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 Trabecular Surface Remodeling Simulation for Cancellous Bone Using Microstructural Voxel Finite Element Models A computational simulation method for three-dimensional trabecular surface remodeling was proposed, using voxel finite element models of cancellous bone, and was applied to the experimental data. In the simulation, the trabecular microstructure was modeled based on digital images, and its morphological changes due to surface movement at the trabecular level were directly expressed by removing/adding the voxel elements from/to the trabecular surface. A remodeling simulation at the single trabecular level under uniaxial compressive loading demonstrated smooth morphological changes even though the trabeculae were modeled with discrete voxel elements. Moreover, the trabecular axis rotated toward the loading direction with increasing stiffness, simulating functional ad- aptation to the applied load. In the remodeling simulation at the trabecular structural level, a cancellous bone cube was modeled using a digital image obtained by microcom- puted tomography (CT), and was uniaxially compressed. As a result, the apparent stiff- ness against the applied load increased by remodeling, in which the trabeculae reoriented to the loading direction. In addition, changes in the structural indices of the trabecular architecture coincided qualitatively with previously published experimental observations. Through these studies, it was demonstrated that the newly proposed voxel simulation technique enables us to simulate the trabecular surface remodeling and to compare the results obtained using this technique with the in vivo experimental data in the investiga- tion of the adaptive bone remodeling phenomenon. DOI: 10.1115/1.1392315 1 Introduction Bone remodeling, defined as the coupled formation and resorp- tion by cellular activities on the bone surfaces, has been investi- gated through both experimental and computational approaches. The computational mechanics approach allows one to test the in- fluence of mechanical factors sequentially on bone remodeling, isolating the influence of these factors from their complex cou- pling with biological influences. Theoretical modeling and com- putational simulations of bone remodeling were developed for cortical and cancellous bone as a continuum 1,2, and could suc- cessfully predict changes in the external shape and apparent den- sity of bone. However, it has been recognized that anisotropic modeling and simulations are essential for evaluating local me- chanical stimuli at the microstructural level, which affect the cel- lular activities in the bone remodeling process 3,4. Anisotropic continuum models have been proposed to describe the evolution of both apparent bone density and the orientation of trabecular architecture by using the fabric tensor 5, the aniso- tropic stiffness tensor 6, and the lattice continuum model 7. Even though the anisotropy is not explicitly considered in the rate equation, the osteocyte-regulated bone-remodeling theory 8,9 could predict the emergence of the anisotropic trabecular micro- structure. Furthermore, the direct simulation method of trabecular surface remodeling has been proposed using a boundary element method 10,11 and a pixel/voxel finite element method 12. For the prediction of three-dimensional trabecular structural changes caused by remodeling, detailed modeling of the complex trabecular microstructure is essential. Digital-image-based voxel models of cancellous bone with high resolutions, which can be obtained by X-ray CT scanning 13, enable modeling and stress analysis 14,15 of the trabecular microstructure. In addition, this voxel finite element modeling technique is a useful tool for pre- dicting microstructural changes in cancellous bone caused by re- modeling; for example, structural changes in the case of os- teoporosis were predicted by solving the evolution of bone relative density as a continuum 16. However, since trabecular remodeling is due to cellular activities on the trabecular surface 17, the morphological changes due to surface movement by re- modeling should be directly modeled and simulated at the trabe- cular level. The purpose of this study is to propose a simulation method for three-dimensional trabecular surface remodeling by using the mi- crostructural voxel finite element modeling technique. First, a rate equation for trabecular surface remodeling 12, based on the local uniform stress hypothesis 18, is applied to voxel finite element models of cancellous bone. Second, to investigate the basic fea- tures of the proposed simulation method, remodeling simulations are conducted for single trabeculae under compressive loading. Third, a remodeling simulation is carried out for a cancellous bone cube under compressive loading and is compared with an in vivo experiment 4. 2 Methods 2.1 Voxel Simulation Method for Trabecular Surface Re- modeling. A voxel finite element model of trabeculae 14,15,19,20 can be reconstructed from digital images such as those obtained by CT scanning 13,21, and used to represent the trabecular architecture in detail. This technique enabled the direct estimation of the stress and strain at the trabecular level that regu- late cellular activities in bone remodeling. In this study, a model of trabecular surface remodeling, which was proposed to express morphological changes in the trabeculae as a local stress regula- tion process 12, is applied to the three-dimensional microstruc- Contributed by the Bioengineering Division for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Divi- sion February 22, 2000; revised manuscript received April 25, 2001. Associate Edi- tor: T. M. Keaveny. Copyright © 2001 by ASME Journal of Biomechanical Engineering OCTOBER 2001, Vol. 123 Õ 403