The cellular dynamics of bone remodeling: A mathematical model

SIAM Journal on Applied Mathematics

Volumn 70, Issue 6, 2010, Pages 1899-1921

  Ryser, Marc D ^a   Komarova, Svetlana V ^a   Nigam, Nilima ^b  

^a MCGILL UNIVERSITY   (Canada)

^b SIMON FRASER UNIVERSITY   (Canada)

Author keywords

Bone multicellular units; Bone remodeling; Cellular dynamics; Nonlinear PDE; Scaling; Time delay

Indexed keywords

BONE MATRIX; BONE REMODELING; CELL TYPES; CELLULAR DYNAMICS; COMPLEX ENTITIES; COMPUTATIONAL RESULTS; DELAY EQUATIONS; FINITE DIFFERENCE SCHEME; IN-SILICO; IN-VIVO; MECHANOSENSING; NON LINEAR PDE; NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS; OSTEOCYTES; PARACRINE; PARAMETER SENSITIVITIES; SCALING; SCALING THEORIES; TWO SPACE DIMENSIONS;

AIRCRAFT ENGINES; BIOMECHANICS; BONE; DIFFERENCE EQUATIONS; DYNAMICS; MECHANICAL PROPERTIES; NONLINEAR EQUATIONS; OSTEOBLASTS; PARTIAL DIFFERENTIAL EQUATIONS; TIME DELAY;

MATHEMATICAL MODELS;

EID: 77951148825     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/090746094     Document Type: Article

References (37)

1. A. BARKER, Shear stress inhibits while disuse promotes osteocyte apoptosis, Biochem. Biophys. Res. Commun., 320 (2004), pp.1163-1168.
2. P. A. BALDOCK, G. P. THOMAS, J. M. HODGE, S. U. BAKER, U. DRESSEL, P. D. O'LOUGHLIN, G. C. NICHOLSON, K. H. BRIFFA, J. A. EISMAN, AND E. M. GARDINER, Vitamin D ac-tion and regulation of bone remodeling: Suppression of osteoclastogenesis by the mature osteoblast, J. Bone Miner. Res., 21 (2006), pp.1618-1626.
3. L. BONEWALD AND M. JOHNSON, Osteocytes, mechanosensing and Wnt signaling, Bone, 42 (2008), pp.606-615.
4. W. J. BOYLE, W. S. SIMONET, AND D. L. LACEY, Osteoclast differentiation and activation, Nature, 423 (2003), pp.337-342.
5. N. BUCAY, I. SAROSI, C. R. DUNSTAN, S. MORONY, J. TARPLEY, C. CAPPARELLI, S. SCULLY, H. L. TAN, W. XU, D. L. LACEY, W. J. BOYLE, AND W. S. SIMONET, Osteoprotegerin-deficient mice develop early onset osteoporosis and arterial calcification, Genes & Devel-opment, 12 (1998), pp.1260-1268.
6. E. H. BURGER, J. KLEIN-NULEND, AND T. H. SMIT, Strain-derived canalicular fluid flow regulates osteoclast activity in a remodelling osteon-a proposal, J. Biomech., 36 (2003), pp.1453-1459.
7. D. B. BURR, Remodeling and the repair of fatigue damage, Calcified Tissue International, 53 Suppl 1 (1993).
8. D. B. BURR, Muscle strength, bone mass, and age-related bone loss, J. Bone Miner. Res., 12 (1997), pp.1547-1551.
9. E. CANALIS AND D. AGNUSDEI, Insulin-like growth factors and their role in osteoporosis, Cal-cified Tissue International, 58 (1996), pp.133-134.
10. D. M. COOPER, C. D. THOMAS, J. G. CLEMENT, AND B. HALLGRIMSSON, Three-dimensional microcomputed tomography imaging of basic multicellular unit-related resorption spaces in human cortical bone, The Anatomical Record. Part A, Discoveries in Molecular, Cellular, and Evolutionary Biology, 288 (2006), pp.806-816.
11. C. EBMEYER, Regularity in Sobolev spaces for the fast diffusion and the porous medium equation, J. Math. Anal. Appl., 307 (2005), pp.134-152. (Pubitemid 40633661)
12. L. C. EVANS, Partial Differential Equations, Grad. Stud. Math.19, AMS, Providence, RI, 1998.
13. T. A. FRANZ-ODENDAAL, B. K. HALL, AND E. P. WITTEN, Buried alive: How osteoblasts become osteocytes, Developmental Dynamics, 235 (2006), pp.176-190.
14. F. GORI, L. C. HOFBAUER, C. R. DUNSTAN, T. C. SPELSBERG, S. KHOSLA, AND L. B. RIGGS, The expression of osteoprotegerin and rank ligand and the support of osteoclast formation by stromal-osteoblast lineage cells is developmentally regulated, Endocrinology, 141 (2000), pp.4768-4776.
15. S. HARADA AND G. A. RODAN, Control of osteoblast function and regulation of bone mass, Nature, 423 (2003), pp.349-355.
16. E. M. HAUGE, D. QVESEL, E. F. ERIKSEN, L. MOSEKILDE, AND F. MELSEN, Cancellous bone remodeling occurs in specialized compartments lined by cells expressing osteoblastic markers, J. Bone Miner. Res., 16 (2001), pp.1575-1582.
17. J. C. HUANG, T. SAKATA, L. L. PFLEGER, M. BENCSIK, B. P. HALLORAN, D. D. BIKLE, AND R. A. NISSENSON, Pth differentially regulates expression of Rankl and opg, J. Bone Miner. Res., 19 (2004), pp.235-244.
18. H. ITO, M. KOEFOED, P. TIYAPATANAPUTI, K. GROMOV, J. J. GOATER, J. CARMOUCHE, X. ZHANG, P. T. RUBERY, J. RABINOWITZ, R. J. SAMULSKI, T. NAKAMURA, K. SOBALLE, R. J. O'KEEFE, B. F. BOYCE, AND E. M. SCHWARZ, Remodeling of cortical bone allografts mediated by adherent Raav-Rankl and vegfgene therap y, Nat. Med., 11 (2005), pp.291-297.
19. H. D. JONES, T. NAKASHIMA, O. H. SANCHEZ, I. KOZIERADZKI, S. V. KOMAROVA, I. SAROSI, S. MORONY, E. RUBIN, R. SARAO, C. V. HOJILLA, V. KOMNENOVIC, Y.-Y. KONG, M. SCHREIBER, J. S. DIXON, S. M. SIMS, R. KHOKHA, T. WADA, AND J. M. PENNINGER, Regulation of cancer cell migration and bone metastas is by Rankl, Nature, 440 (2006), pp.692-696.
20. H. KANZAKI, M. CHIBA, Y. SHIMIZU, AND H. MITANI, Periodontal ligament cells under mechanical stress induce osteoclastogenesis by receptor activator of nuclear factor kappab ligand up-regulation via prostaglandin e2 synthesis, J. Bone Miner. Res., 17 (2002), pp.210-220.
21. A. E. KEARNS, S. KHOSLA, AND P. J. KOSTENUIK, Receptor activator of nuclear factor kappab ligand and osteoprotegerin regulation of bone remode ling in health and disease, Endocr. Rev., 29 (2008), pp.155-192.
22. S. KHOSLA, Minireview: The opg/Rankl/rank system, J. Endocrinol., 142 (2001), pp.5050-5055.
23. S. V. KOMAROVA, Mathematical model of paracrine interactions between osteoclasts and osteo-blasts predicts anabolic action ofparathyroid hormone on bone, J. Endocrinol., 146 (2005), pp.3589-3595.
24. S. V. KOMAROVA, R. J. SMITH, S. J. DIXON, S. M. SIMS, AND L. M. WAHL, Mathematical model predicts a critical role for osteoclast autocrine regulation in the control ofbone remodeling, Bone, 33 (2003), pp.206-215.
25. Y. Y. KONG, U. FEIGE, I. SAROSI, B. BOLON, A. TAFURI, S. MORONY, C. CAPPARELLI, J. LI, R. ELLIOTT, S. MCCABE, T. WONG, G. CAMPAGNUOLO, E. MORAN, E. R. BOGOCH, G. VAN, L. T. NGUYEN, P. S. OHASHI, D. L. LACEY, E. FISH, W. J. BOYLE, AND J. M. PENNINGER, Activated t cells regulate bone loss and joint destruction in adjuvant arthritis through osteoprotegerin ligand, Nature, 402 (1999), pp.43-47.
26. K. KURATA, T. J. HEINO, H. HIGAKI, AND H. K. VAANANEN, Bone marrow cell differentiation induced by mechanically damaged osteocytes in 3d gel-embedded culture, J. Bone Miner. Res., 21 (2006), pp.616-625.
27. V. LEMAIRE, Modeling the interactions between osteoblast and osteoclast activities in bone remodeling, J. Theoret. Biol., 229 (2004), pp.293-309.
28. R. MULLER, Three-dimensional finite element modelling of non-invasively assessed trabecular bone structures, Medical Engineering & Physics, 17 (1995), pp.126-133.
29. A. M. PARFITT, Osteonal and hemi-osteonal remodeling: The spatial and temporal framework for signal traffic in adult human bone, J. Cell. Biochem., 55 (1994), pp.273-286.
30. J. M. QUINN, K. ITOH, N. UDAGAWA, K. HAUSLER, H. YASUDA, N. SHIMA, A. MIZUNO, K. HIGASHIO, N. TAKAHASHI, T. SUDA, T. J. MARTIN, AND M. T. GILLESPIE, Transforming growth factor beta affects osteoclast differentiation via direct and indirect actions, J. Bone Miner. Res., 16 (2001), pp.1787-1794.
31. A. G. ROBLING, A. B. CASTILLO, AND C. H. TURNER, Biomechanical and molecular regulation bone remodeling, Ann. Rev. Biomed. Engrg., 8 (2006), pp.455-498.
32. M. D. RYSER, N. NIGAM, AND S. V. KOMAROVA, Mathematical modeling of spatio-temporal dynamics of a single bone multicellular unit, J. Bone Miner. Res., 24 (2009), pp.860-870.
33. T. H. SMIT AND E. H. BURGER, Is bmu-coupling a strain-regulated phenomenon? A finite element analysis, J. Bone Miner. Res., 15 (2000), pp.301-307.
34. G. P. THOMAS, S. U. BAKER, J. A. EISMAN, AND E. M. G ARDINER, Changing Rankl/opg mrna expression in differentiating murine primary osteoblasts, J. Endocrinol., 170 (2001), pp.451-460.
35. H. YASUDA, N. SHIMA, N. NAKAGAw A, K. YAMAGUc HI, M. KINOSAKI, S. I. MOc HIz UKI, A. TOMOy ASU, K. YANO, M. GOTO, A. MURAKAMI, E. TSUDA, T. MORINAGA, K. HIGASHIO, N. UDAGAWA, N. TAKAHASHI, AND T. SUDA, Osteoclast differentiation factor is a ligand for osteoprotegerin/osteoclastogenesis-inhibitory factor and is identical to trance/Rankl, Proc. Natl. Acad. Sci. USA, 95 (1998), pp.3597-3602.
36. Z. Yosi BASH, N. TRABELSI, AND C. MILGROM, Reliable simulations of the human proximal femur by high-order finite element analysis validated by experimental observations, J. Biomech., 40 (2007), pp.3688-3699.
37. L. You, S. TEMIYASATHIT, P. LEE, C. KIM, P. TUMMALA, W. YAO, W. KINGERY, A. MAL-ONE, R. KWON, AND C. JACOBS, Osteocytes as mechanosensors in the inhibition of bone resorption due to mechanical loading, Bone, 42 (2008), pp.172-179.