Bone remodeling and biological effects of mechanical stimulus

Chao Hu; Qing-Hua Qin; Chao Hu; Qing-Hua Qin

doi:10.3934/bioeng.2020002

AIMS Bioengineering

2020, Volume 7, Issue 1: 12-28. doi: 10.3934/bioeng.2020002

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Review

Bone remodeling and biological effects of mechanical stimulus

Chao Hu ,
Qing-Hua Qin ^,

Research School of Electrical, Energy and Materials Engineering, The Australian National University, Canberra, ACT 2601, Australia

Received: 05 November 2019 Accepted: 17 January 2020 Published: 19 January 2020

This review describes the physiology of normal bone tissue as an introduction to the subsequent discussion on bone remodeling and biomechanical stimulus. As a complex architecture with heterogeneous and anisotropic hierarchy, the skeletal bone has been anatomically analysed with different levelling principles, extending from nano- to the whole bone scale. With the interpretation of basic bone histomorphology, the main compositions in bone are summarized, including various organic proteins in the bone matrix and inorganic minerals as the reinforcement. The cell populations that actively participate in the bone remodeling—osteoclasts, osteoblasts and osteocytes—have also been discussed since they are the main operators in bone resorption and formation. A variety of factors affect the bone remodeling, such as hormones, cytokines, mechanical stimulus and electromagnetic stimulus. As a particularly potent stimulus for bone cells, mechanical forces play a crucial role in enhancing bone strength and preventing bone loss with aging. By combing all these aspects together, the information lays the groundwork for systematically understanding the link between bone physiology and orchestrated process of mechanically mediated bone homoestasis.
- bone tissue,
- osteoclasts,
- osteoblasts,
- osteocytes,
- bone remodeling,
- mechanical stimulus
Citation: Chao Hu, Qing-Hua Qin. Bone remodeling and biological effects of mechanical stimulus[J]. AIMS Bioengineering, 2020, 7(1): 12-28. doi: 10.3934/bioeng.2020002

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Abstract

This review describes the physiology of normal bone tissue as an introduction to the subsequent discussion on bone remodeling and biomechanical stimulus. As a complex architecture with heterogeneous and anisotropic hierarchy, the skeletal bone has been anatomically analysed with different levelling principles, extending from nano- to the whole bone scale. With the interpretation of basic bone histomorphology, the main compositions in bone are summarized, including various organic proteins in the bone matrix and inorganic minerals as the reinforcement. The cell populations that actively participate in the bone remodeling—osteoclasts, osteoblasts and osteocytes—have also been discussed since they are the main operators in bone resorption and formation. A variety of factors affect the bone remodeling, such as hormones, cytokines, mechanical stimulus and electromagnetic stimulus. As a particularly potent stimulus for bone cells, mechanical forces play a crucial role in enhancing bone strength and preventing bone loss with aging. By combing all these aspects together, the information lays the groundwork for systematically understanding the link between bone physiology and orchestrated process of mechanically mediated bone homoestasis.

Acknowledgments

The authors would like to acknowledge the financial support from Australian Research Council (Grant No. DP160102491).

Conflict of interest

The authors declare no conflict of interests.

References

[1]	Hu C, Ashok D, Nisbet DR, et al. (2019) Bioinspired surface modification of orthopedic implants for bone tissue engineering. Biomaterials 119366. doi: 10.1016/j.biomaterials.2019.119366
[2]	Karsenty G, Olson EN (2016) Bone and muscle endocrine functions: unexpected paradigms of inter-organ communication. Cell 164: 1248-1256. doi: 10.1016/j.cell.2016.02.043
[3]	Rossi M, Battafarano G, Pepe J, et al. (2019) The endocrine function of osteocalcin regulated by bone resorption: A lesson from reduced and increased bone mass diseases. Int J Mol Sci 20: 4502. doi: 10.3390/ijms20184502
[4]	Loebel C, Burdick JA (2018) Engineering stem and stromal cell therapies for musculoskeletal tissue repair. Cell Stem Cell 22: 325-339. doi: 10.1016/j.stem.2018.01.014
[5]	Dimitriou R, Jones E, McGonagle D, et al. (2011) Bone regeneration: current concepts and future directions. BMC Med 9: 66. doi: 10.1186/1741-7015-9-66
[6]	Nordin M, Frankel VH (2001) Basic Biomechanics of the Musculoskeletal System, 3 Eds USA: Lippincott Williams & Wilkins.
[7]	Kobayashi S, Takahashi HE, Ito A, et al. (2003) Trabecular minimodeling in human iliac bone. Bone 32: 163-169. doi: 10.1016/S8756-3282(02)00947-X
[8]	Bartl R, Bartl C (2019) Control and regulation of bone remodelling. The Osteoporosis Manual Cham: Springer, 31-39. doi: 10.1007/978-3-030-00731-7_4
[9]	Kenkre JS, Bassett JHD (2018) The bone remodelling cycle. Ann Clin Biochem 55: 308-327. doi: 10.1177/0004563218759371
[10]	Prendergast PJ, Huiskes R (1995) The biomechanics of Wolff's law: recent advances. Irish J Med Sci 164: 152-154. doi: 10.1007/BF02973285
[11]	Wegst UGK, Bai H, Saiz E, et al. (2015) Bioinspired structural materials. Nat Mater 14: 23-36. doi: 10.1038/nmat4089
[12]	Reznikov N, Shahar R, Weiner S (2014) Bone hierarchical structure in three dimensions. Acta Biomater 10: 3815-3826. doi: 10.1016/j.actbio.2014.05.024
[13]	Weiner S, Wagner HD (1998) The material bone: structure-mechanical function relations. Annu Rev Mater Sci 28: 271-298. doi: 10.1146/annurev.matsci.28.1.271
[14]	Recker RR, Kimmel DB, Dempster D, et al. (2011) Issues in modern bone histomorphometry. Bone 49: 955-964. doi: 10.1016/j.bone.2011.07.017
[15]	Eriksen EF, Vesterby A, Kassem M, et al. (1993) Bone remodeling and bone structure. Physiology and Pharmacology of Bone Heidelberg: Springer, 67-109. doi: 10.1007/978-3-642-77991-6_2
[16]	Augat P, Schorlemmer S (2006) The role of cortical bone and its microstructure in bone strength. Age Ageing 35: ii27-ii31. doi: 10.1093/ageing/afl081
[17]	Kozielski M, Buchwald T, Szybowicz M, et al. (2011) Determination of composition and structure of spongy bone tissue in human head of femur by Raman spectral mapping. J Mater Sci: Mater Med 22: 1653-1661. doi: 10.1007/s10856-011-4353-0
[18]	Cross LM, Thakur A, Jalili NA, et al. (2016) Nanoengineered biomaterials for repair and regeneration of orthopedic tissue interfaces. Acta Biomater 42: 2-17. doi: 10.1016/j.actbio.2016.06.023
[19]	Zebaze R, Seeman E (2015) Cortical bone: a challenging geography. J Bone Miner Res 30: 24-29. doi: 10.1002/jbmr.2419
[20]	Liu Y, Luo D, Wang T (2016) Hierarchical structures of bone and bioinspired bone tissue engineering. Small 12: 4611-4632. doi: 10.1002/smll.201600626
[21]	Brodsky B, Persikov AV (2005) Molecular structure of the collagen triple helix. Adv Protein Chem 70: 301-339. doi: 10.1016/S0065-3233(05)70009-7
[22]	Cui FZ, Li Y, Ge J (2007) Self-assembly of mineralized collagen composites. Mater Sci Eng R Rep 57: 1-27. doi: 10.1016/j.mser.2007.04.001
[23]	Wang Y, Azaïs T, Robin M, et al. (2012) The predominant role of collagen in the nucleation, growth, structure and orientation of bone apatite. Nat Mater 11: 724-733. doi: 10.1038/nmat3362
[24]	Bentmann A, Kawelke N, Moss D, et al. (2010) Circulating fibronectin affects bone matrix, whereas osteoblast fibronectin modulates osteoblast function. J Bone Miner Res 25: 706-715.
[25]	Szweras M, Liu D, Partridge EA, et al. (2002) α2-HS glycoprotein/fetuin, a transforming growth factor-β/bone morphogenetic protein antagonist, regulates postnatal bone growth and remodeling. J Biol Chem 277: 19991-19997. doi: 10.1074/jbc.M112234200
[26]	Boskey AL, Robey PG (2013) The regulatory role of matrix proteins in mineralization of bone. Osteoporosis, 4 Eds Academic Press, 235-255. doi: 10.1016/B978-0-12-415853-5.00011-X
[27]	Boskey AL (2013) Bone composition: relationship to bone fragility and antiosteoporotic drug effects. Bonekey Rep 2: 447. doi: 10.1038/bonekey.2013.181
[28]	Stock SR (2015) The mineral–collagen interface in bone. Calcified Tissue Int 97: 262-280. doi: 10.1007/s00223-015-9984-6
[29]	Nikel O, Laurencin D, McCallum SA, et al. (2013) NMR investigation of the role of osteocalcin and osteopontin at the organic–inorganic interface in bone. Langmuir 29: 13873-13882. doi: 10.1021/la403203w
[30]	He G, Dahl T, Veis A, et al. (2003) Nucleation of apatite crystals in vitro by self-assembled dentin matrix protein 1. Nat Mater 2: 552-558. doi: 10.1038/nmat945
[31]	Clarke B (2008) Normal bone anatomy and physiology. Clin J Am Soc Nephro 3: S131-S139. doi: 10.2215/CJN.04151206
[32]	Olszta MJ, Cheng X, Jee SS, et al. (2007) Bone structure and formation: A new perspective. Mater Sci Eng R Rep 58: 77-116. doi: 10.1016/j.mser.2007.05.001
[33]	Nair AK, Gautieri A, Chang SW, et al. (2013) Molecular mechanics of mineralized collagen fibrils in bone. Nature Commun 4: 1724. doi: 10.1038/ncomms2720
[34]	Landis WJ (1995) The strength of a calcified tissue depends in part on the molecular structure and organization of its constituent mineral crystals in their organic matrix. Bone 16: 533-544. doi: 10.1016/8756-3282(95)00076-P
[35]	Hunter GK, Hauschka PV, POOLE RA, et al. (1996) Nucleation and inhibition of hydroxyapatite formation by mineralized tissue proteins. Biochem J 317: 59-64. doi: 10.1042/bj3170059
[36]	Oikeh I, Sakkas P, Blake D P, et al. (2019) Interactions between dietary calcium and phosphorus level, and vitamin D source on bone mineralization, performance, and intestinal morphology of coccidia-infected broilers. Poult Sci 11: 5679-5690. doi: 10.3382/ps/pez350
[37]	Boyce BF, Rosenberg E, de Papp AE, et al. (2012) The osteoclast, bone remodelling and treatment of metabolic bone disease. Eur J Clin Invest 42: 1332-1341. doi: 10.1111/j.1365-2362.2012.02717.x
[38]	Teitelbaum SL (2000) Bone resorption by osteoclasts. Science 289: 1504-1508. doi: 10.1126/science.289.5484.1504
[39]	Yoshida H, Hayashi SI, Kunisada T, et al. (1990) The murine mutation osteopetrosis is in the coding region of the macrophage colony stimulating factor gene. Nature 345: 442-444. doi: 10.1038/345442a0
[40]	Roodman GD (2006) Regulation of osteoclast differentiation. Ann NY Acad Sci 1068: 100-109. doi: 10.1196/annals.1346.013
[41]	Martin TJ (2013) Historically significant events in the discovery of RANK/RANKL/OPG. World J Orthop 4: 186-197. doi: 10.5312/wjo.v4.i4.186
[42]	Coetzee M, Haag M, Kruger MC (2007) Effects of arachidonic acid, docosahexaenoic acid, prostaglandin E2 and parathyroid hormone on osteoprotegerin and RANKL secretion by MC3T3-E1 osteoblast-like cells. J Nutr Biochem 18: 54-63. doi: 10.1016/j.jnutbio.2006.03.002
[43]	Steeve KT, Marc P, Sandrine T, et al. (2004) IL-6, RANKL, TNF-alpha/IL-1: interrelations in bone resorption pathophysiology. Cytokine Growth F R 15: 49-60. doi: 10.1016/j.cytogfr.2003.10.005
[44]	Mellis DJ, Itzstein C, Helfrich M, et al. (2011) The skeleton: a multi-functional complex organ. The role of key signalling pathways in osteoclast differentiation and in bone resorption. J Endocrinol 211: 131-143. doi: 10.1530/JOE-11-0212
[45]	Silva I, Branco J (2011) Rank/Rankl/opg: literature review. Acta Reumatol Port 36: 209-218.
[46]	Martin TJ, Sims NA (2015) RANKL/OPG; Critical role in bone physiology. Rev Endocr Metab Dis 16: 131-139. doi: 10.1007/s11154-014-9308-6
[47]	Wang Y, Qin QH (2012) A theoretical study of bone remodelling under PEMF at cellular level. Comput Method Biomec 15: 885-897. doi: 10.1080/10255842.2011.565752
[48]	Weitzmann MN, Pacifici R (2007) T cells: unexpected players in the bone loss induced by estrogen deficiency and in basal bone homeostasis. Ann NY Acad Sci 1116: 360-375. doi: 10.1196/annals.1402.068
[49]	Duong LT, Lakkakorpi P, Nakamura I, et al. (2000) Integrins and signaling in osteoclast function. Matrix Biol 19: 97-105. doi: 10.1016/S0945-053X(00)00051-2
[50]	Stenbeck G (2002) Formation and function of the ruffled border in osteoclasts. Semin Cell Dev Biol 13: 285-292. doi: 10.1016/S1084952102000587
[51]	Jurdic P, Saltel F, Chabadel A, et al. (2006) Podosome and sealing zone: specificity of the osteoclast model. Eur J Cell Biol 85: 195-202. doi: 10.1016/j.ejcb.2005.09.008
[52]	Väänänen HK, Laitala-Leinonen T (2008) Osteoclast lineage and function. Arch Biochem Biophys 473: 132-138. doi: 10.1016/j.abb.2008.03.037
[53]	Vaananen HK, Zhao H, Mulari M, et al. (2000) The cell biology of osteoclast function. J cell Sci 113: 377-381.
[54]	Sabolová V, Brinek A, Sládek V (2018) The effect of hydrochloric acid on microstructure of porcine (Sus scrofa domesticus) cortical bone tissue. Forensic Sci Int 291: 260-271. doi: 10.1016/j.forsciint.2018.08.030
[55]	Delaissé JM, Engsig MT, Everts V, et al. (2000) Proteinases in bone resorption: obvious and less obvious roles. Clin Chim Acta 291: 223-234. doi: 10.1016/S0009-8981(99)00230-2
[56]	Logar DB, Komadina R, Preželj J, et al. (2007) Expression of bone resorption genes in osteoarthritis and in osteoporosis. J Bone Miner Metab 25: 219-225. doi: 10.1007/s00774-007-0753-0
[57]	Lorget F, Kamel S, Mentaverri R, et al. (2000) High extracellular calcium concentrations directly stimulate osteoclast apoptosis. Biochem Bioph Res Co 268: 899-903. doi: 10.1006/bbrc.2000.2229
[58]	Nesbitt SA, Horton MA (1997) Trafficking of matrix collagens through bone-resorbing osteoclasts. Science 276: 266-269. doi: 10.1126/science.276.5310.266
[59]	Xing L, Boyce BF (2005) Regulation of apoptosis in osteoclasts and osteoblastic cells. Biochem Bioph Res Co 328: 709-720. doi: 10.1016/j.bbrc.2004.11.072
[60]	Hughes DE, Wright KR, Uy HL, et al. (1995) Bisphosphonates promote apoptosis in murine osteoclasts in vitro and in vivo. J Bone Miner Res 10: 1478-1487. doi: 10.1002/jbmr.5650101008
[61]	Choi Y, Arron JR, Townsend MJ (2009) Promising bone-related therapeutic targets for rheumatoid arthritis. Nat Rev Rheumatol 5: 543-548. doi: 10.1038/nrrheum.2009.175
[62]	Harvey NC, McCloskey E, Kanis JA, et al. (2017) Bisphosphonates in osteoporosis: NICE and easy? Lancet 390: 2243-2244. doi: 10.1016/S0140-6736(17)32850-7
[63]	Ducy P, Schinke T, Karsenty G (2000) The osteoblast: a sophisticated fibroblast under central surveillance. Science 289: 1501-1504. doi: 10.1126/science.289.5484.1501
[64]	Katagiri T, Takahashi N (2002) Regulatory mechanisms of osteoblast and osteoclast differentiation. Oral dis 8: 147-159. doi: 10.1034/j.1601-0825.2002.01829.x
[65]	Kretzschmar M, Liu F, Hata A, et al. (1997) The TGF-beta family mediator Smad1 is phosphorylated directly and activated functionally by the BMP receptor kinase. Gene Dev 11: 984-995. doi: 10.1101/gad.11.8.984
[66]	Bennett CN, Longo KA, Wright WS, et al. (2005) Regulation of osteoblastogenesis and bone mass by Wnt10b. P Natl A Sci 102: 3324-3329. doi: 10.1073/pnas.0408742102
[67]	Wang Y, Qin QH, Kalyanasundaram S (2009) A theoretical model for simulating effect of parathyroid hormone on bone metabolism at cellular level. Mol Cell Biomech 6: 101-112.
[68]	Elefteriou F, Ahn JD, Takeda S, et al. (2005) Leptin regulation of bone resorption by the sympathetic nervous system and CART. Nature 434: 514-520. doi: 10.1038/nature03398
[69]	Proff P, Römer P (2009) The molecular mechanism behind bone remodelling: a review. Clin Oral Invest 13: 355-362. doi: 10.1007/s00784-009-0268-2
[70]	Katsimbri P (2017) The biology of normal bone remodelling. Eur J Cancer Care 26: e12740. doi: 10.1111/ecc.12740
[71]	Fratzl P, Weinkamer R (2007) Nature's hierarchical materials. Prog Mater Sci 52: 1263-1334. doi: 10.1016/j.pmatsci.2007.06.001
[72]	Athanasiou KA, Zhu CF, Lanctot DR, et al. (2000) Fundamentals of biomechanics in tissue engineering of bone. Tissue Eng 6: 361-381. doi: 10.1089/107632700418083
[73]	Takahashi N, Udagawa N, Suda T (1999) A new member of tumor necrosis factor ligand family, ODF/OPGL/TRANCE/RANKL, regulates osteoclast differentiation and function. Biocheml Bioph Res Co 256: 449-455. doi: 10.1006/bbrc.1999.0252
[74]	Nakashima T, Hayashi M, Fukunaga T, et al. (2011) Evidence for osteocyte regulation of bone homeostasis through RANKL expression. Nat Med 17: 1231-1234. doi: 10.1038/nm.2452
[75]	Prideaux M, Findlay DM, Atkins GJ (2016) Osteocytes: the master cells in bone remodelling. Curr Opin Pharmacol 28: 24-30. doi: 10.1016/j.coph.2016.02.003
[76]	Dallas SL, Prideaux M, Bonewald LF (2013) The osteocyte: an endocrine cell… and more. Endocr Rev 34: 658-690. doi: 10.1210/er.2012-1026
[77]	Rochefort GY, Pallu S, Benhamou CL (2010) Osteocyte: the unrecognized side of bone tissue. Osteoporosis Int 21: 1457-1469. doi: 10.1007/s00198-010-1194-5
[78]	Rowe PSN (2012) Regulation of bone–renal mineral and energy metabolism: The PHEX, FGF23, DMP1, MEPE ASARM pathway. Crit Rev Eukaryot Gene Expr 22: 61-86. doi: 10.1615/CritRevEukarGeneExpr.v22.i1.50
[79]	Pajevic PD, Krause DS (2019) Osteocyte regulation of bone and blood. Bone 119: 13-18. doi: 10.1016/j.bone.2018.02.012
[80]	Frost HM (1987) The mechanostat: a proposed pathogenic mechanism of osteoporoses and the bone mass effects of mechanical and nonmechanical agents. Bone Miner 2: 73-85.
[81]	Tate MLK, Adamson JR, Tami AE, et al. (2004) The osteocyte. Int J Biochem Cell Biol 36: 1-8. doi: 10.1016/S1357-2725(03)00241-3
[82]	Bonewald LF, Johnson ML (2008) Osteocytes, mechanosensing and Wnt signaling. Bone 42: 606-615. doi: 10.1016/j.bone.2007.12.224
[83]	Manolagas SC, Parfitt AM (2010) What old means to bone. Trends Endocrinol Metab 21: 369-374. doi: 10.1016/j.tem.2010.01.010
[84]	Wang Y, Qin QH (2010) Parametric study of control mechanism of cortical bone remodeling under mechanical stimulus. Acta Mech Sinica 26: 37-44. doi: 10.1007/s10409-009-0313-z
[85]	Qu C, Qin QH, Kang Y (2006) A hypothetical mechanism of bone remodeling and modeling under electromagnetic loads. Biomaterials 27: 4050-4057. doi: 10.1016/j.biomaterials.2006.03.015
[86]	Parfitt AM (2002) Targeted and nontargeted bone remodeling: relationship to basic multicellular unit origination and progression. Bone 1: 5-7. doi: 10.1016/S8756-3282(01)00642-1
[87]	Hadjidakis DJ, Androulakis II (2006) Bone remodeling. Ann NYAcad Sci 1092: 385-396. doi: 10.1196/annals.1365.035
[88]	Vaananen HK, Zhao H, Mulari M, et al. (2000) The cell biology of osteoclast function. J cell Sci 113: 377-381.
[89]	Goldring SR (2015) The osteocyte: key player in regulating bone turnover. RMD Open 1: e000049. doi: 10.1136/rmdopen-2015-000049
[90]	Silver IA, Murrills RJ, Etherington DJ (1988) Microelectrode studies on the acid microenvironment beneath adherent macrophages and osteoclasts. Exp Cell Res 175: 266-276. doi: 10.1016/0014-4827(88)90191-7
[91]	Delaissé JM, Andersen TL, Engsig MT, et al. (2003) Matrix metalloproteinases (MMP) and cathepsin K contribute differently to osteoclastic activities. Microsc Res Techniq 61: 504-513. doi: 10.1002/jemt.10374
[92]	Delaisse JM (2014) The reversal phase of the bone-remodeling cycle: cellular prerequisites for coupling resorption and formation. Bonekey Rep 3: 561. doi: 10.1038/bonekey.2014.56
[93]	Bonewald LF, Mundy GR (1990) Role of transforming growth factor-beta in bone remodeling. Clin Orthop Relat R 250: 261-276.
[94]	Locklin RM, Oreffo ROC, Triffitt JT (1999) Effects of TGFβ and bFGF on the differentiation of human bone marrow stromal fibroblasts. Cell Biol Int 23: 185-194. doi: 10.1006/cbir.1998.0338
[95]	Lee B, Oh Y, Jo S, et al. (2019) A dual role of TGF-β in human osteoclast differentiation mediated by Smad1 versus Smad3 signaling. Immunol Lett 206: 33-40. doi: 10.1016/j.imlet.2018.12.003
[96]	Koseki T, Gao Y, Okahashi N, et al. (2002) Role of TGF-β family in osteoclastogenesis induced by RANKL. Cell Signal 14: 31-36. doi: 10.1016/S0898-6568(01)00221-2
[97]	Anderson HC (2003) Matrix vesicles and calcification. Curr Rheumatol Rep 5: 222-226. doi: 10.1007/s11926-003-0071-z
[98]	Bellido T, Plotkin LI, Bruzzaniti A (2019) Bone cells. Basic and Applied Bone Biology, 2 Eds Elsevier, 37-55. doi: 10.1016/B978-0-12-813259-3.00003-8
[99]	Weinstein RS, Jilka RL, Parfitt AM, et al. (1998) Inhibition of osteoblastogenesis and promotion of apoptosis of osteoblasts and osteocytes by glucocorticoids. Potential mechanisms of their deleterious effects on bone. J Clin Invest 102: 274-282. doi: 10.1172/JCI2799
[100]	Vezeridis PS, Semeins CM, Chen Q, et al. (2006) Osteocytes subjected to pulsating fluid flow regulate osteoblast proliferation and differentiation. Biochem Bioph Res Co 348: 1082-1088. doi: 10.1016/j.bbrc.2006.07.146
[101]	Lind M, Deleuran B, Thestrup-Pedersen K, et al. (1995) Chemotaxis of human osteoblasts: Effects of osteotropic growth factors. Apmis 103: 140-146. doi: 10.1111/j.1699-0463.1995.tb01089.x
[102]	Russo CR, Lauretani F, Seeman E, et al. (2006) Structural adaptations to bone loss in aging men and women. Bone 38: 112-118. doi: 10.1016/j.bone.2005.07.025
[103]	Ozcivici E, Luu YK, Adler B, et al. (2010) Mechanical signals as anabolic agents in bone. Nat Rev Rheumatol 6: 50-59. doi: 10.1038/nrrheum.2009.239
[104]	Rosa N, Simoes R, Magalhães FD, et al. (2015) From mechanical stimulus to bone formation: a review. Med Eng Phys 37: 719-728. doi: 10.1016/j.medengphy.2015.05.015
[105]	Noble BS, Peet N, Stevens HY, et al. (2003) Mechanical loading: biphasic osteocyte survival and targeting of osteoclasts for bone destruction in rat cortical bone. Am J Physiol-Cell Ph 284: C934-C943. doi: 10.1152/ajpcell.00234.2002
[106]	Robling AG, Castillo AB, Turner CH (2006) Biomechanical and molecular regulation of bone remodeling. Annu Rev Biomed Eng 8: 455-498. doi: 10.1146/annurev.bioeng.8.061505.095721
[107]	Qin QH, Mai YW (1999) A closed crack tip model for interface cracks inthermopiezoelectric materials. Int J Solids Struct 36: 2463-2479. doi: 10.1016/S0020-7683(98)00115-2
[108]	Yu SW, Qin QH (1996) Damage analysis of thermopiezoelectric properties: Part I—crack tip singularities. Theor Appl Fract Mec 25: 263-277. doi: 10.1016/S0167-8442(96)00026-2
[109]	Qin QH, Mai YW, Yu SW (1998) Effective moduli for thermopiezoelectric materials with microcracks. Int J Fracture 91: 359-371. doi: 10.1023/A:1007423508650
[110]	Jirousek J, Qin QH (1996) Application of hybrid-Trefftz element approach to transient heat conduction analysis. Comput Struct 58: 195-201. doi: 10.1016/0045-7949(95)00115-W
[111]	Qin QH (1995) Hybrid-Trefftz finite element method for Reissner plates on an elastic foundation. Comput Method Appl M 122: 379-392. doi: 10.1016/0045-7825(94)00730-B
[112]	Qin QH (1994) Hybrid Trefftz finite-element approach for plate bending on an elastic foundation. Appl Math Model 18: 334-339. doi: 10.1016/0307-904X(94)90357-3
[113]	Qin QH (2013) Mechanics of Cellular Bone Remodeling: Coupled Thermal, Electrical, and Mechanical Field Effects CRC Press. doi: 10.1201/b13728
[114]	Wang H, Qin QH (2010) FE approach with Green's function as internal trial function for simulating bioheat transfer in the human eye. Arch Mech 62: 493-510.
[115]	Qin QH (2003) Fracture analysis of cracked thermopiezoelectric materials by BEM. Electronic J Boundary Elem 1: 283-301.
[116]	Qin QH, Ye JQ (2004) Thermoelectroelastic solutions for internal bone remodeling under axial and transverse loads. Int J Solids Struct 41: 2447-2460. doi: 10.1016/j.ijsolstr.2003.12.026
[117]	Qin QH, Qu C, Ye J (2005) Thermoelectroelastic solutions for surface bone remodeling under axial and transverse loads. Biomaterials 26: 6798-6810. doi: 10.1016/j.biomaterials.2005.03.042
[118]	Ducher G, Jaffré C, Arlettaz A, et al. (2005) Effects of long-term tennis playing on the muscle-bone relationship in the dominant and nondominant forearms. Can J Appl Physiol 30: 3-17. doi: 10.1139/h05-101
[119]	Robling AG, Hinant FM, Burr DB, et al. (2002) Improved bone structure and strength after long-term mechanical loading is greatest if loading is separated into short bouts. J Bone Miner Res 17: 1545-1554. doi: 10.1359/jbmr.2002.17.8.1545
[120]	Rubin J, Rubin C, Jacobs CR (2006) Molecular pathways mediating mechanical signaling in bone. Gene 367: 1-16. doi: 10.1016/j.gene.2005.10.028
[121]	Tatsumi S, Ishii K, Amizuka N, et al. (2007) Targeted ablation of osteocytes induces osteoporosis with defective mechanotransduction. Cell Metab 5: 464-475. doi: 10.1016/j.cmet.2007.05.001
[122]	Robling AG, Turner CH (2009) Mechanical signaling for bone modeling and remodeling. Crit Rev Eukar Gene 19: 319-338. doi: 10.1615/CritRevEukarGeneExpr.v19.i4.50
[123]	Galli C, Passeri G, Macaluso GM (2010) Osteocytes and WNT: the mechanical control of bone formation. J Dent Res 89: 331-343. doi: 10.1177/0022034510363963
[124]	Robling AG, Duijvelaar KM, Geevers JV, et al. (2001) Modulation of appositional and longitudinal bone growth in the rat ulna by applied static and dynamic force. Bone 29: 105-113. doi: 10.1016/S8756-3282(01)00488-4
[125]	Burr DB, Milgrom C, Fyhrie D, et al. (1996) In vivo measurement of human tibial strains during vigorous activity. Bone 18: 405-410. doi: 10.1016/8756-3282(96)00028-2
[126]	Sun W, Chi S, Li Y, et al. (2019) The mechanosensitive Piezo1 channel is required for bone formation. Elife 8: e47454. doi: 10.7554/eLife.47454
[127]	Goda I, Ganghoffer JF, Czarnecki S, et al. (2019) Topology optimization of bone using cubic material design and evolutionary methods based on internal remodeling. Mech Res Commun 95: 52-60. doi: 10.1016/j.mechrescom.2018.12.003
[128]	Goda I, Ganghoffer JF (2018) Modeling of anisotropic remodeling of trabecular bone coupled to fracture. Arch Appl Mech 88: 2101-2121. doi: 10.1007/s00419-018-1438-y
[129]	Louna Z, Goda I, Ganghoffer JF, et al. (2017) Formulation of an effective growth response of trabecular bone based on micromechanical analyses at the trabecular level. Arch Appl Mech 87: 457-477. doi: 10.1007/s00419-016-1204-y
[130]	Goda I, Ganghoffer JF (2017) Construction of the effective plastic yield surfaces of vertebral trabecular bone under twisting and bending moments stresses using a 3D microstructural model. ZAMM Z Angew Math Mech 97: 254-272. doi: 10.1002/zamm.201600141
[131]	Qin QH, Wang YN (2012) A mathematical model of cortical bone remodeling at cellular level under mechanical stimulus. Acta Mech Sinica-Prc 28: 1678-1692. doi: 10.1007/s10409-012-0154-z

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