2013, Number 1
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Revista Cubana de Ortopedia y Traumatología 2013; 27 (1)
Theoretical and conceptual proposal for appearance modeling of ossification centers in different types of flat and long bones
Calixto LF, Gutiérrez ML, Garzón ADA
Language: Spanish
References: 56
Page: 2-21
PDF size: 248.52 Kb.
ABSTRACT
A work context on the modeling of endocondral formation process in any type of ossification present in the bones of the human body was shown. Assuming that PTHrP and Ihh form a biochemical regulatory loop for the endocondral process and BMP2 and Noggin for the intramembranous one, regulatory mechanisms for this formation process were implemented. For this purpose, a set of widely used diffusion reaction equations in morphogenesis were used in which the biochemical factors are supposed to be secreted by precursor cells, mesenchymal and chondrocytes in the case of intramembranous and chondroidal respectively. It was concluded that the solution led to the denominated Turing patterns which represent these ossification processes in a highly estimated form.
REFERENCES
Van Der Meulen MC, Huikes R. Why Mechanobiology? J Biomech. 2002;35(4):401-14.
Sadler TW. Langman's medical embryology. 9th ed. Maryland: Lippincott Williams and Wilkins Ed. Baltimore; 2010. p. 1-534.
Holleville N, Quilhac A, Bontoux M, Monsoro-Burq AH. BMP signals regulate Dlx5 during early avian skull development. Dev Biol. 2003;257(1):177-89.
Franceschini MP. On the appearance and evolution of secondary centers of ossification in the tibia of Gallus gallus. Acta Anat. 1967;68:169-88.
Kronenberg HM. Development regulation of the growth plate. Nature. 2003;423:332-6.
Morini S, Continenza M, Ricciardi AG, Gaudio E, Pannarale L. Development of the microcirculation of the secondary ossification center in rat humeral head. Anat Rec Part A. 2004;278A:41927.
De Crombrugghe B, Lefebvre V, Nakashima K. Regulatory mechanisms in the pathways of cartilage and bone formation. Curr Opin Cell Biol. 2001;13(6):721-8.
Provot S, Schipani E. Molecular mechanisms of endochondral bone development. Biochem Bioh Res Co. 2005;328(3):658-65.
Karp S, Schipani E, St-Jacques B, Hunzelman J, Kronenberg H, Mcmahon AP. Indian Hedgehog coordinates endochondral bone growth and morphogenesis via parathyroid hormone related-protein -dependent and -independent pathways. Development. 2000;127:543-8.
Sundaramurthy S, Mao J. Modulation of endochondral development of the distal femoral condyle by mechanical loading. J Orthop Res. 2006;24:229-41.
Carter DR, Wong MA. Theoretical model of endochondral ossification and bone architectural construction in long bone ontogeny. Anat Embryol. 1990;181(6):523-32.
Henderson J, Carter DR. Mechanical induction in limb morphogenesis: The role of growth-generated strains and pressures. Bone. 2002;31(6):645-53.
Kobayashi T, Soegiarto DW, Yang Y, Lanske B, Schipani E, Mcmahon AP, Kronenberg HM. Indian Hedgehog stimulates periarticular chondrocyte differentiation to regulate growth plate length independently of PTHrP. J Clin Invest. 2005;115:1734-42.
Chung U, Schipani E, Mcmahon AP, Kronenberg HM. Indian Hedgehog couples chondrogenesis to osteogenesis in endochondral bone development. J Clin Invest. 2001;107(3):295-304.
Kindblom JM, Nilsson O, Hurme T, Ohlsson C, Savendah JL. Expression and localization of Indian Hedgehog (Ihh) and Parathyroid hormone related protein (PTHrP) in the human growth plate during pubertal development. J Endocrinol. 2002;174:R1-R6.
Kobayashi T, Chung UI, Schipani E, Starbuck M, Karsenty G, Katagiri T, et al. PTHrP and Indian Hedgehog control differentiation of growth plate chondrocytes at multiple steps. Development. 2002;129:2977-86.
Zelzer E, Mamluk R, Ferrara N, Johnson R, Schipani E, Olsen B. Vegfa is necessary for chondrocytes survival during bone development. Development. 2003;131:2161-71.
St-Jacques B, Hammerschmidt M, Mcmahon A. Indian Hedgehog signaling regulates proliferation and differentiation of chondrocytes and is essential for bone formation. Gene Dev. 1999;13:2072-86.
Fisher MC, Meyer C, Garber G, Dealy C. Role of IGFBP2, IGF-I and IGF-II in regulating long bone growth. Bone. 2005;37(6):741-50.
Vortkamp A, Lee K, Lanske B, Segre GV, Kronenberg HM, Tabin CJ. Regulation of rate of cartilage differentiation by Indian hedgehog and PTH- related protein. Science. 1996;273:613-22.
Madzvamuse A, Maini PK, Wathen AJ. A moving grid finite element method for the simulation of pattern generation by Turing models on growing domains. J Sci Comput. 2005;24:247-62.
Crampin EJ, Maini PK. Reaction-diffusion models for biological pattern formation. Methods Applications Analysis. 2001;8(3):415-28.
Page KM, Maini PK, Monk NAM. Complex pattern formation in reaction-diffusion systems with spatially varying parameters. Physica D: Nonlinear Phenomena. 2005;202(1-2):95-115.
Murray JD, Maini PK. A new approach to the generation of pattern and form in embriology. Sci Prog. 1986;70:539-53.
Maini PK, Baker RE, Chuong CM. The Turing model comes of molecular age. Science. 2006;314:1397-8.
Maini PK, Murray JD. A nonlinear analysis of a mechanical model for pattern formation. SIAM J Appl Math. 1998;48:1064-72.
Garzón-Alvarado DA, García-Aznar JM, Doblaré M. Appearance and location of secondary ossification centres may be explained by a reaction-diffusion mechanism. Computers Biology Medicine. 2009;39(6):554-61.
Farnum CE, Lee R, Ohara K, Urban JPG. Volume increase in growth plate chondrocytes during hypertrophy: the contribution of organic osmolytes. Bone. 2002;30(4):574-81.
Kronenberg H. Development regulation of the growth plate. Nature. 2003;423:332-6.
DeCrombrugghe B, Lefebvre V, Nakashima K. Regulatory mechanisms in the pathways of cartilage and bone formation. Current Opinion Cell Biology. 2001;13(6):721-8.
Kobayashi T, Soegiarto DW, Yang Y, Lanske B, Schipani E, McMahon AP, et al. Indian Hedgehog stimulates periarticular chondrocyte differentiation to regulate growth plate length independently of PTHrP. J Clin Invest. 2005;115:1734-42.
Provot S, Schipani E. Molecular mechanisms of endochondral bone development. Biochemical Biophysical Research Communications. 2005;328(3):658-65.
Madzvamuse AA. Numerical approach to the study of spatial pattern formation. Oxford University, UK: D. Phil Thesis; 2000. p. 1-125.
Madzvamuse A. Time-stepping schemes for moving grid finite elements applied to reaction-diffusion systems on fixed and growing domains. J Computational Physics. 2006;214:239-63.
Maini PK. Using mathematical models to help understand biological pattern formation. C R Biologies. 2004;327:225-34.
Chung U, Schipani E, McMahon U, Kronenberg HM. Indian Hedgehog couples chondrogenesis to osteogenesis in endochondral bone development. J Clin Invest. 2001;107(3):295-304.
Fisher MC, Meyer C, Garber G, Dealy C. Role of IGFBP2, IGF-I and IGF-II in regulating long bone growth. Bone. 2005;37(6):741-50.
Johnsen SL, Wilsgaard T, Rasmussen S, Sollien R, Kiserud T. Longitudinal reference charts for growth of the fetal head, abdomen and femur. European J Obst Gynecol Reprod Biol. 2006;85(3):286-97.
Zylan T, Murshid KW. An assessment of femur growth parameters in human fetuses and their relationship to gestational age. Turk J Med Sci. 2003;33:27-32.
Chitty LS, Altman DG. Charts of fetal size: limb bones. BJOG: International J Obst Gynecol. 2002;109:919-29.
Zelzer E, Mamluk R, Ferrara N, Johnson R, Schipani E, Olsen B. VEGFA is necessary for chondrocytes survival during bone development. Development. 2003;131:2161-71.
Mackie EJ, Ahmed YA, Tatarczuch L, Chen K-S, Mirams M. Endochondral ossification: how cartilage is converted into bone in the developing skeleton. International J Biochemistry Cell Biology. 2008;40(1):46-62.
Krane SM, Inada M. Matrix metalloproteinases and bone. Bone. 2008;43(1):7-18.
Troeberg L, Nagase H. Proteases involved in cartilage matrix degradation in osteoarthritis. Biochimica Biophysica Acta (BBA)-Proteins Proteomics. 2011;1824(1):133-45.
Filvaroff EH. VEGF and bone. J Musculoskeletal Neuronal Interactions. 2003;3(4):304-7.
Turing AM. The chemical basis of morphogenesis. Biological Sciences. 1952;237(641):37-72.
Garzon-Alvarado DA, Ramírez Martínez AM. A biochemical hypothesis on the formation of fingerprints using a turing patterns approach. Theor Biol Med Model. 2011;8:24.
Murray JD. Parameter space for turing instability in reaction diffusion mechanisms: a comparison of models. J Theor Biol. 1982;98(1):143-63.
Zhu W, Kim J, Cheng C, Rawlins BA, Boachie-Adjei O, Crystal RG, Hidaka C. Noggin regulation of bone morphogenetic protein (BMP) 2/7 heterodimer activity in vitro. Bone. 2006;39(1):61-71.
Walsh DW, Godson C, Brazil DP, Martin F. Extracellular BMP-antagonist regulation in development and disease: tied up in knots. Trends Cell Biol. 2010;20(5):244-56.
Plikus MV, Zeichner-David M, Mayer JA, Reyna J, Bringas P, Thewissen JG, et al. Morphoregulation of teeth: modulating the number, size, shape and differentiation by tuning Bmp activity. Evol Dev. 2005;7(5):440-57.
Ruch JV, Lesot H, Begue-Kirn C. Odontoblast differentiation. Int J Dev Biol. 1995;39(1):51-68.
Schmitt R, Ruch JV. In vitro synchronization of embryonic mouse incisor preodontoblasts and preameloblasts: repercussions on terminal differentiation. Eur J Oral Sci. 2000;108(4):311-9.
Tubbs RS, Bosmia AN, Cohen-Gadol A. The human calvaria: a review of embriology, anatomy, pathology, and molecular development. Childs Nerv Syst. 2012Apr;28(4):23-31.
Sick S, Reinker S, Timmer J, Schlake T. Wtn and Dkk determine hair follicle spacing through a reaction-diffusion mechanism. Science. 2006;314:1447-50.
Carter DR, Wong M. The role of mechanical loading histories in the development of diarthrodial joints. J Orthop Res. 1988;6:804-16.