Multiscale Characterisation of Cortical Bone Tissue

The authors gratefully acknowledge the Ministry of Economy and Competitiveness [Ministerio de Economia y Competitividad] of the Government of Spain (DPI2014-58233-P, DPI2017-82501-P, PGC2018-097257-B-C31) for research funding.

[1]  Yang Ning,et al.  A review of computational models of bone fracture healing , 2017 .

[2]  J. Domínguez,et al.  Analysis of fretting fatigue initial crack path in Al7075-T651 using cylindrical contact , 2017 .

[3]  H. Schryver.  Bending properties of cortical bone of the horse. , 1978, American journal of veterinary research.

[4]  S J Hollister,et al.  Trabecular surface remodeling simulation for cancellous bone using microstructural voxel finite element models. , 2001, Journal of biomechanical engineering.

[5]  Ralph Müller,et al.  In silico models of bone remodeling from macro to nano—from organ to cell , 2011, Wiley interdisciplinary reviews. Systems biology and medicine.

[6]  N. Kikuchi,et al.  A class of general algorithms for multi-scale analyses of heterogeneous media , 2001 .

[7]  Bernd Eggers,et al.  Bones Structure And Mechanics , 2016 .

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

[9]  S. Cowin,et al.  Bone remodeling I: theory of adaptive elasticity , 1976 .

[10]  V. Kouznetsova,et al.  Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme , 2002 .

[11]  José Manuel García-Aznar,et al.  Micro–macro numerical modelling of bone regeneration in tissue engineering , 2008 .

[12]  Jacob Fish,et al.  Toward realization of computational homogenization in practice , 2008 .

[13]  J. A. Sanz-Herrera,et al.  A mathematical approach to bone tissue engineering , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[14]  D. Burr,et al.  Stiffness of compact bone: effects of porosity and density. , 1988, Journal of biomechanics.

[15]  G. Beaupré,et al.  An approach for time‐dependent bone modeling and remodeling—application: A preliminary remodeling simulation , 1990, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[16]  E. Reina-Romo,et al.  Modeling distraction osteogenesis: analysis of the distraction rate , 2009, Biomechanics and modeling in mechanobiology.

[17]  M. Warner,et al.  Determination of orthotropic bone elastic constants using FEA and modal analysis. , 2002, Journal of biomechanics.

[18]  Gaffar Gailani,et al.  Hierarchical poroelasticity: movement of interstitial fluid between porosity levels in bones , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[19]  Ralph Müller,et al.  Guidelines for assessment of bone microstructure in rodents using micro–computed tomography , 2010, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[20]  Ning Yang,et al.  A review of computational models of bone fracture healing , 2017, Medical & Biological Engineering & Computing.

[21]  L. Geris,et al.  A computational model for cell/ECM growth on 3D surfaces using the level set method: a bone tissue engineering case study , 2014, Biomechanics and modeling in mechanobiology.

[22]  Stephen C. Cowin,et al.  The estimated elastic constants for a single bone osteonal lamella , 2008, Biomechanics and modeling in mechanobiology.

[23]  L. Claes,et al.  Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing. , 1998, Journal of biomechanics.

[24]  Patrick J Prendergast,et al.  Prediction of the optimal mechanical properties for a scaffold used in osteochondral defect repair. , 2006, Tissue engineering.

[25]  Rik Huiskes,et al.  Bone regeneration during distraction osteogenesis: mechano-regulation by shear strain and fluid velocity. , 2007, Journal of biomechanics.

[26]  J. A. Sanz-Herrera,et al.  A mathematical model for bone tissue regeneration inside a specific type of scaffold , 2008, Biomechanics and modeling in mechanobiology.

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

[28]  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.

[29]  E Reina-Romo,et al.  Effect of the fixator stiffness on the young regenerate bone after bone transport: computational approach. , 2011, Journal of biomechanics.

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

[31]  Sandra J. Shefelbine,et al.  Ex vivo determination of bone tissue strains for an in vivo mouse tibial loading model , 2014, Journal of biomechanics.

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

[33]  L. Lanyon,et al.  Mechanical implications of collagen fibre orientation in cortical bone of the equine radius , 1993, Anatomy and Embryology.

[34]  J M García-Aznar,et al.  On scaffold designing for bone regeneration: A computational multiscale approach. , 2009, Acta biomaterialia.

[35]  A. Burstein,et al.  The elastic and ultimate properties of compact bone tissue. , 1975, Journal of biomechanics.

[36]  G S Beaupré,et al.  Correlations between mechanical stress history and tissue differentiation in initial fracture healing , 1988, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[37]  J. A. Sanz-Herrera,et al.  Multiscale simulation of particle-reinforced elastic–plastic adhesives at small strains , 2011 .

[38]  Christian Hellmich,et al.  A multiscale analytical approach for bone remodeling simulations: linking scales from collagen to trabeculae. , 2014, Bone.

[39]  T. Adachi,et al.  Framework for optimal design of porous scaffold microstructure by computational simulation of bone regeneration. , 2006, Biomaterials.

[40]  Gaffar Gailani,et al.  Experimental determination of the permeability in the lacunar-canalicular porosity of bone. , 2009, Journal of biomechanical engineering.

[41]  S. Cowin,et al.  Candidates for the mechanosensory system in bone. , 1991, Journal of biomechanical engineering.

[42]  O. Carpentier,et al.  Numerical optimization of cell colonization modelling inside scaffold for perfusion bioreactor: A multiscale model. , 2018, Medical engineering & physics.

[43]  G. Reilly,et al.  Postexercise and positional variation in mechanical properties of the radius in young horses. , 2010, Equine veterinary journal.

[44]  B. van Rietbergen,et al.  Bone remodelling in humans is load-driven but not lazy , 2014, Nature Communications.

[45]  C. Miehe,et al.  On multiscale FE analyses of heterogeneous structures: from homogenization to multigrid solvers , 2007 .

[46]  J. Domínguez,et al.  Mechanical characterization via nanoindentation of the woven bone developed during bone transport. , 2017, Journal of the mechanical behavior of biomedical materials.

[47]  A. Sadegh,et al.  An evolutionary Wolff's law for trabecular architecture. , 1992, Journal of biomechanical engineering.

[48]  Kenneth E. Newhouse,et al.  Handbook of Bioengineering , 1987, The Yale Journal of Biology and Medicine.

[49]  Pascal Laugier,et al.  Accurate measurement of cortical bone elasticity tensor with resonant ultrasound spectroscopy. , 2013, Journal of the mechanical behavior of biomedical materials.

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

[51]  S C Cowin,et al.  Mechanosensation and fluid transport in living bone. , 2002, Journal of musculoskeletal & neuronal interactions.

[52]  Hwj Rik Huiskes,et al.  Trabecular Bone Tissue Strains in the Healthy and Osteoporotic Human Femur , 2003, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[53]  G N Duda,et al.  Digital image correlation: a technique for determining local mechanical conditions within early bone callus. , 2007, Medical engineering & physics.

[54]  J. Currey,et al.  The adaptation of bones to stress. , 1968, Journal of theoretical biology.

[55]  Philippe H. Geubelle,et al.  Coupled multi‐scale cohesive modeling of failure in heterogeneous adhesives , 2010 .

[56]  G. Reilly,et al.  The development of microcracking and failure in bone depends on the loading mode to which it is adapted. , 1999, The Journal of experimental biology.

[57]  P. Prendergast,et al.  A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading. , 2002, Journal of biomechanics.

[58]  Josep A Planell,et al.  Simulation of tissue differentiation in a scaffold as a function of porosity, Young's modulus and dissolution rate: application of mechanobiological models in tissue engineering. , 2007, Biomaterials.

[59]  Ralph Müller,et al.  Local Mechanical Stimuli Regulate Bone Formation and Resorption in Mice at the Tissue Level , 2013, PloS one.

[60]  M. V. D. van der Meulen,et al.  A mathematical framework to study the effects of growth factor influences on fracture healing. , 2001, Journal of theoretical biology.

[61]  S. Hall,et al.  Linking multiscale deformation to microstructure in cortical bone using in situ loading, digital image correlation and synchrotron X-ray scattering. , 2018, Acta biomaterialia.

[62]  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.

[63]  Christian Hellmich,et al.  Mineral–collagen interactions in elasticity of bone ultrastructure – a continuum micromechanics approach , 2004 .

[64]  Damien Lacroix,et al.  In Vitro Bone Cell Models: Impact of Fluid Shear Stress on Bone Formation , 2016, Front. Bioeng. Biotechnol..

[65]  D. Carter,et al.  Mechanobiological predictions of growth front morphology in developmental hip dysplasia , 2004, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[66]  Schryver Hf,et al.  Bending properties of cortical bone of the horse. , 1978 .

[67]  A. Curnier,et al.  A three-dimensional elastic plastic damage constitutive law for bone tissue , 2009, Biomechanics and modeling in mechanobiology.

[68]  Manuel Doblaré,et al.  Computational Multiscale Solvers for Continuum Approaches , 2019, Materials.

[69]  Christian Hellmich,et al.  'Universal' microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: micromechanics-based prediction of anisotropic elasticity. , 2007, Journal of theoretical biology.

[70]  A. Palazoglu,et al.  Nanoscale heterogeneity promotes energy dissipation in bone. , 2007, Nature materials.