Medical & Biological Engineering & Computing

, Volume 45, Issue 10, pp 977–988 | Cite as

Finite element modeling of the growth plate in a detailed spine model

  • Pierre-Luc Sylvestre
  • Isabelle VillemureEmail author
  • Carl-Éric Aubin
Original Article


Very few computer models of the spine integrate vertebral growth plates to investigate their mechanical behavior and potential impacts on bone growth. An approach was developed to generate a finite element (FE) model of the lumbar spine and their connective tissues including the growth plate, which allowed a personalization of the geometry based on patients’ bi-planar radiographs. The geometrical validation was performed by deforming meshed vertebrae to reference vertebral specimens and comparing geometrical indices. No significant difference was found between the measured parameters, with errors under 1% in 83% of the geometrical parameters. Mechanical validation was done by simulating loading cases on a functional unit representing experimental testing on cadaveric spines. The flexibility of the functional unit remained between expected ranges of motion, but was more linear than experimental data. The mechanical behavior of the growth plate was evaluated under various loading cases: greater stresses were located in the proliferative zone for the different spinal loading cases tested. This modeling approach is a useful tool to study the effect of mechanical stresses on bone growth.


Growth plate Spine Finite element model Geometrical kriging 



This study was funded by the Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT), the Natural Sciences and Engineering Research Council of Canada (NSERC) and by the Canadian Institute of Health Research (CIHR).


  1. 1.
    Abad V, Meyers JL, Weise M, Gafni RI, Barnes KM, Nilsson O, Bacher JD, Baron J (2002) The role of the resting zone in growth plate chondrogenesis. Endocrinology 143:1851–1857CrossRefGoogle Scholar
  2. 2.
    Alberty A, Peltonen J, Ritsilä V (1993) Effects of distraction and compression on proliferation of growth plate chondrocytes. Acta Orthop Scand 64:449–455CrossRefGoogle Scholar
  3. 3.
    Arriola F, Forriol F, Canadell J (2001) Histomorphometric study of growth plate subjected to different mechanical conditions (compression, tension and neutralization): an experimental study in lambs. J Pediatr Orthop B 10:334–338CrossRefGoogle Scholar
  4. 4.
    Aubin CE, Descrimes JL, Dansereau J, Skalli W, Lavaste F, Labelle H (1995) Geometrical modeling of the spine and the thorax for the biomechanical analysis of scoliotic deformities using the finite element method. Ann Chir 49:749–761Google Scholar
  5. 5.
    Ballock T, O’Keefe R (2003) The biology of the growth plate. J Bone Joint Surg 85A:715–726Google Scholar
  6. 6.
    Bradford DS, Hensinger RM (1985) The pediatric spine. Thieme-Stratton Corp, New YorkGoogle Scholar
  7. 7.
    Breau C, Shirazi-Adl A, de Guise J (1991) Reconstruction of a human ligamentous lumbar spine using CT images. Ann Biomed Eng 19:291–302CrossRefGoogle Scholar
  8. 8.
    Breur GJ, Turgai J, Vanenkevort BA, Farnum CE, Wilsman NJ (1994) Stereological and serial section analysis of chondrocytic enlargement in the proximal tibial growth plate of the rat. Anat Rec 239:255–268CrossRefGoogle Scholar
  9. 9.
    Bursac PM, Obitz TW, Eisenberg SR, Stamenovic D (1999) Confined and unconfined stress relaxation of cartilage: appropriateness of a transversely isotropic analysis. J Biomech 32:1125–1130CrossRefGoogle Scholar
  10. 10.
    Cheriet F, Dansereau J, Petit Y, Aubin CE, Labelle H, de Guise J (1999) Towards the self-calibration of a multiview radiographic imaging system for the 3D reconstruction of the human spine and rib cage. Int J Pattern Recognit Artif Intell 13:761–779CrossRefGoogle Scholar
  11. 11.
    Chosa E, Totoribe K, Tajima N (2004) A biomechanical study of lumbar spondylolysis based on a three-dimensional finite element method. J Orthop Res 22:158–163CrossRefGoogle Scholar
  12. 12.
    Cohen B, Chorney GS, Phillips DP, Dick HM, Buckwalter JA, Ratcliffe A, Mow VC (1992) The microstructural tensile properties and biochemical composition of the bovine distal femoral growth plate. J Orthop Res 10:263–275CrossRefGoogle Scholar
  13. 13.
    Cohen B, Chorney G, Phillips D, Dick H, Mow V (1994) Compressive Stress-relaxation behavior of bovine growth plate may be described by the nonlinear biphasic theory. J Orthop Res 12:804–813CrossRefGoogle Scholar
  14. 14.
    Cohen B, Lai WM, Mow VC (1998) A transversely isotropic biphasic model for unconfined compression of growth plate and chondroepiphysis. J Biomech Eng 120:491–496Google Scholar
  15. 15.
    de Guise JA, Martel Y (1988) 3D-biomedical modeling: merging image processing and computer aided design. In: Proceedings of the annual international conference of the IEEE engineering in medicine and biology society, Piscataway, NJ, USA pp 426–427Google Scholar
  16. 16.
    Delorme S, Petit Y, de Guise JA, Labelle H, Aubin CE, Dansereau J (2003) Assessment of the 3-D reconstruction and high-resolution geometrical modeling of the human skeletal trunk from 2-D radiographic images. IEEE Trans Biomed Eng 50:989–998CrossRefGoogle Scholar
  17. 17.
    Farnum C, Nixon A, Lee A, Kwan D, Belanger L, Wilsman N (2000) Quantitative three-dimensional analytic responses to chondrocytic kinetic responses to short-term stapling of the rat proximal tibial growth plate. Cells Tissues Organs 167:247–258CrossRefGoogle Scholar
  18. 18.
    Frost H (1990) Skeletal structural adaptations to mechanical usage: the hyaline cartilage modeling problem. Anat Rec 226:423–432CrossRefGoogle Scholar
  19. 19.
    Gafni RI, Weise M, Robrecht DT, Meyers JL, Barnes KM, De-Levi S, Baron J (2001) Catch-up growth is associated with delayed senescence of the growth plate in rabbits. Pediatr Res 50:618–623CrossRefGoogle Scholar
  20. 20.
    Gibson LJ, Ashby MF (1998) Cellular solid: structure and properties. Pergamon Press, OxfordGoogle Scholar
  21. 21.
    Hobatho M, Rho J, Ashman R (1997) Mechanical properties of the lumbar spine. Res Spinal Deformities 1:181–184Google Scholar
  22. 22.
    Hunziker E, Schenk R (1989) Physiological mechanisms adopted by chondrocyt regulating longitudinal bone growth in rats. J Physiol 414:55–71Google Scholar
  23. 23.
    Konz RJ, Goel VK, Grobler LJ, Grosland NM, Spratt KF, Scifert JL, Sairyo K (2001) The pathomechanism of spondylolytic spondylolisthesis in immature primate lumbar spines in vitro and finite element assessments. Spine 26:38–49CrossRefGoogle Scholar
  24. 24.
    Kopperdahl DL, Morgan EF, Keaveny TM (2002) Quantitative computed tomography estimates of the mechanical properties of human vertebral trabecular bone. J Orthop Res 20:801–805CrossRefGoogle Scholar
  25. 25.
    Kumaresan S, Yoganandan N, Pintar FA, Maiman DJ, Kuppa S (2000) Biomechanical study of pediatric human cervical spine: a finite element approach. J Biomech Eng 122:60–71CrossRefGoogle Scholar
  26. 26.
    LeVeau B, Bernhardt D (1984) Developmental biomechanics: effect of forces on the growth, development, and maintenance of the human body. Phys Ther 64:1874–1882Google Scholar
  27. 27.
    Myers RH, Montgomery DC, Vining GG (2002) Generalized linear models. Wiley, New YorkzbMATHGoogle Scholar
  28. 28.
    Niehoff A, Kersting U, Zaucke F, Morlock M, Brüggeman G (2004) Adaptation of mechanical, morphological, and biomecahnical properties of the rat growth plate to dose-dependent voluntary exercise. Bone 35:899–908CrossRefGoogle Scholar
  29. 29.
    Panjabi MM, Oxland TR, Lin RM, McGowen TW (1994) Thoracolumbar burst fracture: a biomechanical investigation of its multidirectional flexibility. Spine 19:578–585CrossRefGoogle Scholar
  30. 30.
    Perie D, Sales De Gauzy J, Baunin C, Hobatho MC (2001) Tomodensitometry measurements for in vivo quantification of mechanical properties of scoliotic vertebrae. Clin Biomech 16:373–379CrossRefGoogle Scholar
  31. 31.
    Perie D, Aubin CE, Petit Y, Labelle H, Dansereau J (2004) Personalized biomechanical simulations of orthotic treatment in idiopathic scoliosis. Clin Biomech 19:190–195CrossRefGoogle Scholar
  32. 32.
    Polikeit A, Ferguson SJ, Nolte LP, Orr TE (2003) Factors influencing stresses in the lumbar spine after the insertion of intervertebral cages: finite element analysis. Eur Spine J 12:413–420CrossRefGoogle Scholar
  33. 33.
    Radhakrishnan P, Lewis NT, Mao JJ (2004) Zone-specific micromechanical properties of the extracellular matrices of growth plate cartilage. Ann Biomed Eng 32:284–291CrossRefGoogle Scholar
  34. 34.
    Rho JY, Hobatho MC, Ashman RB (1995) Relations of mechanical properties to density and CT numbers in human bone. Med Eng Phys 17:347–355CrossRefGoogle Scholar
  35. 35.
    Sairyo K, Goel VK, Masuda A, Vishnubhotla S, Faizan A, Biyani A, Ebraheim N, Yonekura D, Murakami R, Terai T (2006) Three-dimensional finite element analysis of the pediatric lumbar spine. Part I: pathomechanism of apophyseal bony ring fracture. Eur Spine J 15:923–929Google Scholar
  36. 36.
    Sarwark J, Aubin CE (2007) Growth considerations of the immature spine. J Bone Joint Surg 89(Suppl. 1):8–13CrossRefGoogle Scholar
  37. 37.
    Shirazi-Adl A (1991) Finite element evaluation of contact loads on facets of an L2-L3 lumbar segment in complex loads. Spine 16:533–541CrossRefGoogle Scholar
  38. 38.
    Stokes I, Spence H, Aronsson D, Kilmer N (1996) Mechanical modulation of vertebral body growth. Spine 21:1162–1167CrossRefGoogle Scholar
  39. 39.
    Stokes IA, Mente PL, Iatridis JC, Farnum CE, Aronsson DD (2002) Enlargement of growth plate chondrocytes modulated by sustained mechanical loading. J Bone Joint Surg 84A:1842–1848Google Scholar
  40. 40.
    Templeton A, Cody D, Liebschner M (2004) Updating a 3-D vertebral body finite element model using 2-D images. Med Eng Phys 26:329–333CrossRefGoogle Scholar
  41. 41.
    Trochu F (1993) A contouring program based on dual kriging interpolation. Eng Comp 9:160–177CrossRefGoogle Scholar
  42. 42.
    Villemure I, Aubin CE, Dansereau J, Labelle H (2002) Simulation of progressive deformities in adolescent idiopathic scoliosis using a biomechanical model integrating vertebral growth modulation. J Biomech Eng 124:784–790CrossRefGoogle Scholar
  43. 43.
    Villemure I, Cloutier L, Matyas JR, Duncan NA (2007) Non-uniform strain distribution within rat cartilaginous growth plate under uniaxial compression. J Biomech 40:149–156CrossRefGoogle Scholar
  44. 44.
    Wang JL, Parnianpour M, Shirazi-Adl A, Engin AE, Li S, Patwardhan A (1997) Development and validation of a viscoelastic finite element model of an L2/L3 motion segment. Theor Appl Fract Mech 28:81–93CrossRefGoogle Scholar
  45. 45.
    Wang X, Mao JJ (2002) Accelerated chondrogenesis of the rabbit cranial base growth plate by oscillatory mechanical stimuli. J Bone Miner Res 17:1843–1850CrossRefGoogle Scholar
  46. 46.
    White A, Panjabi M (1990) Clinical biomechanics of the spine. JB Lippincott Company, PhiladelphiaGoogle Scholar
  47. 47.
    Williams JL, Do PD, Eick JD, Schmidt TL (2001) Tensile properties of the physis vary with anatomic location, thickness, strain rate and age. J Orthop Res 19:1043–1048CrossRefGoogle Scholar

Copyright information

© International Federation for Medical and Biological Engineering 2007

Authors and Affiliations

  • Pierre-Luc Sylvestre
    • 1
    • 2
  • Isabelle Villemure
    • 1
    • 2
    Email author
  • Carl-Éric Aubin
    • 1
    • 2
  1. 1.Department of Mechanical EngineeringEcole Polytechnique of MontrealMontrealCanada
  2. 2.Sainte-Justine University Hospital CenterMontrealCanada

Personalised recommendations