Skip to main content

Advertisement

Log in

Recent Advance in Evaluation Methods for Characterizing Mechanical Properties of Bone

  • Original Paper
  • Published:
Archives of Computational Methods in Engineering Aims and scope Submit manuscript

Abstract

Skeletal biomechanics focuses on both transient and long-term effects of bone stress, using the basic theory and method of material mechanics, elasto-plasticity theory, and fracture mechanics,is considered to be one of the most important branches in biomechanics. In order to achieve complete and comprehensive evaluation of skeletal biomechanics, researchers developed a variety of levels of skeletal biomechanical evaluation methods, including mechanical testing, theoretical research, microstructure research and finite element analyses. At present, most of the mechanical evaluation methods were performed by a combination of mechanical tests and finite element (FE) simulation studies for the evaluation of mechanical properties. This study summerized the research in multi-level mechanical test methods, different research methods of microstructure, and the reconstruction of various FE skeletal models to study bone mechanics. The mentioned methods and techniques can be served as the basis for systematic studies of the biomechanical properties of bones.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Xiaogang Z, Daping Q, Min S, Yiwei J (2012) Application and research progress of bone biomechanical. China J Osteoporos 18:850–860

    Google Scholar 

  2. Cao ZCZ, Zhu DZD, Sun DSD, Zhang XZX (2010) A finite element analysis of mechanics about the long head of biceps brachii tendon. In: 2010 3rd international conference biomed eng informatics (BMEI), vol 3, pp 1098–1101. https://doi.org/10.1109/bmei.2010.5639620

  3. Johnstone B, Alini M, Cucchiarini M et al (2013) Tissue engineering for articular cartilage repair—the state of the art. Eur Cells Mater 25:248–267. https://doi.org/10.22203/eCM.v025a18

    Article  Google Scholar 

  4. Newell N, Little JP, Christou A et al (2017) Biomechanics of the human intervertebral disc: a review of testing techniques and results. J Mech Behav Biomed Mater 69:420–434. https://doi.org/10.1016/j.jmbbm.2017.01.037

    Article  Google Scholar 

  5. Claes L, Recknagel S, Ignatius A (2012) Fracture healing under healthy and inflammatory conditions. Nat Rev Rheumatol 8:133–143. https://doi.org/10.1038/nrrheum.2012.1

    Article  Google Scholar 

  6. Brainerd EL, Baier DB, Gatesy SM et al (2010) X-ray reconstruction of moving morphology (XROMM): precision, accuracy and applications in comparative biomechanics research. J Exp Zool Part A Ecol Genet Physiol. https://doi.org/10.1002/jez.589

    Article  Google Scholar 

  7. Chirchir H, Kivell TL, Ruff CB et al (2015) Recent origin of low trabecular bone density in modern humans. Proc Natl Acad Sci 112:366–371. https://doi.org/10.1073/pnas.1411696112

    Article  Google Scholar 

  8. Gailey R (2008) Review of secondary physical conditions associated with lower-limb amputation and long-term prosthesis use. J Rehabil Res Dev 45:15–30. https://doi.org/10.1682/JRRD.2006.11.0147

    Article  Google Scholar 

  9. Ryan TM, Shaw CN (2015) Gracility of the modern Homo sapiens skeleton is the result of decreased biomechanical loading. Proc Natl Acad Sci 112:372–377. https://doi.org/10.1073/pnas.1418646112

    Article  Google Scholar 

  10. Weber JF, Waldman SD (2016) In situ and ex vivo biomechanical testing of articular cartilage. Elsevier Inc, Amsterdam

    Google Scholar 

  11. Weißmann V, Bader R, Hansmann H, Laufer N (2016) Influence of the structural orientation on the mechanical properties of selective laser melted Ti6Al4 V open-porous scaffolds. Mater Des 95:188–197. https://doi.org/10.1016/j.matdes.2016.01.095

    Article  Google Scholar 

  12. Lopes VMM, Neto MA, Amaro AM et al (2017) FE and experimental study on how the cortex material properties of synthetic femurs affect strain levels. Med Eng Phys 46:96–109. https://doi.org/10.1016/j.medengphy.2017.06.001

    Article  Google Scholar 

  13. Tchanque-Fossuo CN, Donneys A, Deshpande SS et al (2018) Radioprotection with amifostine enhances bone strength and regeneration and bony union in a rat model of mandibular distraction osteogenesis. Ann Plast Surg 80:176–180. https://doi.org/10.1097/SAP.0000000000001209

    Article  Google Scholar 

  14. Huang J, Liu W, Zhou F, Peng Y (2018) Effect of multiscale structural parameters on the mechanical properties of rice stems. J Mech Behav Biomed Mater. https://doi.org/10.1016/j.jmbbm.2018.03.040

    Article  Google Scholar 

  15. Ma JX, He WW, Zhao J et al (2017) Bone microarchitecture and biomechanics of the necrotic femoral head. Sci Rep 7:1–10. https://doi.org/10.1038/s41598-017-13643-2

    Article  Google Scholar 

  16. Yeh SCA, Wilk K, Lin CP, Intini G (2018) In vivo 3D histomorphometry quantifies bone apposition and skeletal progenitor cell differentiation. Sci Rep 8:2–11. https://doi.org/10.1038/s41598-018-23785-6

    Article  Google Scholar 

  17. Xinlong M, Jianxiong M, Weiguo X et al (2014) Expert consensus about the methodology of bone biomechanical measurement. Chin J Osteoporos 20:1039–1054. https://doi.org/10.3969/j.issn.1006-7108.2014.09.004

    Article  Google Scholar 

  18. Yuan H, Xiao L, Min W et al (2018) Bu-Shen-Tong-Luo decoction prevents bone loss via inhibition of bone resorption and enhancement of angiogenesis in ovariectomy-induced osteoporosis of rats. J Ethnopharmacol. https://doi.org/10.1016/j.jep.2018.01.007

    Article  Google Scholar 

  19. Ramezanzadehkoldeh M, Skallerud BH (2017) MicroCT-based finite element models as a tool for virtual testing of cortical bone. Med Eng Phys 46:12–20. https://doi.org/10.1016/j.medengphy.2017.04.011

    Article  Google Scholar 

  20. Muszyński S, Kwiecień M, Tomaszewska E et al (2017) Effect of caponization on performance and quality characteristics of long bones in Polbar chickens. Poult Sci 96:491–500. https://doi.org/10.3382/ps/pew301

    Article  Google Scholar 

  21. Pengzhen C, Fenru N, Dan L (2016) Effects of different preservation methods on mechanical prop erties of mouse femur. J Biomed Eng 33:1133–1138. https://doi.org/10.7507/1001-5515.20160180

    Article  Google Scholar 

  22. Xiao W, Zaeem MA, Li G et al (2017) Tough and strong porous bioactive glass-PLA composites for structural bone repair. J Mater Sci 52:9039–9054. https://doi.org/10.1007/s10853-017-0777-3

    Article  Google Scholar 

  23. Cheong VS, Karunaratne A, Amis AA, Bull AMJ (2017) Strain rate dependency of fractures of immature bone. J Mech Behav Biomed Mater 66:68–76. https://doi.org/10.1016/j.jmbbm.2016.10.023

    Article  Google Scholar 

  24. Vargas G, Mujika F (2017) Greenstick fracture in composite pultruded rods. Compos Part B Eng 110:106–115. https://doi.org/10.1016/j.compositesb.2016.11.001

    Article  Google Scholar 

  25. Narsaria N, Singh AK, Rastogi A, Singh V (2014) Biomechanical analysis of distal femoral fracture fixation: dynamic condylar screw versus locked compression plate. J Orthop Sci 19:770–775. https://doi.org/10.1007/s00776-014-0583-6

    Article  Google Scholar 

  26. Lenz M, Stoffel K, Kielstein H et al (2016) Plate fixation in periprosthetic femur fractures Vancouver type B1—trochanteric hook plate or subtrochanterical bicortical locking? Injury 47:2800–2804. https://doi.org/10.1016/j.injury.2016.09.037

    Article  Google Scholar 

  27. Zhang ZM, Li ZC, Jiang LS et al (2010) Micro-CT and mechanical evaluation of subchondral trabecular bone structure between postmenopausal women with osteoarthritis and osteoporosis. Osteoporos Int 21:1383–1390. https://doi.org/10.1007/s00198-009-1071-2

    Article  Google Scholar 

  28. Podshivalov L, Fischer A, Bar-Yoseph PZ (2014) On the road to personalized medicine: multiscale computational modeling of bone tissue. Arch Comput Methods Eng 21(4):399–479

    Article  Google Scholar 

  29. Pharr GM, Oliver WC (1992) Measurement of thin film mechanical properties using nanoindentation. MRS Bull 17:28–33. https://doi.org/10.1557/S0883769400041634

    Article  Google Scholar 

  30. Baker MI, Eberhardt AW, Martin DM et al (2010) Bone properties surrounding hydroxyapatite-coated custom osseous integrated dental implants. J Biomed Mater Res Part B Appl Biomater 95:218–224. https://doi.org/10.1002/jbm.b.31693

    Article  Google Scholar 

  31. Seong WJ, Kim UK, Swift JQ et al (2009) Elastic properties and apparent density of human edentulous maxilla and mandible. Int J Oral Maxillofac Surg 38:1088–1093. https://doi.org/10.1016/j.ijom.2009.06.025

    Article  Google Scholar 

  32. Yoon HI, Jeon MJ, Kim HL et al (2018) Spatial variation of bone biomechanical properties around a dental implant using nanoindentation: a case study. J Mech Behav Biomed Mater 79:168–172. https://doi.org/10.1016/j.jmbbm.2017.12.027

    Article  Google Scholar 

  33. 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 85:335–343. https://doi.org/10.1007/s00223-009-9289-8

    Article  Google Scholar 

  34. Springall GAC, Yin L (2018) Nano-scale mechanical behavior of pre-crystallized CAD/CAM zirconia-reinforced lithium silicate glass ceramic. J Mech Behav Biomed Mater 82:35–44. https://doi.org/10.1016/j.jmbbm.2018.03.010

    Article  Google Scholar 

  35. Can Z, Ru-chun D (2011) Nanoindentation technology in bone tissue micro-or nano-structure research applications oliver-pharr cube-corner. Chin J Med Phys 28:3052–3054. https://doi.org/10.3969/j.issn.1005-202X.2011.06.025

    Article  Google Scholar 

  36. Haidekker MA, Andresen R, Evertsz CJG et al (1997) Evaluation of the cortical structure in high resolution CT images of lumbar vertebrae by analysing low bone mineral density clusters and cortical profiles. Br J Radiol 70:1222–1228. https://doi.org/10.1259/bjr.70.840.9505840

    Article  Google Scholar 

  37. Sarkalkan N, Waarsing JH, Bos PK et al (2014) Statistical shape and appearance models for fast and automated estimation of proximal femur fracture load using 2D finite element models. J Biomech 47:3107–3114. https://doi.org/10.1016/j.jbiomech.2014.06.027

    Article  Google Scholar 

  38. Wegrzyn J, Roux JP, Arlot ME et al (2010) Role of trabecular microarchitecture and its heterogeneity parameters in the mechanical behavior of ex vivo human L3 vertebrae. J Bone Miner Res 25:2324–2331. https://doi.org/10.1002/jbmr.164

    Article  Google Scholar 

  39. Wear KA, Nagaraja S, Dreher ML et al (2017) Relationships among ultrasonic and mechanical properties of cancellous bone in human calcaneus in vitro. Bone 103:93–101. https://doi.org/10.1016/j.bone.2017.06.021

    Article  Google Scholar 

  40. Ben Kahla R, Barkaoui A, Merzouki T (2018) Age-related mechanical strength evolution of trabecular bone under fatigue damage for both genders: fracture risk evaluation. J Mech Behav Biomed Mater 84:64–73. https://doi.org/10.1016/j.jmbbm.2018.05.006

    Article  Google Scholar 

  41. Vidal B, Pinto A, Galvão MJ et al (2012) Bone histomorphometry revisited. Acta Reumatol Port 37:294–300. https://doi.org/10.1177/002215549704500215

    Article  Google Scholar 

  42. Peng J, Lai ZG, Fang ZL et al (2014) Dimethyloxalylglycine prevents bone loss in ovariectomized C57BL/6J mice through enhanced angiogenesis and osteogenesis. PLoS ONE 9:1–12. https://doi.org/10.1371/journal.pone.0112744

    Article  Google Scholar 

  43. Saalfeld S, Fetter R, Cardona A, Tomancak P (2012) Elastic volume reconstruction from series of ultra-thin microscopy sections. Nat Methods 9:717–720. https://doi.org/10.1038/nmeth.2072

    Article  Google Scholar 

  44. Muller R, Van Campenhout H, Van Damme B et al (1998) Morphometric analysis of human bone biopsies: a quantitative structural comparison of histological sections and micro-computed tomography. Bone 23:59–66. https://doi.org/10.1016/S8756-3282(98)00068-4

    Article  Google Scholar 

  45. Majumdar S, Kothari M, Augat P et al (1998) High-resolution magnetic resonance imaging: three-dimensional trabecular bone architecture and biomechanical properties. Bone 22:445–454. https://doi.org/10.1016/S8756-3282(98)00030-1

    Article  Google Scholar 

  46. Ueo T, Tsutsumi S, Yamamuro T et al (1985) Biomechanical aspects of the development of aseptic necrosis of the femoral head. Arch Orthop Trauma Surg 104:145–149

    Article  Google Scholar 

  47. Hao Z (2011) The effect of boundary condition on the biomechanics of a human pelvic joint under an axial compressive load: a three-dimensional finite element model. J Biomech Eng 133:101006. https://doi.org/10.1115/1.4005223

    Article  Google Scholar 

  48. Jaecques SVN, Van Oosterwyck H, Muraru L et al (2004) Individualised, micro CT-based finite element modelling as a tool for biomechanical analysis related to tissue engineering of bone. Biomaterials 25:1683–1696. https://doi.org/10.1016/S0142-9612(03)00516-7

    Article  Google Scholar 

  49. Lacroix D, Planell JA, Prendergast PJ (2009) Computer-aided design and finite-element modelling of biomaterial scaffolds for bone tissue engineering. Philos Trans R Soc A Math Phys Eng Sci 367:1993–2009. https://doi.org/10.1098/rsta.2009.0024

    Article  MATH  Google Scholar 

  50. Xiao W, Zaeem MA, Bal BS, Rahaman MN (2016) Creation of bioactive glass (13–93) scaffolds for structural bone repair using a combined finite element modeling and rapid prototyping approach. Mater Sci Eng, C 68:651–662. https://doi.org/10.1016/j.msec.2016.06.011

    Article  Google Scholar 

  51. Delye H, Clijmans T, Mommaerts MY et al (2015) Creating a normative database of age-specific 3D geometrical data, bone density, and bone thickness of the developing skull: a pilot study. J Neurosurg Pediatr 16:687–702. https://doi.org/10.3171/2015.4.PEDS1493

    Article  Google Scholar 

  52. Hage IS, Hamade RF (2013) Micro-FEM orthogonal cutting model for bone using microscope images enhanced via artificial intelligence. Procedia CIRP 8:385–390. https://doi.org/10.1016/j.procir.2013.06.121

    Article  Google Scholar 

  53. Mauldin FW, Owen K, Hossack JA (2011) Three-dimensional spinal bone imaging with medical ultrasound for epidural anesthesia guidance. In: IEEE international ultrasonics symposium (IUS), pp 238–241. https://doi.org/10.1109/ultsym.2011.0058

  54. Bingzhi C (2008) Bone remodeling numerical simulation on the basis of bone adaptive theory. J Biomed Eng 25:364–367

    Google Scholar 

  55. Sheng-wei HE, Bing-zhi C, Rui-xian QIN et al (2018) Effects of percutaneous vertebroplasty on biomechanics of patients with osteoporotic thoracolumbar fractures. Prog Mod Biomed 18:705–709. https://doi.org/10.13241/j.cnki.pmb.2018.04.022

    Article  Google Scholar 

  56. Luo Y, Ferdous Z, Leslie William D (2013) Precision study of DXA-based patient-specific finite element modeling for assessing hip fracture risk. Int J Numer Method Biomed Eng 29:615–629. https://doi.org/10.1002/cnm.2548

    Article  MathSciNet  Google Scholar 

  57. Op Den Buijs J, Dragomir-Daescu D (2011) Validated finite element models of the proximal femur using two-dimensional projected geometry and bone density. Comput Methods Programs Biomed 104:168–174. https://doi.org/10.1016/j.cmpb.2010.11.008

    Article  Google Scholar 

  58. Quevedo González FJ, Reimeringer M, Nuño N (2017) On the two-dimensional simplification of three-dimensional cementless hip stem numerical models. J Biomech Eng 139:031011. https://doi.org/10.1115/1.4035368

    Article  Google Scholar 

  59. Grassi L, Väänänen SP, Ristinmaa M et al (2017) Prediction of femoral strength using 3D finite element models reconstructed from DXA images: validation against experiments. Biomech Model Mechanobiol 16:989–1000. https://doi.org/10.1007/s10237-016-0866-2

    Article  Google Scholar 

  60. Heimann T, Meinzer HP (2009) Statistical shape models for 3D medical image segmentation: a review. Med Image Anal 13:543–563. https://doi.org/10.1016/j.media.2009.05.004

    Article  Google Scholar 

  61. Calì M, Zanetti EM, Oliveri SM et al (2018) Influence of thread shape and inclination on the biomechanical behaviour of plateau implant systems. Dent Mater 34:460–469. https://doi.org/10.1016/j.dental.2018.01.012

    Article  Google Scholar 

  62. Gok K, Inal S, Gok A, Gulbandilar E (2017) Comparison of effects of different screw materials in the triangle fixation of femoral neck fractures. J Mater Sci Mater Med. https://doi.org/10.1007/s10856-017-5890-y

    Article  Google Scholar 

  63. Dong F, Anmin J (2007) Reconstructing a finite element model of human skeleton using ct images. J Clin Rehabil Tissue Eng Res 11:1620–1623

    Google Scholar 

  64. An-an L, Qian L, Hui G (2006) High quality 3D skeketon system modeling of virtual Chinese Human male No.1. Chin J Clin Anat 24:292–294

    Google Scholar 

  65. Ping GW, Xinmin Y, Fengmin W (2005) Set-up of three-dimensional solid and finite element model of teeth and dental arch with images of Chinese visible human. J Stomatol 25:1–2. https://doi.org/10.13591/j.cnki.kqyx.2005.01.002

    Article  Google Scholar 

  66. Soodmand E, Kluess D, Varady PA et al (2018) Interlaboratory comparison of femur surface reconstruction from CT data compared to reference optical 3D scan. Biomed Eng Online 17:1–10. https://doi.org/10.1186/s12938-018-0461-0

    Article  Google Scholar 

  67. Väänänen SP, Grassi L, Flivik G et al (2015) Generation of 3D shape, density, cortical thickness and finite element mesh of proximal femur from a DXA image. Med Image Anal 24:125–134. https://doi.org/10.1016/j.media.2015.06.001

    Article  Google Scholar 

  68. Langton CM, Pisharody S, Keyak JH (2009) Generation of a 3D proximal femur shape from a single projection 2D radiographic image. Osteoporos Int 20:455–461. https://doi.org/10.1007/s00198-008-0665-4

    Article  Google Scholar 

  69. Thevenot J, Koivumäki J, Kuhn V et al (2014) A novel methodology for generating 3D finite element models of the hip from 2D radiographs. J Biomech 47:438–444. https://doi.org/10.1016/j.jbiomech.2013.11.004

    Article  Google Scholar 

  70. Whitmarsh T, Humbert L, De Craene M et al (2011) Reconstructing the 3D shape and bone mineral density distribution of the proximal femur from dual-energy x-ray absorptiometry. IEEE Trans Med Imaging 30:2101–2114. https://doi.org/10.1109/TMI.2011.2163074

    Article  Google Scholar 

  71. Falcinelli C, Schileo E, Pakdel A et al (2016) Can CT image deblurring improve finite element predictions at the proximal femur? J Mech Behav Biomed Mater 63:337–351. https://doi.org/10.1016/j.jmbbm.2016.07.004

    Article  Google Scholar 

  72. Ni J, Li D, Mao M et al (2018) A method of accurate bone tunnel placement for anterior cruciate ligament reconstruction based on 3-dimensional printing technology: a cadaveric study. Arthrosc J Arthrosc Relat Surg 34:546–556. https://doi.org/10.1016/j.arthro.2017.08.288

    Article  Google Scholar 

  73. Sreenivasan D, Tu PT, Dickinson M et al (2016) Computer modelling integrated with micro-CT and material testing provides additional insight to evaluate bone treatments: application to a beta-glycan derived whey protein mice model. Comput Biol Med 68:9–20. https://doi.org/10.1016/j.compbiomed.2015.10.017

    Article  Google Scholar 

  74. Wang J, Zhou B, Liu XS et al (2015) Trabecular plates and rods determine elastic modulus and yield strength of human trabecular bone. Bone 72:71–80. https://doi.org/10.1016/j.bone.2014.11.006

    Article  Google Scholar 

  75. Zhou B, Wang J, Yu YE et al (2016) High-resolution peripheral quantitative computed tomography (HR-pQCT) can assess microstructural and biomechanical properties of both human distal radius and tibia: ex vivo computational and experimental validations. Bone 86:58–67. https://doi.org/10.1016/j.bone.2016.02.016

    Article  Google Scholar 

  76. Giovannelli L, Ródenas JJ, Navarro-Jiménez JM, Tur M (2017) Direct medical image-based finite element modelling for patient-specific simulation of future implants. Finite Elem Anal Des 136:37–57. https://doi.org/10.1016/j.finel.2017.07.010

    Article  Google Scholar 

  77. Grassi L, Schileo E, Boichon C et al (2014) Comprehensive evaluation of PCA-based finite element modelling of the human femur. Med Eng Phys 36:1246–1252

    Article  Google Scholar 

  78. Grassi L, Väänänen SP, Amin Yavari S et al (2014) Full-field strain measurement during mechanical testing of the human femur at physiologically relevant strain rates. J Biomech Eng 136:111010–111011. https://doi.org/10.1115/1.4028415

    Article  Google Scholar 

  79. Grassi L, Väänänen SP, Ristinmaa M et al (2016) How accurately can subject-specific finite element models predict strains and strength of human femora? Investigation using full-field measurements. J Biomech 49:802–806. https://doi.org/10.1016/j.jbiomech.2016.02.032

    Article  Google Scholar 

  80. Matsunaga S, Takano N, Tamatsu Y et al (2011) Biomechanics of jaw bone considering structural properties of trabecular bone. J Oral Biosci 53:143–147. https://doi.org/10.1016/S1349-0079(11)80017-4

    Article  Google Scholar 

  81. Wen Z, Lan W, Qin S et al (2014) Finite element analysis on lumbar interbody fusion treatment. J Med Biomech 29:405–410. https://doi.org/10.16156/j.1004-7220.2014.05.006

    Article  Google Scholar 

  82. Pakdel A, Mainprize JG, Robert N et al (2014) Model-based PSF and MTF estimation and validation from skeletal clinical CT images. Med Phys. https://doi.org/10.1118/1.4835515

    Article  Google Scholar 

  83. Roca X, Sarrate J (2013) Least-squares approximation of affine mappings for sweep mesh generation: functional analysis and applications. Eng Comput 29:1–15. https://doi.org/10.1007/s00366-012-0260-3

    Article  Google Scholar 

  84. Legrain G, Chevaugeon N, Dréau K (2012) High order X-FEM and levelsets for complex microstructures: uncoupling geometry and approximation. Comput Methods Appl Mech Eng 241–244:172–189. https://doi.org/10.1016/j.cma.2012.06.001

    Article  MathSciNet  MATH  Google Scholar 

  85. Ooi ET, Yang ZJ (2011) Modelling dynamic crack propagation using the scaled boundary finite element method. Int J Numer Methods Eng 88:329–349. https://doi.org/10.1002/nme.3177

    Article  MathSciNet  MATH  Google Scholar 

  86. Saputra A, Talebi H, Tran D et al (2016) Automatic image-based stress analysis by the scaled boundary finite element method. Int J Numer Methods Eng. https://doi.org/10.1002/nme.5304

    Article  Google Scholar 

  87. Schillinger D, Düster A, Rank E (2012) The hp-d-adaptive finite cell method for geometrically nonlinear problems of solid mechanics. Int J Numer Methods Eng 89:1171–1202. https://doi.org/10.1002/nme.3289

    Article  MathSciNet  MATH  Google Scholar 

  88. Watson PJ, Dostanpor A, Fagan MJ, Dobson CA (2017) The effect of boundary constraints on finite element modelling of the human pelvis. Med Eng Phys 43:48–57. https://doi.org/10.1016/j.medengphy.2017.02.001

    Article  Google Scholar 

  89. Haider IT, Speirs AD, Frei H (2013) Effect of boundary conditions, impact loading and hydraulic stiffening on femoral fracture strength. J Biomech 46:2115–2121. https://doi.org/10.1016/j.jbiomech.2013.07.004

    Article  Google Scholar 

  90. Schillinger D, Rank E (2011) An unfitted hp-adaptive finite element method based on hierarchical B-splines for interface problems of complex geometry. Comput Methods Appl Mech Eng 200:3358–3380. https://doi.org/10.1016/j.cma.2011.08.002

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by Major Research & Development Program of Shandong Province (No. 2015GGX103022), Program of Science and Technology Development of Jinan (201401227) and Shandong Provincial Natural Science Foundation, China (No. ZR2016HM02).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yanbin Shi.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kong, D., Shi, Y., Lin, G. et al. Recent Advance in Evaluation Methods for Characterizing Mechanical Properties of Bone. Arch Computat Methods Eng 27, 711–723 (2020). https://doi.org/10.1007/s11831-019-09322-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11831-019-09322-2

Navigation