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Bone formation: biological aspects and modelling problems

dc.contributor.authorHerrero, Miguel A.
dc.contributor.authorLópez, J. M.
dc.date.accessioned2023-06-20T10:36:51Z
dc.date.available2023-06-20T10:36:51Z
dc.date.issued2005-03
dc.description.abstractIn this work we succintly review the main features of bone formation in vertebrates. Out of the many aspects of this exceedingly complex process, some particular stages are selected for which mathematical modelling appears as both feasible and desirable. In this way, a number of open questions are formulated whose study seems to require interaction among mathematical analysis and biological experimentation
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipEuropean Contract
dc.description.sponsorshipSpanish Ministry of Science
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/22502
dc.identifier.doi10.1080/10273660412331336883
dc.identifier.issn1027-3662
dc.identifier.officialurlhttp://www.hindawi.com/journals/cmmm/2005/197567/abs/
dc.identifier.relatedurlhttp://www.hindawi.com
dc.identifier.urihttps://hdl.handle.net/20.500.14352/50775
dc.issue.number1
dc.journal.titleJournal of Theoretical Medicine
dc.language.isoeng
dc.page.final55
dc.page.initial41
dc.publisherTaylor & Francis
dc.relation.projectIDMRTN-CT-2004-503661
dc.relation.projectIDGrant MCT-00-BMC-0446
dc.rights.accessRightsrestricted access
dc.subject.cdu51-76
dc.subject.cdu519.87
dc.subject.keywordBone formation
dc.subject.keywordmathematical modelling
dc.subject.keywordhuman skeleton
dc.subject.keywordskeletal morphogenesis
dc.subject.ucmBiomatemáticas
dc.subject.ucmInvestigación operativa (Matemáticas)
dc.subject.unesco2404 Biomatemáticas
dc.subject.unesco1207 Investigación Operativa
dc.titleBone formation: biological aspects and modelling problems
dc.typejournal article
dc.volume.number6
dcterms.referencesWolpert, L., 1998, Principles of Development (Oxford University Press). Turing, A.M., 1952, The chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond., 237, 37–72. Von Dassow, G., Meir, E., Munro, E.M. and Odell, G.M., 2000, The segment polarity network is a robust developmental module. Nature, 406, 188–192, 13 July. Raya, M., Kawakami, Y., Rodriguez-Esteban, C., Ibañes, M., Russkin-Gutman, D., Rodriguez-León, J., Buscher, D., Feijó, J.A. and Izpisúa-Belmonte, J.C., 2004, Notch activity acts as a sensor for extracellular calcium during vertebrate left–right determination. Nature, 427, 121–128. Carmeliet, P., 2000, Mechanisms of angiogenesis and arterogenesis. Nat. Med., 6(3), 389–395. Yancopoulos, G.D., Davis, S., Gale, N.W., Rudge, J.S., Wiegand, S.J. and Holash, J., 2000, Vascular-specific growth factors and blood vessel formation. Nature. 407, 242–248. Bussolino, F., Arese, M., Audero, E., Giraudo, E., Marchiò, S., Mittola, S., Primo, L. and Serini, G., 2003, Biological aspects of tumour angiogenesis. In: L. Preziosi (Ed.) Cancer Modeling and Simulation (Chapman and Hall), pp. 1–22. Sleeman, B.D. and Levine, H.A., 2001, Partial differential equations of chemotaxis and angiogenesis. Math. Meth. Appl. Sci., 24, 405–426. Levine, H.A., Sleeman, B.D. and Preziosi, L., 2003, Modelling tumour-induced angiogenesis. Cancer Modeling and Simulation (Chapman and Hall), pp. 147–184. Chaplain, M.A.J. and Anderson, A.R.A., 2003, Mathematical modeling of tissue invasion. In: L. Preziosi (Ed.) Cancer Modeling and Simulation (Chapman and Hall), pp. 269–298. Gardiner, D.M., Blumberg, B., Komine, Y. and Bryant, B.V., 1995, Regulation of HoxA expression in developing and regenerating axolotl limbs. Development, June 121(6), 1731–1741. Brand-Saberi, B. and Christ, B., 2000, Evolution and development of distinct cell lineages derived from somites. Curr. Top. Dev. Biol., 48, 1–42. Capdevila, J. and Izpisúa-Belmonte, J.C., 2001, Patterning mechanisms controlling vertebrate limb development. Annu. Rev. Cell. Dev. Biol., 17, 87–132. Meinhardt, H., 1982, Models of Biological Pattern Formation (London: Academic Press). Meinhardt, H., 1983a, A boundary model for pattern formation in vertebrate limbs. J. Embryol. Exp. Morph., 76, 115–137. Maden, M., 1983, A test of the predictions of the boundary model regarding supernumerary limb structures. J. Embryol. Exp. Morph., 76, 147–155. Meinhardt, H., 2004, Different strategies for midline formation in bilaterians. Nat. Rev. Neurosci., 5, 502–509. Gierer, A. and Meinhardt, H., 1972, A theory of biological pattern formation. Kybernetik, 12, 30–39. Koch, A.J. and Meinhardt, H., 1994, Biological pattern formation: From basic mechanisms to complex structures. Rev. Mod. Phys., 66(4), 1481–1507. De Lise, A.M., Fischer, L. and Tuan, R.S., 2000, Cellular interactions and signaling in cartilage development. Osteoarthritis Cartilage, 8, 309–334. Rowe, D.A. and Fallon, J.F., 1982, Normal anterior pattern formation after barrier placement in the chick leg: Further evidence on the action of the polarizing zone. J. Embryol. Exp. Morph., 69, 1–6. Summerbell, D., 1974, A quantitative analysis of the effect of excision of the AER from the chick limb-bud. J. Embryol. Exp. Morph., 32, 651–660. Summerbell, D., 1978, Normal and experimental variations in preparations of skeleton of chick embryo wing. Nature, 274(5670), 472–473. Wolpert, L., 2002, The progress zone model for specifying positional information. Int. J. Dev. Biol., 46(7), 869–870. Ng, J.K., Tamura, K., Buscher, D. and Izpisúa-Belmonte, J.C., 1999, Molecular and cellular basis of pattern formation during vertebrate limb development. Curr. Top. Dev. Biol., 41, 37–66. Mercader, N., Leonardo, E., Azpiazu, N., Serrano, A., Morata, G., Martinez, C. and Torres, M., 1999, Conserved regulation of proximodistal limb axis development by Meis1/Htb. Nature, 402(6760), 425–429. Meinhardt, H., 1983b, A bootstrap model for the proximodistal pattern formation in vertebrate limbs. J. Embryol. Exp. Morph., 76, 139–146. Maden, M. and Mustafa, K., 1982, The structure of 180 degrees supernumerary limbs and a hypothesis of their formation. Dev. Biol., 93(19), 257–265. Tickle, C., Alberts, B., Wolpert, L. and Lee, J., 1982, Local application of retinoic acid to the limb bud mimics the action of the polarizing region. Nature, 296(5857), 564–566. Summerbell, D., 1983, The effect of the application of retinoic acid to the anterior margin of the developing chick limb. J. Embryol. Exp. Morph., 78, 269–289. Thaller, C. and Eichele, G., 1996, Retinoid signaling in vertebrate limb development. Ann. N Y Acad. Sci., 785, 1–11. Mic, F.A., Sirbu, I.O. and Duester, G., 2004, Retinoic acid synthesis controlled by Raldh2 is required early for limb bud initiation and then later as a proximodistal signal during apical ectodermal ridge formation. J. Biol. Chem., 279(25), 26698–26706. Dillon, R. and Othmer, H.G., 1999, A mathematical model for outgrowth and spatial patterning of the vertebrate limb and bud. J. Theor. Biol., 197, pp 295–330. Gadgil, C., Dillon, R., and Othmer, H.G., 2003, Short and longrange efects of Sonic hedgehog in limb development. Proc. Nat. Acad. Sci. USA, 100, pp 819–835. Hall, B.K. and Miyake, T., 2000, All for one and one for all: condensations and the initiation of skeletal development. BioEssays, 22, 138–147. Rivas, R. and Shapiro, F., 2002, Structural stages in the development of the long bones and epiphysis. J. Bone Joint Surg., 84(1), 85–100. Keller, E.F. and Segel, L.A., 1970, Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol., 26, 399–415. Gomer, R., Gao, T., Tang, Y., Knecht, D. and Titus, M.A., 2002, Cell motility mediates tissue size regulation in Dictyostelium. J. Muscle Res. Cell Motil., 23, 809–815. Escalante, R. and Vicente, J.J., 2000, Dictyostelium discoideum: a model system for differentiation and patterning. Int. J. Dev. Biol., 44, pp 819–835. Herrero, M.A., 2003, Reaction-diffusion systems: A mathematical biology approach. In: L. Preziosi (Ed.) Cancer Modeling and Simulation (Chapman and Hall), pp. 367–420. Horstmann, D., 2003, From 1970 until present: The Keller–Segel model in chemotaxis and its consequences I. Jahresbericht der DMV, 105(3), 103–165. Herrero, M.A. and Velázquez, J.J.L., 1996, Chemotactic collapse for the Keller–Segel model. J. Math. Biol., 75, 177–196. Velázquez, J.J.L., 2002, Stability of some mechanisms of chemotactic aggregation. SIAM J. Appl. Math., 62, 1581–1633. Hentschel, H.G.E., Glimm, T., Glazier, J.A. and Newman, S.A., 2004, Dynamical mechanisms for skeletal pattern formation in the vertebrate limb. Proc. R. Soc. Lond. B, 271(1549), 1713–1722. Hunziker, E.B., 1994, Mechanism of longitudinal bone growth and its regulation by growth plate chondrocytes. Microsc. Res. Tech., 28, 505–519. Kronenberg, H.M., 2003, Developmental regulation of the growth plate. Nature, 423, 332–336. Alvarez, J., Balbín, M., Santos, F., Fernández, M., Ferrando, S. and López, J.M., 2000, Different growth rates are associated with changes in the expression pattern of types II and X collagens and collagenase 3 in proximal growth plates of the rat tibia. J. Bone. Miner. Res., 15(1), 82–94. Roach, H.I., Baker, J.E. and Clarke, N.M.P., 1998, Initiation of bone epiphysis in long bones: Chronology of interactions between the vascular system and the chondrocytes. J. Bone Miner. Res., 13(6), 950–961. Cancedda, R., Descalzi Cancedda, F. and Castagnola, P., 1995, Chondrocyte differentiation. Int. Rev. Cytol., 159, 265–358. Olsen, B.R., Reginato, A.M. and Wenfang, W., 2000, Bone development. Ann. Rev. Cell Dev. Biol., 16, 191–220. Mikhailov, A.S., 1994, Foundations of Synergetics I (Springer-Verlag). Murray, J.D., 2000, Mathematical Biology II, Springer Interdisciplinary Applied Mathematics, Vol. 18. Fisher, R.A., 1937, The wave of advance of an advantageous gene. Ann. Eugen., 7, 353–369. Kolmogorov, A. Petrovsky, I. and Piskunov, N., 1988. Study of the diffusion equation with growth of the quantity of matter and its application to a biology problem. In: P. Pelcé (Ed.) (Trans.) (London: Academic Press) (Original work published 1937, Bul. Moskovskovo G.S. Univ. 17, 1–26). Grindrod, P., 1991, Patterns and Waves (Oxford: Oxford University Press). Larson, D.A., 1978, Transient bounds and time-asymptotic behaviour of solutions to nonlinear equations of Fisher type. SIAM J. Appl. Math., 34, 93–103. Needham, D.J. and Barnes, A.N., 1999, Reaction-diffusion and phase waves occurring in a class of scalar reaction-diffusion equations. Nonlinearity, 12, 41–58. Kay, A.L., Sherratt, J.A. and Mc Leod, J.B., 2001, Comparison theorems and variable speed waves for a scalar reaction–diffusion equation. Proc. R. Soc. Edinb. A, 131, 1133–1161. Alvarez, J., Costales, L., Serra, R., Balbín, M. and Lopez, J.M., 2005, Expression patterns of matrix metalloproteinases and vascular endothelium growth factor during epiphyseal ossification. J. Bone. Miner. Res., To appear. Ataullakhanov, F.I., Guria, G.T., Sarbash, V.I. and Volkova, R.I., 1998, Spatio-temporal dynamics of clotting and pattern formation in human blood. Biochim. Biophys. Acta, 1425, 453–468. Ataullakhanov, F.I., Krasotkina, V., Sarbash, V.I., Volkova, R.I., Sinavridse, E.I. and Kondratovich, A.Y., 2002, Spatiotemporal dynamics of blood coagulation and pattern formation: An experimental study. Int. J. Bifurcat. Chaos, 12(9), 1969–1983.
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