Trabecular Surface Remodeling Simulation for Cancellous Bone Using Microstructural Voxel Finite Element Models

[+] Author and Article Information
Taiji Adachi, Ken-ichi Tsubota, Yoshihiro Tomita

Department of Mechanical Engineering, Faculty of Engineering, Kobe University, Nada, Kobe 657-8501 Japan

Scott J. Hollister

Departments of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109-2125

J Biomech Eng 123(5), 403-409 (Apr 25, 2001) (7 pages) doi:10.1115/1.1392315 History: Received February 22, 2000; Revised April 25, 2001
Copyright © 2001 by ASME
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Cowin,  S. C., 1993, “Bone Stress Adaptation Models,” ASME J. Biomech. Eng., 115, pp. 528–533.
Huiskes,  R., and Hollister,  S. J., 1993, “From Structure to Process, From Organ to Cell: Recent Developments of FE-Analysis in Orthopaedic Biomechanics,” ASME J. Biomech. Eng., 115, pp. 520–527.
Cowin,  S. C., Moss-Salentijn,  L., and Moss,  M. L., 1991, “Candidates for the Mechanosensory System in Bone,” ASME J. Biomech. Eng., 113, pp. 191–197.
Guldberg,  R. E., Richards,  M., Caldwell,  N. J., Kuelske,  C. L., and Goldstein,  S. A., 1997, “Trabecular Bone Adaptation to Variations in Porous-Coated Implant Topology,” J. Biomech., 30, pp. 147–153.
Cowin,  S. C., Sadegh,  A. M., and Luo,  G. M., 1992, “An Evolutionary Wolff’s Law for Trabecular Architecture,” ASME J. Biomech. Eng., 114, pp. 129–136.
Jacobs,  C. R., Simo,  J. C., Beaupre,  G. S., and Carter,  D. R., 1997, “Adaptive Bone Remodeling Incorporating Simultaneous Density and Anisotropy Considerations,” J. Biomech., 30, pp. 603–613.
Adachi,  T., Tomita,  Y., and Tanaka,  M., 1999, “Three-Dimensional Lattice Continuum Model of Cancellous Bone for Structural and Remodeling Simulation,” JSME Int. J., 42, pp. 470–480.
Mullender,  M. G., Huiskes,  R., and Weinans,  H., 1994, “A Physiological Approach to the Simulation of Bone Remodeling as a Self Organization Control Process,” J. Biomech., 27, pp. 1389–1394.
Huiskes,  R., Ruimerman,  R., Van Lenthe,  G. H., and Janssen,  J. D., 2000, “Effects of Mechanical Forces on Maintenance and Adaptation of Form in Trabecular Bone,” Nature (London), 405, pp. 704–706.
Sadegh,  A. M., Luo,  G. M., and Cowin,  S. C., 1993, “Bone Ingrowth: An Application of the Boundary Element Method to Bone Remodeling at the Implant Interface,” J. Biomech., 26, pp. 167–182.
Luo,  G., Cowin,  S. C., Sadegh,  A. M., and Arramon,  Y. P., 1995, “Implementation of Strain Rate as a Bone Remodeling Stimulus,” ASME J. Biomech. Eng., 117, pp. 329–338.
Adachi,  T., Tomita,  Y., Sakaue,  H., and Tanaka,  M., 1997, “Simulation of Trabecular Surface Remodeling Based on Local Stress Nonuniformity,” JSME Int. J., 40, pp. 782–792.
Feldkamp,  L. A., Goldstein,  S. A., Parfitt,  A. M., Jesion,  G., and Kleerekoper,  M., 1989, “The Direct Examination of Three-Dimensional Bone Architecture In Vitro by Computed Tomography,” J. Bone Miner. Res., 4, pp. 3–11.
Hollister,  S. J., and Kikuchi,  N., 1994, “Homogenization Theory and Digital Imaging: A Basis for Studying the Mechanics and Design Principles of Bone Tissue,” Biotechnol. Bioeng., 43, pp. 586–596.
Van Rietbergen,  B., Weinans,  H., Huiskes,  R., and Odgaard,  A., 1995, “A New Method to Determine Trabecular Bone Elastic Properties and Loading Using Micromechanical Finite-Element Models,” J. Biomech., 28, pp. 69–81.
Mullender,  M., Van Rietbergen,  B., Rüegsegger,  P., and Huiskes,  R., 1998, “Effect of Mechanical Set Point of Bone Cells on Mechanical Control of Trabecular Bone Architecture,” Bone, 22, pp. 125–131.
Parfitt,  A. M., 1994, “Osteonal and Hemi-Osteonal Remodeling: The Spatial and Temporal Framework for Signal Traffic in Adult Human Bone,” J. Cell. Biochem., 55, pp. 273–286.
Adachi,  T., Tanaka,  M., and Tomita,  Y., 1998, “Uniform Stress State in Bone Structure With Residual Stress,” ASME J. Biomech. Eng., 120, pp. 342–347.
Hollister,  S. J., Brennan,  J. M., and Kikuchi,  N., 1994, “A Homogenization Sampling Procedure for Calculating Trabecular Bone Effective Stiffness and Tissue-Level Stress,” J. Biomech., 27, pp. 433–444.
Ulrich,  D., Van Rietbergen,  B., Weinans,  H., and Rüegsegger,  P., 1998, “Finite Element Analysis of Trabecular Bone Structure: A Comparison of Image-Based Meshing Techniques,” J. Biomech., 31, pp. 1187–1192.
Rüegsegger,  P., Koller,  B., and Muller,  R., 1996, “A Microtomographic System for the Nondestructive Evaluation of Bone Architecture,” Calcif. Tissue Int., 58, pp. 24–29.
Van Rietbergen,  B., Odgaard,  A., Kabel,  J., and Huiskes,  R., 1996, “Direct Mechanics Assessment of Elastic Symmetries and Properties of Trabecular Bone Architecture,” J. Biomech., 29, pp. 1653–1657.
Hughes,  T. J. R., Ferencz,  R. M., and Hallquist,  J. O., 1987, “Large-Scale Vectorized Implicit Calculations in Solid Mechanics on a Cray X-MP/48 Utilizing EBE Preconditioned Conjugate Gradients,” Comput. Methods Appl. Mech. Eng., 61, pp. 215–248.
Carter,  D. R., 1984, “Mechanical Loading Histories and Cortical Bone Remodeling,” Calcif. Tissue Int., 36, pp. S19–S24.
Huiskes,  R., Weinans,  H., Grootenboer,  H. J., Dalstra,  M., Fudala,  B., and Slooff,  T. F., 1987, “Adaptive Bone-Remodeling Theory Applied to Prosthetic-Design Analysis,” J. Biomech., 20, pp. 1135–1150.
Frost,  H. M., 1988, “Structural Adaptations to Mechanical Usage: A Proposed ‘Three-Way Rule’ for Bone Modeling,” Veterinary Comparative Orthopaedics Traumatology, 1, pp. 7–17.
Tsubota, K., Adachi, T., and Tomita, Y., 2001, “Simulation Study on Model Parameters of Trabecular Surface Remodeling Model,” in: Computer Methods in Biomechanics & Biomedical Engineering—3, Middleton, J., Jones, M. L., Shrive, N. G., and Pande, G. N., eds., Gordon and Breach Science Publishers, pp. 129–135.
Goldstein,  S. A., Matthews,  L. S., Kuhn,  J. L., and Hollister,  S. J., 1991, “Trabecular Bone Remodeling: An Experimental Model,” J. Biomech., 24, pp. 135–150.
Cowin,  S. C., 1985, “The Relationship between the Elasticity Tensor and the Fabric Tensor,” Mech. Mater., 4, pp. 137–147.
Guldberg,  R. E., Hollister,  S. J., and Charras,  G. T., 1998, “The Accuracy of Digital Image-Based Finite Element Models,” ASME J. Biomech. Eng., 120, pp. 289–295.
Laib,  A., and Ruegsegger,  P., 1999, “Calibration of Trabecular Bone Structure Measurements of In Vivo Three-Dimensional Peripheral Quantitative Computed Tomography With 28-μm-Resolution Microcomputed Tomography,” Bone, 24, pp. 35–39.
Donahue,  H. J., McLeod,  K. J., Rubin,  C. T., Andersen,  J., Grine,  E. A., Hertzberg,  E. L., and Brink,  P. R., 1995, “Cell-to-Cell Communication in Osteoblastic Networks: Cell Line-Dependent Hormonal Regulation of Gap Junction Function,” J. Bone Miner. Res., 10, pp. 881–889.
Guldberg,  R. E., Caldwell,  N. J., Guo,  X. E., Goulet,  R. W., Hollister,  S. J., and Goldstein,  S. A., 1997, “Mechanical Stimulation of Tissue Repair in the Hydraulic Bone Chamber,” J. Bone Miner. Res., 12, pp. 1295–1302.
Xia,  S.-L., and Ferrier,  J., 1992, “Propagation of a Calcium Pulse Between Osteoblastic Cells,” Biochem. Biophys. Res. Commun., 186, pp. 1212–1219.
Hollister, S. J., Chu, T. M., Guldberg, R. E., Zysset, P. K., Levy, R. A., Halloran, J. W., and Feinberg, S. E., 1999, “Image Based Design and Manufacture of Scaffolds for Bone Reconstruction,” in: Synthesis in Bio Solid Mechanics, Pedersen, P., and Bendsoe, M. P., eds., Kluwer Academic Publishers, pp. 163–174.


Grahic Jump Location
Model of trabecular surface remodeling driven by nonuniformity of the mechanical stimulus σ on the trabecular surface. (a) Driving force of remodeling Γ is defined as the relative difference between stress σc at xc and σd determined by integrating stress σr at xr at the neighboring point (l<lL) with weight function w(l). (b) Remodeling rate equation Ṁ=Ṁ(Γ) as a function of the driving force of remodeling Γ representing nonuniformity in mechanical stimulus σ at xc on the trabecular surface.
Grahic Jump Location
Remodeling simulation for single trabecula under compressive loading, σ3=F3/a1a2: (a) Model Z; (b) Model Y; (c) Model X
Grahic Jump Location
Changes of three-dimensional architecture of cancellous bone cube and fabric ellipsoid; X1–X3 cross section and fabric ellipse, due to trabecular surface remodeling under compressive loading: (a) initial voxel finite element model (200×200×200 voxel elements) based on μCT digital image obtained from canine distal femur, (b) 10th step, (c) 20th step, and (d) 50th step
Grahic Jump Location
Changes in structural indices, principal direction of trabecular architecture and apparent stiffness of cancellous bone due to remodeling under compressive load: (a) bone volume fraction (BV/TV); (b) trabecular bone thickness (Tb.Th); (c) trabecular bone number (Tb.N); (d) trabecular bone separation (Tb.Sp); (e) angle Θi3 between principal direction of Hi and loading axis X3; and (f) apparent stiffness σii in Xi direction



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