Towards a new spatial representation of bone remodeling

Mathematical Biosciences and Engineering

Volumn 9, Issue 2, 2012, Pages 281-295

  Graham, Jason M ^a   Ayati, Bruce P ^a   Ramakrishnan, Prem S ^b   Martin, James A ^b  

^a UNIVERSITY OF IOWA   (United States)

^b UNIVERSITY OF IOWA   (United States)

Author keywords

Bone remodeling; Cytokines; Level set equation; Osteoblast; Osteoclast

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; BONE DISEASE; BONE REMODELING; COMPUTER SIMULATION; HUMAN; OSTEOBLAST; OSTEOCLAST; PATHOPHYSIOLOGY; PHYSIOLOGY;

ANIMALS; BONE DISEASES; BONE REMODELING; COMPUTER SIMULATION; HUMANS; MODELS, BIOLOGICAL; OSTEOBLASTS; OSTEOCLASTS;

EID: 84863294575     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2012.9.281     Document Type: Article

References (32)

1. T. Akchurin, T. Aissiou, N. Kemeny, E. Prosk, N. Nigam and S. V. Komarova, Complex dynamics of osteoclast formation and death in long-term cultures, PLoS One, 3 (2008).
2. B. P. Ayati, C. M. Edwards, G. F. Webb and J. P. Wikswo, A mathematical model of bone remodeling dynamics for normal bone cell populations and myeloma bone disease, Biology Direct, 5 (2010).
3. J. P. Bilezikian, L. G. Raisz and G. A. Rodan, "Principles ofBone Biology," Second edition, Academic Press, Boston, 2002.
4. L. Geris, A. Gerisch, C. Maes, G. Carmeliet, R. Weiner, J. Vander Sloten and H. Van Oosterwyck, Mathematical modeling of fracture healing in mice: Comparison between experimental data and numerical simulation results, Med. Biol. Eng. Comput., 44 (2006), 280-289. (Pubitemid 43949704)
5. L. Geris, A. Gerisch and R. C. Schugart, Mathematical modeling in wound healing, bone regeneration and tissue engineering, Acta Biotheor, 58 (2010), 355-367.
6. L. Geris, A. Gerisch, J. Vander Sloten, R. Weiner and H. Van Oosterwyck, Angiogenesis in bone fracture healing: A bioregulatory model, J. Theor. Bio., 25 (2008), 137-158.
7. L. Geris, A. A. C. Reed, J. Vander Sloten, A. Hamish, R. W. Simpson and H. Van Oosterwyck, Occurrence and treatment of bone atrophic non-unions investigated by an integrative approach, PLoS Comput. Bio., 6 (2010), 189-193.
8. L. Geris, J. Vander Sloten and H. Van oosterwyck, Connecting biology and mechanics in fracture healing: An integrated mathematical modeling framework for the study of nonunions, Biomech. Model. Mechanobiol., 9 (2010), 713-724.
9. C. T. Kelley, "Iterative Methods for Linear and Nonlinear Equations," With separately avail- able software, Frontiers in Applied Mathematics, 16, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1995.
10. C. T. Kelley, "Solving Nonlinear Equations with Newton's Method," Fundamentals of Algorithms, 1, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2003.
11. S. V. Komarova, Mathematical model ofparacrine interactions between osteoclasts and osteoblasts predicts anabolic action of parathyroid hormone on bone, J. Endocrinol., 146 (2005), 3589-3595. (Pubitemid 41058130)
12. S. V. Komarova, R. J. Smith, S. J. Dixon, S. M. Sims and L. H. Wahl, Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling, Bone, 33 (2003), 225-234.
13. M. J. Martin and J. C. Buckland-Wright, Sensitivity analysis of a novel mathematical model identifies factors determining bone resorption rates, Bone, 35 (2004), 918-928. (Pubitemid 39349223)
14. M. J. Martin and J. C. Buckland-Wright, A novel mathematical model identifies potential factors regulating bone apposition, Calcif. Tissue Int., 77 (2005), 250-260. (Pubitemid 41531505)
15. I. M. Mitchell, The flexible, extensible and efficient toolbox oflevel set methods, J. Sci. Comp., 35 (2008), 300-329.
16. S. Osher and R. Fedkiw, "Level Set Methods and Dynamic Implicit Surfaces," Applied Math- ematical Sciences, 153, Springer-Verlag, New York, 2003.
17. S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobiformulations, J. Comput. Phys., 79 (1988), 12-49.
18. S. Osher and C. Shu, High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations, SIAM J. Numer. Anal., 28 (1991), 907-922. (Pubitemid 21682139)
19. 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), 273-286. (Pubitemid 24218802)
20. V. Peiffer, A. Gerisch, D. Vandepitte, H. Van Oosterwyck and L. Geris, A hybrid bioregulatory model of angiogenesis during bonefracture healing, Biomech. Model. Mechanobiol., 10 (2011), 383-395.
21. D. Peng, B. Merriman, S. Osher, H. Zhao and M. Kang, A PDE-based fast local level set method, J. Comput. Phys., 155 (1999), 410-438.
22. P. Pivonka and S. V. Komarova, Mathematical modeling in bone biology: From intracellular signaling to tissue mechanics, Bone, 47 (2010), 181-189.
23. P. Pivonka, J. Zimak, D. W. Smith, B. S. Gardiner, C. R. Dunstan, N. A. Sims, T. J. Martin and G. R. Mundy, Model structure and control of bone remodeling: A theoretical study, Bone, 43 (2008), 249-263.
24. L. G. Raisz, Physiology and pathophysiology of bone remodeling, Clinical Chemistry, 45 (1999), 1353-1358. (Pubitemid 29422075)
25. A. G. Robling, A. B. Castillo and C. H. Turner, Biomechanical and molecular regualtion of bone remodeling, Annu. Rev. Biomed. Eng., 8 (2006), 455-498. (Pubitemid 44314825)
26. M. D. Ryser, S. V. Komarova and N. Nigam, The cellular dynamics of bone remodeling: A mathematical model, SIAM J. Appl. Math., 70 (2010), 1899-1921.
27. M. D. Ryser, N. Nigam and S. V. Komarova, Mathematical modeling of spatio-temporal dyanmics of a single bone multicellular unit, J. Bone Miner. Res., 24 (2009), 860-870.
28. D. Salac and W. Lu, A local semi-implicit level-set method for interface motion, J. Sci. Comput., 35 (2008), 330-349.
29. J. A. Sethian, "Level Set Methods and Fast Marching Methods. Evolving Interfaces in Com- putational Geometry, Fluid Mechanics, Computer Vision, and Materials Science," Second edition, Cambridge Monographs on Applied and Computational Mathematics, 3, Cambridge University Press, Cambridge, 1999.
30. B. Sumengen, A matlab toolbox implementing level set methods, 2004. Available from: http: //barissumengen.com/level-set-methods/.
31. H. Zhao, T. Chan, B. Merriman and S. Osher, A variational level set approach to multiphase motion, J. Comput. Phys., 127 (1996), 179-195. (Pubitemid 126162336)
32. H. Zhao, B. Merriman, S. Osher and L. Wang, Capturing the behavior of bubbles and drops using the variational level set approach, J. Comput. Phys., 143 (1998), 495-518. (Pubitemid 128345945)