Publication: On the dynamics of the growth plate in primary ossification
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2010-08-21
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Elsevier
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Abstract
In this work a mathematical model for the interaction of two key signalling molecules in rat tibia ossification is presented and discussed. The molecules under consideration are Indian hedgehog (Ihh) and parathyroid hormone-related peptide (PTHrP). These are known to be major agents in the dynamics of the so-called growth plate, where transition from pristine cartilage to advancing bone takes place. Our model consists in a steady-state linear approximation to a reaction-diffusion system where only diffusion and absorption mechanisms are retained. Estimates on some system parameters are given, on the basis of the knowledge of a few measurable quantities. This allows for explicitly solving our model, whereupon a discussion on robustness and regulatory properties thereof is provided. In particular, we show that the size of the Proliferative Zone in the growth plate is rather insensitive to variations in the flux coefficients for Ihh and PTHrP at their boundaries. Besides, we also show that the model is also insensitive to large changes in the (comparatively small) critical value of the PTHrP concentration which marks the transition form Proliferative to Hyperthropic Regions within the Growth Plate. These results hold irrespective of the particular diffusivities selected for Ihh and PTHrP.
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J. Alvarez, M. Balbín, F. Santos, M. Fernández, S. Ferrando, J.M. López. Different bone growth rates are associated with changes in the expression patterns of types II and X collagensand collagenase 3 in proximal growth plates of the rat tibia J. Bone Miner. Res., 15 (2000), pp. 82–94
J.E.M. Brouwers, C.C. van Donkelaar, B.G. Sengers, R. Huiskes. Can the growth factors PTHrP, Ihh and VGEF, together regulate the development of a long bone? J. Biomech., 39 (2006), pp. 2774–2782
C. Colnot, C. Lu, D. Hu, J.A. Helms. Distinguishing the contributions of the perichondrium, cartilage and vascular endothelium to skeletal development Dev. Biol., 269 (2004), pp. 55–69
R.C. Edwards, W.A. Ratcliffe, J. Walls, J.M. Morrison, J.G. Ratcliffe, R. Holder, N.J. Bundred. Parathyroid hormone-related protein (PTHrP) in breastcancer and in benign breast tissue Eur. J. Cancer, 31 (3) (1995), pp. 334–339
G.A. Garzón-Alvarado, J.M. García-Aznar, M. Doblaré. A reaction–diffusion model for long bones growth Biomech. Model. Mechanobiol., 8 (2009), pp. 381–395
G.A. Garzón-Alvarado, J.M. García-Aznar, M. Doblaré. Appearance and location of secondary ossification centres may be explained by a reaction–diffusion mechanism Comput. Biol. Med., 39 (2009), pp. 554–561
M.A. Herrero, J.M. Lopez. Bone formation: biological aspects and modelling problems J. Theor. Med. (now Computational and Mathematical Methods in Medicine), 6 (1) (2005), pp. 41–55
E.B. Hunziker. Mechanism of longitudinal bone growth and its regulation by growth plate chondrocyte Microsc. Res. Tech., 28 (1994), pp. 505–519
D. Kalderon. Similarities between the Hedgehog and Wnt signalling pathways Trends Cell Biol., 12 (2002), pp. 523–531
T. Kobayashi, U.I. Chung, E. Schipani, M. Starbuck, G. Karsenty, T. Katagiri, D.L. Goad, B. Lanske, H.M. Kronenberg PTHrP and Indian hedgehog control differentiation of growth plate chondrocytes at multiple steps Development, 129 (2002), pp. 2977–2986
H.M. Kronenberg. Developmental regulation of the growth plate Nature, 423 (2003), pp. 332–336
E.J. Mackie, Y.A. Ahmed, L. Tatarczuch, K.S. Chen, M. Mirams. Endochondral ossification: how cartilage is converted into bone in the developing skeleton The Int. J. Biochem. Cell Biol., 40 (2008), pp. 46–62
H. Meinhardt. Models of Biological Pattern Formation Academic Press, London (1982)
E. Minina, H.M. Wenzel, C. Kreschel, S. Karp, W. Gaffield, A. McMahon, A. Wortkamp. Bmp AND Ihh/PTHrP signalling interact to coordinate chondrocyte proliferation and differentiation Development, 128 (2001), pp. 4523–4534
P. Moreo, J.M. García-Aznar, M. Doblaré. Bone ingrowth on the surface of endosseous implants. Part 1: mathematical model J. Theor. Biol., 260 (2009), pp. 1–12
O. Nilsson, R. Marino, F. De Luca, M. Phillip, J. Baron. Endocrine regulation of the growth plate Horm Res., 64 (2005), pp. 157–165
S. Pathi, S. Pagan-Westphal, D.P. Baker, E.A. Garber, P. Rayhorn, D. Bumcrot, C.J. Tabin, R. Blake Pepinsky, K.P. Williams. Comparative biological responses to human Sonic, Indian and desert hedgehog Mech. Dev., 106 (2001), pp. 107–117
R. Rivas, F. Shapiro. Structural stages in the development of the long bones and epiphysis J. Bone Joint Surg., 84 (1) (2002), pp. 85–100
D. Saha, D. Schaffer. Signal dynamics in Sonic Hedgehog tissue patterning Development, 133 (2006), pp. 889–900
T. Shimo, C. Gentili, M. Iwamoto, C. Wu, E. Koyama, M. Pacifici. Indian hedgehog and syndecans-3 coregulate chondrocyte proliferation and function during chick limb skeletogenesis Dev. Dyn., 229 (2004), pp. 607–617
C.C. Van Donkelaar, R. Huiskes. The PTHrP-Ihh fedback loop in the embryonic growth plate allows PTHrPto control hypertrophy and Ihh to regulate proliferation Biomech. Model. Mechanobiol., 6 (2007), pp. 55–62
A. Vortkamp, K. Lee, B. Lanske, G.V. Segre, H.M. Kronenberg, C.J. Tabin. Regulation of rate of cartilage differentiation by Indian Hedgehog and PTH-related protein Science, 273 (1996), pp. 613–622
E.C. Weir, W.M. Philbrick, M. Amling, L.N. Neff, R. Baron, A.E. Broadus. Targeted overexpression of parathyroid hormone-related peptide in chondrocytes causes chondrodysplasia and delayed endochondral bone formation Proc. Natl. Acad. Sci. USA, 93 (1996), pp. 10240–10245
R.M. Williams, W.R. Zipfel, M.L. Tinsley, C.E. Farnum. Solute transport in growth plate cartilage: in vitro and in vivo Biophys. J., 93 (2007), pp. 1039–1050
Q. Zhao, P.R. Brauer, L. Xiao, M.H. Mc Guire, J.A. Yee. Expression of parathyroid hormone-related peptide (PthrP) and its receptor (PTH1R) during the histogenesis of cartilage and bone in the chicken mandibular process J. Anat., 201 (2002), pp. 137–151