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Journal of Biomechanical Engineering | Volume 132 | Issue 11 | Technical Brief
Technical Briefs

Application of Neural Networks and Finite Element Computation for Multiscale Simulation of Bone Remodeling

[+] Author and Article Information
Ridha Hambli

 Institut Prisme/MMH, 8 Rue Léonard de Vinci, 45072 Orléans Cedex 2, Franceridha.hambli@univ-orleans.fr

J Biomech Eng 132(11), 114502 (Oct 12, 2010) (5 pages) doi:10.1115/1.4002536 History: Received January 10, 2010; Revised September 08, 2010; Posted September 10, 2010; Published October 12, 2010; Online October 12, 2010
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In this paper, a novel multiscale hierarchical model based on finite element analysis and neural network computation was developed to link mesoscopic and macroscopic scales to simulate the bone remodeling process. The finite element calculation is performed at the macroscopic level, and trained neural networks are employed as numerical devices for substituting the finite element computation needed for the mesoscale prediction. Based on a set of mesoscale simulations of representative volume elements of bones taken from different bone sites, a neural network is trained to approximate the responses at the meso level and transferred at the macro level.
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References

1
Rho, J. Y., Kuhn-Spearing, L., and Zioupos, P., 1998, “Mechanical Properties and the Hierarchical Structure of Bone,” Med. Eng. Phys., 20 , pp. 92–102.  [CrossRef]
2
Carter, D. R., and Beaupré, G. S., 2001, "Skeletal Function and Form: Mechanobiology of Skeletal Development, Aging and Regeneration", 1st ed., Cambridge University Press, Cambridge, UK.
3
Weiner, S., and Traub, W., 1992, “Bone Structure: From Ångstroms to Microns,” FASEB J., 6 , pp. 879–885.
4
Fazzalari, N. L., Kuliwaba, J. S., and Forwood, M. R., 2002, “Cancellous Bone Microdamage in the Proximal Femur: Influence of Age and Osteoarthritis on Damage Morphology and Regional Distribution,” Bone31 (6), pp. 697–702.  [CrossRef]
5
Yoo, A., and Jasiuk, I., 2006, “Couple-Stress Moduli of a Trabecular Bone Idealized as a 3D Periodic Cellular Network,” J. Biomech., 39 , pp. 2241–2252.  [CrossRef]
6
Viceconti, M., Taddei, F., Jan, S. V. S., Leardini, A., Cristofolini, A., Stea, S., Baruffaldi, F., and Baleani, M., 2008, “Multiscale Modelling of the Skeleton for the Prediction of the Risk of Fracture,” Clin. Biomech. (Bristol, Avon), 23 , pp. 845–852.  [CrossRef]
7
Unger, J. F., and Konke, C., 2008, "Coupling of Scales in Multiscale Simulation Using Neural Networks", Elsevier, New York.
8
Hambli, R., 2009, “Statistical Damage Analysis of Extrusion Processes Using Finite Element Method and Neural Networks Simulation,” Finite Elem. Anal. Design, 45 (10), pp. 640–649.  [CrossRef]
9
Rafiq, M. Y., Bugmann, G., and Easterbrook, D. J., 2001, “Neural Network Design for Engineering Applications,” Comput. Struct., 79 (17), pp. 1541–1552.  [CrossRef]
10
Hambli, R., Chamekh, A., and Bel Hadj Salah, H., 2006, “Real-Time Deformation of Structure Using Finite Element and Neural Networks in Virtual Reality Applications,” Finite Elem. Anal. Design, 42 (11), pp. 985–991.  [CrossRef]
11
Chaboche, J. L., 1981, “Continuum Damage Mechanics—A Tool to Describe Phenomena Before Crack Initiation,” Nucl. Eng. Des., 64 , pp. 233–247.  [CrossRef]
12
McNamara, L. M., and Prendergast, J. P., 2007, “Bone Remodeling Algorithms Incorporating Both Stain and Microdamage Stimuli,” J. Biomech., 40 (6), pp. 1381–1391.  [CrossRef]
13
Hambli, R., Soulat, D., Gasser, A., and Benhamou, C. L., 2009, “Strain-Damage Coupled Algorithm for Cancellous Bone Mechano-Regulation With Spatial Function Influence,” Comput. Methods Appl. Mech. Eng., 198 (33–36), pp. 2673–2682.  [CrossRef]
14
Cowin, S. C., 2002, “Mechanosensation and Fluid Transport in Living Bone,” J. Musculoskeletal and Neuronal Interact., 2 (3), pp. 256–260.

Figures

Grahic Jump Location
+Multiscale hierarchical approach for bone analysis. Two level analysis for the prediction of the remodeling process. Macroscale level: a whole bone computed using FE analysis. Mesoscale level: μ-CT FE model computed using trained NN. 2 mm3 RVE obtained using digital image-based modeling technique meshed using about 200,000 eight-node 3D brick elements.
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Multiscale hierarchical approach for bone analysis. Two level analysis for the prediction of the remodeling process. Macroscale level: a whole bone computed using FE analysis. Mesoscale level: μ-CT FE model computed using trained NN. 2 mm3 RVE obtained using digital image-based modeling technique meshed using about 200,000 eight-node 3D brick elements.
Figure 1

Multiscale hierarchical approach for bone analysis. Two level analysis for the prediction of the remodeling process. Macroscale level: a whole bone computed using FE analysis. Mesoscale level: μ-CT FE model computed using trained NN. 2 mm3 RVE obtained using digital image-based modeling technique meshed using about 200,000 eight-node 3D brick elements.

Grahic Jump Location
+Meso-to-macro transition: NN is incorporated into the FE code ABAQUS via the routine UMAT
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Meso-to-macro transition: NN is incorporated into the FE code ABAQUS via the routine UMAT
Figure 2

Meso-to-macro transition: NN is incorporated into the FE code ABAQUS via the routine UMAT

Grahic Jump Location
+Contour of trabecular bone damage predicted by the hybrid method. (a) Macroscopic contour predicted by NN computation. (b) RVE predicted results are averaged and passed to the macroscopic finite element level.
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Contour of trabecular bone damage predicted by the hybrid method. (a) Macroscopic contour predicted by NN computation. (b) RVE predicted results are averaged and passed to the macroscopic finite element level.
Figure 3

Contour of trabecular bone damage predicted by the hybrid method. (a) Macroscopic contour predicted by NN computation. (b) RVE predicted results are averaged and passed to the macroscopic finite element level.

Grahic Jump Location
+Contour of trabecular bone density predicted by the hybrid method. (a) Macroscopic contour predicted by NN computation. (b) RVE predicted results are averaged and passed to the macroscopic finite element level.
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Contour of trabecular bone density predicted by the hybrid method. (a) Macroscopic contour predicted by NN computation. (b) RVE predicted results are averaged and passed to the macroscopic finite element level.
Figure 4

Contour of trabecular bone density predicted by the hybrid method. (a) Macroscopic contour predicted by NN computation. (b) RVE predicted results are averaged and passed to the macroscopic finite element level.

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