FE Model and Operational Modal Analysis of Lower Limbs

Human lower limbs are exposed to vibrations on a daily basis, during work, transport or sports. However, most of the FE (Finite Elements) and OMA (Operational Modal Analysis) studies focus either on the whole body or on the hand-arm system. The study presented herein aims at identifying the modal pa...

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Autores:
Munera Ramirez, Marcela Cristina
Pionteck, Aymeric
Chiementin, Xavier
Murer, Sébastien
Chadefaux, Delphine
Rao, Guillaume
Tipo de recurso:
Article of investigation
Fecha de publicación:
2017
Institución:
Escuela Colombiana de Ingeniería Julio Garavito
Repositorio:
Repositorio Institucional ECI
Idioma:
eng
OAI Identifier:
oai:repositorio.escuelaing.edu.co:001/1570
Acceso en línea:
https://repositorio.escuelaing.edu.co/handle/001/1570
https://doi.org/10.3390/app7080853
Palabra clave:
Método de elementos finitos - Análisis numérico
Vibración
OMA
OMA
Miembros inferiores
Análisis de elementos finitos
Lower limbs;
Finite element analysis
Rights
openAccess
License
https://creativecommons.org/licenses/by/4.0/
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network_acronym_str ESCUELAIG2
network_name_str Repositorio Institucional ECI
repository_id_str
dc.title.eng.fl_str_mv FE Model and Operational Modal Analysis of Lower Limbs
title FE Model and Operational Modal Analysis of Lower Limbs
spellingShingle FE Model and Operational Modal Analysis of Lower Limbs
Método de elementos finitos - Análisis numérico
Vibración
OMA
OMA
Miembros inferiores
Análisis de elementos finitos
Lower limbs;
Finite element analysis
title_short FE Model and Operational Modal Analysis of Lower Limbs
title_full FE Model and Operational Modal Analysis of Lower Limbs
title_fullStr FE Model and Operational Modal Analysis of Lower Limbs
title_full_unstemmed FE Model and Operational Modal Analysis of Lower Limbs
title_sort FE Model and Operational Modal Analysis of Lower Limbs
dc.creator.fl_str_mv Munera Ramirez, Marcela Cristina
Pionteck, Aymeric
Chiementin, Xavier
Murer, Sébastien
Chadefaux, Delphine
Rao, Guillaume
dc.contributor.author.none.fl_str_mv Munera Ramirez, Marcela Cristina
Pionteck, Aymeric
Chiementin, Xavier
Murer, Sébastien
Chadefaux, Delphine
Rao, Guillaume
dc.contributor.researchgroup.spa.fl_str_mv GiBiome
dc.subject.armarc.none.fl_str_mv Método de elementos finitos - Análisis numérico
Vibración
topic Método de elementos finitos - Análisis numérico
Vibración
OMA
OMA
Miembros inferiores
Análisis de elementos finitos
Lower limbs;
Finite element analysis
dc.subject.proposal.spa.fl_str_mv OMA
OMA
Miembros inferiores
Análisis de elementos finitos
dc.subject.proposal.eng.fl_str_mv Lower limbs;
Finite element analysis
description Human lower limbs are exposed to vibrations on a daily basis, during work, transport or sports. However, most of the FE (Finite Elements) and OMA (Operational Modal Analysis) studies focus either on the whole body or on the hand-arm system. The study presented herein aims at identifying the modal parameters of the lower limbs using a 2D FE model updated using OMA. A numerical model is proposed, and a modal analysis has been performed on 11 subjects. Two repeatable modal frequencies were extracted: 52.54 ± 2.05 Hz and 118.94 ± 2.70 Hz, which were used to update the mechanical properties of the numerical model. The knowledge of these modal characteristics makes it possible to design new equipment that would absorb these specific vibrations and possibly reduce the risk of related diseases in the field of sports and transport.
publishDate 2017
dc.date.issued.none.fl_str_mv 2017
dc.date.accessioned.none.fl_str_mv 2021-06-14T00:27:29Z
2021-10-01T17:16:54Z
dc.date.available.none.fl_str_mv 2021-06-14T00:27:29Z
2021-10-01T17:16:54Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.type.content.spa.fl_str_mv Text
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dc.identifier.issn.none.fl_str_mv 2076-3417
dc.identifier.uri.none.fl_str_mv https://repositorio.escuelaing.edu.co/handle/001/1570
dc.identifier.doi.none.fl_str_mv 10.3390/app7080853
dc.identifier.url.none.fl_str_mv https://doi.org/10.3390/app7080853
identifier_str_mv 2076-3417
10.3390/app7080853
url https://repositorio.escuelaing.edu.co/handle/001/1570
https://doi.org/10.3390/app7080853
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.citationendpage.spa.fl_str_mv 865
dc.relation.citationstartpage.spa.fl_str_mv 853
dc.relation.citationvolume.spa.fl_str_mv 7
dc.relation.indexed.spa.fl_str_mv N/A
dc.relation.ispartofjournal.eng.fl_str_mv Applied Sciences
dc.relation.references.eng.fl_str_mv Gómez-Cabello, A.; González-Agüero, A.; Morales, S.; Ara, I.; Casajús, J.A.; Vicente-Rodríguez, G. Effects of a short-term whole body vibration intervention on bone mass and structure in elderly people. J. Sci. Med. Sport 2014, 17, 160–164.
Madou, K.H.; Cronin, J.B. The Effects of Whole Body Vibration on Physical and Physiological Capability in Special Populations. Hong Kong Physiother. J. 2008, 26, 24–38.
Matute-Llorente, Á.; González-Agüero, A.; Gómez-Cabello, A.; Vicente-Rodríguez, G.; Casajús Mallén, J.A. Effect of Whole-Body Vibration Therapy on Health-Related Physical Fitness in Children and Adolescents With Disabilities: A Systematic Review. J. Adolesc. Health 2014, 54, 385–396.
Carlsöö, S. The effect of vibration on the skeleton, joints and muscles. A review of the literature. Appl. Ergon. 1982, 13, 251–258.
Wang, Y.J.; Huang, X.L.; Yan, J.W.; Wan, Y.N.; Wang, B.X.; Tao, J.H.; Chen, B.; Li, B.Z.; Yang, G.J.; Wang, J. The association between vibration and vascular injury in rheumatic diseases: A review of the literature. Autoimmunity 2015, 48, 61–68.
Jordan, M.J.; Norris, S.R.; Smith, D.J.; Herzog, W. Vibration Training: An Overview of the Area, Training Consequences, and Future Considerations. J. Strength Cond. Res. 2005, 19, 459.
Gurram, R. A Study of Vibration Response Characteristics of the Human Hand-Arm System. Ph.D. Thesis, Concordia University, Montreal, QC, Canada, 1993.
Munera, M.; Chiementin, X.; Crequy, S.; Bertucci, W. Physical risk associated with vibration at cycling. Mech. Ind. 2014, 15, 535–540.
Fridén, J. Vibration damage to the hand: Clinical presentation, prognosis and length and severity of vibration required. J. Hand Surg. 2001, 26, 471–474.
Ayari, H.; Thomas, M.; Doré, S.; Serrus, O. Evaluation of lumbar vertebra injury risk to the seated human body when exposed to vertical vibration. J. Sound Vib. 2009, 321, 454–470.
Grassi, L.; Väänänen, S.; Ristinmaa, M.; Jurvelin, J.S.; Isaksson, H. How accurately can subject-specific finite element models predict strains and strength of human femora? Investigation using full-field measurements. J. Biomech. 2016, 49, 802–806.
Adewusi, S.; Thomas, M.; Vu, V.; Li, W. Modal parameters of the human hand-arm using finite element and operational modal analysis. Mech. Ind. 2014, 15, 541–549.
Hostens, I.; Ramon, H. Descriptive analysis of combine cabin vibrations and their effect on the human body. J. Sound Vib. 2003, 266, 453–464.
Kitazaki, S.; Griffin, M.J. Resonance behaviour of the seated human body and effects of posture. J. Biomech. 1998, 31, 143–149.
Hobatho, M.C.; Darmana, R.; Pastor, P.; Barrau, J.J.; Laroze, S.; Morucci, J.P. Development of a three-dimensional finite element model of a human tibia using experimental modal analysis. J. Biomech. 1991, 24, 371–383.
Munera, M.; Chiementin, X.; Murer, S.; Bertucci, W. Model of the risk assessment of hand-arm system vibrations in cycling: Case of cobblestone road. Proc. Inst. Mech. Eng. Part P 2015, 229, 231–238.
Thuong, O.; Griffin, M.J. The vibration discomfort of standing persons: 0.5–16 Hz fore-and-aft, lateral, and vertical vibration. J. Sound Vib. 2011, 330, 816–826.
Wakeling, J.M.; Liphardt, A.M.; Nigg, B.M. Muscle activity reduces soft-tissue resonance at heel-strike during walking. J. Biomech. 2003, 36, 1761–1769
Lafortune, M.A.; Lake, M.J.; Hennig, E.M. Differential shock transmission response of the human body to impact severity and lower limb posture. J. Biomech. 1996, 29, 1531–1537.
Peeters, B.; Van Der Auweraer, H. Polymax: A revolution in operational modal analysis. In Proceedings of the 1st International Operational Modal Analysis Conference, Copenhagen, Denmark, 26–27 April 2005.
Van der Auweraer, H.; Guillaume, P.; Verboven, P.; Vanlanduit, S. Application of a Fast-Stabilizing Frequency Domain Parameter Estimation Method. J. Dyn. Syst. Meas. Control 2001, 123, 651.
Heylen, W.; Lammens, S.; Sas, P. Modal Analysis Theory and Testing; Katholieke Universiteit Leuven, Faculty of Engineering, Department of Mechanical Engineering, Division of Production Engineering, Machine Design and Automation: Leuven, Belgium, 1998
Afnor. ISO 2631-1:1997—Mechanical Vibration and Shock—Evaluation of Human Exposure to Whole-Body Vibration—Part 1: General Requirements; ISO: Geneva, Switzerland, 1997.
Beillas, P.; Papaioannou, G.; Tashman, S.; Yang, K. A new method to investigate in vivo knee behavior using a finite element model of the lower limb. J. Biomech. 2004, 37, 1019–1030.
De Mendonça, M.C. Estimation of height from the length of long bones in a Portuguese adult population. Am. J. Phys. Anthropol. 2000, 112, 39–48.
Atilla, B.; Oznur, A.; Ca ˘glar, O.; Tokgözo ˘glu, M.; Alpaslan, M. Osteometry of the femora in Turkish individuals: A morphometric study in 114 cadaveric femora as an anatomic basis of femoral component design. Acta Orthop. Traumatol. Turc. 2007, 41, 64–68.
Beauthier, J.; Mangin, P.; Hédouin, V. Traité de Médecine Légale; De Boeck: Bruxelles, Belgique, 2011
Schmidt, W.; Reyes, M.; Fischer, F.; Geesink, R.; Nolte, L.; Racanelli, J.; Reimers, N. Quantifying human knee anthropometric differences between ethnic groups and gender using shape analysis techniques. In Proceedings of the Annual Meeting American Society of Biomechanics, State College, PA, USA, 26–29 August 2009.
NASA. Volume I: Man-Systems Integration Standards (MSIS); Chapter Anthropometry and Biomechanics; NASA: Washington, DC, USA, 1995.
Giladi, M.; Milgrom, C.; Simkin, A.; Stein, M.; Kashtan, H.; Margulies, J.; Rand, N.; Chisin, R.; Steinberg, R.; Aharonson, Z. Stress fractures and tibial bone width. A risk factor. J. Bone Jt. Surg. Br. Vol. 1987, 69, 326–329
Radzi, S.; Uesugi, M.; Baird, A.; Mishra, S.; Schuetz, M.; Schmutz, B. Assessing the bilateral geometrical differences of the tibia—Are they the same? Med. Eng. Phys. 2014, 36, 1618–1625.
Ozden, H.; Balci, Y.; Demirüstü, C.; Turgut, A.; Ertugrul, M. Stature and sex estimate using foot and shoe dimensions. Forensic Sci. Int. 2005, 147, 181–184.
Kanaani, J.; Mortazavi, S.B.; Khavanin, A.; Mirzai, R.; Rasulzadeh, Y.; Mansurizadeh, M. Foot Anthropometry of 18–25 Years Old Iranian Male Students. Asian J. Sci. Res. 2010, 3, 62–69.
Pionteck, A.; Munera, M.; Chiementin, X. Modélisation 2D des Membres Inférieurs et Comportement Modale Face aux Paramètres Biomécaniques; 22ème Congrès Français de Mécanique, Lyon, France (FR); AFM, Association Française de Mécanique: Courbevoie, France, 2015
Cornelissen, P.; Cornelissen, M.; Van der Perre, G.; Christensen, A.B.; Ammitzbøll, F.; Dyrbye, C. Assessment of tibial stiffness by vibration testing in situ–II. Influence of soft tissues, joints and fibula. J. Biomech. 1986, 19, 551–561.
Dumas, R.; Camomilla, V.; Bonci, T.; Cheze, L.; Cappozzo, A. Generalized mathematical representation of the soft tissue artefact. J. Biomech. 2014, 47, 476–481.
Munera, M.; Bertucci, W.; Duc, S.; Chiementin, X. Transmission of whole body vibration to the lower body in static and dynamic half-squat exercises. Sports Biomech. 2016, 15, 409–428.
Kiiski, J.; Heinonen, A.; Järvinen, T.L.; Kannus, P.; Sievänen, H. Transmission of Vertical Whole Body Vibration to the Human Body. J. Bone Miner. Res. 2008, 23, 1318–1325.
Van der Perre, G.; Cornelissen, P. On the mechanical resonances of a human tibia in vitro. J. Biomech. 1983, 16, 549–552.
Taylor, W.R.; Roland, E.; Ploeg, H.; Hertig, D.; Klabunde, R.; Warner, M.D.; Hobatho, M.C.; Rakotomanana, L.; Clift, S.E. Determination of orthotropic bone elastic constants using FEA and modal analysis. J. Biomech. 2002, 35, 767–773.
Kumar, A.; Jaiswal, H.; Garg, T.; Patil, P.P. Free Vibration Modes Analysis of Femur Bone Fracture Using Varying Boundary Conditions based on FEA. Procedia Mater. Sci. 2014, 6, 1593–1599.
Gupta, A.; Ming Tse, K. Finite Element Analysis on Vibration Modes of Femur Bone. In Proceedings of the International Conference on Advances in Mechanical Engineering, NCR-Delhi Region, India, December 2013.
Tsuchikane, A.; Nakatsuchi, Y.; Nomura, A. The influence of joints and soft tissue on the natural frequency of the human tibia using the impulse response method. Proc. Inst. Mech. Eng. Part H 1995, 209, 149–155.
Tseng, J.G.; Huang, B.W.; Liang, S.H.; Yen, K.T.; Tsai, Y.C.; Tseng, J.G. Normal Mode Analysis of a Human Fibula. Life Sci. J. 2014, 11, 711-718.
Kassab, G.; Sacks, M. Structure-Based Mechanics of Tissues and Organs; Springer: New York, NY, USA, 2016.
Gruber, A.H.; Boyer, K.A.; Derrick, T.R.; Hamill, J. Impact shock frequency components and attenuation in rearfoot and forefoot running. J. Sport Health Sci. 2014, 3, 113–121
Taiar, R.; Chiementin, X. Ergonomics and biomechanics on the impact of mats on decreasing whole body vibration. In Proceedings of the 8th International Conference on Applied Human Factors and Ergonomics, Los Angeles, CA, USA, 7–17 July 2017.
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spelling Munera Ramirez, Marcela Cristinac7b2f5daa754327476b7992dea703f6a600Pionteck, Aymeric9a70af606111071f405f46a59ccc16d9600Chiementin, Xavier5381418aa944cc4518e7bd78724f965c600Murer, Sébastienda991093bb14c78028ea897f96665e0b600Chadefaux, Delphine28bc66cc62460a6519338ab5de1e55a4600Rao, Guillaumead7079f8c0ad5d05b0d7f787ecbe2484600GiBiome2021-06-14T00:27:29Z2021-10-01T17:16:54Z2021-06-14T00:27:29Z2021-10-01T17:16:54Z20172076-3417https://repositorio.escuelaing.edu.co/handle/001/157010.3390/app7080853https://doi.org/10.3390/app7080853Human lower limbs are exposed to vibrations on a daily basis, during work, transport or sports. However, most of the FE (Finite Elements) and OMA (Operational Modal Analysis) studies focus either on the whole body or on the hand-arm system. The study presented herein aims at identifying the modal parameters of the lower limbs using a 2D FE model updated using OMA. A numerical model is proposed, and a modal analysis has been performed on 11 subjects. Two repeatable modal frequencies were extracted: 52.54 ± 2.05 Hz and 118.94 ± 2.70 Hz, which were used to update the mechanical properties of the numerical model. The knowledge of these modal characteristics makes it possible to design new equipment that would absorb these specific vibrations and possibly reduce the risk of related diseases in the field of sports and transport.Las extremidades inferiores del ser humano están expuestas a vibraciones a diario, durante el trabajo, el transporte o el deporte. Sin embargo, la mayoría de los estudios de EF (elementos finitos) y OMA (análisis modal operacional) se centran en el cuerpo entero o en el sistema mano-brazo. El estudio que aquí se presenta tiene como objetivo identificar los parámetros modales de las extremidades inferiores mediante un modelo de EF 2D actualizado con OMA. Se propone un modelo numérico y se ha realizado un análisis modal en 11 sujetos. Se extrajeron dos frecuencias modales repetibles 52,54 ± 2,05 Hz y 118,94 ± 2,70 Hz, que se utilizaron para actualizar las propiedades mecánicas del modelo numérico. El conocimiento de estas características modales permite diseñar nuevos equipos que absorban estas vibraciones específicas y posiblemente reduzcan el riesgo de enfermedades relacionadas en el ámbito del deporte y el transporte.12 páginasapplication/pdfengMDPI Multidisciplinary Digital Publishing InstituteSwitzerlandhttps://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessAtribución 4.0 Internacional (CC BY 4.0)http://purl.org/coar/access_right/c_abf2https://www.mdpi.com/2076-3417/7/8/853FE Model and Operational Modal Analysis of Lower LimbsArtículo de revistainfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARThttp://purl.org/coar/version/c_970fb48d4fbd8a858658537N/AApplied SciencesGómez-Cabello, A.; González-Agüero, A.; Morales, S.; Ara, I.; Casajús, J.A.; Vicente-Rodríguez, G. Effects of a short-term whole body vibration intervention on bone mass and structure in elderly people. J. Sci. Med. Sport 2014, 17, 160–164.Madou, K.H.; Cronin, J.B. The Effects of Whole Body Vibration on Physical and Physiological Capability in Special Populations. Hong Kong Physiother. J. 2008, 26, 24–38.Matute-Llorente, Á.; González-Agüero, A.; Gómez-Cabello, A.; Vicente-Rodríguez, G.; Casajús Mallén, J.A. Effect of Whole-Body Vibration Therapy on Health-Related Physical Fitness in Children and Adolescents With Disabilities: A Systematic Review. J. Adolesc. Health 2014, 54, 385–396.Carlsöö, S. The effect of vibration on the skeleton, joints and muscles. A review of the literature. Appl. Ergon. 1982, 13, 251–258.Wang, Y.J.; Huang, X.L.; Yan, J.W.; Wan, Y.N.; Wang, B.X.; Tao, J.H.; Chen, B.; Li, B.Z.; Yang, G.J.; Wang, J. The association between vibration and vascular injury in rheumatic diseases: A review of the literature. Autoimmunity 2015, 48, 61–68.Jordan, M.J.; Norris, S.R.; Smith, D.J.; Herzog, W. Vibration Training: An Overview of the Area, Training Consequences, and Future Considerations. J. Strength Cond. Res. 2005, 19, 459.Gurram, R. A Study of Vibration Response Characteristics of the Human Hand-Arm System. Ph.D. Thesis, Concordia University, Montreal, QC, Canada, 1993.Munera, M.; Chiementin, X.; Crequy, S.; Bertucci, W. Physical risk associated with vibration at cycling. Mech. Ind. 2014, 15, 535–540.Fridén, J. Vibration damage to the hand: Clinical presentation, prognosis and length and severity of vibration required. J. Hand Surg. 2001, 26, 471–474.Ayari, H.; Thomas, M.; Doré, S.; Serrus, O. Evaluation of lumbar vertebra injury risk to the seated human body when exposed to vertical vibration. J. Sound Vib. 2009, 321, 454–470.Grassi, L.; Väänänen, S.; Ristinmaa, M.; Jurvelin, J.S.; Isaksson, H. How accurately can subject-specific finite element models predict strains and strength of human femora? Investigation using full-field measurements. J. Biomech. 2016, 49, 802–806.Adewusi, S.; Thomas, M.; Vu, V.; Li, W. Modal parameters of the human hand-arm using finite element and operational modal analysis. Mech. Ind. 2014, 15, 541–549.Hostens, I.; Ramon, H. Descriptive analysis of combine cabin vibrations and their effect on the human body. J. Sound Vib. 2003, 266, 453–464.Kitazaki, S.; Griffin, M.J. Resonance behaviour of the seated human body and effects of posture. J. Biomech. 1998, 31, 143–149.Hobatho, M.C.; Darmana, R.; Pastor, P.; Barrau, J.J.; Laroze, S.; Morucci, J.P. Development of a three-dimensional finite element model of a human tibia using experimental modal analysis. J. Biomech. 1991, 24, 371–383.Munera, M.; Chiementin, X.; Murer, S.; Bertucci, W. Model of the risk assessment of hand-arm system vibrations in cycling: Case of cobblestone road. Proc. Inst. Mech. Eng. Part P 2015, 229, 231–238.Thuong, O.; Griffin, M.J. The vibration discomfort of standing persons: 0.5–16 Hz fore-and-aft, lateral, and vertical vibration. J. Sound Vib. 2011, 330, 816–826.Wakeling, J.M.; Liphardt, A.M.; Nigg, B.M. Muscle activity reduces soft-tissue resonance at heel-strike during walking. J. Biomech. 2003, 36, 1761–1769Lafortune, M.A.; Lake, M.J.; Hennig, E.M. Differential shock transmission response of the human body to impact severity and lower limb posture. J. Biomech. 1996, 29, 1531–1537.Peeters, B.; Van Der Auweraer, H. Polymax: A revolution in operational modal analysis. In Proceedings of the 1st International Operational Modal Analysis Conference, Copenhagen, Denmark, 26–27 April 2005.Van der Auweraer, H.; Guillaume, P.; Verboven, P.; Vanlanduit, S. Application of a Fast-Stabilizing Frequency Domain Parameter Estimation Method. J. Dyn. Syst. Meas. Control 2001, 123, 651.Heylen, W.; Lammens, S.; Sas, P. Modal Analysis Theory and Testing; Katholieke Universiteit Leuven, Faculty of Engineering, Department of Mechanical Engineering, Division of Production Engineering, Machine Design and Automation: Leuven, Belgium, 1998Afnor. ISO 2631-1:1997—Mechanical Vibration and Shock—Evaluation of Human Exposure to Whole-Body Vibration—Part 1: General Requirements; ISO: Geneva, Switzerland, 1997.Beillas, P.; Papaioannou, G.; Tashman, S.; Yang, K. A new method to investigate in vivo knee behavior using a finite element model of the lower limb. J. Biomech. 2004, 37, 1019–1030.De Mendonça, M.C. Estimation of height from the length of long bones in a Portuguese adult population. Am. J. Phys. Anthropol. 2000, 112, 39–48.Atilla, B.; Oznur, A.; Ca ˘glar, O.; Tokgözo ˘glu, M.; Alpaslan, M. Osteometry of the femora in Turkish individuals: A morphometric study in 114 cadaveric femora as an anatomic basis of femoral component design. Acta Orthop. Traumatol. Turc. 2007, 41, 64–68.Beauthier, J.; Mangin, P.; Hédouin, V. Traité de Médecine Légale; De Boeck: Bruxelles, Belgique, 2011Schmidt, W.; Reyes, M.; Fischer, F.; Geesink, R.; Nolte, L.; Racanelli, J.; Reimers, N. Quantifying human knee anthropometric differences between ethnic groups and gender using shape analysis techniques. In Proceedings of the Annual Meeting American Society of Biomechanics, State College, PA, USA, 26–29 August 2009.NASA. Volume I: Man-Systems Integration Standards (MSIS); Chapter Anthropometry and Biomechanics; NASA: Washington, DC, USA, 1995.Giladi, M.; Milgrom, C.; Simkin, A.; Stein, M.; Kashtan, H.; Margulies, J.; Rand, N.; Chisin, R.; Steinberg, R.; Aharonson, Z. Stress fractures and tibial bone width. A risk factor. J. Bone Jt. Surg. Br. Vol. 1987, 69, 326–329Radzi, S.; Uesugi, M.; Baird, A.; Mishra, S.; Schuetz, M.; Schmutz, B. Assessing the bilateral geometrical differences of the tibia—Are they the same? Med. Eng. 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