Multiscale modeling of osseous tissues

• Autorzy: Burczyński T. , Kuś W. , Brodacka A.

Warianty tytułu

PL

Modelowanie wieloskalowe tkanki kostnej

• Języki publikacji: EN

Abstrakty

EN

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.

PL

W artykule przedstawiono metodologię wieloskalowego modelowania thanki kostnej, w której zagadnienie identyfikacji parametrów materiałowych odgrywa kluczową rolę. Rozpatrzono analizę dwuskalową kości, a problem identyfikacji sformułowano jako zagadnienie odwrotne, będące ważnym etapem procesu modelowania. Jako przykład tkanki kostnej rozważono kość udową zbudowaną z kości gąbczastej i korowej.

Słowa kluczowe

EN

multiscale modeling of bone; computational homogenization; identification of material parameters

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2010
• Tom: Vol. 48 nr 4
• Strony: 855--870
• Opis fizyczny: Bibliogr. 18 poz., rys., tab.

Twórcy

autor

Burczyński T.

autor

Kuś W.

autor

Brodacka A.

• Silesian University of Technology, Department of Strength of Materials and Computational Mechanics, Gliwice, Poland; Cracow University of Technology, Institute of Computer Science, Kraków, Poland,

Bibliografia

• 1. Agić A., Nikolić V., Mijović B., 2006, The cancellous bone multiscale morphology-elasticity relationship, Collegium Antropologicum, 30, 2, 409-414
• 2. Bąk R., Burczyński T., 2009, Computational Strength of Materials (in Polish Wytrzymałość materiałów z elementami ujęcia komputerowego), WNT, Warszawa
• 3. Burczyński T., 2010, Evolutionary and immune computations in optimal design and inverse problems, Chapter 2 in: Advances of Soft Computing in Engineering, Z. Waszczyszyn (Edit.), Springer, 57-132
• 4. Burczyński T., KuśW., 2009,Microstructure optimization and identification in multi-scale modellig, Chapter in: New Computational Challenges in Materials, Structures and Fluids, J. Eberhadstener et al. (Edit.), Springer, 169-181
• 5. Burczyński T., Mrozek A., Górski R., Kuś W., 2010, Molecular statics coupled with the subregion boundary element method in multiscale analysis, Int. Journal for Multiscale Computational Engineering, 8, 3, 319-331
• 6. Ghanbari J., Naghdabadi R., 2009, Nonlinear hierarchical multiscale modeling of cortical bone considering its nanoscale microstructure, Journal of Biomechanics, 42, 1560-1565
• 7. Hamed E., Lee Y., Jasiuk I., 2010, Multiscale modeling of elastic properties of cortical bone, Acta Mechanica (online)
• 8. Ilic S., Hackl K., Gilbert R., 2010, Application of the multiscale FEM to the modeling of cancellous bone, Biomech. Model Mechanobiol., 9, 87-102
• 9. Kouznetsova V.G., 2002, Computational homogenization for the multi-scale analysis of multi-phase materials, Ph.D. Thesis, TU Eindhoven.
• 10. Kowalczyk P., 2010, Simulation of orthotropic microstructure remodelling of cancellous bone, Journal of Biomechanics, 43, 563-569
• 11. Madej Ł., Mrozek A., Kuś W., Burczyński T., Pietrzyk M., 2008, Concurrent and upscaling methods in multi scale modelling – case studies, Computer Methods in Material Science, 8, 1, AGH, Krakow
• 12. Sansalone V., Lemaire T., Naili S., 2009, Variational homogenization for modeling fibrillar structures in bone, Mechanics Research Communications, 36, 265-273
• 13. Schneider R., Faust G., Hindenlang U., Helwig P., 2009, Inhomogeneous, orthotropic material model for the cortical structure of long bones modeled on the basis of clinical CT or density data, Comput. Methods Appl. Mech. Engrg., 1298, 2167-2174
• 14. Terada K., Kikuchi N., 2001, A class of general algorithms for multi-scale analyses for heterogeneous media, Computer Methods in Applied Mechanics and Engineering, 190, 5427-5464
• 15. Trębacz H., Gawda H., 2001, The estimation of structural anisotropy of trabecular and cortical bone tissues based on ultrasonic velocity and attenuation, Acta of Bioengineering and Biomechanics, 3, 2, 41-48
• 16. Tsubota K., Adachi T., Nishiumi S., Tomita Y., 2003, Elastic properties of single trabeculae measured by micro-three-point bending test, Proc. of the International Conference on Advanced Technology in Experimental Mechanics
• 17. Wirtz D.C., Schiffers N., Pandorf T., Radermacher K., Weichert D., Forst R., 2000, Critical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur, Journal of Biomechanics, 33, 1325-1330
• 18. Zienkiewicz O.C., Taylor R.L., Zhu J.Z., 2005, The Finite Element Method: Its Basis and Fundamentals, 6th Edition, Butterworth-Heinemann