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The Computational Mechanics of Bone Tissue pp 179–202Cite as

Finite Element Analysis of Bone and Experimental Validation

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Part of the book series: Lecture Notes in Computational Vision and Biomechanics ((LNCVB,volume 35))

Abstract

This chapter describes the application of the finite element (FE) method to bone tissues. The aspects that differ the most between bone and other materials’ FE analysis are the type of elements used, constitutive models and experimental validation. These aspects are observed from a historical evolution point of view. Several types of elements can be used to simulate similar bone structures, and within the same analysis, many types of elements may be needed to realistically simulate an anatomical part. Special attention is made to constitutive models, including the use of density–elasticity relationships enabled through CT scanned images. Other more complex models are also described, such as viscoelastic and anisotropic models. The importance of experimental validation is discussed, describing several methods used by different authors in this challenging field. The use of cadaveric human bones is not always possible or desirable and other options are described, as the use of animal or artificial bones. Strain and strain rate measuring methods are also discussed, such as rosette strain gauges and optical devices.

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References

  1. Brekelmans W, Poort H, Slooff T (1972) A new method to analyse the mechanical behavior of skeletal parts. Acta Orthop Scand 43:301–317

    Article  CAS  PubMed  Google Scholar 

  2. Ascenzi A (1993) Biomechanics and galileo galilei. J Biomech 26(2):95–100

    Article  CAS  PubMed  Google Scholar 

  3. Huiskes R, Chao E (1983) A survey of finite element analysis in orthopedic biomechanics: the first decade. J Biomech 16(6):385–409

    Article  CAS  PubMed  Google Scholar 

  4. Taylor M, Prendergast P (2015) Four decades of finite element analysis of orthopaedic devices: where are we now and what are the opportunities. J Biomech 48:767–778

    Article  PubMed  Google Scholar 

  5. Schmidt H, Galbusera F, Rohlmann A, Shirazi-Adl A (2013) What have we learned from finite element model studies of lumbar intervertebral discs in the past four decades? J Biomech 46:2342–2355

    Article  PubMed  Google Scholar 

  6. Kumaresan S, Yoganandan N, Pintar F, Maiman D (1999) Finite element modeling of the cervical spine: role of the intervertebral disc under axial and eccentric loads. Med Eng Phys 21:689–700

    Article  CAS  PubMed  Google Scholar 

  7. Zander T, Rohlmann A, Calisse J, Bergmann G (2001) Estimation of muscle forces in the lumbar spine during upper-body inclination. Clin Biomech 16(1):S73–S80

    Article  Google Scholar 

  8. Schmidt H et al (2007) Application of a calibration method provides more realistic results for a finite element model of a lumbar spinal segment. Clin Biomech 22:377–384

    Article  Google Scholar 

  9. Papaioannou G et al (2008) Patient-specific knee joint finite element model validation with high-accuracy kinematics from biplane dynamic Roentgen. J Biomech 41:2633–2638

    Article  CAS  PubMed  Google Scholar 

  10. Faizan A et al (2009) Do design variations in the artificial disc influence cervical spine biomechanics? A finite element investigation. Eur Spine J 21(Suppl. 5):S653–S662

    PubMed  Google Scholar 

  11. Wolfram U, Wilke H, Zysset P (2010) Valid u finite element models of vertebral trabecular bone can be obtained using tissue properties measured with nanoindentation under wet conditions. J Biomech 43:1731–1737

    Article  PubMed  Google Scholar 

  12. Zhang J, Wang F, Zhou RXQ (2011) A three-dimensional finite element model of the cervical spine: an investigation of whiplash injury. Med Biol Eng Comput 49:193–201

    Article  PubMed  Google Scholar 

  13. Niemeyer F, Wilke H, Schmidt H (2012) Geometry strongly influences the response of numerical models of the lumbar spine—a probabilistic finite element analysis. J Biomech 45:1414–1423

    Article  PubMed  Google Scholar 

  14. Kinzl M, Wolfram U, Pahr D (2013) Identification of a crushable foam material model and application to strength and damage prediction of human femur and vertebral body. J Mech Beha Biom Mat 26:136–147

    Article  CAS  Google Scholar 

  15. Liu S et al (2014) Effect of bone material properties on effective region in screw-bone model: an experimental and finite element study. Biomed Eng Onl 13:83

    Article  PubMed  PubMed Central  Google Scholar 

  16. Lughmani W, Marouf K, Ashcroft I (2015) Drilling in cortical bone: a finite element model and experimental investigations. J Mech Beha Biom Mat 42:32–42

    Article  Google Scholar 

  17. Donald B (2011) Pracrical stress analysis with finite elements, 2nd edn. Glasnevin Publishing, Dublin

    Google Scholar 

  18. Burkhart T, Andrews D, Dunning C (2013) Finite element modeling mesh quality, energy balance and validation methods: a review with recommendations associated with the modeling of bone tissue. J Biomech 46:1477–1488

    Article  PubMed  Google Scholar 

  19. Gu K, Li L (2011) A human knee joint model considering fluid pressure and fiber orientation in cartilages and menisci. Med Eng Phys 33:497–503

    Article  CAS  PubMed  Google Scholar 

  20. Evans S et al (2012) Finite element analysis of a micromechanical model of bone and a new approach to validation. J Biomech 45:2702–2705

    Article  CAS  PubMed  Google Scholar 

  21. Hussain M et al (2012) Corpectomy versus discectomy for the treatment of multilevel cervical spine pathology: a finite element model analysis. Spine J. 12:401–408

    Article  PubMed  Google Scholar 

  22. Parr W et al (2013) Finite element micro-modelling of a human ankle bone reveals the importance of the trabecular network to mechanical performance: new methods for generation and comparison of 3D models. J Biomech 46:200–205

    Article  CAS  PubMed  Google Scholar 

  23. Taddei F et al (2006) Subject-specific finite element models of long bones: an in vitro evaluation of the overall accuracy. J Biomech 39:2457–2467

    Article  PubMed  Google Scholar 

  24. Austman R, Milner J, Holdsworth D, Dunning C (2008) The effect of the density-modulus relationship selected to apply material properties in a finite element model of long bone. J Biomech 41:3172–3176

    Article  Google Scholar 

  25. Nazemi S et al (2015) Prediction of proximal tibial subchondral bone structural stiffness using subject-specific finite element modelling: effect of selected density-modulus relationship. Clin Biomech 30:703–712

    Article  Google Scholar 

  26. Denozière G, Ku D (2006) Biomechanical comparison between fusion of two vertebrae and implantation of an artificial intervertebral disc. J Biomech 39:766–775

    Article  PubMed  Google Scholar 

  27. Ezquerro F et al (2011) Calibration of the finite element model of a lumbar functional spinal unit using an optimization technique based on differential evolution. Med Eng Phys 33:89–95

    Article  CAS  PubMed  Google Scholar 

  28. Beillas P, Lee S, Tashman S, Yang K (2007) Sensitivity of the tibio-femoral response to finite element modeling parameters. Comp Meth Biomech Biomed Eng 10(3):209–221

    Article  CAS  Google Scholar 

  29. Bowden A et al (2008) Quality of motion considerations in numerical analysis of motion restoring implants of the spine. Clin Biomech 23:536–544

    Article  Google Scholar 

  30. Little J, Adam C (2011) Effects of surgical joint destabilization on load sharing between ligamentous structures in the thoracic spine: a finite element investigation. Clin Biomech 26:895–903

    Article  CAS  Google Scholar 

  31. Dong L et al (2013) Development and validation of a 10-year-old child ligamentous cervical spine finite element model. A Biomed Eng 41(12):2538–2552

    Article  Google Scholar 

  32. Wang W, Zhang H, Sadeghipour K, Baran G (2013) Effect of posterolateral disc replacement on kinematics and stress distribution in the lumbar spine: a finite element study. Med Eng Phys 35:357–364

    Article  PubMed  Google Scholar 

  33. Bendjaballah M, Shirazi-Adl A, Zukor D (1995) Biomechanics of the human knee joint in compression: reconstruction, mesh generation and finite element analysis. Knee 2(2):69–79

    Article  Google Scholar 

  34. Moglo K, Shirazi-Adl A (2003) On the coupling between anterior and posterior cruciate ligaments, and knee joint response under anterior femoral drawer in flexion: a finite element study. Clin Biomech 18:751–759

    Article  CAS  Google Scholar 

  35. Donahue T, Hull M, Rashid M, Jacobs C (2003) How the stiffness of meniscal attachments and meniscal material properties affect tibio-femoral contact pressure computed using a validated finite element model of the human knee joint. J Biomech 36:19–34

    Article  Google Scholar 

  36. Ramaniraka N, Terrier A, Theumann N, Siegrist O (2005) Effects of the posterior cruciate ligament reconstruction on the biomechanics of the knee joint: a finite element analysis. Clin Biomech 20:434–442

    Article  CAS  Google Scholar 

  37. Peña E, Calvo B, Martínez M, Doblaré M (2006) A three-dimensional finite element analysis of the combined behavior of ligaments and menisci in the healthy human knee joint. J Boimech 39:1686–1701

    Article  Google Scholar 

  38. Li L, Cheung J, Herzog W (2009) Three-dimensional fibril-reinforced finite element model of articular cartilage. Med Biol Eng Comput 47:607–615

    Article  CAS  PubMed  Google Scholar 

  39. Rohlmann A, Boustani H, Bergmann G, Zander T (2010) Effect of a pedicle-screw-based motion preservation system on lumbar spine biomechanics: A probabilistic finite element study with subsequent sensitivity analysis. J Biomech 43:2963–2969

    Article  PubMed  Google Scholar 

  40. Yue-fu D et al (2011) Accurate 3D reconstruction of subject-specific knee finite element model to simulate the articular cartilage defects. J Shang Jiaot Univ (Sci) 16(5):620–627

    Article  Google Scholar 

  41. Carter D, Hayes W (1977) The compressive behaviour of bone as a two-phase porous structure. J Bone Joint Surg 954–962

    Google Scholar 

  42. Cowin SC (2001) Bone mechanics handbook, 2nd edn. CRC Press, Boca Raton

    Book  Google Scholar 

  43. Mow V, Huiskes R (2005) Basic orthopaedic biomechanics and mechano-biology, 3rd edn. Lippincott Williams & Wilkins, Philadelphia

    Google Scholar 

  44. Dempster W, Liddicoat R (1952) Compact bone as a non-isotropic material. Am J Anat 91(3):331–362

    Article  CAS  PubMed  Google Scholar 

  45. Huiskes R, Janssen J, Slooff T (1981) A detailed comparison of experimental and theoretical stress-analyses of a human femur. Mech Proper Bone 45:211–234

    Google Scholar 

  46. Brown T, Ferguson A (1980) Mechanical property distributions in the cancellous bone of the human proximal femur. Acta Orthop Scand 51:429–437

    Article  CAS  PubMed  Google Scholar 

  47. Taylor M et al (1995) Cancellous bone stresses surrounding the femoral component of a hip prosthesis: an elastic-plastic finite element analysis. Med Eng Phys 17:544–550

    Article  CAS  PubMed  Google Scholar 

  48. Kopperdahl D, Keaveny T (1998) Yield strain behaviour of trabecular bone. J Biomech 31:601–608

    Article  CAS  PubMed  Google Scholar 

  49. Morgan E, Keaveny T (2001) Dependence of yield strain of human trabecular bone on anatomical site. J Biomech 34:569–577

    Article  CAS  PubMed  Google Scholar 

  50. Chang W et al (1999) Uniaxial yield strains for bovine trabecular bone are isotropic and asymmetric. J Orthop Res 17:582–585

    Article  CAS  PubMed  Google Scholar 

  51. Iyo T et al (2004) Anisotropic viscoelastic properties of cortical bone. J Biomech 37:1433–1437

    Article  PubMed  Google Scholar 

  52. Galante J, Rostoker W, Ray R (1970) Physical properties of trabecular bone. Calc Tiss Res 5:236–246

    Article  CAS  Google Scholar 

  53. Lotz J, Gerhart T, Hayes W (1990) Mechanical properties of trabecular bone from the proximal femur: a quantitative CT study. J Comp Assist Tomogr 14:107–114

    Article  CAS  Google Scholar 

  54. Hodgskinson R, Currey J (1992) Young’s modulus, density and material properties in cancellous bone over a large density range. J Mat Sci Mat Med 3:377–381

    Article  Google Scholar 

  55. Kalender W et al (1995) The European spine phantom—a tool for standardization and quality control in spinal bone mineral measurements by DXA and QCT. Eur J Radiol 20:83–92

    Article  CAS  PubMed  Google Scholar 

  56. Rho J, Hobatho M, Ashman R (1995) Relations of mechanical properties to density and CT numbers in human bone. Med Eng Phys 17:347–355

    Article  CAS  PubMed  Google Scholar 

  57. Wirtz D et al (2000) Critical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur. J Biomech 33:1325–1330

    Article  CAS  PubMed  Google Scholar 

  58. Adams J (2009) Quantitative computed tomography. Eur J Radiol 71:415–424

    Article  PubMed  Google Scholar 

  59. Carter D, Hayes W (1976) Bone compressive strength: the influence of density and strain rate. Science 194:1174–1175

    Article  CAS  PubMed  Google Scholar 

  60. Taylor W et al (2002) Determination of orthotropic bone elastic constants using FEA and modal analysis. J Biomech 35:767–773

    Article  CAS  PubMed  Google Scholar 

  61. Pancanti A, Bernakiewicz M, Viceconti M (2003) The primary stability of a cementless stem varies between subjects as much as between activities. J Biomech 36:777–785

    Article  PubMed  Google Scholar 

  62. Taddei F, Pancanti A, Viceconti M (2004) An improved method for the automatic mapping of computed tomography numbers onto finite element models. Med Eng Phys 26:61–69

    Article  PubMed  Google Scholar 

  63. Morgan E, Bayraktar H, Keaveny T (2003) Trabecular bone modulus-density relationships depend on anatomic site. J Biomech 36:897–904

    Article  PubMed  Google Scholar 

  64. Marangalou J et al (2013) A novel approach to estimate trabecular bone anisotropy using a database approach. J Biomech 46:2356–2362

    Article  Google Scholar 

  65. Rietbergen B, Ito K (2015) A survey of micro-finite element analysis for clinical assessment of bone strength: the first decade. J Biomech 48:832–841

    Article  PubMed  Google Scholar 

  66. Scholz R et al (2013) Validation of density-elasticity relationships for finite element modelling of human pelvic bone by modal analysis. J Biomech 46:2667–2673

    Article  PubMed  Google Scholar 

  67. Liu S et al (2010) High-resolution peripheral quantitative computed tomography can assess microstructural and mechanical properties of human distal tibial bone. J Bone Min Res 25(4):746–756

    CAS  Google Scholar 

  68. Carnelli D et al (2010) A finite element model for direction-dependent mechanical response to nanoindentation of cortical bone allowing for anisotropic post-yield behaviour of the tissue. J Biomech Eng 132:081008.1–081008.10

    Google Scholar 

  69. Carnelli D et al (2011) Nanoindentation testing and finite element simulations of cortical bone allowing for anisotropic elastic and inelastic mechanical response. J Biomech 44:1852–1858

    Article  PubMed  Google Scholar 

  70. Koivumaki J et al (2012) Cortical bone finite element models in the estimation of experimentally measured failure loads in the proximal femur. Bone 51:737–740

    Article  PubMed  Google Scholar 

  71. Nelly N et al (2013) An investigation of the inelastic behaviour of trabecular bone during the press-fit implantation of a tibial component in total knee arthroplasty. Med Eng Phys 35:1599–1606

    Article  Google Scholar 

  72. Viceconti M, Olsen S, Burton K (2005) Extracting clinically relevant data from finite element simulations. Clin Biomech 20:451–454

    Article  Google Scholar 

  73. Neugebauer R et al (2011) Experimental modal analysis on fresh-frozen human hemipelvic bones employing a 3D laser vibrometer for the purpose of modal parameter identification. J Biomech 44:1610–1613

    Article  CAS  PubMed  Google Scholar 

  74. Cristofolini L, Viceconti M, Cappello A, Toni A (1996) Mechanical validation of whole bone composite femur models. J Biomech 29(4):525–535

    Article  CAS  PubMed  Google Scholar 

  75. Completo A, Fonseca F, Simões J (2007) Experimental validation of intact and implanted distal femur finite element models. J Biomech 40:2467–2476

    Article  CAS  PubMed  Google Scholar 

  76. Castro A, Completo A, Simões J, Flores P (2015) Biomechanical behaviour of cancellous bone on patellofemoral arthroplasty with Journey prosthesis: a finite element study. Comp Meth Biomech Biomed Eng 18(10):1090–1098

    Article  CAS  Google Scholar 

  77. Meireles S, Completo A, Simões J, Flores P (2010) Strain shielding in distal femur after patellofemoral arthroplasty under different activity conditions. J Biomech 43:477–484

    Article  PubMed  Google Scholar 

  78. Abdul-Kadir M et al (2008) Finite element modelling of primary hip stem stability: the effect of interference fit. J Biomech 41:587–594

    Article  PubMed  Google Scholar 

  79. Chong D, Hansen U, Andrew A (2010) Analysis of bone-prosthesis interface micromotion for cementless tibial prosthesis fixation and the influence of loading conditions. J Biomech 43:1074–1080

    Article  PubMed  Google Scholar 

  80. Viceconti M, Davinelli M, Taddei F, Cappello A (2004) Automatic generation of accurate subject-specific bone finite element models to be used in clinical studies. J Biomech 37:1597–1605

    Article  PubMed  Google Scholar 

  81. Weiss J et al (2005) Three-dimensional finite element modeling of ligaments: technical aspects. Med Eng Phys 27:845–861

    Article  PubMed  Google Scholar 

  82. Laville A, Laporte S, Skalli W (2009) Parametric and subject-specific finite element modelling of the lower cervical spine. Influence of geometrical parameters on the motion patterns. J Biomech 42:1409–1415

    Article  CAS  PubMed  Google Scholar 

  83. Rothstock S et al (2010) Primary stability of uncemented femoral resurfacing implants for varying interface parameters and material formulations during walking and stair climbing. J Biomech 43:521–526

    Article  PubMed  Google Scholar 

  84. Taylor M, Bryan R, Galloway F (2013) Accounting for patient variability in finite element analysis of the intact and implanted hip and knee: a review. Int J Numer Methods Biomed Eng 29(2):273–292

    Article  Google Scholar 

  85. Pankaj P (2013) Patient-specific modelling of bone and bone-implant systems: the challenges. J Numer Methods Biomed Eng 29(2):233–249

    Article  Google Scholar 

  86. Arregui-Mena J, Margetts L, Mummery P (2014) Practical application of the stochastic finite element method. Comp Meth Eng. https://doi.org/10.1007/s11831-014-9139-3

    Article  Google Scholar 

  87. Amirouche F et al (2014) Factors influencing initial cup stability in total hip arthroplasty. Clin Biomech 29:1177–1185

    Article  Google Scholar 

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Acknowledgements

This work is supported by the project POCI-01-0145-FEDER-028424, funded by Programa Operacional Competitividade e Internacionalização (COMPETE 2020) on its component FEDER and by funding from FCT—Fundação para a Ciência e Tecnologia on its component OE.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Aveiro, Aveiro, Portugal

    Francisco M. P. Almeida & António M. G. Completo

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  1. Francisco M. P. Almeida
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  2. António M. G. Completo
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Correspondence to António M. G. Completo .

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Editors and Affiliations

  1. Department of Mechanical Engineering, School of Engineering, Polytechnic of Porto (ISEP), Porto, Portugal

    Jorge Belinha

  2. Departament de Patologia i Terapèutica Experimental, University of Barcelona, Barcelona, Spain

    Maria-Cristina Manzanares-Céspedes

  3. Department of Mechanical Engineering, University of Aveiro, Aveiro, Portugal

    António M. G. Completo

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Almeida, F.M.P., Completo, A.M.G. (2020). Finite Element Analysis of Bone and Experimental Validation. In: Belinha, J., Manzanares-Céspedes, MC., Completo, A. (eds) The Computational Mechanics of Bone Tissue. Lecture Notes in Computational Vision and Biomechanics, vol 35. Springer, Cham. https://doi.org/10.1007/978-3-030-37541-6_7

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