Numerical modeling of bone tissue adaptation-A hierarchical approach for bone apparent density and trabecular structure

Journal of Biomechanics

Volumn 42, Issue 7, 2009, Pages 830-837

  Coelho, P G ^a   Fernandes, P R ^b   Rodrigues, H C ^b   Cardoso, J B ^a   Guedes, J M ^b  

^a UNIVERSIDADE NOVA DE LISBOA   (Portugal)

^b UNIVERSITY OF LISBON   (Portugal)

Author keywords

Anisotropy; Bone remodeling; Bone surface; Hierarchical; Porosity

Indexed keywords

APPARENT DENSITIES; BIOLOGICAL FACTORS; BONE MICROSTRUCTURES; BONE REMODELING; BONE SURFACE; BONE TISSUES; CELLULAR MATERIALS; COMPACT BONES; DENSITY-BASED; DESIGN VARIABLES; DUAL-ENERGY X-RAY ABSORPTIOMETRY; EXPERIMENTAL DATUM; FUNCTIONAL DEMANDS; GLOBAL LEVELS; GLOBAL SCALE; HIERARCHICAL; HIERARCHICAL APPROACHES; HIERARCHICAL STRUCTURES; ISOTROPIC BEHAVIORS; LOCAL SCALE; LOCAL STRESS; MACRO-SCALE; MATERIAL DISTRIBUTIONS; MATERIAL SYMMETRIES; MICRO-SCALE; MICROSTRUCTURAL DESIGNS; NUMERICAL MODELING; NUMERICAL RESULTS; PROXIMAL FEMURS; RELATIVE DENSITIES; THREE-DIMENSIONAL MODELS; TRABECULAR STRUCTURES;

ANISOTROPY; BIOMECHANICS; DENSITY (SPECIFIC GRAVITY); MECHANICAL PROPERTIES; MICROSTRUCTURE; POROSITY; SURFACES; THREE DIMENSIONAL;

BONE;

ANISOTROPY; ARTICLE; BONE DENSITY; BONE REMODELING; BONE STRUCTURE; DUAL ENERGY X RAY ABSORPTIOMETRY; MATHEMATICAL MODEL; PRIORITY JOURNAL; TRABECULAR BONE;

ADAPTATION, BIOLOGICAL; ALGORITHMS; BONE DENSITY; FEMUR; FINITE ELEMENT ANALYSIS; MODELS, BIOLOGICAL;

EID: 64549103367     PISSN: 00219290     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jbiomech.2009.01.020     Document Type: Article

References (46)

1. Bendsøe M.P., and Sigmund O. Topology Optimization Theory, Methods and Applications (2003), Springer, Berlin Heidelberg, New York
2. Beaupré G.S., Orr T.E., and Carter D.R. An approach for time-dependent bone modeling and remodeling-theoretical development. Journal of Orthopaedic Research 8 (1990) 651-661
3. Bergmann, G., 1998. Hip98-Loading of the hip joint. Free University of Berlin. Compact disc, ISBN 3980784800.
4. Bergmann G., Deuretzbacher G., Heller M., Graichen F., Rohlmann A., Strauss J., and Duda G. Hip contact forces and gait patterns from routine activities. Journal of Biomechanics 34 (2001) 859-871
5. Carter D.R., and Beaupré G.S. Skeletal Function and Form (2001), Cambridge University Press
6. Carter D.R., Fyhrie D.P., and Whalen R.T. Trabecular bone density and loading history: regulation of tissue biology by mechanical energy. Journal of Biomechanics 20 (1987) 785-795
7. Carter D.R., Orr T.E., and Fyhrie D.P. Relationships between loading history and femoral cancellous bone architecture. Journal of Biomechanics 22 (1989) 231-244
8. Coelho P., Fernandes P., Guedes J., and Rodrigues H. A hierarchical model for concurrent material and topology optimization of three-dimensional structures. Structural and Multidisciplinary Optimization 35 (2008) 107-115
9. Cowin S.C. Bone poroelasticity. Journal of Biomechanics 32 (1999) 217-238
10. Doblaré M., and Garcia J.M. Application of an anisotropic bone-remodelling model based on a damage-repair theory to the analysis of the proximal femur before and after total hip replacement. Journal of Biomechanics 34 (2001) 1157-1170
11. Doblaré M., and Garcia J.M. Anisotropic bone remodelling model based on a continuum damage-repair theory. Journal of Biomechanics 35 (2002) 1-17
12. Fazzalari N.L., Crisp D.J., and Vernon-Roberts B. Mathematical modeling of trabecular bone structure: the evaluation of analytical and quantified surface to volume relationships in the femoral head and iliac crest. Journal of Biomechanics 22 (1989) 901-910
13. Fernandes P., Rodrigues H., and Jacobs C. A model of bone adaptation using a global optimization criterion based on the trajectorial theory of Wolff. Computer Methods in Biomechanics and Biomedical Engineering 2 (1999) 125-138
14. Fernandes P., Guedes J.M., and Rodrigues H. Topology optimization of three-dimensional structures with a constraint on perimeter. Computers and Structures 73 (1999) 583-594
15. Fleury C. CONLIN: an efficient dual optimizer based on convex approximation concepts. Structural Optimization 1 (1989) 81-89
16. Fyhrie D.P., Fazzalari N.L., Goulet R., and Goldstein S.A. Direct calculation of the surface-to-volume ratio for human cancellous bone. Journal of Biomechanics 26 (1993) 955-967
17. Fyhrie D.P., Lang S.M., Hoshaw S.J., Shaffler M.B., and Kuo R.F. Human vertebral cancellous bone surface distribution. Bone 17 (1995) 287-291
18. Garcia-Aznar J.M., Rueberg T., and Doblaré M. A bone remodelling model coupling microdamage growth and repair by 3D BMU-activity. Biomechanics and Modeling Mechanobiology 4 (2005) 147-167
19. Gibson L., and Ashby M. Cellular Solids, Structure and Properties (1988), Pergamon Press, Oxford, England
20. Guedes J., and Kikuchi N. Preprocessing and postprocessing for materials based on the homogenisation method with adaptive finite element method. Computer Methods in Applied Mechanics and Engineering 83 (1990) 143-198
21. Hart R.T., Davy D.T., and Heiple K.G. A computational model for stress analysis of adaptive elastic materials with a view toward applications in strain-induced bone remodeling. Journal of Biomechanical Engineering 106 (1984) 342-350
22. Hart R.T., and Fritton S.P. Introduction to finite element based simulation of functional adaptation of cancellous bone. Forma 12 (1997) 277-299
23. Hazelwood S.J., Martin R.B., Rashid M.M., and Rodrigo J.J. A mechanistic model for internal bone remodeling exhibits different dynamic responses in disuse and overload. Journal of Biomechanics 34 (2001) 299-308
24. Hernandez C.J., Beaupré G.S., and Carter D.R. A model of mechanobiologic and metabolic influences on bone adaptation. Journal Rehabilitation Research and Development 37 (2000) 235-244
25. Hernandez, C.J., 2001. Simulation of bone remodeling during the development and treatment of osteoporosis. PhD thesis, Stanford University, Stanford, CA.
26. Huiskes R., Weinans H., Grootenboer H.J., Dalstra M., Fudala B., and Sloof T.J. Adaptive bone-remodeling theory applied to prosthetic-design analysis. Journal of Biomechanics 20 (1987) 1135-1150
27. Huiskes R., Ruimerman R., van Lenthe G.H., and Janssen J.D. Effects of mechanical forces on maintenance and adaptation of form in trabecular bone. Nature 405 (2000) 704-706
28. Jacobs C.R., Simo J.C., Beaupré G.S., and Carter D.R. Adaptive bone remodeling incorporating simultaneous density and anisotropy considerations. Journal of Biomechanics 30 (1997) 603-613
29. Keaveny T.M., Morgan E.F., Niebur G.L., and Yeh O.C. Biomechanics of trabecular bone. Annual Review of Biomedical Engineering 3 (2001) 307-333
30. Lucas G., Cook F., and Friis E. A Primer of Biomechanics (1999), Springer, NY
31. Lucchinetti E. Composite model of bone properties. In: Cowin S.C. (Ed). Bone Mechanics Handbook. 2nd Edition (2001), CRC Press 121-1219
32. Martin R.B. Porosity and specific surface of bone. CRC Critical Reviews in Biomedical Engineering 10 (1984) 179-222
33. Martin R.B. A mathematical model for fatigue damage repair and stress fracture in osteonal bone. Journal Orthopaedic Research 13 (1995) 309-316
34. Martin R.B., Burr D.B., and Sharkey N.A. Skeletal Tissue Mechanics (1998), Springer, NY
35. Mullender M.G., Huiskes R., and Weinans H. A Physiological approach to the simulation of bone remodeling as a self-organisational control process. Journal of Biomechanics 27 (1994) 1389-1394
36. Parfitt A.M., Mathews C.H., Villanueva A.R., Kleerekoper M., Frame B., and Rao D.S. Relationships between surface, volume, and thickness of iliac trabecular bone in aging and in osteoporosis. Journal Clinical Investigation 72 (1983) 1396-1409
37. Prendergast P.J., and Taylor D. Prediction of bone adaptation using damage accumulation. Journal of Biomechanics 27 (1994) 1067-1076
38. Rodrigues H., Jacobs C., Guedes J., and Bendsøe M. Global and local material optimization applied to anisotropic bone adaptation. In: Perdersen P., and Bendsoe M.P. (Eds). Synthesis in Bio Solid Mechanics (1999), Kluwer Academic Publishers 209-220 ISBN 0-7923-5615-2
39. Santos, L., Coelho, P., Fonseca, J., Rodrigues, H., Fernandesm, P., 2008. A DXA validation of a bone remodeling model for the assessment of osteoporotic bone quality. Sixth International Conference on Engineering Computational Technology, M. Papadrakakis and B.H.V. Topping, (Eds), Civil-Comp Press, Stirlingshire, Scotland.
40. Sigmund O. On the optimality of bone structure. In: Perdersen P., and Bendsoe M.P. (Eds). Synthesis in Bio Solid Mechanics (1999), Kluwer Academic Publishers 221-234 ISBN 0-7923-5615-2
41. Svanberg K. The method of moving asymptotes-a new method for structural optimisation. International Journal for Numerical Methods in Engineering 24 (1987) 359-373
42. Taylor D., and Lee T.C. Microdamage and mechanical behavior: predicting failure and remodeling in compact bone. Journal of Anatomy 203 (2003) 203-211
43. Taylor D., Casolari E., and Bignardi C. Predicting stress fractures using a probabilistic model of damage, repair and adaptation. Journal of Orthopaedic Research 22 (2004) 487-494
44. Viceconti M., Casali M., Massari B., Cristofolini L., Bassini S., and Toni A. The 'standardized femur program' proposal for a reference geometry to be used for the creation of finite element models of the femur. Journal of Biomechanics 29 (1996) 1241
45. Weinans H., Huiskes R., and Grootenboer H.J. The behavior of adaptive bone-remodeling simulation models. Journal of Biomechanics 25 (1992) 1425-1441
46. Wolff, J., 1986. The law of bone remodeling (Das Gesetz der Transformation der Knochen, Hirschwald, 1892). Translated by Maquet P. and Furlong R. Springer, Berlin.