Abstract
This chapter describes a three-dimensional computer simulation of trabecular surface remodeling using voxel finite element models. The rate equation and the simulation method for the trabecular surface remodeling described in Chap. 8 are extended to the three-dimensional problems of trabecular-level and cancellous-bone-level structures under compressive loading. While Z, X, and Y shaped trabeculae are constructed as models of simplified trabecular-level structure, a cancellous-bone-level structure is modeled on the basis of digital images obtained from X-ray microcomputed tomography (μCT). Remodeling simulations predict the increasing apparent stiffness against the applied load by the trabecular reorientation to the loading direction, in both models of trabecular-level and cancellous-bone-level structures. This demonstrates functional adaptation to the applied load. Simulated structural changes in cancellous bone are anisotropic, although the loading condition is that of simple compression, and thus, changes in the structural and mechanical properties of cancellous-bone-level structures are essentially anisotropic and should be expressed by tensorial quantities. Changes in the structural indices of the trabecular architecture coincide well with reported experimental data.
This Chapter was adapted from Adachi et al. (2001) and Tsubota and Adachi (2004) with permission from The American Society of Mechanical Engineers and Taylor & Francis Ltd., respectively.
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References
Adachi T, Tomita Y, Sakaue H, Tanaka M (1997) Simulation of trabecular surface remodeling based on local stress nonuniformity. JSME Int J C 40(4):782–792. https://doi.org/10.1299/jsmec.40.782
Adachi T, Tsubota K, Tomita Y, Hollister SJ (2001) Trabecular surface remodeling simulation for cancellous bone using microstructural voxel finite element models. J Biomech Eng-T Asme 123(5):403–409. https://doi.org/10.1115/1.1392315
Badilatti SD, Christen P, Levchuk A, Marangalou JH, van Rietbergen B, Parkinson I, Muller R (2016) Large-scale microstructural simulation of load-adaptive bone remodeling in whole human vertebrae. Biomech Model Mechanobiol 15(1):83–95. https://doi.org/10.1007/s10237-015-0715-8
Cowin SC (1985) The relationship between the elasticity tensor and the fabric tensor. Mech Mater 4(2):137–147. https://doi.org/10.1016/0167-6636(85)90012-2
Cowin SC (1986) Wolff's law of trabecular architecture at remodeling equilibrium. J Biomech Eng 108(1):83–88
Cowin SC, Moss-Salentijn L, Moss ML (1991) Candidates for the mechanosensory system in bone. J Biomech Eng 113(2):191–197
Cowin SC, Sadegh AM, Luo GM (1992) An evolutionary Wolff's law for trabecular architecture. J Biomech Eng 114(1):129–136
Feldkamp LA, Goldstein SA, Parfitt AM, Jesion G, Kleerekoper M (1989) The direct examination of three-dimensional bone architecture in vitro by computed tomography. J Bone Miner Res 4(1):3–11. https://doi.org/10.1002/jbmr.5650040103
Frost H (1988) Structural adaptations to mechanical usage. A proposed “Three-Way Rule” for bone modeling, part I. Vet Comp Orthop Traumatol 1(1):13–23
Goldstein SA, Matthews LS, Kuhn JL, Hollister SJ (1991) Trabecular bone remodeling: an experimental model. J Biomech 24(Suppl 1):135–150
Guedes JM, Kikuchi N (1990) Preprocessing and Postprocessing for materials based on the homogenization method with adaptive finite-element methods. Comput Method Appl M 83(2):143–198
Guldberg RE, Caldwell NJ, Guo XE, Goulet RW, Hollister SJ, Goldstein SA (1997a) Mechanical stimulation of tissue repair in the hydraulic bone chamber. J Bone Miner Res 12(8):1295–1302. https://doi.org/10.1359/jbmr.1997.12.8.1295
Guldberg RE, Richards M, Caldwell NJ, Kuelske CL, Goldstein SA (1997b) Trabecular bone adaptation to variations in porous-coated implant topology. J Biomech 30(2):147–153
Harrigan TP, Mann RW (1984) Characterization of microstructural anisotropy in orthotropic materials using a 2nd rank tensor. J Mater Sci 19(3):761–767
Hollister SJ, Kikuchi N (1994) Homogenization theory and digital imaging: a basis for studying the mechanics and design principles of bone tissue. Biotechnol Bioeng 43(7):586–596. https://doi.org/10.1002/bit.260430708
Hollister SJ, Brennan JM, Kikuchi N (1994) A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stress. J Biomech 27(4):433–444
Hughes TJR, Ferencz RM, Hallquist JO (1987) Large-scale vectorized implicit calculations in solid mechanics on a Cray X-Mp/48 utilizing Ebe preconditioned conjugate gradients. Comput Method Appl M 61(2):215–248
Huiskes R, Ruimerman R, van Lenthe GH, Janssen JD (2000) Effects of mechanical forces on maintenance and adaptation of form in trabecular bone. Nature 405(6787):704–706. https://doi.org/10.1038/35015116
Jacobs CR, Simo JC, Beaupre GS, Carter DR (1997) Adaptive bone remodeling incorporating simultaneous density and anisotropy considerations. J Biomech 30(6):603–613
Luo G, Cowin SC, Sadegh AM, Arramon YP (1995) Implementation of strain rate as a bone remodeling stimulus. J Biomech Eng 117(3):329–338
Mullender MG, Huiskes R, Weinans H (1994) A physiological approach to the simulation of bone remodeling as a self-organizational control process. J Biomech 27(11):1389–1394
Mullender M, van Rietbergen B, Ruegsegger P, Huiskes R (1998) Effect of mechanical set point of bone cells on mechanical control of trabecular bone architecture. Bone 22(2):125–131
Odgaard A, Kabel J, van Rietbergen B, Dalstra M, Huiskes R (1997) Fabric and elastic principal directions of cancellous bone are closely related. J Biomech 30(5):487–495
Parfitt AM (1994) Osteonal and hemi-osteonal remodeling: the spatial and temporal framework for signal traffic in adult human bone. J Cell Biochem 55(3):273–286. https://doi.org/10.1002/jcb.240550303
Sadegh AM, Luo GM, Cowin SC (1993) Bone ingrowth: an application of the boundary element method to bone remodeling at the implant interface. J Biomech 26(2):167–182
Schulte FA, Lambers FM, Kuhn G, Muller R (2011) In vivo micro-computed tomography allows direct three-dimensional quantification of both bone formation and bone resorption parameters using time-lapsed imaging. Bone 48(3):433–442. https://doi.org/10.1016/j.bone.2010.10.007
Schulte FA, Ruffoni D, Lambers FM, Christen D, Webster DJ, Kuhn G, Muller R (2013) Local mechanical stimuli regulate bone formation and resorption in mice at the tissue level. PLoS One 8(4):e62172. https://doi.org/10.1371/journal.pone.0062172
Tsubota K, Adachi T (2004) Changes in the fabric and compliance tensors of cancellous bone due to trabecular surface remodeling, predicted by a digital image-based model. Comput Methods Biomech Biomed Engin 7(4):187–192. https://doi.org/10.1080/10255840410001729524
Tsubota K, Adachi T (2005) Spatial and temporal regulation of cancellous bone structure: characterization of a rate equation of trabecular surface remodeling. Med Eng Phys 27(4):305–311. https://doi.org/10.1016/j.medengphy.2004.09.013
Tsubota K, Adachi T, Tomita Y (2002) Functional adaptation of cancellous bone in human proximal femur predicted by trabecular surface remodeling simulation toward uniform stress state. J Biomech 35(12):1541–1551. https://doi.org/10.1016/S0021-9290(02)00173-2
Tsubota K, Suzuki Y, Yamada T, Hojo M, Makinouchi A, Adachi T (2009) Computer simulation of trabecular remodeling in human proximal femur using large-scale voxel FE models: approach to understanding Wolff's law. J Biomech 42(8):1088–1094. https://doi.org/10.1016/j.jbiomech.2009.02.030
Ulrich D, van Rietbergen B, Weinans H, Ruegsegger P (1998) Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques. J Biomech 31(12):1187–1192
van Rietbergen B, Weinans H, Huiskes R, Odgaard A (1995) A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J Biomech 28(1):69–81
van Rietbergen B, Odgaard A, Kabel J, Huiskes R (1996) Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture. J Biomech 29(12):1653–1657
van Rietbergen B, Odgaard A, Kabel J, Huiskes R (1998) Relationships between bone morphology and bone elastic properties can be accurately quantified using high-resolution computer reconstructions. J Orthop Res 16(1):23–28. https://doi.org/10.1002/jor.1100160105
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Kameo, Y., Tsubota, Ki., Adachi, T. (2018). Trabecular Surface Remodeling Simulation of Cancellous Bone Using Image-Based Voxel Finite Element Models. In: Bone Adaptation. Frontiers of Biomechanics, vol 2. Springer, Tokyo. https://doi.org/10.1007/978-4-431-56514-7_11
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