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

[1]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[2]  J. M. García-Aznar,et al.  A bone remodelling model coupling microdamage growth and repair by 3D BMU-activity , 2005, Biomechanics and modeling in mechanobiology.

[3]  David Taylor,et al.  Predicting stress fractures using a probabilistic model of damage, repair and adaptation , 2004, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[4]  D. Taylor.,et al.  Microdamage and mechanical behaviour: predicting failure and remodelling in compact bone , 2003, Journal of anatomy.

[5]  M Doblaré,et al.  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. , 2001, Journal of biomechanics.

[6]  G. Niebur,et al.  Biomechanics of trabecular bone. , 2001, Annual review of biomedical engineering.

[7]  G. Bergmann,et al.  Hip contact forces and gait patterns from routine activities. , 2001, Journal of biomechanics.

[8]  S. Cowin Bone mechanics handbook , 2001 .

[9]  M. Rashid,et al.  A mechanistic model for internal bone remodeling exhibits different dynamic responses in disuse and overload. , 2001, Journal of biomechanics.

[10]  Rik Huiskes,et al.  Effects of mechanical forces on maintenance and adaptation of form in trabecular bone , 2000, Nature.

[11]  G S Beaupré,et al.  A model of mechanobiologic and metabolic influences on bone adaptation. , 2000, Journal of rehabilitation research and development.

[12]  H. Rodrigues,et al.  Topology optimization of three-dimensional linear elastic structures with a constraint on “perimeter” , 1999 .

[13]  Francis W. Cooke,et al.  A Primer of Biomechanics , 1998, Springer New York.

[14]  R. T. Hart,et al.  Introduction to Finite Element Based Simulation of Functional Adaptation of Cancellous Bone , 1998 .

[15]  J. C. Simo,et al.  Adaptive bone remodeling incorporating simultaneous density and anisotropy considerations. , 1997, Journal of biomechanics.

[16]  L Cristofolini,et al.  The 'standardized femur program' proposal for a reference geometry to be used for the creation of finite element models of the femur. , 1996, Journal of biomechanics.

[17]  D P Fyhrie,et al.  Human vertebral cancellous bone surface distribution. , 1995, Bone.

[18]  B. Martin,et al.  Mathematical model for repair of fatigue damage and stress fracture in osteonal bone , 1995, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[19]  H Weinans,et al.  A physiological approach to the simulation of bone remodeling as a self-organizational control process. , 1994, Journal of biomechanics.

[20]  P J Prendergast,et al.  Prediction of bone adaptation using damage accumulation. , 1994, Journal of biomechanics.

[21]  N L Fazzalari,et al.  Direct calculation of the surface-to-volume ratio for human cancellous bone. , 1993, Journal of biomechanics.

[22]  H. Grootenboer,et al.  The behavior of adaptive bone-remodeling simulation models. , 1992, Journal of biomechanics.

[23]  N. Kikuchi,et al.  Preprocessing and postprocessing for materials based on the homogenization method with adaptive fini , 1990 .

[24]  G S Beaupré,et al.  An approach for time‐dependent bone modeling and remodeling—theoretical development , 1990, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[25]  M. Wolcott Cellular solids: Structure and properties , 1990 .

[26]  Claude Fleury,et al.  CONLIN: An efficient dual optimizer based on convex approximation concepts , 1989 .

[27]  K. Svanberg The method of moving asymptotes—a new method for structural optimization , 1987 .

[28]  D T Davy,et al.  A computational method for stress analysis of adaptive elastic materials with a view toward applications in strain-induced bone remodeling. , 1984, Journal of biomechanical engineering.

[29]  M. Kleerekoper,et al.  Relationships between surface, volume, and thickness of iliac trabecular bone in aging and in osteoporosis. Implications for the microanatomic and cellular mechanisms of bone loss. , 1983, The Journal of clinical investigation.

[30]  Helder C. Rodrigues,et al.  A hierarchical model for concurrent material and topology optimisation of three-dimensional structures , 2008 .

[31]  P. Coelho A DXA validation of a bone remodelling model for the assessment of osteoporotic bone quality , 2008 .

[32]  J. M. Garcı́a,et al.  Anisotropic bone remodelling model based on a continuum damage-repair theory. , 2002, Journal of biomechanics.

[33]  H. Rodrigues,et al.  A Model of Bone Adaptation Using a Global Optimisation Criterion Based on the Trajectorial Theory of Wolff. , 1999, Computer methods in biomechanics and biomedical engineering.

[34]  Martin P. Bendsøe,et al.  Global and Local Material Optimization Models Applied to Anisotropic Bone Adaptation , 1999 .

[35]  Martin P. Bendsøe,et al.  Synthesis in Bio Solid Mechanics , 1999 .

[36]  S. Cowin Bone poroelasticity. , 1999, Journal of biomechanics.

[37]  D. Carter,et al.  Relationships between loading history and femoral cancellous bone architecture. , 1989, Journal of biomechanics.

[38]  N L Fazzalari,et al.  Mathematical modelling of trabecular bone structure: the evaluation of analytical and quantified surface to volume relationships in the femoral head and iliac crest. , 1989, Journal of biomechanics.

[39]  M. Ashby,et al.  Cellular solids: Structure & properties , 1988 .

[40]  D P Fyhrie,et al.  Trabecular bone density and loading history: regulation of connective tissue biology by mechanical energy. , 1987, Journal of biomechanics.

[41]  H. Grootenboer,et al.  Adaptive bone-remodeling theory applied to prosthetic-design analysis. , 1987, Journal of biomechanics.

[42]  Martin Rb Porosity and specific surface of bone. , 1984 .

[43]  R. Martin Porosity and specific surface of bone. , 1984, Critical reviews in biomedical engineering.