Abstract
A theoretical model for surface bone remodeling under electromagnetic loads is proposed in this paper. In the model, surface bone remodeling is assumed to be related to growth factors. Growth factors in latent form in osteocytes are released to the bone fluid after the osteocytes are absorbed by osteoclasts, and then regulate the bone formation process. At the same time, environmental loadings can influence the generation of growth factors. This paper shows how surface bone remodeling is triggered under the influence of growth factors. Based on this hypothesis, a computational model is established that simulates the bone coupling remodeling process, including internal and surface bone remodeling. The effects of various loadings, including electrical and magnetic loadings, are simulated and compared. The interactions between internal and surface bone remodeling are investigated via the numerical method. The results indicate that an electromagnetic field can strongly influence the bone remodeling process and that the remodeling process will be altered after surface bone remodeling is triggered, compared to the sole effect of the internal remodeling process.
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References
Bessett C.A., Valdes M.G., Hernandez E. (1982) Modification of fracture repair with selected pulsing electromagnetic fields. J. Bone Joint Surg. 64: 888–895
Mcleod K.J., Rubin C.T. (1992) The effect of low-frequency electrical fields on osteogenesis. J. Bone Joint Surg. 74: 920–929
Giordano N., Battisti E. (2001) Effect of electromagnetic fields on bone mineral density and biochemical markers of bone turnover in osteoporosis: a single-blind, randomized pilot study. Curr. Ther. Res. 62: 187–193
Frost H.M. (1998) Changing concepts in skeletal physiology: Wolff’s Law, the Mechanostat, and the “Utah Paradigm.” Am. J. Hum. Biol. 10: 599–605
Frost H.M. (1964) Dynamics of bone remodeling. In: Frost H.M. (ed.) Bone biodynamics. Little, Brown and Co., Boston
Cowin S.C., Hegedus D.M. (1976) Bone remodeling I: Theory of adaptive elasticity. J. Elasticity 6: 313–326
Hegedus D.H., Cowin S.C. (1976) Bone remodeling II: Small strain adaptive elasticity. J. Elasticity 6: 337–352
Cowin S.C., Nachlinger R.R. (1978) Bone remodeling III: Uniqueness and stability in adaptive elasticity theory. J. Elasticity 8: 285–295
Martin R.B. (1995) A mathematical model for fatigue damage repair and stress fracture in osteonal bone. J. Orthop. Res. 13: 309–316
Beaupré, G.S., Orr, T.E., Carter, D.R.: An approach for time-dependent bone remodeling and remodeling: theoretical development. J. Orthop. Res. 651–661 (1990a)
Beaupré G.S., Orr T.E., Carter D.R. (1990b) An approach for time-dependent bone remodeling and remodeling: Application: A preliminary remodeling simulation. J. Orthop. Res. 8: 662–670
Gjelsvik A. (1973a) Bone remodeling and piezoelectricity—I. J. Biomech. 6: 69–77
Gjelsvik A. (1973b) Bone remodeling and piezoelectricity—II. J. Biomech. 6: 187–197
Qin Q.H., Ye J.Q. (2004) Thermolectroelastic solutions for internal bone remodeling under axial and transverse loads. Int. J. Solids and Struct. 41: 2447–2460
Qin Q.H., Qu C.Y., Ye J.Q. (2005) Thermolectroelastic solutions for surface bone remodeling under axial and transverse loads. Biomaterials 26: 6798–6810
Qu, C.Y., Qin, Q.H., Kang, Y.L.: Thermomagnetoelectroelastic prediction of the bone surface remodeling under axial and transverse loads. In: Proceedings of the 9th International Conference on Inspection, Appraisal, Repairs & Maintenance of Structures, 373–380, Fuzhou, China, October 20–21 (2005)
Qu C.Y., Qin Q.H., Kang Y.L. (2006) A hypothetical mechanism of bone remodeling and remodeling under electromagnetic loads. Biomaterials 27: 4050–4057
Fukada E., Yasuda I. (1957) On the piezoelectric effect of bone. J. Physiol. Soc. Jpn. 12: 1158–1162
Frost H.M. (1987) The mechanostat: a proposed pathogenic mechanism of osteoporosis and the bone mass effects of mechanical and nonmechanical agents. Bone 2: 73–85
Frost H.M. (2003) Bone’s mechanostat: A 2003 update. Anat. Rec. 275A: 1081–1101
Frost H.M. (1990) Structural adaptations to mechanical usage (SATMU): 1. Redefining Wolff’s Law: The bone remodeling problem. Anat. Rec. 226: 403–413
Rubin C.T., Lanyon L.E. (1985) Regulation of bone mass by mechanical strain magnitude. Calcified. Tissue Int. 37: 411–417
Jee W.S.S., Li X.J., Ke H.Z. (1991) Skeletal adaptations to mechanical usage in the rat. Cells. Mat. S1: 131–142
Batra G.S., Hainey L., Freemont A.J., Andrew G., Saunders P.T., Hoyland J.A., Braidman I.P. (2003) Evidence for ellspecific changes with age in expression of oestrogen receptor (ER) alpha and beta in bone fractures from men and women. J. Pathol. 200: 65–73
Oursler, M.J., Kassem, M., Turner, R., Riggs, B.L., Spelsberg, T.C.: Regulation of bone cell function by gonadal steroids. In: Marcus, R., Feldman, D., Kelsey, J. (eds.) Osteoporosis, pp. 237–260. Academic, San Diego (1996)
Skerry T.M., Bitensky L., Chayen J., Lanyon L.E. (1989) Early strain-related changes in enzyme activity in osteocytes following bone loading in vivo. J. Bone Miner. Res. 4: 783–788
Klein-Nulend J., Van der Plas A., Semeins C.M., Ajubi N.E., Frangos J.A., Nijweide P.J., Burger E.H. (1995) Sensitivity of osteocytes to biomechanical stress in vitro. FASEB J. 9: 441–445
Bakker A., Klein-Nulend J., Burger E. (2004) Shear stress inhibits while disuse promotes osteocyte apoptosis. Biochem. Bioph. Res. 320: 1163–1168
Mullender M.G., Huiskes R. (1995) A proposal for the regulatory mechanism of Wolff’s law. J. Orthop. Res. 13: 503–512
Nielsen H.M., Andreassen T.T., Leder T. (1994) Local injection of TGF-β increasing the strength of tibial fracture in the rat. Acta. Orthop. Scand. 65(1): 37–41
Asahina J., Waranabe M., Sakurai N. (1997) Repair of bone defect in primate mandible using a bone morphogenetic protein (BMP)-hydroxyapatite-collagen composite. J. Med. Dent. Sci. 44(3): 63–70
Weinreb M., Suponiyzky I., Keila S. (1997) Systematic administration of an anabolic dose of PGE2 in young rats increases the osteogenic capacity of bone marrow. Bone 20(6): 521–526
Lammens J., Liu Z., Aerssans J. (1998) Distraction bone healing versus osteotomy healing: A comparative biochemical analysis. J. Bone. Miner. Res. 13(2): 279–286
Fitzsimmons R.J., Strong D.D., Mohan S. (1992) Low-amplitude, low-frequency electric field-stimulated bone cell proliferation may in part be mediated by increased IGF-I release. J. Cell Physiol. 150(1): 84–89
Nagai M., Ots M. (1994) Pulsing electromagnetic fields stimulates mRNA expression of bone morphogenetic protem-2 and −4. J. Dent. Res. 73(10): 1601–1605
Zhung H.M., Wei W., Seldes R.M. (1997) Electrical stimulation induces the level of TGF-β mRNA in osteoblastic cells by a mechanism involving a calcium/ calmodulin pathway. Biochem. Bioph. Res. 237(2): 225–229
Currey J.D. (1988) The effect of porosity and mineral content on the Young’s modulus of elasticity of compact bone. J. Biomech. 21: 131–139
Hillsley M.V., Frangos J.A. (1994) Bone tissue engineering: The role of interstitial fluid flow. Biotechnol. Bioeng. 43: 573–581
Frost, H.M. (2002) Emerging views about “osteoporosis,” bone health, strength, fragility, and their determinants. J. Bone. Miner. Metab. 20: 319–325
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He, X.Q., Qu, C. & Qin, Q.H. A theoretical model for surface bone remodeling under electromagnetic loads. Arch Appl Mech 78, 163–175 (2008). https://doi.org/10.1007/s00419-007-0144-y
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DOI: https://doi.org/10.1007/s00419-007-0144-y