Mechanical Behaviour of Femoral Diaphyseal Cortical Bone using the Computed Tomography Data: A Numerical Investigation

Document Type : Research Paper


1 Young Researchers and Elite Club, Central Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Mechanical Engineering, Islamic Azad University, Najafabad Branch, Najafabad

3 Department of Mechanical Engineering, Islamic Azad University, Najafabad Branch, Najafabad, Iran

4 School of Mechanical Engineering, College of Engineering, University of Tehran, P.O. Box 111554563, Tehran, Iran

5 Corresponding Author, Department of Mechanical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran


In this paper, mechanical behaviour and buckling analysis of human femoral bone are performed using the finite element method. A method is proposed to model the geometry and mechanical properties of Femur specimens. Mechanical properties of the bone are regarded both as homogeneous and nonhomogeneous quantities. Compressive tests are performed in three regions of the midshaft to validate the mechanical properties obtained by the CT scan. Waterjet cutting method is used to cut the samples which are used in compressive tests, and the 3D-printed models are used to locate the samples between the jaws of the test machine. Critical axial buckling loads of the femurs are studied, applying both of the homogeneous and nonhomogeneous material properties. Results show that the buckling load which is obtained by proposed homogenous modeling technique is close to the one which is obtained by nonhomogeneous modeling, and the proposed method is quite capable to simplify the FE analysis of the diaphyseal cortical bone.


Main Subjects

[1] Peng, L., Bai, J., Zeng, X., and Zhou, Y., "Comparison of isotropic and orthotropic material property assignments on femoral finite element models under two loading conditions", Med Eng Phys, Vol. 28, pp. 227-233, (2006).
[2] Trabelsi, N., and Yosibash, Z., "Patient-specific finite-element analyses of the proximal femur with orthotropic material properties validated by experiments", Journal of Biomechanical Engineering, 133, (2011).
[3] Zysset, P., Pahr, D., Engelke, K., Genant, H.K., McClung, M.R., Kendler, D.L., Recknor, C., Kinzl, M., Schwiedrzik, J., Museyko, O., Wang, A., and Libanati, C., "Comparison of proximal femur and vertebral body strength improvements in the FREEDOM trial using an alternative finite element methodology", Bone, Vol. 81, pp.122-130, (2015).
[4] Mathukumar, S., Nagarajan, V.A., and Radhakrishnan, A., "Analysis and validation of femur bone data using finite element method under static load condition", Proc IMechE Part C: J Mechanical Engineering Science, Vol. 233(16), pp. 5547-5555, (2019).
[5] Amini, M., Nazemi, S.M., Lanovaz, J.L., Kontulainen, S., Masri, B.A., Wilson, D.R., Szyszkowski, W., and Johnston, J.D., "Individual and combined effects of OA-related subchondral bone alterations on proximal tibial surface stiffness: A parametric finite element modeling study", Med Eng Phys, Vol. 37, pp. 783-791, (2015).
[6] Enns-Bray, W.S., Owoc, J.S., Nishiyama, K.K., and Boyd, S.K., "Mapping anisotropy of the proximal femur for enhanced image based finite element analysis", J Biomech, Vol. 47, pp. 3272-3278, (2014).
[7] Enns-Bray, W.S., Ariza, O., Gilchrist, S., Widmer Soyka, R.P., Vogt, P.J., Palsson, H., Boyd, S.K., Guy, P., Cripton, P.A., Ferguson, S.J., and Helgason, B., "Morphology based anisotropic finite element models of the proximal femur validated with experimental data", Med Eng Phys, Vol. 38, pp. 1339-1347, (2016).
[8] San Antonio, T., Ciaccia, M., Müller-Karger, C., and Casanova, E., "Orientation of
orthotropic material properties in a femur FE model: A method based on the principal stresses directions", Med Eng Phys, Vol. 34, pp. 914–919, (2012).
[9] Varga, P., Schwiedrzik, J., Zysset, P.K., Fliri-Hofmann, L., Widmer, D., Gueorguiev, B., Blauth, M., and Windolf, M., "Nonlinear quasi-static finite element simulations predict in vitro strength of human proximal femora assessed in a dynamic sideways fall setup", J Mech Behav Biomed Mater, Vol. 57, pp. 116-127, (2016).
[10] van de Laarschot, D.M., and Zillikens, M.C., "Atypical femur fracture in an adolescent boy treated with bisphosphonates for X-linked osteoporosis based on PLS3 mutation", Bone, Vol. 91, pp. 148-151, (2016).
[11] Voo, L., Armand, M., and Kleinberger, M., "Stress fracture risk analysis of the human femur based on computational biomechanics", JOHNS HOPKINS APL Tech Dig, Vol. 25(3), pp. 223-230, (2004).
[12] Mahmoudi, M., Amini, S., Vatankhahan, F., and Mahbadi, H., "Buckling analysis of human Tibia and Fibula bones", 25th Annual International Conference on Mechanical Engineering, Tarbiat Modares University, Tehran, Iran. April 16-18, (2017).
[13] Mahmoudi, M., Vatankhahan, F., Salehi, M., and Mahbadi, H., "Experimental investigation of compressive strength in diaphysis of human Tibia and Fibula bones", 25th Annual International Conference on Mechanical Engineering. Tarbiat Modares University, Tehran, Iran. April 16-18, (2017).
[14] Havaldar, R., Pilli, S.C., and Putti, B.B., "Insights into the effects of tensile and compressive loadings on human femur bone", Adv Biomed Res, 3:101, (2014).
[15] Avery, C.M.E., Bujtár, P., Simonovics, J., Dézsi, T., Váradi, K., Sándor, G.K.B., and Pan, J., "A finite element analysis of bone plates available for prophylactic internal fixation of the radial osteocutaneous donor site using the sheep tibia model", Med Eng Phys, Vol. 35, pp. 1421-1430, (2013).
[16] Naidubabu, Y., Mohana Rao, G., Rajasekhar, K., and Ratna Sunil B., "Design and simulation of polymethyl methacrylate-titanium composite bone fixing plates using finite element analysis: Optimizing the composition to minimize the stress shielding effect", Proc IMechE Part C: J Mechanical Engineering Science, Vol. 231(23), pp. 4402-4412, (2017).
[17] Morgan, E.F., Bayraktar, H.H., and Keaveny, T.M., "Trabecular bone modulus-density relationships depend on anatomic site", J Biomech, Vol. 36, pp. 897-904, (2003).
[18] Batawil, N., and Sabiq, S., "Hounsfield unit for the diagnosis of bone mineral density disease: A proof of concept study", Radiography, Vol. 22, pp. e93-98, (2016).
[19] Faisal, T.R., and Luo, Y., "Stress variations owing to single-stance load and sideways fall result in fracture at proximal femur", Proceedings - International Symposium on Biomedical Imaging, (2015).
[20] Knowles, N.K., Reeves, J.M., and Ferreira, L.M., "Quantitative computed tomography (QCT) derived Bone Mineral Density (BMD) in finite element studies: a review of the literature", J Exp Orthop, 3:36, (2016).
[21] den Dunnen, S., Dankelman, J., Kerkhoffs, G.M.M.J., and Tuijthof, G.J.M., "How do jet time, pressure and bone volume fraction influence the drilling depth when waterjet drilling in porcine bone?", J Mech Behav Biomed Mater, Vol. 62, pp. 495-503, (2016).
[22] den Dunnen, S., Mulder, L., Kerkhoffs, G.M.M.J., Dankelman, J., and Tuijthof, G.J.M., "Waterjet drilling in porcine bone: The effect of the nozzle diameter and bone architecture on the hole dimensions", J Mech Behav Biomed Mater, Vol. 27, pp. 84-93, (2013).
[23] Kraaij, G., Tuijthof, G.J.M., Dankelman, J., Nelissen, R.G.H.H., and Valstar, E.R., "Waterjet cutting of periprosthetic interface tissue in loosened hip prostheses: An in vitro feasibility study", Med Eng Phys, Vol. 37, pp. 245-250, (2015).
[24] Wang, J., and Shanmugam, D.K., "Cutting meat with bone using an ultrahigh pressure abrasive waterjet", Meat Sci, Vol. 81, pp. 671-677, (2009).
[25] Zhang, G., Wang, S., Xu, S., Guan, F., Bai, Z., and Mao, H., "The Effect of Formalin Preservation Time and Temperature on the Material Properties of Bovine Femoral Cortical Bone Tissue", Annals of Biomedical Engineering, (2019).
[26] Boehm, H.F., Horng, A., Notohamiprodjo, M., Eckstein, F., Burklein, D., Panteleon, A., Lutz, J., and Reiser, M., "Prediction of the fracture load of whole proximal femur specimens by topological analysis of the mineral distribution in DXA-scan images", Bone, Vol. 43, pp. 826-831, (2008).
[27] Soodmand, E., Kluess, D., Varady, P.A., Cichon, R., Schwarze, M., Gehweiler, D., Niemeyer, F., Pahr, D., and Woiczinski, M., "Interlaboratory comparison of femur surface reconstruction from CT data compared to reference optical 3D scan", BioMedical Engineering OnLine, 2;17(1):29, (2018).
[28] Mahmoudi, M., Dorali, M.R., Heydari Beni, M., and Mahbadi, H., "Bio-CAD modeling of femoral bones with Dual X-ray absorptiometry and Spiral CT-scan technique", The 26th Annual International Conference of Iranian Society of Mechanical Engineers. Semnan University, Semnan, Iran. 24-26 April, (2018).
[29] Alavi, F., and Mirzaei, M., "Experimental and Computational Analysis of Fracture Load and Pattern of Human Femur using Cohesive Zone Model", Modares Mechanical Engineering, Vol. 15(10), pp. 192-200, (2015), (In Persian).
[30] Schileo, E., Dall’Ara, E., Taddei, F., Malandrino, A., Schotkamp, T., Baleani, M., and Viceconti, M., "An accurate estimation of bone density improves the accuracy of subject-specific finite element models", J Biomech 41, pp. 2483-91, (2008).
[31] Helgason, B., Gilchrist, S,. Ariza, O., Vogt, P., Enns-Bray, W., Widmer, R.P., Fitze, T., Pálsson, H., Pauchard, Y., Guy, P., Ferguson, S.J., and Cripton, P.A., "The influence of the modulus-density relationship and the material mapping method on the simulated mechanical response of the proximal femur in side-ways fall loading configuration", Med Eng Phys, Vol. 38, pp. 679-689, (2016).
[32] Kemper, A., McNally, C., Kennedy, E., Manoogian, S., and Duma, S., "The material properties of human tibia cortical bone in tension and compression: implacations for the tibia index", Paper Number 07-0470.
[33] Wang, X., Nyman, J.S., Dong, X., Leng, H., and Reyes, M., "Fundamental Biomechanics in Bone Tissue Engineering", Morgan & Claypool, (2010).