نوع مقاله: مقاله کامل پژوهشی

نویسندگان

1 دانش آموخته دکترا دانشکده مهندسی پزشکی، دانشگاه صنعتی امیرکبیر

2 دانشیاردانشکده مهندسی پزشکی، دانشگاه صنعتی امیرکبیر

3 استاد دانشکده مهندسی مکانیک، دانشگاه صنعتی امیرکبیر

4 دانشیار دانشکده مهندسی صنایع، دانشگاه ایلینویز

10.22041/ijbme.2007.13497

چکیده

در این تحقیق، یک مدل میکرومکانیک المان محدود برای استخوان متراکم هاورس انسان به صورت دو بعدی ارایه شده است. با توجه به شباهت استخوان متراکم هاورس انسان با مواد مرکب فیبری- سرامیکی، بافت بینابینی، استخوانک و بافت سمنت لاین به ترتیب به عنوان زمینه، فیبر و فصل مشترک این دو فاز در نظر گرفته شد. سپس با اعمال تئوری مکانیک شکست الاستیک خطی و فرض شرایط کرنش صفحه ای، فاکتور شدت تنش در نزدیکی نوک یک میکروترک محاسبه شد. همچنین تاثیر ریز ساختار و خصوصیات مکانیکی استخوان متراکم انسان بر مسیر رشد میکروترک مورد مطالعه قرار گرفت. نتایج این مطالعه نشان داد که تاثیر ریز ساختار و خصوصیات مکانیکی استخوان متراکم انسان بر رفتار شکست، محدود به نزدیکی استخوانک می باشد. اگر استخوانک و سمنت لاین نرم تر از بافت بینابینی باشند، هر چه میکروترک به استخوانک نزدیک تر باشد، فاکتور شدت تنش در نوک های میکروترک بیشتر خواهد بود. در صورتی که این دو فاز سخت تر از بافت بینابینی باشند، تاثیر استخوانک بر میکروترک معکوس می شود. همچنین نتایج نشان داد در صورتی که سمنت لاین و بافت بینابینی سخت تر و یا نرم تر از استخوانک باشند، تاثیر استخوانک بر میکروترک بسیار ناچیز خواهد بود. اگر میکروترک تحت شرایط بارگذاری کششی قرار گیرد، مسیر رشد میکروترک همواره به گونه ای منحرف می گردد که از استخوانک دور شود. این نتیجه به خصوصیات مکانیکی بافت های مختلف وابسته نیست. در واقع میکروترک برای رشد خود مسیر بین استخوانک ها را انتخاب می نماید و این خود باعث افزایش جذب انرژی لازم برای شکست و در نتیجه بالا رفتن چقرمگی استخوان متراکم هاورس انسان می شود. این در صورتی است که میکروترک ها بر اثر بارگذاری فشاری، در راستای بار رشد کرده و تقریبا به صورت مستقیم وارد استخوانک می شوند. نتایج این مدلسازی المان محدود با نتایج تجربی مورد مقایسه قرار گرفت و همخوانی خوبی بین آنها وجود داشت.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Effect Of Microstructure And Mechanical Properties Of Haversian Cortical Bone On Microcrack Propagation Trajectory

نویسندگان [English]

  • Ahmad Raeisi Najafi 1
  • Ahmad Reza Arshi 2
  • Mohammad Reza Eslami 3
  • Shahriar Fariborz 3
  • Mansour Moeinzadeh 4

1 Phd, Biomedical Engineering School, Amirkabir University of Technology

2 Associate Professor, Biomedical Engineering School, Amirkabir University of Technology

3 Professor, Mechanical Engineering School, Amirkabir University of Technology

4 Associate Professor, Industrial and Enterprise Systems Engineering School, University of Illinois

چکیده [English]

A two dimensional finite element model for the human Haversian cortical bone is represented. The interstitial bone tissue, the osteons and the cement line were modeled as the matrix, the fibers and the interface, respectively. This was due to similarities between fiber-ceramic composite materials and the human Haversian cortical bone. The stress intensity factor in the microcrack tips vicinity was computed using the linear elastic fracture mechanics theory and assuming a plane strain condition. It was therefore possible to study the effect of microstructure and mechanical properties of Haversian cortical bone on microcrack propagation trajectory. The results indicated that this effect was limited to the vicinity of the osteon. If both osteon and cement line were assumed to be softer than the interstitial tissue, the stress intensity factor was increased when the crack distance to the osteon reduced. The stress intensity factor decreased if both osteon and cement line were assumed to be stiffer than the interstitial tissue. The resulting simulation indicated that the effect of existence of osteon on the stress intensity factor was no significance, if both the interstitial tissue and cement line were assumed either stiffer or softer than the osteon. Microcrack trajectory was observed to deviate from the osteon under tensile loading; indicating an independence from the mechanical properties of various tissues. In fact, the microcrack adopts a trajectory between the osteons, thereby increasing the necessary absorbed energy for fracture. This results in an increase in the human Haversian cortical bone toughness. The result of this finite element modeling has been confirmed by through evaluation and comparison made with experimental results.

کلیدواژه‌ها [English]

  • Human Haversian Cortical Bone
  • Microstructure
  • Linear Elastic Fracture Mechanics Theory
  • Microcrack
  • stress intensity factor
  • Finite element

[1]     Wang X. D., Masilamani N.S., Mabry J.D., Alder M. E, Agrawal C M; Changes in the fracture toughness of bone may not be reflected in its mineral density, porosity and tensile properties; Bone 1998; 23(1): 67- 72.

[2]     Phelps J.B, Hubbard G B, Wang X., Agrawal C.M; Microstructural heterogeneity and the fracture toughness of bone; J Biomedical Material Research 2000;51: 735-741.

[3]     Courtney A C, Hayes W C, Gibson LJ; Age-related differences in post-yield damage in human cortical bone. Experiment and model; J Biomechanics 1996; 29(11): 1463-1471.

[4]     Knowelden J, Buhr AJ, Dumbar D; Incidence of fracture in person over 35 years of age; Br. J Prev Soc Med 1964;18:130-141.

[5]     Currey JD; Changes in impact energy absorption of bone with age; J Biomechanics 1979; 12:459-469.

[6]     McCalden RW, McGeough JA, Barker MB, Court- Brown CM; Age related changes in the tensile properties of cortical bone. The relative implication of changes in porosity, mineralization and microstructure; J Bone Joint Surgery 1993; 75-A: 1193-1205.

[7]     Burstein AH, Reilly DT, Martens M; Aging of bone tissue: Mechanical properties; J. Bone Joint Surgery 1976; 58-A: 82-86.

[8]     Smith CB, and Smith DA; Relation between age, mineral density and mechanical properties of human femoral compacta; Acta. Orthop. Scand 1976; 47: 496- 502.

[9]     Wall J C, Chatterji S K, Jeffery J W; Age-related changes in the density and tensile strength of human femoral cortical bone; Calcified tissue international 1979; 27: 105-108.

[10] Guo XR, Liang LC, Goldstein SA; Micromechanics of osteonal cortical bone fracture; J Biomechanical Engineering 1998; 120: 112-117.

[11] Hogan H A; Micromechanics modeling of Haversian cortical bone properties; J Biomechanics 1992; 25(5): 549-556.

[12] Braidotti P, Branca FP., Sciubba E, Stagni L; An elastic compound tube model for a single osteon; J Biomechanics 1995; 28(4): 439-444.

[13] Carter D R, Hayes W C, Schurman D J; Fatigue life of compact bone-I. Effects of microstructure and density; J Biomechanics 1976; 9: 211-218.

[14] Carter DR, and Hayes WC; Compact bone fatigue damage. A microscopic examination; Clinical Orthopaedics and Related Research 1977; 127: 265- 276.

[15] Smikin A, and Robin G; Fracture formation in differing collagen fibre pattern of compact bone; J Biomechanics 1974; 7: 183-188.

[16] Ascenzi A, and Bonucci E;Mechanical similarities between alternate osteons and cross-ply laminates; J Biomechanics 1976; 9: 65-71.

[17] Saha S, and Hayes W C; Relation between tensile impact properties and microstructure of compact bone; Calcified tissue research 1977; 24: 65-72.

[18] Piekarski K; Fracture of bone; J Applied Physics 1970; 41(1): 215-223.

[19] Burr D.B., Stafford T; Validity of the bulk-staining technique to separate art factual from In Vivo microdamage; Clinical Orthopaedics and Related Research 1990; 260: 305-308.

[20] Schaffler M.B., Pitchford WC, Choi K, Riddle JM; Examination of compact bone microdamage using back-scattered electron microscopy; Bone 1994; 15(5):483-488.

[21] Norman T.L., Yeni Y.N., Brown CU, Wang Z; Influence of microdamage on fracture toughness of the human femur and tibia; Bone 1998; 23(2): 303-306.

[22] Yeni, YN, Brown CU, Wang Z, Norman T L; The influence of bone morphology on fracture toughness of the human femur and tibia; Bone 1997; 21(5): 453- 459.

[23] Yeni, YN, Brown C U, Norman TL; Influence of bone composition and apparent density on fracture toughness of the human femur and tibia; Bone 1998; 22(1): 79-84.

[24] Yeni YN, and Fyhrie DP; Fatigue damage-fracture mechanics interaction in cortical bone; Bone 2002; 30(3): 509-514.

[25] Reily GC, and Currey JD; The effects of damage and microcracking on the impact strength of bone; J Biomechanics 2000; 33: 337-343.

[26] Norman TL, Nivargikar SV, Burr DB; Resistance to crack growth in human cortical bone is greater in shear that in tension; J Biomechanics 1996; 29(8): 1023- 1031.

[27] Prendergast PJ, Huiskes R; Microdamage and osteocyte-lacuna strain in bone: A microstructural finite element analysis; J Biomechanical Engineering 1996; 118: 240-246.

[28] Norman TL, Vashishth D, Burr DB; Fracture toughness of human bone under tension; J Biomechanics 1995; 28(3): 309-320.

[29] Bonfield W, and Datta PK; Fracture toughness of cortical bone; J Biomechanics 1976; 9: 131-134.

[30] Bonfield W; Advances in the fracture of cortical bone; J Biomechanics 1987; 20(11/12): 1071-1081.

[31] Melvin J W; Fracture mechanics of bone; J Biomechanical Engineering 1993; 115: 549-554.

[32] Robertson DM, Robertson D, Barrett CR; Fracture toughness, critical crack length and plastic zone size in bone; J Biomechanics 1978; 11: 359-364.

[33] Katz JL; Mechanics of hard tissue; The Biomedical Engineering handbook; J. D. Bronzino, eds.; Second edition; CRC Press, Springer, IEEE press; Boca Raton, FL 2000; VOL. 1: 18-11.

[34] Ascenzi A, Benvenuti A, Mango F, Simili R; Mechanical hysteresis loops from single osteons: Technical devices and preliminary results; J Biomechanics 1985; 18: 391-398.

[35] Ascenzi A, Baschieri P, Benvenuti A; The bending properties of single osteons; J Biomechanics 1990; 23(8): 763-771.

[36] Frasca P., Jacyna G., Harper R., Katz J.L.; Strain dependence of dynamic Young’s modules for human single osteons; J Biomechanics 1981; 14: 691-696.

[37] Evans F.G., and Vincentelli R.; Relations of the compressive properties of human cortical bone to histological structure and calcification; J Biomechanics 1974; 7: 1-10.

[38] Dorlot J.M., L’Esperance G., Meunier A.; Characterization of single osteons: microhardness and mineral content; Tras. 32nd Orthop. Res. Soc. 1986; 11: 330.

[39] Burr D.B., Schaffler M.B., Fredericson R.G.; Composition of the cement line and its possible mechanical role as a local interface in human compact bone; J Biomechanics 1988; 21: 939-945.

[40] Lakes R., and Saha S.; Cement line motion in bone; Science 1979; 204: 501-503.

[41] Curry J.; The mechanical adaptations of bones; Princeton University Press, New York, 1984.

[42] Advani S.H., Lee T.S., Martin R.B.; Analysis of crack arrest by cement lines in osteonal bone; In 1987 advances in bioengineering (Edited by Erdman, A. G.); ASME, New York, BED 1987, 3: 57-88.

[43] Burr D.B., Stafford T.; Validity of the bulk-staining technique to separate art factual from In Vivo microdamage; Clinical Orthopaedics and Related Research 1990; 260: 305-308.

[44] Simmons E.D., Pritzker K.P.H., Grynpas M.D.; Agerelated changes in the human femoral cortex; J Orthopaedic Research 1991;9:155-167.

[45] Crofts R.D., Boyce TM, Milgrom C.; Aging changes in osteon mineralization in the human femoral neck; Bone 1994; 15: 137-152.

[46] Burr D.B., Turner C.H., Naick P., Forwood M.R., Ambrosius W., Sayeed Hasan M., Pidaparti R.; Does microdamage accumulation affect the mechanical properties of bone?; J Biomechanics 1998; 31: 337- 345.

[47] Reily G.C., and Currey J.D.; The development of microcracking and failure in bone depends on the loading mode to which it is a adapted; J Experimental Biology 1999; 202: 543-552.

[48] Boyce T.M., Fyhrie D.P., Glotkowski MC, Radin EL, Schaffler MB; Damage type and strain mode association in human compact bone bending fatigue; J Orthopaedic Research 1998; 16: 322-329;

[49] Barth, R.W., Williams J.L., Kaplan F.S.; Osteon morphometry in females with femoral neck fractures; Clinical Orthopaedics and Related Research 1992; 283: 178-186.

[50] Corondan, G., and Haworth W.L.; A fractographic study of human long bone; J Biomechanics 1986; 19: 207-218.

[51] Moyle D.D., Welborn J.W., Cooke F.W.,; Work to fracture of canine femoral bone; J Biomechanics 1978; 11: 435-440.

[52] Squillante R.G., and Williams JL; Videodensitometry of osteons in females with femoral neck fractures, Calcified tissue international 1993; 52: 273-277.

[53] Stover S.M., Martin RB, Gibson V.A., Gibeling JC, Briffin L.V.; Ostonal pullout increases fatigue life of cortical bone; Proc. 41 st Annual Meeting of ORS, Orlando, FL, ORS 1995; 1:129.