The present paper introduces a numerical simulation aided, experimental method for the measurement of Young’s modulus of the trabecular substance in the human mandible. Compression tests were performed on fresh cadaveric samples containing trabecular bone covered with cortical layer, thus avoiding the destruction caused by the sterilization, preservation, and storage and the underestimation of the stiffness resulting from the individual failure of the trabeculae cut on the surfaces. The elastic modulus of the spongiosa was determined by the numerical simulation of each compression test using a specimen specific finite element model of each sample. The received mandibular trabecular bone Young’s modulus values ranged from 6.9 to 199.5？MPa. 1. Introduction The biomechanical behaviour of a dental implant plays an important role in its functional longevity inside the bone. Implants can have either advantageous or destructive effect on the surrounding bone, depending on several physiological, material, and mechanical factors. The mandible—lower jaw bone—like most human bones is divided into an external cortical and an internal trabecular substance (or spongiosa). The aim of the following experiments was to determine the mechanical properties of the human mandibular trabecular bone, to be used in further finite element models. Application of finite element analysis has become an indispensable method for estimating mechanical behaviour, stress and strain distributions under a certain load, of the cortical and cancellous bone surrounding dental implants, since it is nondestructive. These numerical experiments have their importance in making the implantation the most possibly secure, reliable, and efficient and the lifetime of the implant the longest conceivable, by finding the most favourable thread formation, surface, material, and so forth. The measurement of the trabecular bone material properties by means of conventional mechanical tests involves several difficulties [1, 2]. Because of the scale of the human bones, the primary difficulty is to obtain cubic shaped specimens from purely trabecular regions larger than 5？mm, which is taken for the lower limit to be examined in compression tests [2, 3]. This can cause serious problems in the examination of the small bones like mandible. In contradiction to the measurements of artificial materials, further difficulties arise in case of biological materials—especially human tissues. Since the poor availability of specimens, the researchers are often under the necessity of drawing conclusions from small number of
References
[1]
J. Lemaitre, Handbook of Materials Behavior Models, Elsevier, New York, NY, USA, 2001.
[2]
Y. H. An and R. A. Draughn, Mechanical Testing of Bone and the Bone–Implant Interface, CRC Press, New York, NY, USA, 2000.
[3]
F. Linde, “Elastic and viscoelastic properties of trabecular bone by a compression testing approach,” Danish Medical Bulletin, vol. 41, no. 2, pp. 119–138, 1994.
[4]
A. Odgaard and F. Linde, “The underestimation of Young's modulus in compressive testing of cancellous bone specimens,” Journal of Biomechanics, vol. 24, no. 8, pp. 691–698, 1991.
[5]
R. B. Ashman and J. Y. Rho, “Elastic modulus of trabecular bone material,” Journal of Biomechanics, vol. 21, no. 3, pp. 177–181, 1988.
[6]
D. R. Carter and W. C. Hayes, “The compressive behavior of bone as a two-phase porous structure,” Journal of Bone and Joint Surgery. Series A, vol. 59, no. 7, pp. 954–962, 1977.
[7]
M. Soncini, R. Rodriguez Y Baena, R. Pietrabissa, V. Quaglini, S. Rizzo, and D. Zaffe, “Experimental procedure for the evaluation of the mechanical properties of the bone surrounding dental implants,” Biomaterials, vol. 23, no. 1, pp. 9–17, 2002.
[8]
Q. Kang, Y. H. An, and R. F. Friedman, “Mechanical properties and bone densities of canine trabecular bone,” Journal of Materials Science: Materials in Medicine, vol. 9, no. 5, pp. 263–267, 1998.
[9]
S. A. Goldstein, “The mechanical properties of trabecular bone: dependence on anatomic location and function,” Journal of Biomechanics, vol. 20, no. 11-12, pp. 1055–1061, 1987.
[10]
Y. Chevalier, D. Pahr, H. Allmer, M. Charlebois, and P. Zysset, “Validation of a voxel-based FE method for prediction of the uniaxial apparent modulus of human trabecular bone using macroscopic mechanical tests and nanoindentation,” Journal of Biomechanics, vol. 40, no. 15, pp. 3333–3340, 2007.
[11]
E. F. Morgan, H. H. Bayraktar, and T. M. Keaveny, “Trabecular bone modulus-density relationships depend on anatomic site,” Journal of Biomechanics, vol. 36, no. 7, pp. 897–904, 2003.
[12]
T. M. G. J. van Eijden, L. J. van Ruijven, and E. B. W. Giesen, “Bone tissue stiffness in the mandibular condyle is dependent on the direction and density of the cancellous structure,” Calcified Tissue International, vol. 75, no. 6, pp. 502–508, 2004.
[13]
A. M. O'Mahony, J. L. Williams, J. O. Katz, and P. Spencer, “Anisotropic elastic properties of cancellous bone from a human edentulous mandible,” Clinical Oral Implants Research, vol. 11, no. 5, pp. 415–421, 2000.
[14]
C. E. Misch, Z. Qu, and M. W. Bidez, “Mechanical properties of trabecular bone in the human mandible: implications for dental implant treatment planning and surgical placement,” Journal of Oral and Maxillofacial Surgery, vol. 57, no. 6, pp. 700–706, 1999.
[15]
F. G. Evans and A. I. King, “Regional differences in some physical properties of human spongy bone,” in Biomechanical Studies of the Musculo-Skeletal System, F. G. Evans, Ed., p. 19, Charles C Thomas, Springfield, Ill, USA, 1961.
[16]
J. H. McElhaney, J. L. Fogle, J. W. Melvin, R. R. Haynes, V. L. Roberts, and N. M. Alem, “Mechanical properties of cranial bone,” Journal of Biomechanics, vol. 3, no. 5, pp. 495–496, IN5, 497–511, 1970.
[17]
J. W. Pugh, R. M. Rose, and E. L. Radin, “Elastic and viscoelastic properties of trabecular bone: dependence on structure,” Journal of Biomechanics, vol. 6, pp. 475–485, 1973.
[18]
C. M. Schoenfeld, E. P. Lautenschlager, and P. R. Meyer Jr., “Mechanical properties of human cancellous bone in the femoral head,” Medical and Biological Engineering, vol. 12, no. 3, pp. 313–317, 1974.
[19]
O. Lindahl, “Mechanical properties of dried defatted spongy bone,” Acta Orthopaedica Scandinavica, vol. 47, no. 1, pp. 11–19, 1976.
[20]
P. Ducheyne, L. Heymans, M. Martens, E. Aernoudt, P. de Meester, and J. C. Mulier, “The mechanical behaviour of intracondylar cancellous bone of the femur at different loading rates,” Journal of Biomechanics, vol. 10, no. 11-12, pp. 747–762, 1977.
[21]
T. D. Brown and A. B. Ferguson Jr., “Mechanical property distributions in the cancellous bone of the human proximal femur,” Acta Orthopaedica Scandinavica, vol. 51, no. 1–6, pp. 429–437, 1980.
[22]
J. L. Williams and J. L. Lewis, “Properties and an anisotropic model of cancellous bone from the proximal tibial epiphysis,” Journal of Biomechanical Engineering, vol. 104, no. 1, pp. 50–56, 1982.
[23]
M. Martens, R. van Audekercke, P. Delport, P. de Meester, and J. C. Mulier, “The mechanical characteristics of cancellous bone at the upper femoral region,” Journal of Biomechanics, vol. 16, no. 12, pp. 971–983, 1983.
[24]
M. J. Ciarelli, S. A. Goldstein, D. Dickie et al., “Experimental determination of the orthogonal mechanical properties, density, and distribution of human trabecular bone from the major metaphyseal regions utilizing materials testing and computed tomography,” Transactions of the Orthopedic Research Society, p. 42, 1986.
[25]
T. S. Keller, T. H. Hansson, M. M. Panjabi, and D. M. Spengler, “Regional variations in the compressive properties of lumbar trabeculae,” Transactions of the Orthopedic Research Society, p. 378, 1987.
[26]
S. Struhl, S. A. Goldstein, D. L. Dickie, M. J. Flynn, and L. S. Matthews, “The distribution of mechanical properties of trabecular bone within vertebral bodies and iliac crest: correlation with computed tomography density,” Transactions of the Orthopedic Research Society, p. 262, 1987.
[27]
T. M. Keaveny, T. P. Pinilla, R. P. Crawford, D. L. Kopperdahl, and A. Lou, “Systematic and random errors in compression testing of trabecular bone,” Journal of Orthopaedic Research, vol. 15, no. 1, pp. 101–110, 1997.
[28]
K. W. Luczynski, T. Brynk, B. Ostrowska, W. Swieszkowski, R. Reihsner, and C. Hellmich, “Consistent quasistatic and acoustic elasticity determination of poly-L-lactide-based rapid-prototyped tissue engineering scaffolds,” Journal of Biomedical Materials Research Part A, vol. 101, no. 1, pp. 138–144, 2013.
[29]
K. W. Luczynski, A. Dejaco, O. Lahayne, J. Jaroszewicz, W. Swieszkowski, and C. Hellmich, “MicroCT/micromechanics-based finite element models and quasi-static unloading tests deliver consistent values for young's modulus of rapid-prototyped polymer-ceramic tissue engineering scaffold,” Computer Modeling in Engineering and Sciences, vol. 87, no. 6, pp. 505–528, 2012.
[30]
A. Fritsch, C. Hellmich, and L. Dormieux, “Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: experimentally supported micromechanical explanation of bone strength,” Journal of Theoretical Biology, vol. 260, no. 2, pp. 230–252, 2009.
[31]
E. A. Zimmermann, E. Schaible, H. Bale et al., “Age-related changes in the plasticity and toughness of human cortical bone at multiple length scales,” Proceedings of the National Academy of Sciences of the United States of America, vol. 108, no. 35, pp. 14416–14421, 2011.
[32]
A. Malandrino, A. Fritsch, O. Lahayne, et al., “Anisotropic tissue elasticity in human lumbar vertebra, by means of a coupled ultrasound-micromechanics approach,” Materials Letters, vol. 78, pp. 154–158, 2012.
[33]
L. Cardoso, F. Teboul, L. Sedel, C. Oddou, and A. Meunier, “In vitro acoustic waves propagation in human and bovine cancellous bone,” Journal of Bone and Mineral Research, vol. 18, no. 10, pp. 1803–1812, 2003.
[34]
S. C. Cowin and L. Cardoso, “Fabric dependence of wave propagation in anisotropic porous media,” Biomechanics and Modeling in Mechanobiology, vol. 10, no. 1, pp. 39–65, 2011.
