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3D finite element simulation of human proximal femoral fracture under quasi-static load

  • Received : 2012.06.14
  • Accepted : 2013.02.13
  • Published : 2013.03.25
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Abstract

In this paper, a simple and accurate finite element model coupled to quasi-brittle damage law able to describe the multiple cracks initiation and their progressive propagation is developed in order to predict the complete force-displacement curve and the fracture pattern of human proximal femur under quasi-static load. The motivation of this work was to propose a simple and practical FE model with a good compromise between complexity and accuracy of the simulation considering a limited number of model parameters that can predict proximal femur fracture more accurately and physically than the fracture criteria based models. Different damage laws for cortical and trabecular bone are proposed based on experimental results to describe the inelastic damage accumulation under the excessive load. When the damage parameter reaches its critical value inside an element of the mesh, its stiffness matrix is set to zero leading to the redistribution of the stress state in the vicinity of the fractured zone (crack initiation). Once a crack is initiated, the propagation direction is simulated by the propagation of the broken elements of the mesh. To illustrate the potential of the proposed approach, the left femur of a male (age 61) previously investigated by Keyak and Falkinstein, 2003 (Model B: male, age 61) was simulated till complete fracture under one-legged stance quasi-static load. The proposed finite element model leads to more realistic and precise results concerning the shape of the force-displacement curve (yielding and fracturing) and the profile of the fractured edge.

Keywords

References

  1. Abdel-Wahab, A.A. and Silberschmidt, V.V. (2011), "Numerical modeling of impact fracture of cortical bone tissue using X-FEM", J. Theor. Appl. Mech., 49(3), 599-619.
  2. Baca, V., Horak, Z., Mikulenka, P. and Dzupa, V. (2008), "Comparison of an inhomogeneous orthotropic and isotropic material models used for FE analyses", Med. Eng. Phys., 30, 924-930. https://doi.org/10.1016/j.medengphy.2007.12.009
  3. Bayraktar, H.H., Morgan, E.F., Niebur G.L., Morris, G.E., Wong, E.K. and Keaveny, T.M. (2004), "Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue", J. Biomech., 37, 27-35. https://doi.org/10.1016/S0021-9290(03)00257-4
  4. Bessho, M., Ohnishi, I., Matsuyama, J., Matsumoto, T., Imai, K. and Nakamura, K. (2007), "Prediction of strength and strain of the proximal femur by a CT-based finite element method", J. Biomech., 40, 1745-1753. https://doi.org/10.1016/j.jbiomech.2006.08.003
  5. Burr, D.B. (1993), "Remodeling and the repair of fatigue damage", Calcified Tissue Int., 53(1), S75-S81. https://doi.org/10.1007/BF01321881
  6. Cody, D.D., Gross, G.J., Hou, F.J., Spencer, H.J., Goldstein, S.A. and Fyhrie, D. (1999), "Femoral strength is better predicted by finite element models than QCT and DXA", J. Biomech., 32, 1013-1020. https://doi.org/10.1016/S0021-9290(99)00099-8
  7. Currey, J.D. (1990), "Physical characteristics affecting the tensile failure properties of compact bone", J. Biomech., 23(8), 837-844. https://doi.org/10.1016/0021-9290(90)90030-7
  8. Currey, J.D. (2002), Bones: Structure and mechanics, Princeton University Press, Princeton.
  9. Chaboche, J.L. (1981), "Continuum damage mechanics a tool to describe phenomena before crack initiation", Nucl. Eng. Des., 64, 233-247. https://doi.org/10.1016/0029-5493(81)90007-8
  10. Crawford, R.P., Cann, C.E. and Keaveny, T.M. (2003), "Finite element models predict in vitro vertebral body compressive strength better than quantitative computed tomography", Bone, 33, 744-750. https://doi.org/10.1016/S8756-3282(03)00210-2
  11. Dragomir-Daescu, D., Op Den Buijs, J., McEeligot, S., Dai, Y., Entwistle, R.C., Salas, C., Melton, III J., Bennet, E., Khosla, S. and Amin, S. (2010), "Robust QCT/FEA models of proximal femur stiffness and fracture load during a sideways fall on the hip", Ann. Biomed. Eng., 39(2), 742-755.
  12. Ford, C.M., Keaveny, T.M. and Hayes, W.C. (1996), "The effect of impact direction on the structural capacity of the proximal femur during falls", J. Bone Miner. Res., 11, 377-383.
  13. Garden, R. (1961), "Low-angle fixation in fractures of the femoral neck", J. Bone Joint Surg. Br., 43, 647-661.
  14. Hambli, R., Bettamer, A. and Allaoui, S. (2012), "Finite element prediction of proximal femur fracture pattern based on orthotropic behaviour law coupled to quasi-brittle damage", Med. Eng. Phys., 34(2), 202-210. https://doi.org/10.1016/j.medengphy.2011.07.011
  15. Hambli, R. (2011a), "Multiscale prediction of crack density and crack length accumulation in trabecular bone based on neural networks and finite element simulation", Int. J. Numer. Method. Biomed. Eng., 27(4), 461-475. https://doi.org/10.1002/cnm.1413
  16. Hambli, R. (2011b), "Apparent damage accumulation in cancellous bone using neural networks", J. Mech. Behav. Biomed. Mater., 4(6),868-878. https://doi.org/10.1016/j.jmbbm.2011.03.002
  17. Juszczyk, M.M., Cristofolini, L. and Viceconti, M. (2011), "The human proximal femur behaves linearly elastic up to failure under physiological loading conditions", J. Biomech., 44(12), 2259-2266. https://doi.org/10.1016/j.jbiomech.2011.05.038
  18. Kaneko, T.S., Pejcic, M.R., Tehranzadeh, J. and Keyak, J.H. (2003), "Relationships between material properties and CT scan data of cortical bone with and without metastatic lesions", Med. Eng. Phys., 25(6), 445-454. https://doi.org/10.1016/S1350-4533(03)00030-4
  19. Kotha, S.P. and Guzelsu, N. (2003), "Tensile damage and its effects on cortical bone", J. Biomech., 36(11), 1683-1689. https://doi.org/10.1016/S0021-9290(03)00169-6
  20. Keaveny, T.M., Wachtel, E.F., Ford, C.M. and Hayes, W.C. (1994), "Differences between the tensile and compressive strengths of bovine tibial trabecular bone depend on modulus", J. Biomech., 27, 1137-1146. https://doi.org/10.1016/0021-9290(94)90054-X
  21. Keaveny, T.M., Wachtel, E.F. and Kopperdahl, D.L. (1999), "Mechanical behavior of human trabecular bone after overloading", J. Orthopaed. Res., 17, 346-353. https://doi.org/10.1002/jor.1100170308
  22. Keaveny, T.M., Morgan, E.F., Niebur, G.L. and Yeh, O.C. (2001), "Biomechanics of trabecular bone", Ann. Biomed. Eng., 3, 307-333. https://doi.org/10.1146/annurev.bioeng.3.1.307
  23. Keyak, J.H. (2001), "Improved prediction of proximal femoral fracture load using nonlinear finite element models", Med. Eng. Phys., 23, 165-173. https://doi.org/10.1016/S1350-4533(01)00045-5
  24. Keyak, J.H. and Falkinstein, Y. (2003), "Comparison of in situ and in vitro CT scan-based finite element model predictions of proximal femoral fracture load", Med. Eng. Phys., 25, 781-787. https://doi.org/10.1016/S1350-4533(03)00081-X
  25. Link, M., Vieth, V., Langenberg, R., Meier, N., Lotter, A., Newitt, D. and Majumdar, S. (2003), "Structure analysis of high resolution magnetic resonance imaging of the proximal femur: in vitro correlation with biomechanical strength and BMD", Calcified Tissue Int., 72,156-165. https://doi.org/10.1007/s00223-001-2132-5
  26. Lemaitre, J. (1985), "A continuous damage mechanics model for ductile fracture", J. Eng. Mater. Technol., 107, 83-89. https://doi.org/10.1115/1.3225775
  27. Lotz, J.C, Cheal, E.J. and Hayes, W.C. (1991a), "Fracture prediction for the proximal femur using finite element models: Part I - Linear analysis", J. Biomech. Eng., 113, 353-360. https://doi.org/10.1115/1.2895412
  28. Lotz, J.C., Cheal, E.J. and Hayes, W.C. (1991b), "Fracture prediction for the proximal femur using finite element models: Part II - Nonlinear analysis", J. Biomech. Eng., 113, 361-365. https://doi.org/10.1115/1.2895413
  29. Lotz, J.C., Cheal, E.J. and Hayes, W.C. (1995), "Stress distributions within the proximal femur during gait and falls: implications for osteoporotic fracture", Osteopor Int., 5, 252-261. https://doi.org/10.1007/BF01774015
  30. Malik, L., Stover, M., Martin, B. and Gibeling, C. (2003), "Equine cortical bone exhibits rising R-curve fracture mechanics", J. Biomech., 36, 191-198. https://doi.org/10.1016/S0021-9290(02)00362-7
  31. Mazars, J. and Pijaudier-Cabot, G. (1996), "From damage to fracture mechanics and conversely: A combined approach", Int. J. Solid Struct., 33, 3327-3342. https://doi.org/10.1016/0020-7683(96)00015-7
  32. Nagaraja, S., Couse, T.L. and Guldberg, R.E. (2005), "Trabecular bone microdamage and microstructural stresses under uniaxial compression", J. Biomech., 38, 707-716. https://doi.org/10.1016/j.jbiomech.2004.05.013
  33. Nalla, K., Kruzic, J., Kinney, H. and Ritchie, O. (2005), "Mechanistic aspects of fracture and R-curve behavior in human cortical bone", Biomater., 26, 217-231. https://doi.org/10.1016/j.biomaterials.2004.02.017
  34. Ota, T., Yamamoto, I. and Morita, R. (1999), "Fracture simulation of femoral bone using finite-element method: How a fracture initiates and proceeds", J. Bone Miner. Metab., 17(2), 108-112. https://doi.org/10.1007/s007740050072
  35. Pattin, C.A., Caler, W.E. and Carter, D.R. (1996), "Cyclic mechanical property degradation during fatigue loading of cortical bone", J. Biomech., 29, 69-79. https://doi.org/10.1016/0021-9290(94)00156-1
  36. Parsamian, G.P. (2002), Damage mechanics of human cortical bone: Phd, College of Engineering and Mineral Resources at West Virginia University.
  37. Peng, L., Bai, J., Zeng, X. and Zhou, Y. (2006), "Comparison of isotropic and orthotropic material property assignments on femoral finite element models under two loading conditions", Med. Eng. Phys., 28, 227-233. https://doi.org/10.1016/j.medengphy.2005.06.003
  38. Reilly, D.T. and Burstein, A.H. (1974), "Review article. The mechanical properties of cortical bone", J. Bone Jt. Surg. Am., 56, 1001-1022. https://doi.org/10.2106/00004623-197456050-00012
  39. Reilly, D.T. and Burstein, A.H. (1975), "The elastic and ultimate properties of compact bone tissue", J. Biomech., 8, 393-405. https://doi.org/10.1016/0021-9290(75)90075-5
  40. San Antonio, T., Ciaccia, M., Müller-Karger, C. and Casanova, E. (2012), "Orientation of orthotropic material properties in a femur FE model: A method based on the principal stresses directions", Med. Eng. Phys., 34(7), 914-919. https://doi.org/10.1016/j.medengphy.2011.10.008
  41. Schileo, E., Taddei, F., Cristofolini, L. and Viceconti, M. (2008), "Subject-specific finite element models implementing a maximum principal strain criterion are able to estimate failure risk and fracture location on human femurs tested in vitro", J. Biomech., 41(2), 356-367. https://doi.org/10.1016/j.jbiomech.2007.09.009
  42. Taylor, D. and Lee, T.C. (2003), "A crack growth model for the simulation of fatigue in bone", Int. J. Fatigue, 2, 387-395.
  43. Taddei, F., Cristofolini, L., Martelli, S., Gill, H. and Viceconti, M. (2006), "Subject-specific finite element models of long bones: an in vitro evaluation of the overall accuracy", J. Biomech., 39, 2457-2467. https://doi.org/10.1016/j.jbiomech.2005.07.018
  44. Tellache, M., Pithioux, M., Chabrand, P. and Hochard, C. (2009), "Femoral neck fracture prediction by anisotropic yield criteria", Eur. J. Comput. Mech., 1, 33-41.
  45. Ural, A. and Vashishth, D. (2007), "Anisotropy of age-related toughness loss in human cortical bone: A finite element study", J. Biomech., 40, 1606-1614. https://doi.org/10.1016/j.jbiomech.2006.07.023
  46. Vashishth, D., Tanner, E. and Bonfield, W. (2003), "Experimental validation of a microcracking-based toughening mechanism for cortical bone", J. Biomech., 36(1), 121-124. https://doi.org/10.1016/S0021-9290(02)00319-6
  47. Vashishth, D., Behiri, J.C. and Bonfield, W. (1997), "Crack growth resistance in cortical bone: Concept of microcrack toughening", J. Biomech., 30(8), 763-769. https://doi.org/10.1016/S0021-9290(97)00029-8
  48. Verhulp, E., van Rietbergen, B. and Huiskes, R. (2006), "Comparison of micro-level and continuum level voxel models of the proximal femur", J. Biomech. 39, 2951-2957. https://doi.org/10.1016/j.jbiomech.2005.10.027
  49. Wang, X., Zauel, R. and Fyhrie, D.P. (2008a), "Postfailure modulus strongly affects microcracking and mechanical property change in human iliac cancellous bone: A study using a 2D nonlinear finite element method", J. Biomech., 41, 2654- 2658. https://doi.org/10.1016/j.jbiomech.2008.06.011
  50. Wang, X., Zauel, R., Sudhaker Rao, D. and Fyhrie, D.P. (2008b), "Cancellous bone lamellae strongly affect microcrack propagation and apparent mechanical properties: Separation of patients with osteoporotic fracture from normal controls using a 2D nonlinear finite element method (biomechanical)", Bone, 42(6), 1184-1192. https://doi.org/10.1016/j.bone.2008.01.022
  51. Wolfram, U., Wilke, H.J. and Zysset, P.K. (2011), "Damage accumulation in vertebral trabecular bone depends on loading mode and direction", J. Biomech., 44(6),1164-1169. https://doi.org/10.1016/j.jbiomech.2011.01.018
  52. Yang, D., Cox, N., Nalla, K. and Ritchie, O. (2006), "Re-evaluating the toughness of human cortical bone", Bone, 38, 878-887. https://doi.org/10.1016/j.bone.2005.10.014
  53. Yang, H., Shen, L., Demetropoulos, K., King, I., Kolodziej, P., Levine, S. and Fitzgerald, J. (1996), "The relationship between loading conditions and fracture patterns of the proximal femur", J. Biomech. Eng., 118, 575-578. https://doi.org/10.1115/1.2796045
  54. Yosibash, Z., Tal, D. and Trabelsi, N. (2010), "Inhomogeneous orthotropic material properties high-order finite-element analysis with inhomogeneous orthotropic material properties", Phil. Trans. R. Soc. A, 368, 2707-2723. https://doi.org/10.1098/rsta.2010.0074
  55. Zioupos, P., Tong Wang, X. and Currey, J.D. (1996), "Experimental and theoretical quantification of the development of damage in fatigue tests of bone and antler", J. Biomech., 29(8), 989-1002. https://doi.org/10.1016/0021-9290(96)00001-2

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