ENG  Vol.6 No.3 , March 2014
Computational Simulations of Bone Remodeling under Natural Mechanical Loading or Muscle Malfunction Using Evolutionary Structural Optimization Method
Abstract: Live bone inherently responds to applied mechanical stimulus by altering its internal tissue composition and ultimately biomechanical properties, structure and function. The final formation may structurally appear inferior by design but complete by function. To understand the loading response, this paper numerically investigated structural remodeling of mature sheep femur using evolutionary structural optimization method (ESO). Femur images from Computed Tomography scanner were used to determine the elastic modulus variation and subsequently construct finite element model of the femur with stiffest elasticity measured. Major muscle forces on dominant phases of healthy sheep gait were imposed on the femur under static mode. ESO was applied to progressively alter the remodeling of numerically simulated femur from its initial to final design by iteratively removing elements with low strain energy density (SED). The computations were repeated with two different mesh sizes to test the convergence. The elements within the medullary canal had low SEDs and therefore were removed during the optimization. The SEDs in the remaining elements varied with angle around the circumference of the shaft. Those elements with low SED were inefficient in supporting the load and thus fundamentally explained how bone remodels itself with less stiff inferior tissue to meet load demand. This was in line with the Wolff’s law of transformation of bone. Tissue growth and remodeling process was found to shape the sheep femur to a mechanically optimized structure and this was initiated by SED in macro-scale according to traditional principle of Wolff’s law.
Cite this paper: Latifi, H. , Xie, Y. , Huang, X. and Bilgen, M. (2014) Computational Simulations of Bone Remodeling under Natural Mechanical Loading or Muscle Malfunction Using Evolutionary Structural Optimization Method. Engineering, 6, 113-126. doi: 10.4236/eng.2014.63015.

[1]   Fan, Y., et al. (2011) Optimal Principle of Bone Structure. PLoS One, 6, e28868.

[2]   Bouguecha, A., Weigel, N., Behrens, B.-A., Stukenborg-Colsman, C. and Waizy, H. (2011) Numerical Simulation of Strain-Adaptive Bone Remodelling in the Ankle Joint. BioMedical Engineering OnLine, 10, 1-13.

[3]   Comiskey, D.P., MacDonald, B.J., McCartney, W.T., Synnott, K. and O’Byrne, J. (2012) Predicting the External Formation of a Bone Fracture Callus: An Optimisation Approach. Computer Methods in Biomechanics and Biomedical Engineering, 15, 779-785.

[4]   Comiskey, D., MacDonald, B.J., McCartney, W.T., Synnott, K. and O’Byrne, J. (2013) Predicting the External Formation of Callus Tissues in Oblique Bone Fractures: Idealised and Clinical Case Studies. Biomechanics and Modeling in Mechanobiology, 12, 1277-1282.

[5]   Schulte, F.A., et al. (2013) Local Mechanical Stimuli Regulate Bone Formation and Resorption in Mice at the Tissue Level. PLoS One, 8, e62172.

[6]   Xie, Y.M. and Steven, G.P. (1993) A Simple Evolutionary Procedure for Structural Optimization. Computers & Structures, 49, 885-896.

[7]   Hangartner, T.N. and Overton, T.R. (1982) Quantitative Measurement of Bone Density Using Gamma-Ray Computed Tomography. Journal of Computer Assisted Tomography, 6, 1156-1162.

[8]   Latifi, M.H., et al. (2012) Prospects of Implant with Locking Plate in Fixation of Subtrochanteric Fracture: Experimental Demonstration of Its Potential Benefits on Synthetic Femur Model with Supportive Hierarchical Nonlinear Hyperelastic Finite Element Analysis. BioMedical Engineering OnLine, 11, 1-18.

[9]   Agostinho, F., et al. (2012) Gait Analysis in Clinically Healthy Sheep from Three Different Age Groups Using a Pressure-Sensitive Walkway. BMC Veterinary Research, 8, 87-94.

[10]   Bramer, J.A., et al. (1998) Representative Assessment of Long Bone Shaft Biomechanical Properties: An Optimized Testing Method. Journal of Biomechanics, 31, 741-745.

[11]   Yamato, Y., Matsukawa, M., Otani, T., Yamazaki, K. and Nagano, A. (2006) Distribution of Longitudinal Wave Properties in Bovine Cortical Bone in Vitro. Ultrasonics, 44, e233-e237.

[12]   Yosibash, Z., Padan, R., Joskowicz, L. and Milgrom, C. (2007) A CT-Based High-Order Finite Element Analysis of the Human Proximal Femur Compared to in-Vitro Experiments. Journal of Biomechanical Engineering-Transactions of the Asme, 129, 297-309.

[13]   Katz, L.J., et al. (1984) The Effects of Remodeling on the Elastic Properties of Bone. Calcified Tissue International, 36, S31-S36.

[14]   Tomaszewski, P.K., Verdonschot, N., Bulstra, S.K. and Verkerke, G.J. (2010) A Comparative Finite-Element Analysis of Bone Failure and Load Transfer of Osseointegrated Prostheses Fixations. Annals of Biomedical Engineering, 38, 2418-2427.

[15]   Bergmann, G., Graichen, F. and Rohlmann, A. (1999) Hip Joint Forces in Sheep. Journal of Biomechanics, 32, 769-777.

[16]   Orth, P. and Madry, H. (2013) A Low Morbidity Surgical Approach to the Sheep Femoral Trochlea. Bmc Musculoskeletal Disorders, 14, 5.

[17]   Cho, K.H., Park, J.Y., Ryu, S.P. and Han, S.Y. (2011) Reliability-Based Topology Optimization Based on Bidirectional Evolutionary Structural Optimization Using Multi-Objective Sensitivity Numbers. International Journal of Automotive Technology, 12, 849-856.

[18]   Huang, X. and Xie, Y.M. (2007) Convergent and Mesh-Independent Solutions for the Bi-Directional Evolutionary Structural Optimization Method. Finite Elements in Analysis and Design, 43, 1039-1049.

[19]   Petit, M.A., et al. (2008) Proximal Femur Mechanical Adaptation to Weight Gain in Late Adolescence: A Six-Year Longitudinal Study. Journal of Bone and Mineral Research, 23, 180-188.

[20]   Seeman, E. (2008) Bone Quality: The Material and Structural Basis of Bone Strength. Journal of Bone and Mineral Metabolism, 26, 1-8.

[21]   Boyle, C. and Kim, I.Y. (2011) Three-Dimensional Micro-Level Computational Study of Wolff’s Law via Trabecular Bone Remodeling in the Human Proximal Femur Using Design Space Topology Optimization. Journal of Biomechanics, 44, 935-942.

[22]   Robling Ag Fau-Castillo, A.B., Castillo Ab Fau-Turner, C.H. and Turner, C.H. (2006) Biomechanical and Molecular Regulation of Bone Remodeling. Annual Review of Biomedical Engineering, 8, 455-498.

[23]   Huang, X. and Xie, Y.M. (2009) Bi-Directional Evolutionary Topology Optimization of Continuum Structures with One or Multiple Materials. Computational Mechanics, 43, 393-401.

[24]   Woon, S.Y., Tong, L., Querin, O.M. and Steven, G.P. (2005) Effective Optimisation of Continuum Topologies through a Multi-GA System. Computer Methods in Applied Mechanics and Engineering, 194, 3416-3437.

[25]   Machado, M.M., Fernandes, P.R., Cardadeiro, G. and Baptista, F. (2013) Femoral Neck Bone Adaptation to WeightBearing Physical Activity by Computational Analysis. Journal of Biomechanics, 46, 2179-2185.

[26]   R. A. Horch, D. F. Gochberg, J. S. Nyman and M. D. Does, “Non-invasive predictors of human cortical bone mechanical properties: T-2-Discriminated H-1 NMR compared with high resolution X-ray,” PLoS ONE, Vol. 6, No. 1, 2011, p. e16359.

[27]   Müller, R. and Rüegsegger, P. (1995) Three-Dimensional Finite Element Modelling of Non-Invasively Assessed Trabecular Bone Structures. Medical Engineering & Physics, 17, 126-133.

[28]   Cristofolini, L., et al. (2010) Mechanical Testing of Bones: The Positive Synergy of Finite-Element Models and in Vitro Experiments. Philosophical Transactions of the Royal Society A: Mathematical Physical and Engineering Sciences, 368, 2725-2763.

[29]   Kim, H.S., et al. (2012) Finite Element Modeling Technique for Predicting Mechanical Behaviors on Mandible Bone during Mastication. Journal of Advanced Prosthodontics, 4, 218-226.

[30]   Keyak, J.H., Rossi, S.A., Jones, K.A. and Skinner, H.B. (1998) Prediction of Femoral Fracture Load Using Automated Finite Element Modeling. Journal of Biomechanics, 31, 125-133.

[31]   Silva, M.J., Keaveny, T.M. and Hayes, W.C. (1998) Computed Tomography-Based Finite Element Analysis Predicts Failure Loads and Fracture Patterns for Vertebral Sections. Journal of Orthopaedic Research, 16, 300-308.

[32]   Hutzschenreuter, P.O., Sekler, E. and Faust, G. (1993) Loads on Muscles, Tendons and Bones in the Hind Extremities of Sheep—A Theoretical Study. Anatomia Histologia Embryologia—Journal of Veterinary Medicine Series C-Zentralblatt fur Veterinarmedizin Reihe C, 22, 67-82.

[33]   Fraysse, F., et al. (2009) Comparison of Global and Joint-to-Joint Methods for Estimating the Hip Joint Load and the Muscle Forces during Walking. Journal of Biomechanics, 42, 2357-2362.

[34]   Page, A.E., et al. (1993) Determination of Loading Parameters in the Canine Hip in Vivo. Journal of Biomechanics, 26, 571-579.