Abstract
Surgical success of drilling in oral implantology depends on the sense of force on the fingers or feeling of a dental clinician, which is related to the quality of trabecular bone in the jawbone expressed by apparent mechanical characteristics. As the mechanical properties of trabecular bone depend on the bone volume fraction, microstructure, and many other factors closely related to individual differences, a probabilistic numerical procedure to assess drilling force is proposed. Using a micro-CT-based jawbone model, a first-order perturbation-based stochastic homogenization method was employed to estimate the possible scattering of apparent mechanical properties of the trabecular bone region. The complicated drilling problem was simplified to sequential linear static FEAs, to which the predicted apparent Young’s modulus and shearing moduli in the drilling direction were applied. The FEAs demonstrated that the homogenized mechanical properties showed anisotropy, which might lead to differences in the drilling forces at different drilling angles. The numerically estimated drilling forces were shown by the expected value, 50 %-probability result, and 90%-probability result and revealed that one patient among two or ten patients would probably have poor bone quality. There was a remarkable difference in the drilling forces between the expected value and the 90%-probability result.
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Albrektsson T., Sennerby L., Wennerberg A.: State of the art of oral implants. Periodontol 2000 47, 15–26 (2008)
Lambert P.M., Morris H.F., Ochi S.: Positive effect of surgical experience with implants on second-stage implant survival. J. Oral Maxillofac. Surg. 55, 12–18 (1997)
Reingewirtz Y., Szmukler-Moncler S., Senger B.: Influence of different parameters on bone heating and drilling time in implantology. Clin. Oral Implants Res. 8, 189–197 (1997)
Augustin G., Davila S., Mihoci K., Udijak T., Vedrina D.S., Antabak A.: Thermal osteonecrosis and bone drilling parameters revisited. Arch. Orthop. Trauma Surg. 128, 71–77 (2008)
Kim S.J., Yoo J., Kim Y.S., Shin S.W.: Temperature change in pig rib bone during implant site preparation by low-speed drilling. J. Appl. Oral Sci. 18, 522–527 (2010)
Lekholm U., Zarb G.A.: Patient Selection and Preparation, Tissue-Integrated Prosthesis: Osseointegration in clinical dentistry, pp. 199–209. Quintessence, Chicago (1985)
Carter D.R., Hayes W.C.: The compressive behavior of bone as a two-phase porous structure. J. Bone Joint Surg. 59, 954–962 (1977)
Keyak J.H., Lee I.Y., Skinner H.B.: Correlations between orthogonal mechanical properties and density of trabecular bone: use of different densitometric measures. J. Biomed. Mater. Res. 28, 1329–1336 (1994)
Dempster D.W.: The contribution of trabecular architecture to cancellous bone quality. J. Bone Miner. Res. 15, 20–23 (2000)
Pothuaud L., Porion P., Lespessailles E., Benhamou C.L., Levitz P.: A new method for three-dimensional skeleton graph analysis of porous media: application to trabecular bone microarchitecture. J. Microsc. 199(Part 2), 149–161 (2000)
Van der Linden J.C., Birkenhäger-Frenkel D.H., Verhaar J.A.N., Weinans H.: Trabecular bone’s mechanical properties are affected by its non-uniform mineral distribution. J. Biomech. 34, 1573–1580 (2001)
Sansalone V., Naili S., Bousson V., Bergot C., Peyrin F., Zarka J., Laredo J.D., Haiat G.: Determination of the heterogeneous anisotropic elastic properties of human femoral bone: from nanoscopic to organ scale. J. Biomech. 43, 1857–1863 (2010)
Ashman R.B., Rho J.Y., Turner C.H.: Anatomical variation of orthotropic elastic moduli of the proximal human tibia. J. Biomech. 22, 895–900 (1989)
Morgan E.F., Bayraktar H.H., Keaveny T.M.: Trabecular bone modulus–density relationships depend on anatomic site. J. Biomech. 36, 897–904 (2003)
Adachi T., Tsubota K., Tomita Y., Hollister S.J.: Trabecular surface remodeling simulation for cancellous bone using microstructural voxel finite element models. J. Biomech. Eng. 123, 403–409 (2001)
Karim L., Vashishth D.: Role of trabecular microarchitecture in the formation, accumulation, and morphology of microdamage in human cancellous bone. J. Orthop. Res. 29, 1–6 (2011)
Weinans H., Huiskes R., Grootenboer H.J.: The behavior of adaptive bone-remodeling simulation models. J. Biomech. 25, 1425–1441 (1992)
Nakano T., Ishimoto T., Umakoshi Y., Tabata Y.: Texture of biological apatite crystallites and the related mechanical function in regenerated and pathological hard tissues. J. Hard Tissue Biol. 14, 363–364 (2005)
Thomsen J.S., Ebbesen E.N., Mosekilde L.: Age-related differences between thinning of horizontal and vertical trabeculae in human lumbar bone as assessed by a new computerized method. Bone 31, 136–142 (2002)
Wolfram U., Wilke H.J., Zysset P.K.: Transverse isotropic elastic properties of vertebral trabecular bone matrix measured using microindentation under dry conditions (effects of age, gender, and vertebral level). J. Mech. Med. Biol. 10, 139–150 (2010)
Basaruddin K.S., Takano N., Nakano T.: Stochastic multi-scale prediction on the apparent elastic moduli of trabecular bone considering uncertainties of biological apatite (BAp) crystallite orientation and image-based modelling. Comput. Methods Biomech. Biomed. Eng. 18, 162–174 (2015)
Limbert G., Van Lierde C., Muraru O.L., Walboomers X.F., Frank M., Hansson S., Middleton J., Jaecques S.: Trabecular bone strains around a dental implant and associated micromotions—a micro-CT-based three-dimensional finite element study. J. Biomech. 43, 1251–1261 (2010)
Yeniyol S., Jimbo R., Marin C., Tovar N., Janal M.N., Coelho P.G.: The effect of drilling speed on early bone healing to oral implants. Oral Surg. Oral Med. Oral Pathol. Oral Radiol. 116, 550–555 (2013)
Sui J., Sugita N., Ishii K., Harada K., Mitsuishi M.: Mechanistic modeling of bone-drilling process with experimental validation. J. Mater. Process. Technol. 214, 1018–1026 (2014)
Mathieu V., Vayron R., Richard G., Lambert G., Naili S., Meningaud J.P., Haiat G.: Biomechanical determinants of the stability of dental implants: influence of the bone–implant interface properties. J. Biomech. 47, 3–13 (2014)
Ulrich D., Van Rietbergen B., Weinans H., Ruëgsegger P.: Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques. J. Biomech. 31, 1187–1192 (1998)
Van Rietbergen B., Müller R., Ulrich D., Ruëgsegger P., Huiskes R.: Tissue stresses and strain in trabeculae of a canine proximal femur can be quantified from computer reconstructions. J. Biomech. 32, 165–173 (1999)
Van Rietbergen B., Majumdar S., Newitt D., MacDonald B.: High-resolution MRI and micro-FE for the evaluation of changes in bone mechanical properties during longitudinal clinical trials: application to calcaneal bone in postmenopausal women after one year of idoxifene treatment. Clin. Biomech. 17, 81–88 (2002)
Pistoia W., Van Rietbergen B., Laib A., Ruëgsegger P.: High-resolution three-dimensional-pQCT images can be an adequate basis for in-vivo microFE analysis of bone. J. Biomech. Eng. 123, 176–183 (2001)
Jaecques S.V., Van Oosterwyck H., Muraru L., Van Cleynenbreugel T., De Smet E., Wevers M., Naert I., Vander Sloten J.: Individualised, micro CT-based finite element modelling as a tool for biomechanical analysis related to tissue engineering of bone. Biomaterials 25, 1683–1696 (2004)
Feldkamp L.A., Goldstein S.A., Parfitt A.M., Jesion G., Kleerekoper M.: The direct examination of three-dimensional bone architecture in vitro by computed tomography. J. Bone Miner. Res. 4, 3–11 (1989)
Matsunaga S., Naito H., Tamatsu Y., Takano N., Abe S., Ide Y.: Consideration of shear modulus in biomechanical analysis of peri-implant jaw bone: accuracy verification using image-based multi-scale simulation. Dental Mater. J. 32, 425–432 (2013)
Tawara D., Adachi T., Takano N., Nakano T.: High-resolution micro-mechanical analysis of cancellous bone in vertebra considering bone quality (in Japanese). Jpn. J. Clin. Biomech. 29, 7–14 (2008)
Tawara D., Takano N., Adachi T., Nakano T.: Mechanical evaluation of trabecular bone of human vertebra based on multi-scale stress analysis (in Japanese). J. Jpn. Soc. Bone Morphom. 20, S100–S107 (2010)
Yoshiwara Y., Clanche M., Basaruddin K.S., Takano N., Nakano T.: Numerical study on the morphology and mechanical role of healthy and osteoporotic vertebral trabecular bone, J. Biomech. Sci. Eng. 6, 270–285 (2011)
Takano N., Ohnishi Y., Zako M., Nishiyabu K.: Microstructure-based deep-drawing simulation of knitted fabric reinforced thermoplastics by homogenization theory. Int. J. Solids Struct. 38, 6333–6356 (2001)
Takano N., Zako M., Okuno Y.: Multi-scale finite element analysis of porous materials and components by asymptotic homogenization theory and enhanced mesh superposition method. Model. Simul. Mater. Sci. Eng. 11, 137–156 (2003)
Takano N., Fukasawa K., Nishiyabu K.: Structural strength prediction for porous titanium based on micro-stress concentration by micro-CT image-based multiscale simulation. Int. J. Mech. Sci. 52, 229–235 (2010)
Hvid I., Bentzen S.M., Linde F., Mosekilde L., Pongsoipetch B.: X-ray quantitative computed tomography: the relations to physical properties of proximal tibial trabecular bone specimens. J. Biomech. 22, 837–844 (1989)
Linde F., Hvid I.: The effect of constraint on the mechanical behaviour of trabecular bone specimens. J. Biomech. 22, 485–490 (1989)
Keyak J.H.: Improved prediction of proximal femoral fracture load using nonlinear finite element models. Med. Eng. Phys. 23, 165–173 (2001)
Odgaard A., Linde F.: The underestimation of Young’s modulus in compressive testing of cancellous bone specimens. J. Biomech. 24, 691–698 (1991)
Linde F., Hvid I., Madsen F.: The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens. J. Biomech. 25, 359–368 (1992)
Kopperdahl D.L., Keaveny T.M.: Yield strain behavior of trabecular bone. J. Biomech. 31, 601–608 (1998)
Wilmes B., Su Y.Y., Sadigh L., Drescher D.: Pre-drilling force and insertion torques during orthodontic mini-implant insertion in relation to root contact. J. Orofac. Orthop. 69, 51–58 (2008)
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Tawara, D., Nagahata, M., Takano, N. et al. Probabilistic analysis of mechanical behaviour of mandibular trabecular bone using a calibrated stochastic homogenization model. Acta Mech 226, 3275–3287 (2015). https://doi.org/10.1007/s00707-015-1381-8
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DOI: https://doi.org/10.1007/s00707-015-1381-8