medigraphic.com
ISSN 1561-3011 (Electronic)

2011, Number 1

<< Back Next >>

Rev Cubana Invest Bioméd 2011; 30 (1)

A mathematical model of growth plate

Garzón-Alvarado DA, Narváez-Tovar CA, Landinez PNS

Language: Spanish
References: 53
Page: 42-63
PDF size: 391.96 Kb.


ABSTRACT

The growth plate is a structure composed of cells called chondrocytes arranged in columns and causing the bone lengthening due to its proliferation and hypertrophy. In each column it may observed the presence of chondrocytes in proliferation stage (constantly divided) and hypertrophy stage (growing to obtain a almost spherical shape). These cells express different proteins and molecules during half-life and have a special behavior that may to depend on its mechanical or biochemical local environment. In present paper it is developed a mathematical model describing the relationship among the geometry, proliferation and hypertrophy growth and the vascular invasion by biochemical and mechanical factors present during the endochondral development.


REFERENCES

  1. Kronenberg H. Development regulation of the growth plate. Nature. 2003;423:332-36.

  2. 2 Provot S, Schipani E. Molecular mechanisms of endochondral bone development. Biochemical and Biophysical Research Communications. 2005;328(3):65865.

  3. Carter DR, Beaupré GS, Wong M, Smith RL, Andriacchi TP, Schurman DJ. The mechanobiology of articular cartilage development and degeneration. Clin Orthop Relat Res. 2004;427:Suppl:S69-77.

  4. Minina E, Kreschel C, Naski MC, Ornitz DM, Vortkamp A. Interaction of fgf, ihh/pthlh, and bmp signaling integrates chondrocyte proliferation and hypertrophic differentiation. Developmental Cell. 2002;3(3):439-49.

  5. Gao B, Guo J, She C, Shu A, Yang M, Tan Z, et al. Mutations in IHH, encoding Indian hedgehog, cause brachydactyly type A-1. Nat Genet. 2001;28(4):386-88.

  6. Karp S, Schipani E, St-Jacques B, Hunzelman J, Kronenberg H, McMahon A. Indian Hedgehog coordinates endochondral bone growth and morphogenesis via Parathyroid Hormone related-Protein-dependent and -independent pathways. Development. 2000;127:543-48.

  7. Kindblom JM, Nilsson O, Hurme T, Ohlsson C, Savendahl J. Expression and localization of Indian Hedgehog (Ihh) and parathyroid hormone related protein (PTHrP) in the human growth plate during pubertal development. Journal of Endocrinology. 2002;174:R1-R6.

  8. Forriol F, Shapiro F. Bone development. Clinical Orthopaedics and related research. 2005;432:14-33.

  9. Fasano A, Herrero MA, López JM, Medina E. On the dynamics of the growth plate in primary ossification. Journal of Theoretical Biology. 2010; 265(4):543-53.

  10. Blumenkrantz N, Asboe-Hansen G. Cortisol effects on collagen biosynthesis in embryonic explants and in vitro hydroxylation of protocollagen. Acta Endocrinol. 1976;83:665-72.

  11. Delpech JM. De L'Orthomorphie: Par Rapport a L'espece Humaine. 2 vol. Paris: Gabon. 1828.

  12. Stokes IA, Clark KC, Farnum CE, Aronsson DD. Alterations in the growth plate associated with growth modulation by sustained compression or distraction. Bone. 2007;41(2):197-205.

  13. Simon MR, Papierski P. Effects of Experimental Bipedalism on the Growth of the Femur and Tibia in Normal and Hypophysectomized Rats. Acta Anat. 1982;114:321-29.

  14. Stokes IA, Mente PL, Iatridis JC, Farnum CE, Aronsson DD. Enlargement of growth plate chondrocytes modulated by sustained mechanical loading. Journal of Bone and Joint Surgery. 2002;84-A:1842-48.

  15. Stokes IA, Gwadera J, Dimock A, Farnum CE. Modulation of vertebral and tibial growth by compression loading: diurnal versus full-time loading. Journal of Orthopaedic Research. 2005;23:188-95.

  16. Modi HN, Suh SW, Hong JY, Cho JW, Park JH, Yang JH. Treatment and complications in flaccid neuromuscular scoliosis (Duchenne muscular dystrophy and spinal muscular atrophy) with posterior-only pedicle screw instrumentation. Eur Spine J. 2010;19(3):384-93.

  17. Stokes IA. Mechanical Effects on skeletal Growth. J Musculoskel Neuron Interact. 2002;2(3):277-80.

  18. Clarke SE, McCarthy JJ, Davidson RS. Treatment of Blount disease: a comparison between the multiaxial correction system and other external fixators. J Pediatr Orthop. 2009;29 (2):103-09.

  19. Pereira BP, Cavanagh SP, Pho RW. Longitudinal growth rate following slow physeal distraction. The proximal tibial growth plate studied in rabbits. Acta Orthop Scand. 1997;68(3):262-68.

  20. Henderson JH, Carter DR. Mechanical induction in limb morphogenesis: the role of growth-generated strains and pressures. Bone. 2002;31(6):645-53.

  21. Lerner AL, Kuhn JL, Hollister SJ. Are regional variations in bone growth related to mechanical stress and strain parameters? J Biomech. 1998;31(4):327-35.

  22. Stevens SS, Beaupré GS, Carter DR. Computer model of endochondral growth and ossification in long bones: biological and mechanobiological influences. JOrthop Res. 1999;17(5):646-53.

  23. Beaupré GS, Stevens SS, Carter DR. Mechanobiology in the development, maintenance, and degeneration of articular cartilage. J Rehabil Res Dev. 2000;37(2):145-51.

  24. Brouwers JE, Van Donkelaar CC, Sengers BG, Huiskes R. Can the growth factors PTHrP, Ihh and VEGF, together regulate the development of a long bone? J Biomech. 2006;39(15):2774-82.

  25. Garzón-Alvarado DA, García-Aznar JM, Doblaré M. A reaction-diffusion model for long bones growth. Biomech Model Mechanobiol. 2009;8(5):381-95.

  26. Griffiths SF. Developmental biology. 6th ed. Sunderland: Sinauer Associates Inc.; 2000.

  27. Rivas R, Shapiro F. Structural stages in the development of the long bones and epiphyses: a study in the New Zealand white rabbit. J Bone Joint Surg Am. 2002;84-A(1):85-100.

  28. Hunziker EB, Schenk RK. Physiological mechanisms adopted by chondrocytes in regulating longitudinal bone growth in rats. J Physiol. 1989;414:55-71.

  29. Farnum CE, Wilsman NJ. Converting a differentiation cascade into longitudinal growth: stereology and analysis of transgenic animals as tools for understanding growth plate function. Curr Opinion Orthop. 2001;12(5):428-33.

  30. 30.. Ballock RT, O'Keefe RJ. The biology of the growth plate. J Bone Joint Surg Am. 2003;85-A(4):715-26.

  31. Goldberg R, Reshef-Bankai E, Coleman R, Green J, Maor G. Chronic acidosisinduced growth retardation is mediated by proton-induced expression of Gs protein. J Bone Miner Res. 2006;21:703-13.

  32. Olney RC, Wang J, Sylvester JE, Mougey EB. Growth factor regulation of human growth plate chondrocyte proliferation in vitro. Biochem Biophys Res Commun. 2004;317(4):1171-82.

  33. Villemure I, Stokes IA. Growth plate mechanics and mechanobiology. A survey of present understanding. Journal of Biomechanics. 25 August 2009;42(12):1793- 03.

  34. Fasano A, Herrero MA, López JM, Medina E. On the dynamics of the growth plate in primary ossification. Journal of Theoretical Biology. 2010;265(4):543-53.

  35. Garzón-Alvarado DA, García-Aznar JM, Doblaré M. Appearance and location of secondary ossification centres may be explained by a reactiondiffusion mechanism. Comput Biol Med. 2009;39:554-61.

  36. Alberty A, Peltonen J, Ritsila V. Effects of distraction and compression on proliferation of growth plate chondrocytes. A study in rabbits. Acta Orthop Scand. 1993;64 (4):449-55.

  37. Farnum CE, Wilsman NJ. Effects of distraction and compression on growth plate function. En: Buckwalter JA, Ehrlich MG, Sandell LJ, Trippel SB. Skeletal Growth and Development. AAOS, Rosemont, 1998:517-30.

  38. Ehrlich MG, Mankin HJ, Treadwell BV. Biochemical and physiological events during closure of the stapled distal femoral epiphyseal plate in rats. J Bone Joint Surg Am. 1972;54(2):309-22.

  39. Garzón-Alvarado DA, Peinado Cortés LM, Cardenas Sandoval RP. A mathematical model of epiphyseal development: hypothesis on the cartilage canals growth. Comput Methods Biomech Biomed Engin. 2010. 13(6):765-72.

  40. Stokes A, Clark KC, Farnum CE, Aronsson DD. Alterations in the growth plate associated with growth modulation by sustained compression or distraction. Bone. 2007;41(2):197-205.

  41. Stokes A, Aronsson DD, Dimock AN, Cortright V, Beck S. Endochondral growth in growth plates of three species at two anatomical locations modulated by mechanical compression and tension. J Orthop Res. 2006;24(6):132734.

  42. Carter DR, Wong M. Mechanical stresses and endochondral ossification in the chondroepiphysis. J Orthop Res. 1988;6(1):148-54.

  43. Cancel M, Grimard G, Thuillard-Crisinel D, Moldovan F, Villemure I. Effects of in vivo static compressive loading on aggrecan and type II and X collagens in the rat growth plate extracellular matrix. Bone. 2009;44(2):306-15.

  44. Reich A, Jaffe N, Tong A, Lavelin I, Genina O, Pines M, et al. Weight loading young chicks inhibits bone elongation and promotes growth plate ossification and vascularization. J Appl Physiol. 2005;98(6):2381-89.

  45. 45.Villemure I, Chung MA, Seck CS, Kimm MH, Matyas JR, Duncan NA. Static compressive loading reduces the mRNA expression of type II and X collagen in rat growth-plate chondrocytes during postnatal growth. Connect Tissue Res. 2005;46(4-5):211-19.

  46. Herrero MA, López JM. Bone formation: Biological aspects and modelling problems. Computational and Mathematical Methods. 2005;6:41-55.

  47. Cohen B, Chorney GS, Phillips DP, Dick HM, Mow VC. Compressive stressrelaxation behavior of bovine growth plate may be described by the nonlinear biphasic theory. J Orthop Res. 1994;12(6):804-13.

  48. Cohen B, Lai WM, Mow VC. A transversely isotropic biphasic model for unconfined compression of growth plate and chondroepiphysis. J Biomech Eng. 1998;120(4):491-96.

  49. Sergerie K, Lacoursiere MO, Levesque M, Villemure I. Mechanical properties of the porcine growth plate and its three zones from unconfined compression tests. J Biomech. 2009;42(4):510-16.

  50. Kember NF, Sissons HA. Quantitative histology of the human growth plate. J Bone Jt Surg Br. 1976;58-B(4):426-35.

  51. Villemure I, Chung MA, Kimm MH, Matyas FR, Duncan NA. Mechanical properties of rat cartilaginous growth plates vary with developmental stages. En: Sawatzky BJ. International Research Society of Spinal Deformities Vancouver: UBC Press; 2004. 227-30.

  52. Lin H, Aubin C, Parent S, Villemure I. Mechanobiological bone Growth: Comparative analysis of two biomechanical modeling approaches. Medical and Biological Engineering and Computing. 2009;47(4):357-66.

  53. Oñate E. Structural analysis with the finite element methods. Linear Statics. Vol. 1. Barcelona: Ed. Springer Verlag; 2010.




2020     |     www.medigraphic.com