Computer simulation of long bone development: A model of endochondral ossification
Some bones of the body are constituted by cartilaginous supports in which growth is produced both with the ossification process that extends from the center of the bone towards its borders in a process so called endocondral ossification. In this period of bone tissue morphogenesis the factors controlling the process are mainly biochemical, and the mechanical influence is much lower. This paper presents a simulation model using reaction-diffusion equations for the growth and ossification process in the prenatal bone. It is primarily controlled by an interactive inhibitor-activator loop associated with the parathyroid hormone (PTHrP) and the Indian Hedgehog (Ihh). These equations in combination with the simulation of the proliferative process and the cartilage cell growth (chondrogenesis) lead to a quite accurate simulation of the growth process of a long bone, even predicting the development of secondary ossification centers in the epiphysis.
E. Minina, C. Kreschel, M. Naski, D. Ornitz, and A. Vortkamp. “A Interaction of fgf, ihh/pthlh, and bmp signaling integrates chondrocyte proliferation and hypertrophic differentiation”. Developmental Cell. Vol. 3. 2002. pp. 439-449.
B. Gao, J. Guo, C. She, A. Shu, M. Yang, Z. Tan, X. Yang, S. Guo, G. Feng, L. He. “Mutations in IHH, encoding Indian hedgehog, cause brachydactyly type A-1”. Nat Genet. Vol. 28. 2001. pp. 386-388,
S. Karp, E. Schipani, B. St-Jacques, J. Hunzelman, H. Kronenberg, A McMahon. “Indian Hedgehog coordinates endochondral bone growth and morphogenesis via parathyroid hormone related-Protein-dependent and -independent pathways”. Development. Vol. 127. 2000. 543-548.
J. M. Kindblom, O. Nilsson, T. Hurme, C. Ohlsson, J. Savendahl. “Expression and localization of Indian Hedgehog (Ihh) and parathyroid hormone related protein (PTHrP) in the human growth plate during pubertal development”. Journal of Endocrinology. Vol. 174. 2002. pp. R1-R6.
S. Provot, E. Schipani. “Molecular mechanisms of endochondral bone development”. Biochemical and Biophysical Research Communications. Vol. 328. 2005.pp. 658-665.
F. Forriol, F. Shapiro. “Bone development”. Clinical Orthopaedics and related research. Vol. 43. 2005. pp. 214-33.
H. Kronenberg. “Development regulation of the growth plate”. Nature. Vol. 423. 2003. pp. 332-336.
J. Brouwers, C. VanDonkelaar, B. Sengers, R. Huiskes. “Can the growth factors PTHrP, Ihh and VEGF, together regulate the development of a long bone?”. Journal of Biomechanics. Vol. 39. 2006. pp. 2774-2782.
B. DeCrombrugghe, V. Lefebvre, K. Nakashima. “Regulatory mechanisms in the pathways of cartilage and bone formation”. Current Opinion in Cell Biology. Vol. 13. 2001. pp. 721-728.
T. Kobayashi, D. W. Soegiarto, Y. Yang, B. Lanske, E. Schipani, A. P. McMahon, H. M. Kronenberg. “Indian Hedgehog stimulates periarticular chondrocyte differentiation to regulate growth plate length independently of PTHrP”. J. Clin. Invest. Vol.115. 2005. pp. 1734-1742.
C. E. Farnum, R. Lee, K. Ohara, J. P. G Urban. “Volume increase in growth plate chondrocytes during hypertrophy: the contribution of organic osmolytes”. Bone. Vol. 30. 2002. pp. 574-581.
J. E. Marsden, T. J. Hughes. Mathematical Foundations of Elasticity. Courier Dover Publications. New York. 1983. pp. 120-180.
T. J. R. Hughes. The Finite Element Method–Linear Static and Dynamic Finite Element Analysis. Dover Publishers. NewYork. 2000. pp. 459-488
A. Madzvamuse. A Numerical approach to the study of spatial pattern formation, D. Phil Thesis. Oxford University. UK. 2000. pp. 5-125.
A. Madzvamuse, “Time-stepping schemes for moving grid finite elements applied to reaction-diffusion systems on fixed and growing domains”. Journal of Computational Physics. Vol. 214. 2006. pp. 239-263.
P. K. Maini. “Using Mathematical Models to help understand biological pattern formation. C”. R. Biologies. Vol. 327.2004. pp. 225-234.
J. D. Murray. Mathematical Biology I. 3 ed. Ed. Springer. New York. 2001. pp. 44-75
U. Chung, E. Schipani, U. McMahon, H. M. Kronenberg. “Indian Hedgehog couples chondrogenesis to osteogenesis in endochondral bone development”. J. Clin. Invest. Vol. 107.2001. pp. 295-304.
M. C. Fisher, C. Meyer, G. Garber, C. Dealy. “Role of IGFBP2, IGF-I and IGF-II in regulating long bone growth”. Bone. Vol. 37.2005. pp. 741–750.
S. L. Johnsen, T. Wilsgaard, S. Rasmussen, R. Sollien, T. Kiserud. “Longitudinal reference charts for growth of the fetal head, abdomen and femur”. European Journal of Obstetrics and Gynecology and reproductive Biology. Vol. 127. 2006. pp. 172-185.
T. Zylan, K. W. Murshid. “An assesment of femur growth parameters in human fetuses and their relationship to gestational age”. Turk J Med Sci. Vol. 33. 2003. pp. 27-32.
L. S. Chitty, D. G. Altman. “Charts of fetal size: limb bones”. BJOG: An international Journal of Obstetrics and Gynecology. Vol. 109. 2002. pp. 919-929.
W. Floyd, D. Zaleske, A. Schiller, C. Trahan, H. Mankin. “Vascular events associated with the appearance of the secondary center of ossification in the murine distal femoral epiphysis”. Journal of Bone and Joint Surgery. Vol. 69A. 1987. pp. 185-190.
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