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Transversely isotropic and isotropic material considerations in determining the mechanical response of geometrically accurate bovine tibia bone

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Abstract

In finite element method (FEM) simulations of the mechanical response of bones, proper selection of stiffness versus density (E-ρ) formulae for bone constituents is necessary for obtaining accurate results. A considerable number of such formulae can be found in the biomechanics’ literature covering both cortical and cancellous constituents. For determining the first and second modal frequencies (in both cranial-caudal and medial-lateral planes) of bovine tibia bone, this work assembled and numerically tested 22 isotropic and 21 orthotropic stiffness-density formulae combinations (cases). To accurately reproduce bone geometry, anatomical 3D models were generated from computed tomography (CT) scans. By matching the bone’s digital mass to its actual mass, cortical and cancellous constituents were faithfully segmented by utilizing suitable values of three variables: (1) critical cutoff Hounsfield unit (HU) values, (2) cutoff density value, and (3) utilized number of sub-materials. Consequently, a balanced distribution of finite elements was generated with stiffness values congruent with their cancellous or cortical demarcations. Of the considered 22 isotropic formulae cases and 21 orthotropic (reduced to transversely isotropic) cases, only few yielded accurate frequency estimates. For verifying the accuracy of the solutions emanating from the various formulae, experimental vibration tests of corresponding mode frequencies and shapes (ProSig©) were conducted. When compared with the measured experimental frequency values, the most accurate isotropic formulae yielded numerical estimates of + 0.95% and + 10.65% for the first and second cranial-caudal (C-C) frequencies, respectively. The formulae yielding most accurate estimates also proved successful in estimating frequencies of a second tibia bone yielding numerical estimates within + 4.75% and + 1.88% of the said mode frequencies. For the transversely isotropic material assignment, the closest case scenario computed numerical estimates with a percentage difference of + 2.05% and + 9.36% for the first and second cranial-caudal (C-C) frequencies, respectively.

Mode shapes (left) 1 and (right) 2 for transversely isotropic case 15 T (Bone A): (a) cranial-caudal and (b) medial-lateral plane.

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References

  1. Yassine RA, Elham MK, Mustapha S, Hamade RF (2018) Heterogeneous versus homogeneous material considerations in determining the modal frequencies of long tibia bones. J Eng Sc Med Diag 1(021001):1–5

    Google Scholar 

  2. Duchemin L, Bousson V, Roassanaly C, Bergot C, Laredo JD, Skalli W, Mitton D (2008) Prediction of mechanical properties of cortical bone by quantitative computed tomography. Med Eng Phys 30(3):321–328

    Article  CAS  PubMed  Google Scholar 

  3. Taylor WR, Roland E, Ploeg H, Hertig D, Klabunde R, Warner MD, Hobatho MC, Rakotomanana L, Clift SE (2002) Determination of orthotropic bone elastic constants using FEA and modal analysis. Aust J Biotechnol 35(6):767–773

    CAS  Google Scholar 

  4. Lee JW, Kim KJ, Kang KS, Chen S, Rhie JW, Cho DW (2013) Development of a bone reconstruction technique using a solid free-form fabrication (SFF)-based drug releasing scaffold and adipose-derived stem cells. J Bio Mat Res Part A 101(7):1865–1875

    Article  CAS  Google Scholar 

  5. Scholz R, Hoffmann F, Von Sachsen S, Drossel WG, Klohn C, Voigt C (2013) Validation of density-elasticity relationships for finite element modeling of human pelvic bone by modal analysis. Aust J Biotechnol 46(15):2667–2673

    Google Scholar 

  6. Di Puccio F, Mattei L, Longo A, Marchetti S (2017) Fracture healing assessment based on impact testing: in vitro simulation and monitoring of the healing process of a tibial fracture with external fixator. Int J Appl Mech 9(7):1750098

    Article  Google Scholar 

  7. Hobatho MC, Darmana R, Pastor P, Barrau JJ, Laroze S, Morucci JP (1991) Development of a three dimensional finite element model of a human tibia using experimental modal analysis. J Biomech 24(6):371–383

    Article  CAS  PubMed  Google Scholar 

  8. Thomsen JJ (1990) Modelling human tibia structural vibrations. Aust J Biotechnol 23(3):215–228

    CAS  Google Scholar 

  9. Gupta A, Tse KM (2013) Finite element analysis on vibration modes of femur bone. Int Conf Adv Mech Eng (AME), NCR, India 10–13:827–831

    Google Scholar 

  10. Kumar A, Jaiswal H, Garg T, Patil PP (2014) “Free vibration modes analysis of femur bone fracture using varying boundary conditions based on FEA,” 3rd International Conference on Materials Processing and Characterization (ICMPC 2014). Procedia Mater Sci 6:1593–1599

    Article  CAS  Google Scholar 

  11. Liao Z, Chen J, Zhang Z, Li W, Swain M, Li Q (2015) Computational modeling of dynamic behaviors of human teeth. J Bio. 48(16):4214–4220

    Article  Google Scholar 

  12. Al Sukhun J, Kelleway J, Helenius M (2007) Development of a three-dimensional finite element model of a human mandible containing endosseous dental implants. I. Mathematical validation and experimental verification. J Bio Mat Res Part A 80(1):234–246

    Article  CAS  Google Scholar 

  13. Roberge J, Norato J (2018) Computational design of curvilinear bone scaffolds fabricated via direct ink writing. Comput Aided Des 95:1–13

    Article  Google Scholar 

  14. Baek S-Y, Wang J-H, Song I, Lee K, Koo S (2013) Automated bone landmarks prediction on the femur using anatomical deformation technique. Comput Aided Des 45(2):505–510

    Article  Google Scholar 

  15. Snyder SM, Schneider E (1989) Estimation of mechanical properties of cortical bone by computed tomography. J Orthop Res 9(3):422–431

    Article  Google Scholar 

  16. Lotz, J. C., Gerhart, T. N., Hayes, W. C., 1991, “Mechanical properties of metaphyseal bone in the proximal femur,” J. Bio. 24(5), pp. 317–329

    Article  CAS  PubMed  Google Scholar 

  17. Keaveny TM, Morgan EF, Niebeur GL, Yeh OC (2001) Biomechanics of trabecular bone. Annu Rev Biomed Eng 3:307–333

    Article  CAS  PubMed  Google Scholar 

  18. Gupta S, Dan P (2004) Bone geometry and mechanical properties of the human scapula using computed tomography data. Trends Biomater Artif Organs 17(2):61–70

    Google Scholar 

  19. Wirtz DC, Schiffers N, Pandorf T, Radermacher K, Weichert D, Forst R (2000) Critical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur. Aust J Biotechnol 33(10):1325–1330

    CAS  Google Scholar 

  20. Abendschein W, Hyatt GW (1970) Ultrasonics and selected physical properties of bone. Clin Orthop Relat Res 69:294–301

    Article  CAS  PubMed  Google Scholar 

  21. Austman RL, Milner JS, Holdsworth DW, Dunning CE (2009) Development of a customized density-modulus relationship for use in subject-specific finite element models of the ulna. Proc Instit Mech Eng 223(6):787–794

    Article  CAS  Google Scholar 

  22. Austman RL, Milner JS, Holdsworth DW, Dunning CE (2008) The effect of the density-modulus relationship selected to apply material properties in a finite element model of long bone. Aust J Biotechnol 41(15):3171–3176

    Google Scholar 

  23. Morgan EF, Bayraktar HH, Keaveny TM (2003) Trabecular bone modulus-density relationships depend on anatomic site. Aust J Biotechnol 36(7):897–904

    Google Scholar 

  24. Carter DR, Hayes WC (1977) The compressive behavior of bone as a two-phase porous structure. J Bone Jt Surg Ser A 59(7):954–962

    Article  CAS  Google Scholar 

  25. Schileo E, Taddei F, Malandrino A, Cristofolini L, Viceconti M (2007) Subject-specific finite element models can accurately predict stain levels in long bones. Aust J Biotechnol 40(13):2982–2989

    Google Scholar 

  26. Huang HL, Tsai MT, Lin DJ, Chien CS, Hsu JT (2010) A new method to evaluate the elastic modulus of cortical bone by using combined computed tomography and finite element approach. Comput Biol Med 40(4):464–468

    Article  PubMed  Google Scholar 

  27. Yang G, Kabel J, VanRietbergen B, Odgaard A, Huiskes R, Cowin S (1999) The anisotropic Hooke’s law for cancellous bone and wood. J.Elast 53:125–146

    Article  CAS  Google Scholar 

  28. Cowin SC, Yang G (1997) Averaging anisotropic elastic constant data. J Elast 46:151–180

    Article  Google Scholar 

  29. Keller TS (1994) Predicting the compressive mechanical behavior of bone. J Biomech 27(9):1159–1168

    Article  CAS  PubMed  Google Scholar 

  30. Helgason B, Perilli E, Schileo E, Taddei F, Brynjólfsson S, Viceconti M (2008b) Mathematical relationships between bone density and mechanical properties: a literature review. Clin Biomech 23:135–146

    Article  Google Scholar 

  31. Liang P, Bai J, Zeng X, 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

    Article  CAS  Google Scholar 

  32. Rho JY, Hobatho MC, Ashman RB (July 1995) Relations of mechanical properties to density and CT numbers in human bone. Med Eng Phys 17(5):347–355

    Article  CAS  PubMed  Google Scholar 

  33. Rho JY (1996) An ultrasonic method for measuring the elastic properties of human tibial cortical and cancellous bone. Ultrasonics 34:777–783

    Article  CAS  PubMed  Google Scholar 

  34. Chung DH. (2002) Orthotropic elastic structure of human cortical bone. The Texas A&M University System Health Science Center, ProQuest Dissertations Publishing. 10586182

  35. Van Biskirk WC, Cowin SC, Ward RN (1981) Ultrasonic measurement of orthotropic elastic constants of bovine femoral bone. J Biomech Eng 103:67–72

    Article  Google Scholar 

  36. Van Buskirk WC and Ashman R 9. (1981) The elastic moduli of bone mechanical properties of bone. (Edited by Cowin. S. C.). pp. 131-143. American Society 01 Mechanical Engineers, Colorado

  37. Ashman RB, Cowin SC, Van Buckirk WC, Rice JC (1984) A continuous wave technique for the measurement of the elastic properties of cortical bone. J Biomech 17:349–361

    Article  CAS  PubMed  Google Scholar 

  38. Knets IV (1978) Mechanics of biological tissues. A Review Polymer Mech 13:434–441

    Article  Google Scholar 

  39. Mimics student edition course book, Innovation Suite Research, Materialize Technologielaan 15–3001 Leuven-Belgium, http://www.materialise.com/en/medical/software/mimics, Accessed January 10, 2017

  40. Choucair, I., Mustapha, S., Fakhreddine, A., Sayegh, M., and Hamade, R. F., 2016, “Investigation of the dynamic characteristics of bovine tibia using the impulse response method,” ASME Paper No. IMECE2016–66554. Volume 3: Biomedical and Biotechnology Engineering. Phoenix, Arizona, USA, November 11–17, 2016

  41. Yassine R, Fakhreddine A, Sayegh M, Mustafa S, Hamade RF (2018) Dynamic assessment and modeling of the modal frequencies and shapes of bovine tibia. ASME J Nondestruct Eval 1(4):041006

    Article  Google Scholar 

  42. Yang H, Ma X, Guo T (2010) Some factors that affect the comparison between isotropic and orthotropic inhomogeneous finite element material models of femur. Med Eng Phys 32:553–560

    Article  PubMed  Google Scholar 

  43. David C. Lee, PF. Hoffman, DL. Kopperdahl T, Keaveny M. Phantomless calibration of CT scans for measurement of BMD and bone strength-inter-operator reanalysis precision

  44. Novitskaya E, Chen P, Lee S, Castro-Cesena A, Hirata G, Lubardo V, McKittrick J (2011) Anisotropy in the compressive mechanical properties of bovine cortical bone and the mineral and protein constituents. Acta Biomater 7(8):3170–3177

    Article  CAS  PubMed  Google Scholar 

  45. Fatehi P, Nejad MZ (2014) Effects of material gradients on onset of yield in FGM rotating thick cylindrical shells. Int J Appl Mech 6(4):1450038

    Article  Google Scholar 

  46. Yassine, R., Elham, M. K., Mustafa, S., and Hamade, R., 2017, “A detailed methodology for FEM analysis of long bones from CT using Mimics,” ASME Paper No. IMECE2017–72571. November 3–9, 2017, Tampa, Florida, USA

  47. Reilly DT, Burstein A (1975) The elastic and ultimate properties of compact bone tissue. Aust J Biotechnol 8(6):393–405

    CAS  Google Scholar 

  48. Zysset PK, Guo XE, Hoffler CE, Moore KE, Goldstein SA (1992) Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. Aust J Biotechnol 32(10):1005–1012

    Google Scholar 

  49. Sitzer A, Wendlandt R, Barkhausen J, Kovacs A, Weyers I, Schulz AP (2012) Determination of material properties related to quantitative CT in human femoral bone for patient specific finite element analysis - a comparison of material Laws. ORTHOPAEDICS 3(7):WMC003456

    Google Scholar 

  50. Kohles SS (2000) Application of an anisotropic parameter to cortical bone. J Mat Sc Mat Med 11(4):26–265

    Google Scholar 

  51. Hage IS, Hamade RF (2017) Intracortical stiffness of mid-diaphysis femur bovine bone: lacunar–canalicular based homogenization numerical solutions and microhardness measurements. J Mater Sci Mater Med 28(9):135

    Article  PubMed  CAS  Google Scholar 

  52. Knets IV, Pfafrod GO, Saulgozis JZ (1980) Deformation and fracture of hard biological tissue. Zinatne, Riga, p 319

    Google Scholar 

  53. Hage, I. S., Seif, C. Y., and Hamade, R. F., 2016, “Measuring compressive modulus of elasticity across cortical bone thickness of mid-diaphysis bovine femur,” ASME Paper No. IMECE2016–66383. Volume 3: Biomedical and Biotechnology Engineering. Phoenix, Arizona, USA, November 11–17, 2016

  54. Linde F, Hvid I, Madsen F (1992) The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens. Aust J Biotechnol 25(4):359–368

    CAS  Google Scholar 

  55. Lempriere BM (1968) Poisson’s ratio in orthotropic materials. AIAA J 6(11):2226–2227

    Article  Google Scholar 

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Funding

This work was made possible by the financial support of the Lebanese National Council for Scientific Research (CNRS) Award Number 103087 and AUB’s University Research Board.

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  1. Mechanical Engineering Department, American University of Beirut, P.O. Box 11-0236, Riad El-Solh, Beirut, 1107 2020, Lebanon

    Reem A. Yassine & Ramsey F. Hamade

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  1. Reem A. Yassine
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Correspondence to Ramsey F. Hamade.

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Yassine, R.A., Hamade, R.F. Transversely isotropic and isotropic material considerations in determining the mechanical response of geometrically accurate bovine tibia bone. Med Biol Eng Comput 57, 2159–2178 (2019). https://doi.org/10.1007/s11517-019-02019-5

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