Citation: |
[1] |
E. Agyingi, D. S. Ross and K. Bathena, A model of the transmission dynamics of Leismaniasis, J. Bio. Systems, 19 (2011), 237-250.doi: 10.1142/S0218339011003841. |
[2] |
B. P. Ayati, C. M. Edwards, G. F. Webb and J. P. Wikswo, Mathematical model of bone remodeling dynamics for normal bone cell populations and myeloma bone disease, Biology Direct, 5 (2010), 28. |
[3] |
C. Battista, "Mathematical Models of Bone Remodeling at the Cellular Level," M.S. Thesis, Rochester Institute of Technology, 2011. |
[4] |
T. Bellido, A. Ali, L. I. Plotkin, Q. Fu, I. Gubrij, P. K. Roberson, R. S. Weinstein, C. A. O'Brien, S. C. Manolagas and R. I. Jilka, Proteasomal degradation of Runx2 shortens parathyroid hormone-induced anti-apoptotic signaling in osteoblasts; A putatitve explanation for why intermittent administration is needed for bone anabolism, J. Bio. Chem., 278, (2003), 50259-50272. |
[5] |
F. Brohner and W. E. Stein, Calcium homeostasis, an old problem revisited, J. Nutr., 125 (1995), 1987S-1995S. |
[6] |
F. Cosman, N. E. Lane, M. A. Bolognese, J. R. Zanchetta, P. A. Garcia-Hernandez, K. Sees, J. A. Matriano, K. Gaumer and P. E. Daddona, Effect of transdermal teriparatide administration on bone mineral density in postmenopausal women, J. Clin. Endocrinol. Metab., 95 (2010), 151-158.doi: 10.1210/jc.2009-0358. |
[7] |
D. W. Dempster, F. Cosman, M. Parisien and V. Shen, Anabolic action of parathyroid hormone on bone, Endocr. Rev., 14 (1993), 690-709. |
[8] |
P. Ducy, T. Schinke and G. Karsenty, The osteoblast: A sophisticated fibroblast under central surveillance, Science, 289 (2000), 1501-1504.doi: 10.1126/science.289.5484.1501. |
[9] |
J. S. Finkelstein, Jason J. Wyland, B. Z. Leder, S. A. M. Burnett-Bowie, H. Lee, H. Jüppner and R. M. Neer, Effects of teriparatide retreatment in osteoporotic men and women, J. Clin. Endocrinol. Metab., 94 (2009), 2495-2501.doi: 10.1210/jc.2009-0154. |
[10] |
C. Y. Guo, W. E. G. Thomas, A. W. al-Dehaimi, A. M. A. Assiri and R. Eastell, Longitudinal changes in bone mineral density and bone turnover in postmenopausal women with primary hyperparathyroidism, J. Clin. Endocrinol. Metab., 81 (1996), 3487-3491.doi: 10.1210/jc.81.10.3487. |
[11] |
R. L. Jilka, R. S. Weinstein, T. Bellido, P. Roberson, A. M. Parfitt and S. C. Manolagas, Increased bone formation by prevention of osteoblast apoptosis with parathyroid hormone, J. Clin. Invest., 104 (1999), 439-446.doi: 10.1172/JCI6610. |
[12] |
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 of bone remodeling, Bone, 33 (2003), 206-215.doi: 10.1016/S8756-3282(03)00157-1. |
[13] |
M. H. Kroll, Parathyroid hormone temporal effects on bone formation and resorption, Bull. Math. Biol., 62 (2000), 163-688.doi: 10.1006/bulm.1999.0146. |
[14] |
V. Lemaire, F. L. Tobin, L. D. Greller, C. R. Cho and L. J. Suva, Modeling the interactions between osteoblast and osteoclast activities in bone remodeling, J. Theo. Bio., 229 (2004), 293-309.doi: 10.1016/j.jtbi.2004.03.023. |
[15] |
S. C. Manolagas, Birth and death of bone cells: Basic regulatory mechanisms and implications for the pathogenesis and treatment of osteoporosis, Endocrine Reviews, 21 (2000), 115-137.doi: 10.1210/er.21.2.115. |
[16] |
R. M. Neer, C. D. Arnaud, J. R. Zanchetta, R. Prince, G. A. Gaich, J. Y. Reginster, A. B. Hodsman, E. F. Eriksen, S. Ish-Shalom, H. K. Genant, O. Wang and B. H. Mitlak, Effect of parathyroid hormone (1-34) on fractures and bone mineral density in postmenopausal women with osteoporosis, N. Engl. J. Med., 344 (2001), 1434-1441.doi: 10.1056/NEJM200105103441904. |
[17] |
R. O. C. Oreffoi, G. R. Mundyf, S. M. Seyedin and L. F. Bonewald, Activation of the bone-derived latent TGF-beta complex by isolated osteoclasts, Biochem. Biophys. Res. Comm., 158 (1989), 817-823.doi: 10.1016/0006-291X(89)92795-2. |
[18] |
M. Peterson and M. Riggs, A physiologically based mathematical model of integrated calcium homeostasis and bone remodeling, Bone, 46 (2010), 49-63.doi: 10.1016/j.bone.2009.08.053. |
[19] |
K. E. S. Poole and J. Reeve, Parathyroid hormone-a bone anabolic and catabolic agent, Current Opinion in Pharmacology, 5 (2005), 612-617. |
[20] |
J. F. Raposo, L. G. Sobrinho and H. G. Ferriera, A minimal mathematical model of calcium homeostasis, J. Clinical Endocrin. Metab., 87 (2002), 4330-4340.doi: 10.1210/jc.2002-011870. |
[21] |
D. S. Ross, K. Mehta and A. Cabal, A mathematical model of bone biochemistry, in preparation. |
[22] |
E. Seeman and P. D. Delmas, Reconstructing the skeleton with intermittent parathyroid hormone, Trends Endocrinol. Metab., 12 (2001), 281-283.doi: 10.1016/S1043-2760(01)00460-X. |
[23] |
R. P. Shrestha, C. V. Hollot, S. R. Chipkin, C. P. Schmitt and Y. Chait, A mathematical model of parathyroid hormone response to acute changes in plasma ionized calcium concentration in humans, Mathematical Biosciences, 226 (2010), 46-57.doi: 10.1016/j.mbs.2010.04.001. |
[24] |
E. Slatopolsky, A. Brown and A. Dusso, Pathogenesis of secondary hyperparathyroidism, Kidney Int. Suppl., 73 (1999), S14-S19.doi: 10.1046/j.1523-1755.1999.07304.x. |
[25] |
R. V. Talmage, G. E. Lester, P. F. Hirsch and J. Musculoske, Parathyroid hormone and plasma calcium control: An editorial, J. Musculoskel. Neuron. Interact., 1 (2000), 121-126. |
[26] |
S. L. Teitelbaum, Bone resorption by osteoclasts, Science, 289 (2000), 1501-1504.doi: 10.1126/science.289.5484.1504. |
[27] |
H. Vaananen and T. Laitala-Leinonen, Osteoclast lineage and function, Arch. Biochem. Biophys., 473 (2008), 132-138.doi: 10.1016/j.abb.2008.03.037. |
[28] |
L. Xing and B. F. Boyce, Regulation of apoptosis in osteoclasts and osteoblastic cells, Biochemical and Biophysical Research Communications, 328 (2005), 709-720.doi: 10.1016/j.bbrc.2004.11.072. |
[29] |
M. Zumsande, D. Stiefs, S. Siegmund and T. Gross, General analysis of mathematical models for bone remodeling, Bone, 48 (2011), 910-917.doi: 10.1016/j.bone.2010.12.010. |