Growth mixture model of distraction osteogenesis: Effect of pre-traction stresses

Biomechanics and Modeling in Mechanobiology

Volumn 9, Issue 1, 2010, Pages 103-115

  Reina Romo, Esther ^a   Gomez Benito M J ^b,c   Garcia Aznar J M ^b,c   Dominguez J ^a   Doblare M ^b,c  

^a UNIVERSITY OF SEVILLE   (Spain)

^b UNIVERSITY OF ZARAGOZA   (Spain)

^c BIOMATERIALES Y NANOMEDICINA CIBER BBN   (Spain)

Author keywords

Bone distraction; Computational mechanobiology; Finite element; Pre traction stress; Tissue growth

Indexed keywords

FINITE ELEMENT METHOD; MIXTURES;

BONE DISTRACTION; COMPUTATIONAL MECHANOBIOLOGY; DISTRACTION OSTEOGENESIS; FINITE ELEMENT; LIMB LENGTHENING; MIXTURE MODELING; PRE-TRACTION STRESS; TISSUE GROWTH; TRACTION FORCES; TRACTION STRESS;

BONE;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; BIOMECHANICS; DISTRACTION OSTEOGENESIS; MECHANICAL STRESS; TRACTION THERAPY;

ANIMALS; BIOMECHANICS; MODELS, BIOLOGICAL; OSTEOGENESIS, DISTRACTION; STRESS, MECHANICAL; TRACTION;

EID: 74349083400     PISSN: 16177959     EISSN: 16822978     Source Type: Journal    
DOI: 10.1007/s10237-009-0162-5     Document Type: Article

References (80)

1. GT Aarnes H Steen LP Kristiansen P Ludvigsen O Reikerås 2002 Tissue response during monofocal and bifocal leg lengthening in patients J Orthop Res 20 137 141 10.1016/S0736-0266(01)00082-1 (Pubitemid 34071432)
2. S Akizuki VC Mow F Müller JC Pita DS Howell DH Manicourt 1986 Tensile properties of human knee joint cartilage: I. influence of ionic conditions, weight bearing, and fibrillation on the tensile modulus J Orthop Res 4 379 392 10.1002/jor.1100040401
3. V Alastrué E Peña MA Martínez M Doblaré 2007 Assessing the use of the "opening angle method" to enforce residual stresses in patient-specific arteries Ann Biomed Eng 35 1821 1837 10.1007/s10439-007-9352-4 (Pubitemid 47444152)
4. CG Armstrong VC Mow 1982 Variations in the intrinsic mechanical properties of human articular cartilage with age, degeneration, and water content J Bone Joint Surg Am 64 88 94
5. A Bailón-Plaza MC van der Meulen 2003 Beneficial effects of moderate, early loading and adverse effects of delayed or excessive loading on bone healing J Biomech 36 1069 1077 10.1016/S0021-9290(03)00117-9 (Pubitemid 36794102)
6. JE Bertram Y Polevoy DM Cullinane 1998 Mechanics of avian fibrous periosteum: tensile and adhesion properties during growth Bone 22 669 675 10.1016/S8756-3282(98)00035-0 (Pubitemid 28284617)
7. A Boccaccio C Pappalettere DJ Kelly 2007 The influence of expansion rates on mandibular distraction osteogenesis: a computational analysis Ann Biomed Eng 35 1940 1960 10.1007/s10439-007-9367-x (Pubitemid 350001061)
8. CJ Breward HM Byrne CE Lewis 2003 A multiphase model describing vascular tumour growth Bull Math Biol 65 609 640 10.1016/S0092-8240(03)00027-2 (Pubitemid 36821016)
9. UH Brunner J Cordey L Schweiberer SM Perren 1994 Force required for bone segment transport in the treatment of large bone defects using medullary nail fixation Clin Orthop Relat Res 301 147 155
10. DR Carter GS Beaupre NJ Giori JA Helms 1998 Mechanobiology of skeletal regeneration Clin Orthop Relat Res 355S S41 S55 10.1097/00003086-199810001-00006
11. M Charlebois MD McKee MD Buschmann 2004 Nonlinear tensile properties of bovine articular cartilage and their variation with age and depth J Biomech Eng 126 129 137 10.1115/1.1688771 (Pubitemid 38621125)
12. Y Chen A Hoger 2000 Constitutive functions for elastic materials in finite growth and deformation J Elast 59 175 193 0987.74009 10.1023/A: 1011061400438 (Pubitemid 32432070)
13. CJ Chuong YC Fung 1986 On residual stresses in arteries J Biomech Eng 108 189 192 10.1115/1.3138600
14. LE Claes CA Heigele 1999 Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing J Biomech 32 255 266 10.1016/S0021-9290(98)00153-5 (Pubitemid 29125449)
15. A Davol MS Bingham RL Sah SM Klisch 2008 A nonlinear finite element model of cartilage growth Biomech Model Mechanobiol 7 295 307 10.1007/s10237-007- 0098-6 (Pubitemid 352039638)
16. A DiCarlo S Quiligotti 2002 Growth and balance Mech Res Commun 29 449 456 1056.74005 10.1016/S0093-6413(02)00297-5 1944472 (Pubitemid 35401688)
17. M Doblaré JM García-Aznar 2006 On numerical modelling of growth, differentiation and damage in structural living tissues Arch Comput Methods Eng 13 471 513 1171.74030 10.1007/BF02905856
18. M Epstein GA Maugin 2000 Thermomechanics of volumetric growth in uniform bodies Int J Plast 16 951 978 0979.74006 10.1016/S0749-6419(99)00081-9 (Pubitemid 30865271)
19. F Forriol I Goenaga G Mora J Viñolas J Canadell 1997 Measurement of bone lengthening forces; an experimental model in the lamb Clin Biomech 12 17 21 10.1016/S0268-0033(96)00043-5 (Pubitemid 27077639)
20. Fung YC (1984) Biodynamics: circulation. Springer, New York
21. Fung YC (1985) What principle governs the stress distribution in living organs? In: Fung YC, Fukada E, Wang JJ (eds) Biomechanics in China, Japan, and USA. Science Press, Beijing, pp 1-13
22. Fung YC (1990a) Biomechanics: motion, flow, stress, and growth. Springer, New York
23. Fung YC (1990b) Biomechanics: mechanical properties of living tissues. Springer, Berlin
24. JM García-Aznar JH Kuiper MJ Gómez-Benito M Doblaré JB Richardson 2007 Computational simulation of fracture healing: influence of interfragmentary movement on the callus growth J Biomech 40 1467 1476 10.1016/j.jbiomech.2006.06.013 (Pubitemid 46601439)
25. TN Gardner M Evans H Simpson J Kenwright 1998 Force-displacement behaviour of biological tissue during distraction osteogenesis Med Eng Phys 20 708 715 10.1016/S1350-4533(98)00043-5 (Pubitemid 29090705)
26. K Garikipati EM Arruda K Grosh H Narayanan S Calve 2004 A continuum treatment of growth in biological tissue: the coupling of mass transport and mechanics J Mech Phys Solids 52 1595 1625 1159.74381 10.1016/j.jmps.2004.01.004 2066220
27. MJ Gómez-Benito JM García-Aznar JH Kuiper M Doblaré 2005 Influence of fracture gap size on the pattern of long bone healing: a computational study J Theor Biol 235 105 119 10.1016/j.jtbi.2004.12.023 (Pubitemid 40514428)
28. MJ Gómez-Benito JM García-Aznar JH Kuiper M Doblaré 2006 A 3d computational simulation of fracture callus formation: influence of the stiffness of the external fixator J Biomech Eng 128 290 299 10.1115/1.2187045 (Pubitemid 43958631)
29. H Gregersen GS Kassab YC Fung 2000 The zero stress state of the gastrointestinal tract: biomechanical and functional implications Dig Dis Sci 45 2271 2281 10.1023/A:1005649520386 (Pubitemid 32198622)
30. HC Han YC Fung 1996 Direct measurement of transverse residual strains in aorta Am J Physiol 270 H750 H759
31. Hibbit K, Sorensen I (2008) Theory manual, vol 6.8. HKS inc, Pawtucket
32. G Himpel E Kuhl A Menzel P Steinmann 2005 Computational modelling of isotropic multiplicative growth Comput Model Eng Sci 8 119 134 05132438
33. A Hoger 1997 Virtual configurations and constitutive equations for residually stressed bodies with material symmetry J Elast 48 125 144 0924.73047 10.1023/A:1007459331524 1607725
34. RY Hori JL Lewis 1982 Mechanical properties of the fibrous tissue found at the bone-cement interface following total joint replacement J Biomed Mater Res 16 911 927 10.1002/jbm.820160615 (Pubitemid 13202637)
35. CY Huang VC Mow GA Ateshian 2001 The role of flow-independent viscoelasticity in the biphasic tensile and compressive responses of articular cartilage J Biomech Eng 123 410 417 10.1115/1.1392316 (Pubitemid 32938938)
36. Z Huang 1994 The equilibrium equations and constitutive equations of the growing deformable body in the framework of continuum theory Int J Non-Linear Mech 39 951 962 10.1016/S0020-7462(03)00077-5
37. JD Humphrey 2001 Stress, strain, and mechanotransduction in cells J Biomech Eng 123 638 641 10.1115/1.1406131 (Pubitemid 34016558)
38. JD Humphrey KR Rajagopal 2003 A constrained mixture model for arterial adaptations to a sustained step change in blood flow Biomech Model Mechanobiol 2 109 126 10.1007/s10237-003-0033-4
39. H Isaksson O Comas CC van Donkelaar J Mediavilla W Wilson R Huiskes K Ito 2007 Bone regeneration during distraction osteogenesis: mechano-regulation by shear strain and fluid velocity J Biomech 40 2002 2011 10.1016/j.jbiomech.2006. 09.028 (Pubitemid 46843004)
40. H Isaksson W Wilson CC van Donkelaar R Huiskes K Ito 2006 Comparison of biophysical stimuli for mechano-regulation of tissue differentiation during fracture healing J Biomech 39 1507 1516 10.1016/j.jbiomech.2005.01.037
41. SM Klisch SS Chen RL Sah A Hoger 2003 A growth mixture theory for cartilage with application to growth-related experiments on cartilage explants J Biomech Eng 125 169 179 10.1115/1.1560144 (Pubitemid 36506130)
42. SM Klisch RL Sah A Hoger 2005 A cartilage growth mixture model for infinitesimal strains: solutions of boundary-value problems related to in vitro growth experiments Biomech Model Mechanobiol 3 209 223 10.1007/s10237-004-0060-9 (Pubitemid 40920922)
43. SM Klisch TJ Van Dyke A Hoger 2001 A theory of volumetric growth for compressible elastic biological materials Math Mech Solids 6 551 575 1022.74027 10.1177/108128650100600601
44. E Kuhl A Menzel P Steinmann 2003 Computational modeling of growth Comput Mech 32 71 88 1151.74385 10.1007/s00466-003-0463-y
45. E Kuhl P Steinmann 2003 Mass- and volumetric-specific views on thermodynamics for open systems Proc R Soc London 459A 2547 2568 2011354
46. D Lacroix PJ Prendergast 2002 A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading J Biomech 35 1163 1171 10.1016/S0021-9290(02)00086-6 (Pubitemid 34879736)
47. M Lappa 2005 A CFD level-set method for soft tissue growth: theory and fundamental equations J Biomech 38 185 190
48. JC Leong RY Ma JA Clark LS Cornish AC Yau 1979 Viscoelastic behavior of tissue in leg lengthening by distraction Clin Orthop Relat Res 139 102 109
49. PL Leong EF Morgan 2008 Measurement of fracture callus material properties via nanoindentation Acta Biomater 4 1569 1575 10.1016/j.actbio.2008. 02.030
50. JR Levick 1987 Flow through interstitium and other fibrous matrices Q J Exp Physiol 72 409 438
51. G Li JT Bronk KN An PJ Kelly 1987 Permeability of cortical bone of canine tibiae Microvasc Res 34 302 310 10.1016/0026-2862(87)90063-X (Pubitemid 17162151)
52. G Li HRW Simpson J Kenwright JT Triffitt 1997 Assessment of cell proliferation in regenerating bone during distraction osteogenesis at different distraction rates J Orthop Res 15 765 772 10.1002/jor.1100150520 (Pubitemid 28019005)
53. SQ Liu YC Fung 1988 Zero-stress states of arteries J Biomech Eng 110 82 84 10.1115/1.3108410
54. VA Lubarda A Hoger 2002 On the mechanics of solids with a growing mass Int J Solids Struct 39 4627 4664 1045.74035 10.1016/S0020-7683(02)00352-9
55. T Matsushita K Nakamura T Kurokawa 1999 Tensile force in limb lengthening: histogenesis or only mechanical elongation Orthopedics 22 61 63
56. A Menzel 2005 Modelling of anisotropic growth in biological tissues. A new approach and computational aspects Biomech Model Mechanobiol 3 147 171 10.1007/s10237-004-0047-6 (Pubitemid 40454314)
57. Menzel A (2006) Anisotropic remodeling of biological tissue. In: Holzapfel, Ogden (eds) Mechanics of biological tissue. Springer, Berlin, pp 91-104
58. A Nafei C Danielsen F Linde I Hvid 2000 Properties of growing trabecular ovine bone. Part I: mechanical and physical properties J Bone Joint Surg Br 82 910 920 10.1302/0301-620X.82B6.9836 (Pubitemid 30624057)
59. K Nakamura T Matsushita H Okazaki T Kurokawa 1997 Soft tissue responses to limb lengthening J Orthop Sci 2 191 197 10.1007/BF02492977 (Pubitemid 27265377)
60. Ochoa JA, Hillberry BM (1992) Permeability of bovine cancellous bone. In: Transactions of the 38th ORS, Washinton, DC
61. F Pauwels 1960 Eine neue Theorie über den Einfluβ mechanischer Reize auf die Differenzierung der Stützgewebe Z Anat Entwicklungsgesch 121 478 515 10.1007/BF00523401
62. Perren SM, Cordey J (1980) The concept of interfragmentary strain. Currect concepts of internal fixation of fractures. Springer, Berlin, pp 63-77
63. T Popowics Z Zhu S Herring 2002 Mechanical properties of the periosteum in the pig, sus scrofa Arch Oral Biol 47 733 741 10.1016/S0003-9969(02)00065-1 (Pubitemid 35175768)
64. L Preziosi A Farina 2002 On Darcy's law for growing porous media Int J Non-Linear Mech 37 485 491 05138050 10.1016/S0020-7462(01)00022-1
65. S Quiligotti 2002 On bulk growth mechanics of solid-fluid mixtures: kinematics and invariance requirements Theor Appl Mech 28 29 277 288 2025153
66. A Ramasubramanian LA Taber 2008 Computational modeling of morphogenesis regulated by mechanical feedback Biomech Model Mechanobiol 7 77 91 10.1007/s10237-007-0077-y
67. Reina-Romo E, Gómez-Benito MJ, García-Aznar JM, Domínguez J, Doblaré M (2009) Modeling distraction osteogenesis: analysis of the distraction rate. Biomech Model Mechanobiol. doi: 10.1007/s10237-008-0138-x
68. M Richards AS Wineman E Alsberg JA Goulet SA Goldstein 1999 Viscoelastic characterization of mesenchymal gap tissue and consequences for tension accumulation during distraction J Biomech Eng 121 116 123 10.1115/1.2798032
69. EK Rodriguez A Hoger AD McCulloch 1994 Stress-dependent finite growth in soft elastic tissues J Biomech 27 455 467 10.1016/0021-9290(94)90021-3 (Pubitemid 24102058)
70. AH Simpson JL Cunningham J Kenwright 1996 The forces which develop in the tissues during leg lengthening. A clinical study J Bone Joint Surg Br 78 979 983 10.1302/0301-620X78B6.1273
71. Skalak R (1981) Growth as a finite displacement field. In: Carlson DE, Shield RT (eds) Proceedings of IUTAM symposium on finite elasticity. Martinus Nijhoff, The Hague, pp 347-355
72. R Skalak G Dasgupta M Moss E Otten P Dullumeijer H Vilmann 1982 Analytical description of growth J Theor Biol 94 555 577 10.1016/0022-5193(82) 90301-0
73. LA Taber 1998 A model for aortic growth based on fluid shear and fiber stresses J Biomech Eng 120 348 354 10.1115/1.2798001
74. LA Taber DW Eggers 1996 Theoretical study of stress-modulated growth in the aorta J Theor Biol 180 343 357 10.1006/jtbi.1996.0107 (Pubitemid 26258553)
75. LA Taber JD Humphrey 2001 Stress-modulated growth, residual stress, and vascular heterogeneity J Biomech Eng 123 528 535 10.1115/1.1412451 (Pubitemid 34016544)
76. LA Taber R Perucchio 2000 Modeling heart development J Elast 61 165 197 0987.74049 10.1023/A:1011082712497 1852948
77. Vaishnav RN, Vossoughi J (1983) Estimation of residual strain in aortic segments. In: Hall CW (eds) Biomedical engineering II: recent development. Pergamon Press, Oxford, pp 330-333
78. RN Vaishnav J Vossoughi 1987 Residual stress and strain in aortic segments J Biomech 20 235 239 10.1016/0021-9290(87)90290-9 (Pubitemid 17065946)
79. KY Volokh 2004 A simple phenomenological theory of tissue growth Mech Chem Biosyst 1 147 160 1153.74358
80. NA Waanders M Richards H Steen JL Kuhn SA Goldstein JA Goulet 1998 Evaluation of the mechanical environment during distraction osteogenesis Clin Orthop Relat Res 349 225 234 10.1097/00003086-199804000-00028