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Mathematical Biosciences and Engineering (MBE)
 

Towards a new spatial representation of bone remodeling
Pages: 281 - 295, Issue 2, April 2012

doi:10.3934/mbe.2012.9.281      Abstract        References        Full text (664.9K)                  Related Articles

Jason M. Graham - Department of Mathematics/Program, in Applied Mathematical and Computational Sciences, University of Iowa, Iowa City, IA 52242-1419, United States (email)
Bruce P. Ayati - Department of Mathematics/Program, in Applied Mathematical and Computational Sciences, University of Iowa, Iowa City, IA 52242-1419, United States (email)
Prem S. Ramakrishnan - Department of Orthopaedics and Rehabilitation, University of Iowa Hospitals and Clinics, University of Iowa, Iowa City, IA 52242, United States (email)
James A. Martin - Department of Orthopaedics and Rehabilitation, University of Iowa Hospitals and Clinics, University of Iowa, Iowa City, IA 52242, United States (email)

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 of Bone 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.
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 available 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 of paracrine interactions between osteoclasts and osteoblasts predicts anabolic action of parathyroid hormone on bone, J. Endocrinol., 146 (2005), 3589-3595.
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.
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.
15 I. M. Mitchell, The flexible, extensible and efficient toolbox of level set methods, J. Sci. Comp., 35 (2008), 300-329.       
16 S. Osher and R. Fedkiw, "Level Set Methods and Dynamic Implicit Surfaces," Applied Mathematical Sciences, 153, Springer-Verlag, New York, 2003.       
17 S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, 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.       
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.
20 V. Peiffer, A. Gerisch, D. Vandepitte, H. Van Oosterwyck and L. Geris, A hybrid bioregulatory model of angiogenesis during bone fracture 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.
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.
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 Computational 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.       
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.       

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