Abstract
In this chapter the proposed bone tissue remodelling algorithm using the NNRPIM is applied to several problems. First a two-dimensional benchmark example is used to validate the bone trabecular remodelling. In this example distinct material laws are studied as well as the influence of the model nodal discretization and the anisotropy of the biomaterial. Next, the study is extended to the three-dimensional analysis, where a test problem based in another benchmark example is presented. Afterwards, it is numerically simulated the bone tissue remodelling occurring in natural bones. Thus, the calcaneus bone is simulated using a two-dimensional approach, for this example the obtained trabecular bone architecture is in very good agreement with the one that can be found in calcaneus bone X-ray images. The same quality results were found in the two-dimensional approach of the femur example. Additionally, a three-dimensional analysis of the femur is presented. Ending this section, it is studied a two-dimensional model of the maxillary central incisor constructed using the available data in clinical literature. The complete elasto-static analysis of the incisor/maxillary structure, using the NNRPIM, is evaluated and then the nonlinear iterative local NNRPIM analysis of the maxillary bone tissue remodelling is performed. The last section of the present chapter shows the bone tissue remodelling due to the insertion of implants. First it is studied the bone tissue remodelling process of the premolar region of the mandible due to the inclusion of an implant system. Then, the bone tissue remodelling response to the insertion of a femoral implant, after an idealized subcapital or transcervical neck fracture, is studied.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Belinha J, Jorge RMN, Dinis LMJS (2013) A meshless microscale bone tissue trabecular remodelling analysis considering a new anisotropic bone tissue material law. Comput Meth Biomech Biomed Eng 16(11):1170–1184
Belinha J, Jorge RMN, Dinis LMJS (2012) Bone tissue remodelling analysis considering a radial point interpolator meshless method. Eng Anal Boundary Elem 36(11):1660–1670
Mullender MG, Huiskes R, Weinans H (1994) A physiological approach to the simulation of bone remodeling as a selforganizational control process. J Biomech 27(11):1389–1394
Xinghua Z, He G, Dong Z, Bingzhao G (2002) A study of the effect of non-linearities in the equation of bone remodeling. J Biomech 35:951–960
Chen G, Pettet G, Pearcy M, McElwain DLS (2007) Comparison of two numerical approaches for bone remodelling. Med Eng Phys 29:134–139
Shefelbine SJ, Augat P, Claes L, Simon U (2005) Trabecular bone fracture healing simulation with finite element analysis andfuzzy logic. J Biomech 38:2440–2450
Poiate I, Vasconcellos A, Mori M, Poiate E (2011) 2D and 3D finite element analysis of central incisor generated by computerized tomography. Comput Methods Programs Biomed 104(2):292–299
Cheng R, Zhou X, Liu Z, Hu T (2007) Development of a finite element analysis model with curved canal and stress analysis. J Endod 33(6):727–731
Scarfe W, Levin M, Gane G, Farman A (2009) Use of cone beam computed tomography in endodontics. Int J Dent (ID634567):20
Kim W, Voloshin AS (1995) Role of plantar fascia in the load bearing capacity of the human foot. J Biomech 28(9):1025–1033
Gefen A (2002) Stress analysis of the standing foot following surgical plantar fascia release. J Biomech 35(5):629–637
Cheung JTM, Zhang M, An KN (2006) Effect of Achilles tendon loading on plantar fascia tension in the standing foot. Clin Biomech 21:194–203
Cheng HYK, Lin CL, Wang HW, Chou SW (2008) Finite element analysis of plantar fascia under stretch—The relative contribution of windlass mechanism and Achilles tendon force. J Biomech 41(9):1937–1944
Beaupré GS, Orr TE, Carter DR (1990) An approach for time dependent bone modelling and remodelling. Theoretical development. J Orthop Res 8(5):651–661
Beaupré GS, Orr TE, Carter DR (1990) An approach for time dependent bone modelling and remodelling. A preliminary remodelling simulation. J Orthop Res 8(5):662–670
Jacobs CR, Levenston ME, Beaupre GS, Simo JC, Carter DR (1995) Numerical instabilities in bone remodelling simulations: the advantages of a node-based finite element approach. J Biomech 28(4):449–459
Jacobs CR, Simo JC, Beaupré GS, Carter DR (1997) Adaptive bone remodeling incorporating simultaneous density and anisotropy considerations. J Biomech 30(6):603–613
Pettermann H, Reiter T, Rammerstorfer FG (1997) Computational simulation of internal bone remodeling. Arch Comput Meth Eng 4(4):295–323
Doblaré M, GarcÃa JM (2002) Anisotropic bone remodelling model based on a continuum damage-repair theory. J Biomech 35(1):1–17
Rossi JM, Wendling-Mansuy S (2007) A topology optimization based model of bone adaptation. Comput Meth Biomech Biomed Eng 10(6):419–427
Coelho PG, Fernandes PR, Rodrigues HC, Cardoso JB, Guedes JM (2009) Numerical modeling of bone tissue adaptation—A hierarchical approach for bone apparent density and trabecular structure. J Biomech 42(7):830–837
Jang IG, Kim IY (2010) Computational simulation of simultaneous cortical and trabecular bone change in human proximal femur during bone remodeling. J Biomech 43:294–301
Doblare M, Garcia JM (2001) Application of an anisotropic bone-remodelling model based on a damage-repair theory to the analysis of the proximal femur before and after total hip replacement. J Biomech 34:1157–1170
Doblaré M, Cueto E, Calvo B, MartÃnez MA, Garcia JM, Cegoñino J (2005) On the employ of meshless methods in biomechanics. Comput Methods Appl Mech Eng 194:801–821
MartÃnez RJ, GarcÃa JM, DomÃnguez J, Doblaré M (2009) A bone remodelling model including the directional activity of BMUs. Biomech Model Mechanobiol 8:111–127
Jang IG, Kim IY (2010) Application of design space optimization to bone remodeling simulation of trabecular architecture in human proximal femur for higher computational efficiency. Finite Elem Anal Des 46(4):311–319
Lian Z, Guan H, Ivanovski S, Loo YC, Johnson NW, Zhang H (2010) Effect of bone to implant contact percentage on bone remodelling surrounding a dental implant. Int J Oral Maxillofac Surg 39:690–698
Chou HY, Jagodnik JJ, Muftu S (2008) Predictions of bone remodeling around dental implant systems. J Biomech 41:1365–1373
Johnell O, Kanis J (2005) Epidemiology of osteoporotic fractures. Osteoporos Int 16(2):S3–S7
Chen CM, Chiu FY, Lo WE (2001) Avascular necrosis of femoral head after gamma-nailing for unstable intertrochanteric fractures. Arch Orthop Trauma Surg 121:505–507
Vicario C, Marco F, Ortega L, Alcobendas M, Dominguez I, López-Durán L (2003) Necrosis of the femoral head after fixation of trochanteric fractures with Gamma Locking Nail—A cause of late mechanical failure. Int J Care Injured 34:129–134
Guimarães JAM, Guimarães ACA, Franco JS (2008) Evaluating the use of a proximal femoral nail in unstable trochanteric fracture of the femur. Rev Bras Ortop 43(9):406–417
Van der Vis HM, Aspenberg P, Tigchelaar W, Van Noorden CJ (1999) Mechanical compression of a fibrous membrane surrounding bone causes bone resorption. Acta Histochem 101(2):203–212
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Belinha, J. (2014). Bone Tissue Remodelling Analysis. In: Meshless Methods in Biomechanics. Lecture Notes in Computational Vision and Biomechanics, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-319-06400-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-06400-0_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06399-7
Online ISBN: 978-3-319-06400-0
eBook Packages: EngineeringEngineering (R0)