MULTISCALE MODELING OF OSSEOUS TISSUES

The paper presents a methodology of the multiscale bone modeling in which the task of identification of material parameters plays the crucial role. A two-scale analysis of the bone is considered and the problem of identification, formulated as an inverse problem, is examined as an important stage of the modelling process. The human femur bone, built form cancellous and cortical bone, is taken as an example of an osseous tissue, and the computational multiscale approach is considered. The methodology presented in the paper allows one to analyze the two-scale model with the use of computational homogenization. The representative volume element (RVE) is created for the microstructure of the basis of micro-CT scans. The macro and micro model analyses are performed by using the finite element method. The identification of trabeculae material parameters on the micro-level is considered as the minimization problem which is solved using evolutionary computing.

[1]  K. Radermacher,et al.  Critical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur. , 2000, Journal of biomechanics.

[2]  Adam Mrozek,et al.  Molecular Statics Coupled with the Subregion Boundary Element Method in Multiscale Analysis , 2010 .

[3]  V Varvara Kouznetsova,et al.  Computational homogenization for the multi-scale analysis of multi-phase materials , 2002 .

[4]  M. Pietrzyk,et al.  Concurrent and upscaling methods in multi scale modelling - case studies , 2008 .

[5]  H. Trębacz,et al.  The estimation of structural anisotropy of trabecular and cortical bone tissues based on ultrasonic velocity and attenuation , 2001 .

[6]  R. Naghdabadi,et al.  Nonlinear hierarchical multiscale modeling of cortical bone considering its nanoscale microstructure. , 2009, Journal of biomechanics.

[7]  Wacław Kuś,et al.  Microstructure Optimization and Identification in Multi-scale Modelling , 2009 .

[8]  Salah Naili,et al.  Variational homogenization for modeling fibrillar structures in bone , 2009 .

[9]  B. Mijović,et al.  The cancellous bone multiscale morphology-elasticity relationship. , 2006, Collegium antropologicum.

[10]  Iwona M Jasiuk,et al.  Multiscale modeling of elastic properties of cortical bone , 2010 .

[11]  O. C. Zienkiewicz,et al.  The Finite Element Method: Its Basis and Fundamentals , 2005 .

[12]  U. Hindenlang,et al.  Inhomogeneous, orthotropic material model for the cortical structure of long bones modelled on the basis of clinical CT or density data , 2009 .

[13]  R. Gilbert,et al.  Application of the multiscale FEM to the modeling of cancellous bone , 2010, Biomechanics and modeling in mechanobiology.

[14]  Tadeusz Burczyński,et al.  Evolutionary and Immune Computations in Optimal Design and Inverse Problems , 2010 .

[15]  Piotr Kowalczyk,et al.  Simulation of orthotropic microstructure remodelling of cancellous bone. , 2010, Journal of biomechanics.

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