Skip to main content
SpringerLink
Log in

Multiscale Modelling and Simulation of Musculoskeletal Tissues for Orthopaedics

  • Chapter
  • First Online:
Biomaterials for Implants and Scaffolds

Part of the book series: Springer Series in Biomaterials Science and Engineering ((SSBSE,volume 8))

Abstract

Successful development of implants for orthopaedic surgical procedures depends on a comprehensive understanding of the interaction between implant biomaterials and the host tissues of the musculoskeletal system. Mechanical factors are a key part of this interaction. This chapter investigates the potential of computational modelling and simulation approaches at multiple length scales to elucidate the response of musculoskeletal tissues to orthopaedic implants, leading to improved treatment outcomes. To a large extent, musculoskeletal tissues derive their load-bearing function from their hierarchically arranged structure; therefore we pay particular attention to modelling of the musculoskeletal tissues themselves from the nano- and micro-scales to the macro-scale. The most well-characterised musculoskeletal tissue are bone, and this chapter covers recent work on micro- and nanoscale modelling of bone and collagen and on defining the elasto-plastic constitutive response of the bone extracellular matrix using finite element models of bone nanoindentation combined with atomic force microscopy to map the inelastic deformation of the tissues. The use of serial milling and block face imaging techniques to determine soft tissue anatomy at multiple length scales for definition of model geometry is also covered. The potential for further development of multiscale computational biomechanics through modelling cell and tissue mechanobiology is discussed, including more detailed mechanical characterisation of the tissue–implant interface, modelling the strain fields experienced by cells within the extracellular matrix and within scaffolds and coupled modelling of other physical and biological phenomena within tissues and biomaterials.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    We note that it is not possible to deduce from this meta-analysis which of the complications were directly implant related or which were due to other causes.

  2. 2.

    Even in this supposedly simple case of modelling the body as a multi-jointed mechanism, modelling uncertainties abound: muscle lines of action are complex and involve wrapping and contact with other muscles; joints are polycentric, the axis of rotation changing with the degree of rotation. Intra-abdominal pressure affects trunk stiffness, and muscle activation strategies vary during repeated performance of the same task.

  3. 3.

    The physics-based, mechanistic models we refer to here are spatio-temporal models, i.e. they represent tissues and implants as structures in three-dimensional space. Pivonka and Komarova [39] provide an overview of other types of (temporal only) mathematical models used in bone biology.

  4. 4.

    Micro-scale FE models of bone are sometimes described in the literature as ‘high-resolution finite element models’ (see, e.g. [46]).

  5. 5.

    We note that several studies refer to four types of microcracks rather than three.

References

  1. Whitesides G, Wong A (2006) The intersection of biology and materials science. MRS Bulletin 31:19–27

    Article  Google Scholar 

  2. Hunter PJ, Borg TK (2003) Integration from proteins to organs: the Physiome Project. Nat Rev Mol Cell Biol 4:237–43

    Article  Google Scholar 

  3. Horstemeyer MF (2010) Multiscale modelling: a review. In: Leszczynski J, Shukla MK (eds) Practical aspects of computational chemistry. Springer, New York, pp 87–135

    Google Scholar 

  4. Fish J (ed) (2010) Multiscale Methods: Bridging the scales in science and engineering. Oxford University Press, Oxford

    Google Scholar 

  5. Tsubota K, Adachi T, Tomita Y (2003) Effects of a fixation screw on trabecular structural changes in a vertebral body predicted by remodelling simulation. Ann Biomed Eng 31:733–40

    Article  Google Scholar 

  6. Ebraheim NA, Rupp RE, Savolaine ER et al (1994) Use of titanium implants in pedicular screw fixation. J. Spinal Disord 7:478–86

    Google Scholar 

  7. Hawes MC, O'Brien JP (2008) A century of spine surgery: what can patients expect? Disabil Rehabil 30:808–17

    Article  Google Scholar 

  8. Paris O, Zizak I, Lichtenegger H et al (2000) Analysis of the hierarchical structure of biological tissues by scanning X-ray scattering using a micro-beam. Cell Mol Biol 46:993–1004

    Google Scholar 

  9. Mandel U, Dalgaard P, Viidik A (1986) A biomechanical study of the human periodontal ligament. J Biomech 19:637–45

    Article  Google Scholar 

  10. Maroudas A (1976) Balance between swelling pressure and collagen tension in normal and degenerate cartilage. Nature 260:808–809

    Article  Google Scholar 

  11. Evans JH, Nachemson AL (1969) Biomechanical study of human lumbar ligamentum flavum. J Anat 105:188–9

    Google Scholar 

  12. Borg TK, Caulfield JB (1980) Morphology of connective tissue in skeletal muscle. Tissue Cell 12:197–207

    Article  Google Scholar 

  13. Rigozzi S, Müller R, Snedeker JG (2010) Collagen fibril morphology and mechanical properties of the Achilles tendon in two inbred mouse strains. J Anat 216:724–31

    Article  Google Scholar 

  14. Kim SH, Turnbull J, Guimond S (2011) Extracellular matrix and cell signalling: the dynamic cooperation of integrin, proteoglycan and growth factor receptor. J Endocrinol 209:139–51

    Article  Google Scholar 

  15. Chen JH, Liu C, You L et al (2010) Boning up on Wolff's Law: mechanical regulation of the cells that make and maintain bone. J Biomech 43:108–18

    Article  Google Scholar 

  16. Sievänen H (2010) Immobilization and bone structure in humans. Arch Biochem Biophys 503:146–52

    Article  Google Scholar 

  17. LeBlanc A, Schneider V, Shackelford L et al (2000) Bone mineral and lean tissue loss after long duration space flight. J Musculoskelet Neuronal Interact 1:157–60

    Google Scholar 

  18. Merle C, Streit MR, Volz C et al (2011) Bone remodelling around stable uncemented titanium stems during the second decade after total hip arthroplasty: a DXA study at 12 and 17 years. Osteoporos Int 22:2879–86

    Article  Google Scholar 

  19. Burr DB (1993) Remodelling and the repair of fatigue damage. Calcif Tissue Int 53:S75–80

    Article  Google Scholar 

  20. Weiner S, Wagner HD (1998) The material bone: structure mechanical function relations. Annu Rev Mater Sci 28:271–298

    Article  Google Scholar 

  21. Rho JY, Kuhn-Spearing L, Zioupos P (1998) Mechanical properties and the hierarchical structure of bone. Med Eng Phys 20:92–102

    Article  Google Scholar 

  22. Buehler MJ (2007) Nano- and micromechanical properties of hierarchical biological materials and tissues. Mater Sci 42(21):8765–8770

    Article  Google Scholar 

  23. de d’Otreppe BV (2012) From medical imaging to finite element simulations : a contribution to mesh generation and locking-free formulations for tetrahedra. Universite de Liège, PhD Dissertation

    Google Scholar 

  24. Bell CG (2005) A finite element and experimental investigation of the femoral component mechanics in a total hip arthroplasty. Queensland University of Technology, PhD Dissertation

    Google Scholar 

  25. An YH, Draughn RA (eds) (2000) Mechanical testing of bone and the bone-implant interface. CRC Press, Boca Raton

    Google Scholar 

  26. Little JP, de Visser H, Pearcy MJ et al (2008) Are coupled rotations in the lumbar spine largely due to the osseo-ligamentous anatomy?--a modelling study. Comp Meth Biomech Biomed Eng 11:95–103

    Article  Google Scholar 

  27. Nachemson A, Elfström G (1971) Intravital wireless telemetry of axial forces in Harrington distraction rods in patients with idiopathic scoliosis. J Bone Joint Surg Am 53:445–65

    Article  Google Scholar 

  28. Carretta R, Lorenzetti S, Müller R (2013) Towards patient-specific material modelling of trabecular bone post-yield behavior. Int j numer method biomed eng 29:250–72

    Article  Google Scholar 

  29. Hoshaw SJ, Fyhrie DP, Takano Y et al (1997) A method suitable for in vivo measurement of bone strain in humans. J Biomech 30:521–4

    Article  Google Scholar 

  30. Nachemson AL (1981) Disc pressure measurements. Spine 6:93–7

    Article  Google Scholar 

  31. Wilke HJ, Neef P, Caimi M et al (1999) New in vivo measurements of pressures in the intervertebral disc in daily life. Spine 24:755–62

    Article  Google Scholar 

  32. Frost HM (2003) Bone's mechanostat: a 2003 update. Anat Rec A Discov Mol Cell Evol Biol 275:1081–101

    Article  Google Scholar 

  33. Dabirrahmani D, Hogg M, Kohan L et al (2010) Primary and long-term stability of a short-stem hip implant. Proc Inst Mech Eng H 224:1109–19

    Article  Google Scholar 

  34. Dickinson A, Taylor A, Browne M (2012) Implant-bone interface healing and adaptation in resurfacing hip replacement. Comp Meth Biomech Biomed Eng 15:935–47

    Article  Google Scholar 

  35. Geris L, Van Oosterwyck H, Vander Sloten J et al (2003) Assessment of mechanobiological models for the numerical simulation of tissue differentiation around immediately loaded implants. Comp Meth Biomech Biomed Eng 6:277–88

    Article  Google Scholar 

  36. Prendergast PJ, Huiskes R, Søballe K (1997) Biophysical stimuli on cells during tissue differentiation at implant interfaces. J Biomech 30:539–548

    Article  Google Scholar 

  37. Huiskes R, Van Driel WD, Prendergast PJ et al (1997) A biomechanical regulatory model for periprosthetic fibrous-tissue differentiation. J Matl Sci: Materials in Medicine 8:785–788

    Google Scholar 

  38. Claes LE, Heigele CA (1999) Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing. J Biomech 32:255–266

    Article  Google Scholar 

  39. Pivonka P, Komarova SV (2010) Mathematical modelling in bone biology: from intracellular signaling to tissue mechanics. Bone 47:181–9

    Article  Google Scholar 

  40. Meyers MA, Chen PY, Lopez MI et al (2010) Biological materials: a materials science approach. J Mech Behav Biomed Mat 4:626–57

    Article  Google Scholar 

  41. Parfitt AM (2002) Misconceptions (2): turnover is always higher in cancellous than in cortical bone. Bone 30:807–9

    Article  Google Scholar 

  42. Eswaran SK, Gupta A, Adams MF, Keaveny TM (2006) Cortical and trabecular load sharing in the human vertebral body. J Bone Miner Res 21:307–14

    Article  Google Scholar 

  43. Harrigan TP, Jasty M, Mann RW et al (1988) Limitations of the continuum assumption in cancellous bone. J Biomech 21:269–75

    Article  Google Scholar 

  44. McDonnell P, McHugh PE, O’Mahoney D (2007) Vertebral osteoporosis and trabecular bone quality. Ann Biomed Eng 35:170–189

    Article  Google Scholar 

  45. Seeman E, Delmas PD (2006) Bone quality--the material and structural basis of bone strength and fragility. N Engl J Med 354:2250–61

    Article  Google Scholar 

  46. Niebur GL, Feldstein MJ, Yuen JC (2000) High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone. J Biomech 33:1575–83

    Article  Google Scholar 

  47. Müller R, Rüegsegger P (1995) Three-dimensional finite element modelling of non-invasively assessed trabecular bone structures. Med Eng Phys 17:126–33

    Article  Google Scholar 

  48. van Rietbergen B, Weinans H, Huiskes R et al (1995) A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J Biomech 28:69–81

    Article  Google Scholar 

  49. Jacobs CR, Davis BR, Rieger CJ et al (1999) The impact of boundary conditions and mesh size on the accuracy of cancellous bone tissue modulus determination using large-scale finite-element modelling. J Biomech 32:1159–64

    Article  Google Scholar 

  50. van Rietbergen B, Kabel J, Odgaard A et al (1997) Determination of trabecular bone tissue elastic properties by comparison of experimental and finite element results. In: Sol H, Oomens CWJ (eds) Material identification using mixed numerical experimental methods. Kluwer Academic Publisher, Norwell (MA)

    Google Scholar 

  51. Kabel J, van Rietbergen B, Dalstra M et al (1999) The role of an effective isotropic modulus in the elastic properties of cancellous bone. J Biomech 32:673–680

    Article  Google Scholar 

  52. Fyhrie DP, Hou FJ (1995) Prediction of human vertebral cancellous bone strength using non-linear, anatomically accurate, large-scale finite element analysis. Proc Bioeng Conf ASME 29:301–2

    Google Scholar 

  53. Van Rietbergen B, Ulrich D, Pistoia W et al (1998) Prediction of trabecular bone failure parameters using a tissue failure criterion. Trans Orthop Res Soc 23:550

    Google Scholar 

  54. Niebur GL, Yuen JC, Burghardt AJ et al (2001) Sensitivity of damage predictions to tissue level yield properties and apparent loading conditions. J Biomech 34:699–706

    Article  Google Scholar 

  55. Pistoia W, van Rietbergen B, Lochmuller EM et al (2002) Estimation of distal radius failure load with micro-finite element analysis models based on three-dimensional peripheral quantitative computed tomography images. Bone 30:842–8

    Article  Google Scholar 

  56. Stölken JS, Kinney JH (2003) On the importance of geometric nonlinearity in finite-element simulations of trabecular bone failure. Bone 33:494–504

    Article  Google Scholar 

  57. Verhulp E, Van Rietbergen B, Muller R et al (2008) Micro-finite element simulation of trabecular-bone post-yield behaviour-effects of material model, element size and type. Comp Meth Biomech Biomed Eng 11:389–95

    Article  Google Scholar 

  58. Pistoia W, van Rietbergen B, Laib A et al (2001) High-resolution three-dimensional-pQCT images can be an adequate basis for in-vivo microFE analysis of bone. J Biomech Eng 123:176–83

    Article  Google Scholar 

  59. Vilayphiou N, Boutroy S, Szulc P et al (2011) Finite element analysis performed on radius and tibia HR-pQCT images and fragility fractures at all sites in men. J Bone Miner Res 26:965–73

    Article  Google Scholar 

  60. Podshivalov L, Fischer A, Bar-Yoseph PZ (2011) Multiscale FE method for analysis of bone micro-structures. J Mech Behav Biomed Mater 4:888–99

    Article  Google Scholar 

  61. Basaruddin KS, Takano N, Nakano T (2013) Stochastic multiscale prediction on the apparent elastic moduli of trabecular bone considering uncertainties of biological apatite (BAp) crystallite orientation and image-based modelling., Comp Meth Biomech Biomed Eng, (epub ahead of print)

    Google Scholar 

  62. Taylor D, Hazenberg JG, Lee TC (2007) Living with cracks: Damage and repair in human bone. Nature Materials 6:263–8

    Article  Google Scholar 

  63. Fazzalari NL, Forwood MR, Manthey BA et al (1998) Three-dimensional confocal images of microdamage in cancellous bone. Bone 23:373–8

    Article  Google Scholar 

  64. Mori S, Burr DB (1993) Increased intracortical remodelling following fatigue damage. Bone 14:103–9

    Article  Google Scholar 

  65. Mulvihill BM, McNamara LM, Prendergast PJ (2008) Loss of trabeculae by mechano-biological means may explain rapid bone loss in osteoporosis. J R Soc Interface 5:1243–53

    Article  Google Scholar 

  66. Mosekilde L (1990) Consequences of the remodelling process for vertebral trabecular bone structure: a scanning electron microscopy study (uncoupling of unloaded structures). Bone and Mineral 10:13–35

    Article  Google Scholar 

  67. Burr DB, Forwood MR, Fyhrie DP et al (1997) Bone microdamage and skeletal fragility in osteoporotic and stress fractures. J Bone Miner Res 12:6–15

    Article  Google Scholar 

  68. Yeh OC, Keaveny TM (2001) Relative roles of microdamage and microfracture in the mechanical behavior of trabecular bone. J Orthop Res 19:1001–7

    Article  Google Scholar 

  69. Nagaraja S, Couse TL, Guldberg RE (2005) Trabecular bone microdamage and microstructural stresses under uniaxial compression. J Biomech 38:707–16

    Article  Google Scholar 

  70. Jungmann R, Szabo ME, Schitter G et al (2011) Local strain and damage mapping in single trabeculae during three-point bending tests. J Mech Behav Biomed Mater 4:523–34

    Article  Google Scholar 

  71. Ural A, Vashishth D (2006) Cohesive finite element modelling of age-related toughness loss in human cortical bone. J Biomech 39:2974–82

    Article  Google Scholar 

  72. Tomar V (2008) Modelling of dynamic fracture and damage in two-dimensional trabecular bone microstructures using the cohesive finite element method. J Biomech Eng 130:021021

    Article  Google Scholar 

  73. Kosmopoulos V, Keller TS (2003) Finite element modelling of trabecular bone damage. Comp Meth Biomech Biomed Eng 6:209–16

    Article  Google Scholar 

  74. Kosmopoulos V, Keller TS (2008) Predicting trabecular bone microdamage initiation and accumulation using a non-linear perfect damage model. Med Eng Phys 30:725–32

    Article  Google Scholar 

  75. Budyn E, Hoca T (2006) Multiscale Modelling of Human Cortical Bone: Aging and Failure Studies. Mat Res Soc Fall Meeting 975:27–32

    Google Scholar 

  76. Yang QD, Cox BN, Nalla RK et al (2006) Fracture length scales in human cortical bone: the necessity of nonlinear fracture models. Biomaterials 27:2095–113

    Article  Google Scholar 

  77. Renders GA, Mulder L, Langenbach GE et al (2008) Biomechanical effect of mineral heterogeneity in trabecular bone. J Biomech 41:2793–8

    Article  Google Scholar 

  78. Renders GA, Mulder L, van Ruijven LJ et al (2011) Mineral heterogeneity affects predictions of intratrabecular stress and strain. J Biomech 44:402–7

    Article  Google Scholar 

  79. Knothe Tate ML (2003) "Whither flows the fluid in bone?" An osteocyte's perspective. J Biomech 36:1409–24

    Article  Google Scholar 

  80. McNamara LM, Van der Linden JC, Weinans H et al (2006) Stress-concentrating effect of resorption lacunae in trabecular bone. J Biomech 39(4):734–41

    Article  Google Scholar 

  81. Deligianni DD, Apostolopoulos CA (2008) Multilevel finite element modelling for the prediction of local cellular deformation in bone. Biomech Model Mechanobiol 7:151–9

    Article  Google Scholar 

  82. Jacobs CR, Temiyasathit S, Castillo AB (2010) Osteocyte mechanobiology and pericellular mechanics. Annu Rev Biomed Eng 12:369–400

    Article  Google Scholar 

  83. Cardoso L, Fritton SP, Gailani G et al (2013) Advances in assessment of bone porosity, permeability and interstitial fluid flow. J Biomech 46:253–65

    Article  Google Scholar 

  84. Swan CC, Lakes RS, Brand RA et al (2003) Micromechanically based poroelastic modelling of fluid flow in Haversian bone. J Biomech Eng 125:25–37

    Article  Google Scholar 

  85. Galley SA, Michalek DJ, Donahue SW (2006) A fatigue microcrack alters fluid velocities in a computational model of interstitial fluid flow in cortical bone. J Biomech 39:2026–33

    Article  Google Scholar 

  86. Rémond A, Naïli S, Lemaire T (2008) Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study. Biomech Model Mechanobiol 7:487–95

    Article  Google Scholar 

  87. Cowin SC, Gailani G, Benalla M (2009) Hierarchical poroelasticity: movement of interstitial fluid between porosity levels in bones. Philos Trans A Math Phys Eng Sci 367:3401–44

    Article  Google Scholar 

  88. Nguyen VH, Lemaire T, Naili S (2010) Poroelastic behaviour of cortical bone under harmonic axial loading: a finite element study at the osteonal scale. Med Eng Phys 32:384–90

    Article  Google Scholar 

  89. Lemaire T, Naïli S, Rémond A (2006) Multiscale analysis of the coupled effects governing the movement of interstitial fluid in cortical bone. Biomech Model Mechanobiol 5:39–52

    Article  Google Scholar 

  90. Lemaire T, Capiez-Lernout E, Kaiser J (2011) What is the importance of multiphysical phenomena in bone remodelling signals expression? A multiscale perspective. J Mech Behav Biomed Mater 4:909–20

    Article  Google Scholar 

  91. Sansalone V, Kaiser J, Naili S et al (2012) Interstitial fluid flow within bone canaliculi and electro-chemo-mechanical features of the canalicular milieu : A multi-parametric sensitivity analysis., Biomech Model Mechanobiol, (epub ahead of print)

    Google Scholar 

  92. Verbruggen SW, Vaughan TJ, McNamara LM (2013) Fluid flow in the osteocyte mechanical environment: a fluid-structure interaction approach., Biomech Model Mechanobiol, (epub ahead of print)

    Google Scholar 

  93. Goulet GC, Hamilton N, Cooper D (2008) Influence of vascular porosity on fluid flow and nutrient transport in loaded cortical bone. J Biomech 41:2169–75

    Article  Google Scholar 

  94. Steck R, Niederer P, Knothe Tate ML (2003) A finite element analysis for the prediction of load-induced fluid flow and mechanochemical transduction in bone. J Theor Biol 220:249–59

    Article  Google Scholar 

  95. Nguyen VH, Lemaire T, Naili S (2011) Influence of interstitial bone microcracks on strain-induced fluid flow. Biomech Model Mechanobiol 10:963–72

    Article  Google Scholar 

  96. Silva MJ, Gibson LJ (1997) Modelling the mechanical behavior of vertebral trabecular bone: Effects of age-related changes in microstructure. Bone 21:191–199

    Article  Google Scholar 

  97. Langton CM, Haire TJ, Ganney PS et al (1998) Dynamic stochastic simulation of cancellous bone resorption. Bone 22:375–80

    Article  Google Scholar 

  98. Langton CM, Haire TJ, Ganney PS et al (2000) Stochastically simulated assessment of anabolic treatment following varying degrees of cancellous bone resorption. Bone 27:111–8

    Article  Google Scholar 

  99. Huiskes R, Ruimerman R, van Lenthe GH, Janssen JD (2000) Effects of mechanical forces on maintenance and adaptation of form in trabecular bone. Nature 405:704–6

    Article  Google Scholar 

  100. Ruimerman R, Van Rietbergen B, Hilbers P et al (2003) A 3-dimensional computer model to simulate trabecular bone metabolism. Biorheology 40:315–20

    Google Scholar 

  101. Ruimerman R, Van Rietbergen B, Hilbers P (2005) The effects of trabecular-bone loading variables on the surface signaling potential for bone remodelling and adaptation. Ann Biomed Eng 33:71–8

    Article  Google Scholar 

  102. van Oers RF, Ruimerman R, Tanck E et al (2008) A unified theory for osteonal and hemi-osteonal remodelling. Bone 42:250–9

    Article  Google Scholar 

  103. van Oers RF, van Rietbergen B, Ito K et al (2011) Simulations of trabecular remodelling and fatigue: is remodelling helpful or harmful? Bone 48:1210–5

    Article  Google Scholar 

  104. Chen G, Pettet GJ, Pearcy M et al (2007) Modelling external bone adaptation using evolutionary structural optimisation. Biomech Model Mechanobiol 6:275–85

    Article  Google Scholar 

  105. Van Der Linden JC, Verhaar JA, Weinans H (2001) A three-dimensional simulation of age-related remodelling in trabecular bone. J Bone Miner Res 16:688–96

    Article  Google Scholar 

  106. Hernandez CJ, Gupta A, Keaveny TM (2006) A biomechanical analysis of the effects of resorption cavities on cancellous bone strength. J Bone Miner Res 21:1248–55

    Article  Google Scholar 

  107. Smit TH, Burger EH (2000) Is BMU-coupling a strain-regulated phenomenon? A finite element analysis. J Bone Miner Res 15:301–7

    Article  Google Scholar 

  108. McNamara LM, Prendergast PJ (2005) Perforation of cancellous bone trabeculae by damage-stimulated remodelling at resorption pits: a computational analysis. Eur J Morphol 42:99–109

    Article  Google Scholar 

  109. McNamara LM, Prendergast PJ (2007) Bone remodelling algorithms incorporating both strain and microdamage stimuli. J Biomech 40:1381–91

    Article  Google Scholar 

  110. Mulvihill BM, McNamara LM, Prendergast PJ (2008) Loss of trabeculae by mechano-biological means may explain rapid bone loss in osteoporosis. J R Soc Interface 5:1243–53

    Article  Google Scholar 

  111. Ryser MD, Nigam N, Komarova SV (2009) Mathematical modelling of spatio-temporal dynamics of a single bone multicellular unit. J Bone Miner Res 24:860–70

    Article  Google Scholar 

  112. Adachi T, Kameo Y, Hojo M (2010) Trabecular bone remodelling simulation considering osteocytic response to fluid-induced shear stress. Philos Trans A Math Phys Eng Sci 368:2669–82

    Article  Google Scholar 

  113. Gerhard FA, Webster DJ, van Lenthe GH et al (2009) In silico biology of bone modelling and remodelling: adaptation. Philos Trans A Math Phys Eng Sci 367:2011–30

    Article  Google Scholar 

  114. Hambli R (2010) Application of neural networks and finite element computation for multiscale simulation of bone remodelling. J Biomech Eng 132:114502

    Article  Google Scholar 

  115. Hambli R, Katerchi H, Benhamou CL (2011) Multiscale methodology for bone remodelling simulation using coupled finite element and neural network computation. Biomech Model Mechanobiol 10:133–45

    Article  Google Scholar 

  116. Hambli R (2011) Apparent damage accumulation in cancellous bone using neural networks. J Mech Behav Biomed Mater 4:868–78

    Article  Google Scholar 

  117. Mann KA, Miller MA (2013) Fluid-structure interactions in micro-interlocked regions of the cement-bone interface., Comput Methods Biomech Biomed Engin, (epub ahead of print)

    Google Scholar 

  118. Hollister SJ, Fyhrie DP, Jepsen KJ et al (1991) Application of homogenization theory to the study of trabecular bone mechanics. J Biomech 24:825–39

    Article  Google Scholar 

  119. van Lenthe GH, Stauber M, Müller R (2006) Specimen-specific beam models for fast and accurate prediction of human trabecular bone mechanical properties. Bone 39:1182–9

    Article  Google Scholar 

  120. McDonald K, Little J, Pearcy M et al (2010) Development of a multi-scale finite element model of the osteoporotic lumbar vertebral body for the investigation of apparent level vertebra mechanics and micro-level trabecular mechanics. Med Eng Phys 32:653–61

    Article  Google Scholar 

  121. Yeh OC, Keaveny TM (1999) Biomechanical effects of intraspecimen variations in trabecular architecture: A three-dimensional finite element study. Bone 25:223–228

    Article  Google Scholar 

  122. Jensen KS, Mosekilde L, Mosekilde L (1990) A model of vertebral trabecular bone architecture and its mechanical properties. Bone 11:417–423

    Article  Google Scholar 

  123. Hildebrand T, Rüegsegger P (1997) Quantification of Bone Microarchitecture with the Structure Model Index. Comput Methods Biomech Biomed Engin 1:15–23

    Article  Google Scholar 

  124. Odgaard A (1997) Three-dimensional methods for quantification of cancellous bone architecture. Bone 20:315–328

    Article  Google Scholar 

  125. Mosekilde L (1989) Sex differences in age-related loss of vertebral trabecular bone mass and structure-biomechanical consequences. Bone 10:425–432

    Article  Google Scholar 

  126. Pugh JW, Rose RM, Radin EL (1973) A structural model for the mechanical behavior of trabecular bone. Journal of Biomechanics 6:657–670

    Article  Google Scholar 

  127. Gibson LJ, Ashby MF, Schajer GS, et al. (1982) The mechanics of three-dimensional cellular materials. In: Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences A 382

    Google Scholar 

  128. McDonald K (2009) An experimental and finite element investigation of the biomechanics of vertebral compression fractures. Queensland University of Technology, PhD Dissertation

    Google Scholar 

  129. Mizrahi J, Silva MJ, Keaveny TM et al (1993) Finite-element stress analysis of the normal and osteoporotic lumbar vertebral body. Spine 18:2088–2096

    Article  Google Scholar 

  130. Chevalier Y, Pahr D, Allmer H et al (2007) Validation of a voxel-based FE method for prediction of the uniaxial apparent modulus of human trabecular bone using macroscopic mechanical tests and nanoindentation. J Biomech 40:3333–40

    Article  Google Scholar 

  131. Toal V (2013) The mechanics of microdamage and microfracture in trabecular bone. Queensland University of Technology, PhD Dissertation

    Google Scholar 

  132. Galli M, Oyen ML (2009) Fast identification of poroelastic parameters from indentation tests. Comp Model Eng Sci 48:241–268

    Google Scholar 

  133. Fratzl-Zelman N, Roschger P, Gourrier A et al (2009) Combination of nanoindentation and quantitative backscattered electron imaging revealed altered bone material properties associated with femoral neck fragility. Calcif Tissue Int 85:335–43

    Article  Google Scholar 

  134. Tai K, Qi HJ, Ortiz C (2005) Effect of mineral content on the nanoindentation properties and nanoscale deformation mechanisms of bovine tibial cortical bone. J Mater Sci Mater Med 16:947–959

    Article  Google Scholar 

  135. Tai K, Ulm FJ, Ortiz C (2006) Nanogranular origins of the strength of bone. Nano Letters 6:2520–2525

    Article  Google Scholar 

  136. Wang X, Allen MR, Burr DB et al (2008) Identification of material parameters based on Mohr-Coulomb failure criterion for bisphosphonate treated canine vertebral cancellous bone. Bone 43:775–780

    Article  Google Scholar 

  137. Mullins LP, Bruzzi MS, McHugh PE (2009) Calibration of a constitutive model for the post-yield behaviour of cortical bone. J Mech Behav Biomed Mater 2:460–70

    Article  Google Scholar 

  138. Oyen ML, Ko CC (2007) Examination of local variations in viscous, elastic, and plastic indentation responses in healing bone. J Mater Sci Mater Med 18:623–8

    Article  Google Scholar 

  139. Brockaert H, Mazerain PE, Rachik M, Ho Ba Tho MC (2009) Nanoindentation on isotropic and anisotropic materials confrontation with FEM simulations. Comp Meth Biomech Biomed Eng 12:63–64

    Article  Google Scholar 

  140. Paietta R, Campbell SE, Ferguson VL (2011) Influences of spherical tip radius, contact depth and contact area on nanoindentation properties of bone. J Biomech 44:285–90

    Article  Google Scholar 

  141. Carnelli D, Gastaldi D, Sassi V et al (2010) A finite element model for direction-dependent mechanical response to nanoindentation for cortical bone allowing for anisotropic post-yield behavior of the tissue. J Biomech Eng 132:081008

    Article  Google Scholar 

  142. Wolfram U, Wilke HJ, Zysset PK (2010) Valid micro finite element models of vertebral trabecular bone can be obtained using tissue properties measured with nanoindentation under wet conditions. J Biomech 43:1731–7

    Article  Google Scholar 

  143. Reisinger AG, Pahr DH, Zysset PK (2011) Elastic anisotropy of bone lamellae as a function of fibril orientation pattern. Biomech Model Mechanobiol 10:67–77

    Article  Google Scholar 

  144. Carnelli D, Lucchini R, Ponzoni M et al (2011) Nanoindentation testing and finite element simulations of cortical bone allowing for anisotropic elastic and inelastic mechanical response. J Biomech 44:1852–8

    Article  Google Scholar 

  145. Lucchini R, Carnelli D, Ponzoni M et al (2011) Role of damage mechanics in nanoindentation of lamellar bone at multiple sizes: experiments and numerical modelling. J Mech Behav Biomed Mater 4:1852–63

    Article  Google Scholar 

  146. Vaughan TJ, McCarthy CT, McNamara LM (2012) A three-scale finite element investigation into the effects of tissue mineralisation and lamellar organisation in human cortical and trabecular bone. J Mech Behav Biomed Mater 12:50–62

    Article  Google Scholar 

  147. Adam CJ, Swain MV (2011) The effect of friction on indenter force and pile-up in numerical simulations of bone nanoindentation. J Mech Behav Biomed Mater 4:1554–8

    Article  Google Scholar 

  148. Schwiedrzik JJ, Wolfram U, Zysset PK (2013) A generalized anisotropic quadric yield criterion and its application to bone tissue at multiple length scales., Biomech Model Mechanobiol, (epub ahead of print)

    Google Scholar 

  149. Currey JD (2002) Bones: Structure and mechanics. Princeton University Press, Oxfordshire

    Google Scholar 

  150. Jäger I, Fratzl P (2000) Mineralized collagen fibrils: a mechanical model with a staggered arrangement of mineral particles. Biophys J 79:1737–46

    Article  Google Scholar 

  151. Nikolov S, Raabe D (2008) Hierarchical modelling of the elastic properties of bone at submicron scales: the role of extrafibrillar mineralization. Biophys J 94:4220–32

    Article  Google Scholar 

  152. Siegmund T, Allen MR, Burr DB (2008) Failure of mineralized collagen fibrils: modelling the role of collagen cross-linking. J Biomech 41:1427–35

    Article  Google Scholar 

  153. Hambli R, Barkaoui A (2012) Physically based 3D finite element model of a single mineralized collagen microfibril. J Theor Biol 301:28–41

    Article  Google Scholar 

  154. Nair AK, Gautieri A, Chang SW et al (2013) Molecular mechanics of mineralized collagen fibrils in bone. Nat Commun 16:1724

    Article  Google Scholar 

  155. Ganazzoli F, Raffaini G (2005) Computer simulation of polypeptide adsorption on model biomaterials. Phys Chem Chem Phys 7:3651–63

    Article  Google Scholar 

  156. Raffaini G, Ganazzoli F (2007) Understanding the performance of biomaterials through molecular modelling: crossing the bridge between their intrinsic properties and the surface adsorption of proteins. Macromol Biosci 7:552–66

    Article  Google Scholar 

  157. De Nardo L, Raffaini G, Ebramzadeh E et al (2012) Titanium oxide modelling and design for innovative biomedical surfaces: a concise review. Int J Artif Organs 35:629–41

    Article  Google Scholar 

  158. Shim VB, Hunter PJ, Pivonka P et al (2011) A multiscale framework based on the physiome markup languages for exploring the initiation of osteoarthritis at the bone-cartilage interface. IEEE Trans Biomed Eng 58:3532–6

    Article  Google Scholar 

  159. Lavagnino M, Arnoczky SP, Kepich E et al (2008) A finite element model predicts the mechanotransduction response of tendon cells to cyclic tensile loading. Biomech Model Mechanobiol 7:405–16

    Article  Google Scholar 

  160. Hadi MF, Barocas VH (2013) Microscale fiber network alignment affects macroscale failure behavior in simulated collagen tissue analogs. J Biomech Eng 135:021026

    Article  Google Scholar 

  161. Reese SP, Ellis BJ, Weiss JA (2013) Micromechanical model of a surrogate for collagenous soft tissues: development, validation and analysis of mesoscale size effects., Biomech Model Mechanobiol, (epub ahead of print)

    Google Scholar 

  162. Maceri F, Marino M, Vairo G (2010) A unified multiscale mechanical model for soft collagenous tissues with regular fiber arrangement. J Biomech 43:355–63

    Article  Google Scholar 

  163. Maceri F, Marino M, Vairo G (2012) An insight on multiscale tendon modelling in muscle-tendon integrated behavior. Biomech Model Mechanobiol 11:505–17

    Article  Google Scholar 

  164. Gronau G, Krishnaji ST, Kinahan ME et al (2012) A review of combined experimental and computational procedures for assessing biopolymer structure-process-property relationships. Biomaterials 33:8240–55

    Article  Google Scholar 

  165. Israelowitz M, Rizvi SW, Kramer J et al (2005) Computational modelling of type I collagen fibers to determine the extracellular matrix structure of connective tissues. Protein Eng Des Sel 18:329–35

    Article  Google Scholar 

  166. Buehler MJ (2006) Nature designs tough collagen: explaining the nanostructure of collagen fibrils. Proc Natl Acad Sci 103:12285–90

    Article  Google Scholar 

  167. Buehler MJ (2008) Nanomechanics of collagen fibrils under varying cross-link densities: atomistic and continuum studies. J Mech Behav Biomed Mater 1:59–67

    Article  Google Scholar 

  168. Gautieri A, Vesentini S, Redaelli A et al (2011) Hierarchical structure and nanomechanics of collagen microfibrils from the atomistic scale up. Nano Lett 11:757–66

    Article  Google Scholar 

  169. Kim JS, Min J, Recknagel AK et al (2011) Quantitative three-dimensional analysis of embryonic chick morphogenesis via microcomputed tomography. Anat Rec 294:1–10

    Article  Google Scholar 

  170. Kazakia GJ, Lee JJ, Singh M et al (2007) Automated high-resolution three-dimensional fluorescence imaging of large biological specimens. J Microsc 225:109–17

    Article  Google Scholar 

  171. Bigley RF, Singh N, Hernandez CJ et al (2008) Validity of serial milling-based imaging system for microdamage quantification. Bone 42:212–15

    Article  Google Scholar 

  172. Odgaard A, Andersen K, Melsen F et al (1990) A direct method for fast three-dimensional serial reconstruction. J Microsc 159:335–42

    Article  Google Scholar 

  173. Ewald AJ, McBride H, Reddington M et al (2002) Surface imaging microscopy, an automated method for visualizing whole embryo samples in three dimensions at high resolution. Dev Dyn 225:369–75

    Article  Google Scholar 

  174. Boyde A, Lovicar L, Zamecnik J (2005) Combining confocal and BSE SEM imaging for bone block surfaces. Eur Cell Mater 26:33–8

    Google Scholar 

  175. Slyfield CR Jr, Niemeyer KE, Tkachenko EV et al (2009) Three-dimensional surface texture visualization of bone tissue through epifluorescence-based serial block face imaging. J Microsc 236:52–9

    Article  Google Scholar 

  176. Viceconti M (2012) Multiscale modelling of the skeletal system. Cambridge University Press, Cambridge

    Google Scholar 

  177. Fernandez JW, Shim VB, Hunter PJ (2012) Integrating degenerative mechanisms in bone and cartilage: a multiscale approach. In: Proceedings of IEEE Engineering in Medical and Biology Society 6616–6619.

    Google Scholar 

  178. Causin P, Sacco R, Verri M (2012) A multiscale approach in the computational modelling of the biophysical environment in artificial cartilage tissue regeneration., Biomech Model Mechanobiol, (epub ahead of print)

    Google Scholar 

  179. Sacco R, Causin P, Zunino P et al (2011) A multiphysics/multiscale 2D numerical simulation of scaffold-based cartilage regeneration under interstitial perfusion in a bioreactor. Biomech Model Mechanobiol 10:577–89

    Article  Google Scholar 

  180. Stops AJ, McMahon LA, O'Mahoney D et al (2008) A finite element prediction of strain on cells in a highly porous collagen-glycosaminoglycan scaffold. J Biomech Eng 130:061001–1

    Article  Google Scholar 

Download references

Acknowledgements

The author wishes to acknowledge Dr Victoria Toal, Dr Katrina McDonald and Dr Cameron Bell for providing images.

Author information

Authors and Affiliations

  1. School of Chemistry, Physics and Mechanical Engineering, Faculty of Science and Engineering, Queensland University of Technology, GPO Box 2434, 2 George St, Brisbane, Q4000, Australia

    Clayton J. Adam

Authors
  1. Clayton J. Adam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Clayton J. Adam .

Editor information

Editors and Affiliations

  1. School of Aerospace, Mechanical & Mechatronic Engineering, The University of Sydney, Sydney, New South Wales, Australia

    Qing Li

  2. School of Aerospace, Mechanical & Mechatronic Engineering, The University of Sydney, Sydney, New South Wales, Australia

    Yiu-Wing Mai

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer-Verlag GmbH Germany

About this chapter

Cite this chapter

Adam, C.J. (2017). Multiscale Modelling and Simulation of Musculoskeletal Tissues for Orthopaedics. In: Li, Q., Mai, YW. (eds) Biomaterials for Implants and Scaffolds. Springer Series in Biomaterials Science and Engineering, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53574-5_1

Download citation

Publish with us

Policies and ethics

Search

Navigation