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Femoral Fracture load and damage localization pattern prediction based on a quasi-brittle law

  • Nakhli, Zahira (Laboratoire de Recherche Materiaux Mesures et Application (MMA), LR11ES25, National Institute of Sciences and Technology (INSAT)) ;
  • Ben Hatira, Fafa (Laboratoire de Recherche Materiaux Mesures et Application (MMA), LR11ES25, National Institute of Sciences and Technology (INSAT)) ;
  • Pithioux, Martine (Aix Marseille University, UMR CNRS 7287, (ISM) Institute of Movement Sciences) ;
  • Chabrand, Patrick (Aix Marseille University, UMR CNRS 7287, (ISM) Institute of Movement Sciences) ;
  • Saanouni, Khemais (Laboratoire des Systemes Mecaniques et d'Ingenierie Simultanee Institut Charles Delaunay)
  • Received : 2018.07.24
  • Accepted : 2019.05.29
  • Published : 2019.10.25

Abstract

Finite element analysis is one of the most used tools for studying femoral neck fracture. Nerveless, consensus concerning either the choice of material characteristics, damage law and /or geometric models (linear on nonlinear) remains unreached. In this work, we propose a numerical quasi-brittle damage model to describe the behavior of the proximal femur associated with two methods to evaluate the Young modulus. Eight proximal femur finite elements models were constructed from CT scan data (4 donors: 3 women; 1 man). The numerical computations showed a good agreement between the numerical curves (load - displacement) and the experimental ones. A very encouraging result is obtained when a comparison is made between the computed fracture loads and the experimental ones ($R^2=0.825$, Relative error =6.49%). All specific numerical computation provided very fair qualitative matches with the fracture patterns for the sideway fall simulation. Finally, the comparative study based on 32 simulations adopting linear and nonlinear meshing led to the conclusion that the quantitatively results are improved when a nonlinear mesh is used.

Keywords

References

  1. Abedini, M., Khlaghi, E. A., Mehrmashhadi, J., Mussa, M. H., Ansari, M. and Momeni, T. (2017), "Evaluation of concrete structures reinforced with fiber reinforced polymers bars: A Review", J. Asian Sci. Res., 7(5), 165-175.
  2. AbdulKadir, M.R. (2014), "Finite Element Model Construction", Computational Biomechanics of the Hip Joint, Springer, Berlin, Germany. 19-42.
  3. Ariza, O., Gilchrist, S., Widmer, R.P., Guy, P., Ferguson, S.J., Cripton, P.A. and Helgason, B. (2015), "Comparison of explicit finite element and mechanical simulation of the proximal femur during dynamic drop-tower testing", J. Biomech., 48(2015), 224-232. https://doi.org/10.1016/j.jbiomech.2014.11.042.
  4. Bettamer, A., Hambli, R., Allaoui, S. and Almhdie-Imjabber, A. (2015), "Using visual image measurements to validate a novel finite element model of crack propagation and fracture patterns of proximal femur", Comput. Methods Biomech. Biomed. Eng: Imaging Visualization, 5(4), 251-262. https://doi.org/10.1080/21681163.2015.1079505.
  5. Blanco, P.J., Sanchez, P.J., de Souza Neto. E.A. and Feijoo., R.A. (2016), "The method of multiscale virtual power for the derivation of a second order mechanical model", Mech. Mater., 99(2016), 53-67. https://doi.org/10.1016/j.mechmat.2016.05.003.
  6. Briot, K., Cortet, B., Thomas, T., Audran, M., Blain, H., Breuil, L.C., Chapurlat, R., Fardellone, P., Feron, J.M., Gauvain, J.B., Guggenbuhl, P., Kolta, S., Lespessailles, E., Letombe, B., Marcelli, C., Orcel, P., Seret, P., Tremolliere, F. and Roux, C. (2012), "Actualisation 2012 des recommandations francaises du traitement medicamenteux de l'osteoporose postmenopausique", Rev. Rhumatisme, 79 (2012), 264-274. https://doi.org/10.1016/j.rhum.2012.02.006.
  7. Carter, D.R., and Hayes, W.C. (1977), "The compressive behavior of bones as a two-phase porous structure", J. Bone Joint Surg. Am., 59, 954-962. https://doi.org/10.2106/00004623-197759070-00021
  8. Currey, J.D., (1988), "The effect of porosity and mineral content on the Young's modulus elasticity of compact bone", J. Biomech., 21, 131-139. https://doi.org/10.1016/0021-9290(88)90006-1.
  9. Curtis, E.M, Moon, R.J., Harvey, N.C. and Cooper, C. (2017), "The impact of fragility fracture and approaches to osteoporosis risk assessment worldwide", Bone, 104, https://doi.org/10.1016/j.bone.2017.01.024.
  10. Dannilo, C.B. and Pituba, J. (2017), "Analysis of quasi-brittle materials at mesoscopic level using homogenization model", Adv. Concrete Construct., 5(3), 221-240. https://doi.org/10.12989/acc.2017.5.3.221.
  11. Dieter, H.P. and Zysset, P.K. (2009), "A comparison of enhanced continuum FE with micro FE models of human vertebral bodies", J. Biomech., 42, 455-462. https://doi.org/10.1016/j.jbiomech.2008.11.028.
  12. Enns-Bray, W.S., Owoc, J.S., Nishiyama, K.K. and Boyd, S.K. (2014), "Mapping anisotropy of the proximal femur for enhanced image based finite element analysis", J. Biomech., 47(2014), 3272-3278. https://doi.org/10.1016/j.jbiomech.2014.08.020.
  13. Frandsen, P.A., Andersen, E., Madsen, F. and Skjodt, T. (1988), "Garden's Classification of femoral Neck Fractures", J. Bone Joint Surg., 70B(4), 588-590. https://doi.org/10.1302/0301-620X.70B4.3403602.
  14. Haider, I.T., Goldak, J. and Frei, H. (2018), "Femoral fracture load and fracture pattern is accurately predicted using a gradientenhanced quasi-brittle finite element model", Med. Eng. Phys, 55, 1-8. https://doi.org/10.1016/j.medengphy.2018.02.008.
  15. Hambli, R., Bettamer, A. and Allaoui, S. (2012), "Finite element prediction of proximal femur fracture pattern based on orthotropic behavior law coupled to quasi-brittle damage", Med. Eng. Phys., 34, 202- 210. https://doi.org/10.1016/j.medengphy.2011.07.011
  16. Hernandez, C.J., Beaupre, G.S., Keller, T.S. and Carter, D.R. (2001), "The influence of bone volume fraction and ash fraction on bone strength and modulus", Bone, 29(1),74-78. https://doi.org/10.1016/S8756-3282(01)00467-7.
  17. Ju, J.W. (1990), "Isotropic and Anisotropic damage variables in continuum damage mechanics", J. Eng. Mech., 116 (12), 2764-2770. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:12(2764).
  18. Kachanov, L.M. (1986), Introduction to Continuum Damage Mechanics, Martinus Nijhokk Publishers, Netherlands.
  19. Kaneko, T.S., Bell, J.S., Pejcic, M.R., Tehranzadeh, J. and Keyak, J.H. (2004), "Mechanical properties, density and quantitative CT scan data of trabecular bone with and without metastases", J. Biomech., 37, 523-530. https://doi.org/10.1016/j.jbiomech.2003.08.010.
  20. 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.
  21. Krajcinovic, D. (1989), "Damage mechanics", Mech. Mater., 8, 117-197. https://doi.org/10.1016/0167-6636(89)90011-2.
  22. Labergere, C., Rassineux, A. and Saanouni, K. (2007), "Endommagement et procede de mise en forme. Apport du maillage adaptatif", 8e Colloque national en calcul des structures, Giens, France, May 2007.
  23. Le Corroller, T., Halgrin, J., Pithioux, M., Guenoun, F., Chabrand, P. and Champsaur, P. (2012), "Combination of texture analysis and bone mineral density improves the prediction of fracture load in human femurs", Osteoporos Int., 23,163-169. https://doi.org/10.1007/s00198-011-1703-1.
  24. Lekadir, K., Hazrati-Marangalou, J., Hoogendoorn, C., Taylor, Z., van Rietbergen, B. and Frangi, A.F. (2015), "Statistical estimation of femur micro-architecture using optimal shape and density predictors", J. Biomech., 48(2015), 598-603. https://doi.org/10.1016/j.jbiomech.2015.01.002.
  25. Maire, J.F. and Chaboche, J.L. (1997), "A new Formulation of continuum damage mechanics (CDM9 for composite materials", Aerosp. Sci. Technol., 1(4), 247-257. https://doi.org/10.1016/S1270-9638(97)90035-3.
  26. Marco,M., Giner. E., Larrainzar, R., Caeiro, J.R., and Miguelez, M.H. (2017), "Numerical Modelling of Femur Fracture and Experimental Validation Using Bone Simulant", Ann. Biomed. Eng., 45(10), 2395-2408. https://doi.org/10.1007/s10439-017-1877-6.
  27. Mariage, J.F. (2003), "Simulation numerique de l'endommagement ductile en formage de pieces massives", Ph.D. Dissertation, Universite de Technologie de Troyes, France.
  28. Marigo, J. J. (1981), "Formulation of a damage law for an elastic material", Comptes Rendus, Serie II-Mecanique, Physique, Chimie, Sciences de l'Univers, Sciences de la Terre, 292(19), 1309-1312.
  29. Milne, I., Robert O. Ritchie, Bhushan Lal Karihaloo (2003), Comprehensive Structural Integrity, Elsevier, The Netherlands.
  30. Morgan, E.F., Bayraktar, H.H. and Keaveny, T.M. (2003), "Trabecularbonemodulus- density relationships depend on anatomic site", J. Biomech., 36, 897-904. https://doi.org/10.1016/S0021-9290(03)00071-X.
  31. Nakhli, Z., Ben Hatira, F., Pithioux, M. and Chabrand, P. (2017), "Dependance de la modelisation par elements finis du femur humain de la reconstruction tridimensionnelle", International Congress / Congres International Design and Modelling of Mechanical Systems Conception et Modelisation des Systemes Mecaniques, Hammamet, Tunisia, Mars.
  32. Nawathe, S., Yang, H., Fields, A.J., Bouxsein, M.L. and Keaveny, T.M. (2015), "Theoretical effects of fully ductile versus fully brittle behaviors of bone tissue on the strength of the human proximal femur and vertebral body", J. Biomech., 48, 1264-1269. https://doi.org/10.1016/j.jbiomech.2015.02.066.
  33. Pithioux, M., Chabrand, P., Hochard, C.H. and Champsaur, P. (2011), "Improved Femoral Neck fracture predictions using anisotropic failure criteria models", J. Mech. Med. Biol., 11(5), 1333-1346. https://doi.org/10.1142/S0219519412004478.
  34. Pituba, J., Fernandes, G.R. and de Sousa Neto, E.A. (2016), "Modeling of cohesive fracture and plasticity processes in composite microstructures", J. Eng. Mech., 142(10), 1-15. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001123.
  35. Pituba, J.J.C, and Lacerda, M.M.S. (2012), "Simplified damage models applied in the numerical analysis of reinforced concrete structures", Revista Ibracon de Estruturas e Materiais, 5(1), 26-37. http://dx.doi.org/10.1590/S1983-41952012000100004.
  36. Saanouni, K., Forster, Ch., Ben Hatira, F. (1996), "On the Anelastic flow damage", Int. J. Damage Mech., 3(2), 140-169. https://doi.org/10.1177/105678959400300203.
  37. Sanyal, A. (2013), "Bone Strength Multi-axial Behavior - Volume Fraction, Anisotropy and Microarchitecture", Ph.D. Dissertation, University of California, Berkeley, USA.
  38. Schmidt, J., Henderson, A., Ploeg, H., Deluzio, K. and Dunbar, M. (2006), "Finite element analysis of stem dimensions in a revision total knee arthroplasty using visible human computed tomography data" 14th Annual Symposium on Computational Methods in Orthopaedic Biomechanics, Chicago IL, USA, March.
  39. Tellache, M., Pithioux, M., Chabrand, P. and Hochard, C. (2009), "Femoral neck fracture prediction by anisotropic yield criteria", Eur. J. of Comput. Mech. /Rev. Eur. Mec. Num., 18(1), 33-41. https://doi.org/10.3166/ejcm.18.33-41.
  40. Toro, S., Sanchez, P.J., Blanco, P.J., de Souza Neto, E.A., Huespe, A.E. and Feijoo, R.A. (2016), "Multiscale formulation for material failure accounting for cohesive cracks at the macro and micro scales", J. Plasticity, 76(2016), 75-110. https://doi.org/10.1016/j.ijplas.2015.07.001
  41. Varga, P., Schwiedrzik, J., Zysset, Ph. K., Fliri-Hofmanna, L., Widmera, D., Gueorguiev, B., Blauth, M. and Windolf, M. (2016), "Nonlinear quasi-static finite element simulations predict in vitro strength of human proximal femora assessed in a dynamic sideways fall setup", J. Mech. Behav. Biomed. Mater., 57, 116-127. https://doi.org/10.1016/j.jmbbm.2015.11.026.
  42. Viceconti, M., Taddei, F., Cristofolini, L., Martelli, S., Falcinelli, C. and Schileo, E. (2012), "Are spontaneous fractures possible? An example of clinical application for personalised, multiscale neuro-musculo-skeletal modelling", J. Biomech., 45(2012), 421-426. https://doi.org/10.1016/j.jbiomech.2011.11.048.
  43. Wang, E., Nelson, T. and Rauch, R. (2004), "Back to Elements-Tetrahedra vs. Hexahedra", International ANSYS Conference Proceedings (2004), Munich, Germany.
  44. Zagane, M.S., Benbarek, S., Sahli, A., Bouiadjra, B.B. and Boualem, S. (2016), "Numerical simulation of the femur fracture under static loading", Struct. Eng. Mech., 60(3), 405-412. http://dx.doi.org/10.12989/sem.2016.60.3.405.