (2),379-387.
148. Ker R.F. The time-dependent mechanical properties of the human heel pad in the context of locomotion[J].The journal of experimental biology,1996,199(7),1501-1508.
149. Rene E. Weijers, Alphons G.H. Kessels, Gerrit J. Kemerink. The damping properties of the venous plexus of the heel region of the foot during simulated heelstrike[J].Journal of biomechanics,2005,38(12),2423-2430.
150. Amit Gefen, Michal Megido-Ravid, Yacov Itzchak. In vivo biomechanical behavior of the human heel pad during the stance phase of gait[J].Journal of biomechanics,2001,34(12),1661-1665.
151. Chi K.J., Schmitt D. Mechanical energy and effective foot mass during impact loading of walking and running[J] Journal of biomechanics,2005,38(7),1387-1395.
152. Jahss M.H., Michelson J.D., Desai P., Kaye R., Kummer F., Buschman W., Watkins F., Reich S. Investagations into the fat pads of the sole of the foot:Anatomy and histology[J].Foot & Ankle,1992, 13(5),233-242.
153.杨春燕,蔡文.可拓工程[M]第一版.北京：科学技术出版社,2007.
154. Zhi-hui Qian,Yun Hong, Cheng-yu Xu, Lu-quan Ren. A Biological Coupling Extension Model and Coupling Element Identification. Journal of Bionic Engineering,2009,6(2),186-195.
2. Zhihui Qian, Lei Ren, Luquan Ren, John Huchinson. A Dynamic finite element analysis of the human foot complex During Level Walking[J]. Journal of Biomechanics. (In review)
3. 陈宝兴.祝贺我国足病的研究与治疗[J].中华骨科杂志,1994,11(12),707.
4. http://baike.baidu.com/view/62803.htm
5. 陈秉聪.车辆行走机构形态学及仿生减粘脱土理论[M].第1版.北京：机械工业出版社,2001.
6. Cavanagh P.R., Ulbrecht J.S., Caputo G.M. Biomechanical aspects of diabetic foot disease:aetiology, treatment, and prevention [J]. Diabetic medicine,1996,13(1), s17-22.
7. Weng-Pin Chen, Fuk-Tan Tang, Chia-Wei Ju. stress distribution of the foot during mid-stance to push off in bare foot gait, a 3d finite element analysis[J]. Clinical biomechanics,2001,16(7),614-620.
8. Balmaseda M.T., Koozekanani S.H., Fathhi M.T., Gordon C., Dreyfuss P.H., Tanbonliong EC. Ground reaction forces, center of pressure, and duration of stance with and without an ankle-foot orthosis[J]. Arch Phys Med Rehabil,1988,69(12):1009-1012.
9. Lundeen S., Lundquist K., Cornwall M.W., et al. Plantar pressures during level walking compared with other ambulatory activities[J]. Foot & Ankle Int,1994,15(6):324-328.
10. Alexander I.J., Chao E.Y.S., Johnson K.A. The assessment of dynamic foot to ground contact forces and plantar pressure distribution:a review of the evolution of current techniques and clinical applications[J]. Foot & ankle,1990,11(3),152-167.
11. Brown M., Rudicel S., Esquenazi A. Measurement of dynamic pressures at the shoe-foot interface during normal walkingwith various foot orthosis using the FSCAN system[J]. Foot Ankle Int, 1996,17(3):152-156.
12. Rosenbaum D., Bauer G., Augat P.. Calcaneal fractures cause a lateral load shift in chopart joint contact stress and plantar pressure pattern in vitro[J]. Journal of biomechanics, 1996,29(1):1435-1443.
13. Parenteau C.S., Viano D.C., Petit PY. Biomechanical properties of human cadaveric ankle-subtalar joints in quasi-static loading[J]. Journal of biomechanical engineering,1998,120(1):105-111.
14. Stahelin T., Nigg B.M., Stefanyshyn D.J., van den Bogert A.J., Kim S.J. A method to determine bone movement in the ankle joint complex in vitro[J]. Journal of biomechanics,1997,30(5),513-516.
15. Jacob H.A.C, Zollinger H. Biomechanics of the foot-forces in the fore-foot during walking and their clinical relevance[J]. Orthopade,1992,21(1):75-80.
16.林师诚.正常人体足部之三维动态有限元素分析[D].中原大学.
17.王立平,李建设.足底压力测量技术的发展现状与应用研究[J].浙江体育科学,2004,26(1),40-43.
18.林建宏.足底软组织与鞋内垫力学性质对足压分布影响之有限元分析[D].中原大学.
19. Hutton W.C., Drabble G.E. An apparatus to give the distribution of vertical load under the foot[J].
Rheumatology & physical medicine,1972,11(6),313-31
20.李建设,王立平.足底压力测量技术在生物力学研究中的应用于进展[J].北京体育大学学报,2005,28(2),191-193.
21.张潇,卢世璧.人体足底压力的测量与分析[J].医用生物力学,1994,9(2),108-115.
22. Henry A.P.J., Waugh W. The use of footprints in assessing the results of operations for hallux valgus[J]. Journal of bone joint surgery,1975,57(4),478-481.
23.李慧,张欣,陈翔,李毅.足底压力分布测量系统的设计[J].西安工程科技学院学报,2006,20(1),36-40.
24.韦启航,陆文莲,傅祖芸,卢世璧.人体步态分析系统—足底压力测量系统的研制[J].中国生物医学工程学报,2000,19(1),32-40.
25.戴尅戎,徐乃明,汤荣光,高玉兰.S9-1型步态分析系统的研制和平地行走时足-地接触能力的三维分析[J].生物力学,1986,1(1),24.
26.高琴,姜寿山,魏忠义,张欣.携式人体足底压力分布测量系统的研制[J].中国国际毛纺织会议暨WTO羊毛论坛论文集,2006,77-80,中国,西安.
27.王军,徐新智,张伟,刘金祥.足底压力动态图像分析系统与临床应用[J].中国临床康复,2002,6(6),802-803.
28.袁刚,张木勋,张建华.足底压力分布测量系统及临床应用[J].中国康复,2003,18(1),22-25.
29.金观昌,张军,张建中,孙超.一种新型足底压力分布测量系统及其应用[J].生物医学工程学杂志,2005,22(1),133-136.
30. Cavanagh P.R., Rodgers M.M., Iiboshi A. Pressure distribution under sysmptom-free feet during barefoot standing[J]. Foot & Ankle,1987,7(5),262-276.
31. Groundy M., Blackburn T.P.A., McLeish R.D., Smidt L. An investigation of the centers of pressure under the foot while walking[J]. Journal of bone and joint surgery,1975,57(1),98-103.
32. Hessert M.J., Vyas M., Leach L., Hu K., Lipsitz, L.A., Novak V. Foot pressure distribution during walking in young and old adults[J]. BMC Geriatrics,2005,5:8
33. Meyring S., Diehl R.R., Milani T.L., Hennig E.M., Berlit P Dynamic plantar pressure distribution measurement in hemiparetic patients[J]. Clinical biomechanics,1997,12(1),60-65.
34.王兰美,郭业民,潘志国.人体足底压力分布研究与应用[J].机械制造与研究,2005,34(1),35-38.
35.汤荣光.正常人足底静态和动态压力分布的测定[J].中国生物医学工程学报,1994,13(2),175-177.
36.袁刚,张木勋,王中琴,张建华.正常人足底压力分布及其影响因素分析[J].中华物理医学与康复杂志,2004,26(3),156-159.
37.王明鑫,俞光荣,陈雁西,杨云峰,黄四平,胡孙君.正常中国成年人足底压力分析[J].中国矫形外科杂志,2008,1 6(9),687-690.
38. Siegler S., Chen J., Schneck C.D. The three-dimensional kinematics and flexibility characteristics of the human ankle and subtalar joints-part Ⅰ:kinematics[J]. Journal of biomechanical engineering, 1988,110(4):364-73.
39. Ker R.F., Bennett, M.B., Bibby, S.R., Kester, R.C., Alexander, R.M. The spring in the arch of the human foot[J]. Nature,1987.325,147-149.
40. Sammarco G.J., Burstein A.H., Frankel V.H. Biomechanics of the ankle:a kinematic study[J]. Orthop Clin North Am,1973,4(1),75-96.
41. Arndt A., Wolf P., Liu A., Nester C., Stacoff A., Jones R., Lundgren P., Lundberg A. Intrinsic foot kinematics measured in vivo during the stance phase of slow running. Journal of biomechanics,2007, 40(12),2672-2678.
42. Nester C., Jones R.K., Liu A., Howard D., Lunderg A., Arndt A., Lundgren P., Stacoff A., Wolf P. Foot kinematics during walking measured using bone and surface mounted markers[J]. Journal of biomechanics,2007,40(15),3412-3423.
43.董骧,樊瑜波,张明.人体足部生物力学的研究[J].生物医学工程,2002,19(1),148-153.
44. De Cock A., Vanrenterghem., Willems T., Witvrouw E., De Clercq D. The trajectory of the center of pressure during barefoot running as a potential measure for foot function[J]. Gait & Posture,2008, 27(4),669-675.
45. Carrier, D.R., Heglund, N.C., Earls, K.D. Variable gearing during locomotion in the human musculoskeletal system[J]. Science,1994,265(5172),651-653.
46. Scott, S.H., Winter, D.A. Biomechanical model of the human foot:Kinematics and kinetics during the stance phase of walking[J]. Journal of Biomechanics,1993,26 (9),1091-1104.
47. Gilchrist L. A., Winter D. A. A two-part, viscoelastic foot model for use in gait simulations[J]. journal of biomechanics,1996,29(6),795-798.
48. Nester, C.J., Liu, A.M., Ward, E., Howard, D., Cocheba, J., Derrick, T., Paterson, P. In vitro study of foot kinematics using a dynamic walking cadaver model[J]. Journal of Biomechanics 2007,40(9), 1927-1937.
49. Ren Lei, Howard David, Ren Luquan, Nester Chris, Tian Limei. A generic analytical foot rollover model for predicting translational ankle kinematics in gait simulation studies[J]. journal of biomechanics,2009. (In Press)
50. Yettram A.L., Camilleri N.N. The force acting on the human calcaneus[J]. Journal of biomedical engineering,1993,15(1),46-50.
51. Cavanagh P.R., Shiang T.Y. Approaches to finite element analysis of the foot-shoe interface in diabetic patients[J]. Journal of biomechanics.1993,26(3),323-323.
52. Chu T.M., Reddy N.P., Padovan J. Three dimensional finite element stress analysis of the polypropylene, ankle-foot orthosis:static analysis[J]. Medical engineering & physics,1995,17(5), 372-379.
53. Patil K.M., Braak L.H., Huson A. Analysis of stresses in two-dimensional models of normal and neuropathic feet[J]. Medical & biologicall engineering & computing,1996,34(4),280-284.
54. Jacob, S., Patil, K.M., Braak, L.H., Huson, A. Stresses in a 3-D two arch model of a normal human foot[J]. Mechanics Research Communications,1996,23(4),387-393.
55. Jacob, S., Patil, K.M. Three-dimensional foot modeling and analysis of stresses in normal and early stage Hansen's disease with muscle paralysis[J]. Journal of Rehabilitation Research & Development, 1999,36(3),252-263.
56. Lemmon D., Shiang T.Y., Hashmi A. Ulbrecht J.S., Cavanagh P.R. The effect of insoles in therapeutic footwear:a finite element approach[J]. Journal of biomechanics,1997,30(6),615-620.
57. Gefen A.,, Megido-Ravid M., Itzchak Y., Arcan M. Biomechanical analysis of the three-dimensional foot structure during gait:a basic tool for clinical applications[J]. Journal of biomechanics,2000,122 (6),630-639.
58. Gefen A. Stress analysis of the standing foot following surgical plantar fascia release[J]. Journal of Biomechanics,2002,35 (5),629-637.
59. Gefen A. Plantar soft tissue loading under the medial metatarsals in the standing diabetic foot[J]. Medical engineering & physics,2003,25 (6),491-499.
60. Bandak F.A., Tannous R.E., Toridis T. On the development of an osseo-ligamentous finite element model of the human ankle joint[J]. International journal of solids and structures,2001,38 (10-13),1681-1697.
61. 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[J]. Clinical biomechanics,2001,16(7),614-620.
62. Cheung J.T., Zhang M., An K.N. Effects of plantar fascia stiffness on the biomechanical responses of the ankle-foot complex[J]. Clinical biomechanics,2004,19 (8),839-846.
63. Cheung J.T., Zhang M., Leung A.K., Fan Y.B. Three-dimensional finite element analysis of the foot during standing--a material sensitivity study[J]. Journal of biomechanics,2005,38 (5),1045-1054.
64. Cheung J.T., Zhang M. Parametric design of pressure-relieving foot orthosis using statistics-based finite element method[J]. Medical engineering & physics,2008,30 (3),269-277.
65. Garcia-Aznar J.M., Bayod J., Rosas A., Larrainzar R., Garcia-Bogalo R., Doblare M., Llanos L.F. Load transfer mechanism for different metatarsal geometries:a finite element study[J]. Journal of biomechanical engineering,2009,131 (2),1-7.
66. Cheng HY.K., Lin C.L., Wang H.W., Chou S.W. Finite element analysis of plantar fascia under stretch-The relative contribution of windlass mechanism and Achilles tendon force[J]. Journal of biomechanics,2008,41 (9),1937-1944.
67. Wu L.J. Nonlinear finite element analysis for musculoskeletal biomechanics of medial and lateral plantar longitudinal arch of Virtual Chinese Human after plantar ligamentous structure failures[J]. Clinical biomechanics,2007,22 (2),221-229.
68. Dai X.Q., Li Y., Zhang M., Cheung J.T. Effect of sock on biomechanical responses of foot during walking[J]. Clinical biomechanics,2006,21 (3),314-321.
69. Halloran J.P., Erdemir A.,van den Bogert A.J. Adaptive surrogate modeling for efficient coupling of musculoskeletal control and tissue deformation models[J].Journal of biomechanical engineering-transactions of the ASME,2009,131 (1),011014.
70. Alberto Garcia-Gonzalez, Javier Bayod, Juan Carlos Prados-Frutos, Marta Losa-Iglesias, Kevin T. Jules, Ricardo Becerro de Bengoa-Vallejo and Manuel Doblare. Finite-element simulation of flexor digitorum longus or flexor digitorum brevis tendon transfer for the treatment of claw toe deformity [J]. Journal of biomechanics,2009,42 (11),1697-1704.
71.屈钧利,韩江水.工程结构的有限元方法[M].第1版.西安：西北工业大学出版社,2004.
72.曾攀(译著).工程中的有限元方法[M].第3版.北京：清华大学出版社,2006.
73.刘怀横.结构及弹性力学有限元方法[M].第1版.西安：西北工业大学出版社,2007.
74.田杰,林珠,杭洽时,等.x线头颅侧位定位片硬组织形态二维有限元分析模型的建立[J].实用口腔
医学杂志,1999,15(2),129-31.
75.田杰,林珠,杭洽时,等.X线头颅侧位定位片硬组织形态三维有限元分析模型的建立[J].实 用口腔医学杂志,1999,15(2),135-6.
76.周学军,赵志河,赵美英,等.包括下颌骨的颞下颌关节三维有限元模型的建立[J].实用口腔医学杂志,2000,16(1),17-19.
77.苏友新,许书亮,陈日齐,等.用枕不当与颈椎病发病相关性的动态平面有限元分析[J].中国中医骨伤科杂志,1999,7(6),9-12.
78. Yongxiang Lu. Significance and progress of bionics[J].Journal of bionics engineering,2004,1(1),1-3.
79.张美超,钟世镇.国内生物力学中有限元的应用研究进展[J].解剖科学进展,2003,9(1),53-56.
80. Ren L.Q., Liang Y.H. Biological Couplings:Classification and Characteristic Rules[J]. Sci China Ser E-Tech Sci,2009,52(10):2791-2800.
81. Barthlott W., Neinhuis C. Purity of the sacred lotus or escape from contamination in biological surfaces[J]. Planta,1997,202 (1),1-8.
82. Barthlott W, Neinhuis C., Boil D. The lotus-effect:Non-adhesive biological and biomimetic technical surfaces[J]. Proceeding of the 1st International Industrial Conference, Bionik2004, Hannover, Germany,2004,211-214.
83. Xuefeng Gao, Lei Jiang. Biophysics:Water-repellent legs of water striders[J]. Nature,2004,432 (7013),36.
84.任露泉,尚广瑞,杨晓东.禽羽结构及羽表脂质对其润湿性能的影响[J].吉林大学学报(工学版),2007,36(2),213-218.
85.高峰,黄河,任露泉.新疆岩蜥三元耦合耐冲蚀磨损特性及其仿生试验[J].吉林大学学报(工学版),2008,38(3),586-590.
86. Yan Zhang, Changhai Zhou, Luquan Ren. Biology Coupling Characteristics on Soil-engaging Components of Mole Crickets [J]. Journal of Bionic Engineering,2008,5(Supl.),164-171.
87.孙少明,任露泉,徐成宇.长耳鸮皮肤和覆羽耦合吸声降噪特性研究.噪声与振动控制,2008,3,119-123.
88.任露泉,梁云虹.生物耦元及其耦联模式[J].吉林大学学报(工学版),2009,39(06),1504-1511.
89.田捷.医学影像处理与分析[M].第1版.北京：电子工业出版社,2003.
90. Herbert Hatze. The complete optimization of a human motion[J]. Mathematical Biosciences,1976, 28(1-2),99-135.
91. Vaugham C. L., Davis B. L.,O'Connor J. C. Dynamics of human gait[M].The 2nd edition. Illinois:Human Kinetics Publishers, Champaign,1992.
92. Lei Ren, Richard K. J., David H. Whole body inverse dynamics over a complete gait cycle based only on measured kinematics[J]. Journal of biomechanics,2008,41(12),2750-2759.
93.赵国如.基于多刚体逆向运动学原理的人体运动测试技术及运动耦合特性研究[D].吉林大学,2009.
94. Wu G., Cavanagh P. R. ISB recommendations for standardization in the reporting data[J]. Journal of Biomechanics,1995,28(10):1257-1261.
95. Appozzo A., Catani F., Croce U. D., Leardini A.. Position and orientation of bones during movement: anatomical frame definition and determination[J]. Clinical Biomechanics,1995,10(4):171-178.
96. Cappozzo A., Della Croce U; Leardini A,. Chiarid L. Human movement analysis using stereophotogrammetry-Part 1:theoretical background[J]. Gait & Posture,2005,21(2),186-196.
97. Jenkyn T.R., Nicol A.C. A multi-segment kinematic model of the foot with a novel definition of forefoot motion for use in clinical gait analysis during walking[J].Journal of biomechanics,2007, 40(14),3271-3278.
98.石亦平,周玉蓉.ABAQUS有限元分析实例详解[M].第1版.北京：机械工业出版社,2006.
99.张洪武,关振群,李云鹏,顾元宪.有限元分析与CAE技术基础[M].第1版.北京：清华大学出版社,2004.
100.王勖成.有限单元法[M].第1版.北京：清华大学出版社,2003.
101.钱志辉.仿生耦合功能表面应力-应变关系研究[D].吉林大学,2007.
102.庄茁等著.ABAQUS非线性有限元实例[M].第1版.北京：科学技术出版社,2005.
103.孙林松,王德信,谢能刚.接触问题有限元分析方法综述[J].水利水电科技进展,2001,21(3),18-20.
104. Hicks J.H. The mechanics of the foot Ⅱ. The plantar aponeurosis and the arch[J]. Journal of Anatomy, 1954,88,25-30.
105. Cheng HY.K., Lin C.L., Wang H.W., Chou S.W. Finite element analysis of plantar fascia under stretch-The relative contribution of windlass mechanism and Achilles tendon force[J]. Journal of Biomechanics,2008,41 (9),1937-1944.
106. Miller-Young, J.E., Duncan, N.A., Baroud, G..Material properties of the human calcaneal fat pad in compression:experiment and theory[J]. Journal of Biomechanics,2002,35(12),1523-1531.
107.钱志辉,任露泉,田丽梅,孙少明.仿生耦合功能表面应力-应变本构关系[J].吉林大学学报(工学版),2008,38(5),1105-1109.
108. Boulton A.J. The diabetic foot:a global review[J]. Diabetes Metab Res Rev,2000,16(suppl),S2-S5.
109.王爱红,许樟荣.足底压力缓解与糖尿病溃疡的防治[J].中华糖尿病杂志,2005,13(6),478-480.
110. Lavery L.A., Armstrong D.G., Wunderlich R.P., et al. Predictive value of foot pressure assessment as part of a population-based diabetes disease management program[J]. Diabetes Care,2003,26(4), 1069-1073.
111. Freberg R.G, Lavery L.A., Pham H., et al. Role of neuropathy and high foot pressue in diabetic foot ulceration[J]. Diabetes Care,1998,21(10),1714-1719.
112. Pataky Z., Golay A., Faravel L., et al. The impact of callosities on the magnitude and duration of plantar pressure in patients with diabetes mellitus. A callus may cause 18,600 kilograms of excess plantar pressure per day[J]. Diabetes Metab,2002,28 (5),356-361.
113.张发惠,郑和平.足外科临床解剖学[M].第1版.合肥：安徽科学技术出版社,2003.
114.吴永强.精通UG NX5+Imageware逆向工程设计[M].第1版.北京：电子工业出版社,2008.
115.金涛,童永光.逆向工程技术[M].第1版.北京：机械工业出版社,2003.
116.杨加,吴祈耀,田捷,杨骅.几种图像分割算法在CT图像分割上的实现和比较[J].北京理工大学学报,2000,20(6),720-723.
117.李久权,王平,王永强.CT图像分割集中算法[J].微计算机信息(测控自动化),2006,22(2-1),240-242.
118. MIMICS user's manual, version10.0,2006.Materialise Company, Haasrode, Leuven, Belgium.
119. Dicom sample image sets, Osirix. http://pubimage.hcuge.ch:8080/.
120.郭松青.基于CT图像建立人体足部骨骼[D].合肥工业大学,2006.
121.铁瑛.中国力学虚拟人颅骨系统研究及其在颌面骨缺损修复中的应用[D].上海交通大学,2006.
122. Hirokawa S., Tsuruno R.Three-dimensional deformation and stress distribution in an analytical/computational model of the anterior cruciate ligament[J]. Journal of biomechanics, 2000,33(9),1069-1077.
123. Song Y., Debski J.K., Musahl V., Thomas M., L.-Y.Woo S. A three-dimensional finite element model of the human anterior cruciate ligament:a computational analysis with experimental validation[J]. Journal of biomechanics,2004,37(3),383-390.
124.王海鹏,容可,钟砚林,王友,谢叻.膝关节周围韧带三维有限元模型的建立[J].上海交通大学学报,2008,28(4),367-370.
125.胡岩君.基于MR、CT影像下膝关节及交叉韧带重建可视化的初步应用研究[D].第一军医大学,2007.
126. Hsu Y.C., Gung Y.W., Shih S.L., Feng C.H., Wei S.H., Yu C.H., Chen C.S. Using an optimization approach to design an insole for lowering plantar fascia stress-a finite element study[J].Journal of biomedical engineering,2008,36(8),1345-1352.
127.陶凯,王冬梅,王成焘,王旭.韧带和跖腱膜在足部有限元分析中的力学作用[J].生物医学工程学杂志,2008,25(2),336-340.
128. David A.Winter. Biomechanics and motor control of human movement[M].The 4th edition. Canada, John wiley and Sons,2009.
129.郑秀媛,贾书慧,高云峰.现代运动生物力学[M].第1版.北京：国防工业出版社,2002.
130. Seireg A., Arvikar R.J. A m athematical model for evaluation of forces in lower extremeties of the musculo-skeletal system Journal of biomechanics,1973,6(3),313-326.
131. Hoek van Dijke G.A.,Snijders C.J.,Stoeckart R.,etal.A biomechanical model on muscle forces in the transfer of spinal load to the pelvis and legs. Journal of biomechanics,1999,32 (9),927-933.
132. Anderson F.C., Pandy M.G A dynamic optimization solution for vertical jumping in three dimensions[J].Computer methods in biomechanics and biomedical engineering,1999,2(3),201-231.
133.王炜,秦现生.仿肌肉驱动器及其在仿生机器人中的应用[J].微特电机,2009,6,56-60.
134. Cho, K.J., Asada, H. Architecture design of a multiaxis cellular actuator array using segmented binary control of shape memory alloy[J].IEEE transactions of robotics,2006,22(4),831-842.
135. Folgheraiter, M., Gini, G. Human-like hierarchical reflex control for an artificial hand[C].Proceedings of the IEEE-RAS International Conference on Humanoid Robots, Waseda University, Tokyo, Giappone, novembre 2001.
136.高峰,李建军,魏鹏绪,刘舒佳.人工肌肉的研究进展及其在康复医学中的应用[J].中国康复理论与实践,2008,14(12),1146-1148.
137.徐力,郭巧,陈海英.人体下肢肌力分布的仿真模型及参数影响研究[J].计算机仿真,2006,23(1).283-287.
138.余慧杰.具有生理学特性的高精度人体肌肉疲劳建模及其在手臂屈曲运动中的应用研究[D].复旦大学,2008.
139. Jensen R.H., Davy D.T. An investigation of muscle lines of action about the hip:A centroid line approach vs the straight line approach[J].Journal of biomechanics,1975,8(2),103-110.
140. ABAQUS user's manual, version6.8-1,2008. Simulia, Providence, U.S.A.
141.张明,张德文,余嘉,樊瑜波.足部三维有限元建模方法及其生物力学应用[J].医用生物力学,2007,22(4),339-344.
142. Rodgers M.M. Dynamic foot biomechanics [J].Journal of Orthopaedic and Sports Physical Therapy, 1995,21(6),306-316.
143. Hughes J., Clark P., Linge K., Klenerman L. A comparison of two sstudies of the pressure distribution under the feet of normal subjects using different equipments[J]. Foot & Ankle,1993, 14(9),514-519.
144. Margareta N., Victor H.F. Basic biomechanics of the musculoskeletal system[M].The 3rd editon.
145.邝适存,郭霞.泽著：肌肉骨骼系统基础生物力学[M].第一版,北京,人民卫生出版社,2008.
146.郑秀媛.现代运动生物力学[M].第一版.北京：国防工业出版社,2002.
147. Ren L.Q., Liang Y.H. Biological Couplings:function, characteristics and implementation mode[J]. Sci China Ser E-Tech Sci,2010,53 (2),379-387.
148. Ker R.F. The time-dependent mechanical properties of the human heel pad in the context of locomotion[J].The journal of experimental biology,1996,199(7),1501-1508.
149. Rene E. Weijers, Alphons G.H. Kessels, Gerrit J. Kemerink. The damping properties of the venous plexus of the heel region of the foot during simulated heelstrike[J].Journal of biomechanics,2005,38(12),2423-2430.
150. Amit Gefen, Michal Megido-Ravid, Yacov Itzchak. In vivo biomechanical behavior of the human heel pad during the stance phase of gait[J].Journal of biomechanics,2001,34(12),1661-1665.
151. Chi K.J., Schmitt D. Mechanical energy and effective foot mass during impact loading of walking and running[J] Journal of biomechanics,2005,38(7),1387-1395.
152. Jahss M.H., Michelson J.D., Desai P., Kaye R., Kummer F., Buschman W., Watkins F., Reich S. Investagations into the fat pads of the sole of the foot:Anatomy and histology[J].Foot & Ankle,1992, 13(5),233-242.
153.杨春燕,蔡文.可拓工程[M]第一版.北京：科学技术出版社,2007.
154. Zhi-hui Qian,Yun Hong, Cheng-yu Xu, Lu-quan Ren. A Biological Coupling Extension Model and Coupling Element Identification. Journal of Bionic Engineering,2009,6(2),186-195.