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

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Abstract

In thiswork,a three-dimensional model for bone remodeling is presented, taking into account thehierarchical structure of bone. The process of bone tissue adaptation is mathematically described withrespect to functional demands, both mechanical and biological, to obtain the bone apparent densitydistribution (at the macroscale) and the trabecular structure (at the microscale). At global scale bone isassumed as a continuum material characterized by equivalent (homogenized) mechanical properties. Atlocal scale a periodic cellular material model approaches bone trabecular anisotropy as well as bonesurface area density. For each scale there is a material distribution problem governed by density-baseddesign variables which at the global level can be identified with bone relative density. In order to showthe potential of the model, a three-dimensional example of the proximal femur illustrates thedistribution of bone apparent density as well as microstructural designs characterizing both anisotropyand bone surface area density. The bone apparent density numerical results show a good agreementwith Dual-energy X-ray Absorptiometry (DXA) exams. The material symmetry distributions obtainedare comparable to real bone microstructures depending on the local stress field. Furthermore, thecompact bone porosity is modeled giving a transversal isotropic behavior close to the experimentaldata. Since, some computed microstructures have no permeability one concludes that bone tissuearrangement is not a simple stiffness maximization issue but biological factors also play an importantrole.
Original languageUnknown
Pages (from-to)830-837
JournalJournal Of Biomechanics
Volume42
Issue number7
DOIs
Publication statusPublished - 1 Jan 2009

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