Computational Simulation of Cancellous Bone Remodeling Using Digital Image-based Model
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1 1 Computational Simulation of Cancellous Bone Remodeling Using Digital Image-based Model Ken-ichi TSUBOTA, Taiji ADACHI and Yoshihiro TOMITA Kobe University, RIKEN RIKEN Symposium Computational Biomechanics, Suzuki Umetaro Hall, RIKEN, May 2000
2 Introduction: Adaptive Bone Remodeling Macroscopic Phenomenon and Microscopic Mechanism 2 Quiescence Activation Proximal Femur (Tanaka, 1992) Trabecular Structure Lining Cell Bone New Bone Formation Resorption Osteoblast Osteoclast Surface Remodeling (Parfitt, 1994) Relationship between bone morphological change and a mechanical stimulus should be considered at microscopic level in remodeling rate equation.
3 Introduction: Trabecular Surface Remodeling Simulation 3 Bone Morphological Change Related to Mechanical Stimulus at Trabecular Level Large-Scale Pixel Finite Element Model Trabecular remodeling simulation for proximal femur under multiple loading (Adachi et al., 1999)
4 Purpose 4 Application of Trabecular Remodeling Simulation to Digital Image-Based Model (1) Trabecular Remodeling Simulation for 3D Complicated Structure (2) Quantitative Comparison to Experiment
5 1. Digital Image-Based Model 5
6 1.1 Digital Image-Based Model 6 Model of 3D & Complex Trabecular Structure (Hollister et al., 1994; van Rietbergen et al., 1995; Odgaard et al., 1997 ) (1) Voxel Model Generated by Digital Image Direct Modeling of Trabecular Microstructure (2) Large-Scale FEM Using EBE/PCG Manner Evaluation of Trabecular-Level Stress/Strain Digital Image-Based Model for Remodeling Simulation Mechanical Stimulus Trabecular-Level Morphological Change
7 1.2 X-Ray µct System 7 X-Ray µct System (Feldkamp et al., 1989) (1) Obtaining 2D Cross Sections by Detecting X Ray Photons (2) 3D Reconstruction from 2D Images Specimen - Cancellous Bone (Hitachi Medical Co.) - Cortical Bone * Point Source * Obtained by MCT-CB100MF
8 1.3 Iterative Algorithm for Surface Remodeling Simulation Stress Analysis by EBE/PCG FEM 8 Calculation of Remodeling Driving Force Γ 1 step Surface Movement Equilibrium No Yes End
9 2. Simulation Model 9
10 2.1 Bone Remodeling at Trabecular Level 10 Experimental Study (Goldstein et al., 1991; Guldberg et al., 1997) (1) Cancellous Bone in Canine Distal Femoral Metaphysis (2) Hydraulically Controlled Loads Using Platens (3) Quantitative Evaluation of Bone Structural Changes Using Digital Image Obtained by µct Implant body with five 6mm platen designs (left) and embedded within canine distal femoral metaphysis (right) (Guldberg et al., 1997) Trabecular structure around porouscoated platen (Guldberg et al., 1997)
11 2.2 Cancellous Bone Model Under Compressive Loading 11 σ 3 = F 3 /a 2 500µm U 3 a X 3 X 2 X 1 a 3D Image a X 1 -X 3 Cross Section Fabric Ellipsoid Cubic Size: a = 5mm Compressive Loading: σ 3 = 1.24MPa Voxel Size: 25µm = 800 Millions Elements Model Parameters l L = 500µm Γ u = 4.0, Γ l = -5.0
12 3. Results 12
13 Compression Direction(X 3 ) 3.1 Trabecular Remodeling Under Compressive Loading 3D Image 13 X 3 X 2 X 1 -X 3 Cross Section X 1 Formation Resorption X 3 X 1 10th step 20th step 50th step
14 3.2 Change in Structural Indices 14 Simulation Experiment (n=1) (Guldberg et al., 1997) Decrease Not Change (a) Bone Volume Fraction (b) Trabecular Plate Thickness Decrease Increase (c) Trabecular Plate Number (d) Trabecular Plate Separation
15 3.3 Change in Structural Anisotropy 15 Fabric Ellipsoid of Cancellous Bone 500µm Compression Direction(X 3 ) th step 20th step 50th step
16 3.4 Functional Adaptation by Trabecular Reorientation Numerical Mechanical Testing to Obtain Structural Properties (1) Central Region of 4*4*4mm 3 Cube Cancellous Bone (2) Compressive Stress σ i is applied for each direction (i = 1,2,3). (3) Apparent Stiffness: σ i /ε i is Obtained (ε i = U i /a). 16 σ i = F i /a 2 U i a X 3X2 X 1 a a
17 Conclusions 17 - Surface Remodeling Simulation for Trabecular Bone Using Digital Image-Based Model of Cancellous Bone - Large-Scale Voxel Finite Element Model - Remodeling for 3D & Complex Trabecular Structure - Quantitative Comparison to Experimental Results
18 Future Work: Application to Design of Implant 18 Quantitative Evaluation of Bone Structural Changes Due to Implantation Design of Implant Considering Bone Remodeling Trabecular remodeling due to instrumentation of rod screw Digital image-based model of THA stem implanted in proximal femur
19 Acknowledgement 19 Prof. Steven A. Goldstein Prof. Scott J. Hollister Nancy J. Caldwell The University of Michigan
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