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Experimental and simulated studies on the plastic mechanical characteristics of osteoporotic vertebral trabecular bone
Current Applied Physics 10 (2010) 729–733
Contents lists available at ScienceDirect
Current Applied Physics journal homepage: www.elsevier.com/locate/cap
Experimental and simulated studies on the plastic mechanical characteristics of osteoporotic vertebral trabecular bone D.G. Woo a, C.H. Kim a, D. Lim b, H.S. Kim a,* a b
Department of Biomedical Engineering, Yonsei University, Wonju, Gangwon-Do 220-710, Republic of Korea Silver Technology Center, Korea Institute of Industry Technology, Chenan, Chungnam-Do 331-825, Republic of Korea
a r t i c l e
i n f o
Article history: Received 29 May 2009 Accepted 24 July 2009 Available online 6 August 2009 Keywords: Rapid prototyped technology Finite element method Plastic mechanical characteristics Micro-computed tomography Vertebral trabecular bone
a b s t r a c t Osteoporotic vertebral fractures present a major health care burden worldwide, thereby prompting vigorous investigation of the mechanical properties of vertebral bone. Because most vertebral fractures occur gradually and asymptomatically, they are thought to result from loading in daily activities rather than traumatic events. Hence, with respect to stress resistance, the elastic properties of osteoporotic vertebral trabecular bone have generated many studies. A large part of this data describes the linear elastic properties of the bone, with relatively less focus on the plastic mechanical characteristics which may be closely associated with load-induced fracture. We performed experimental and simulated studies of the plastic mechanical characteristics of osteoporotic trabecular bone using non-destructive technologies, rapid-prototyping (RP), and finite element (FE) analysis to build models based on high-resolution micro-computed tomography (micro-CT) data. Two-dimensional geometries for RP and FE models were derived from micro-CT scans of specimens from the central part of the lumbar vertebrae of aged female donors. A cubic specimen (6.5 mm) and a cylindrical specimen (7 mm in diameter and 5 mm long) were generated for the RP and FE models and analysed in place of real bone specimens. We performed simulated compression tests with the FE models to indirectly validate results of the experimental compression tests. To a remarkable degree, results obtained from experimental and simulated compression tests with the RP and FE models concurred. The results of this study support the use of RP technology and FE analysis in the non-destructive evaluation of the plastic mechanical characteristics of osteoporotic bone. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction A large body of research attempts to quantify the effects of agerelated bone loss in trabecular bone [1–3]. Osteoporosis is defined as a systemic skeletal disease caused by low bone mass and microstructural deterioration of the bone. Although bone mass increases during growth, it begins to decrease after approximately 30.5 years of age [4]. About 16% of postmenopausal women and 20% of people over 70 years of age show signs of osteoporotic vertebral fractures in the world, at an estimated annual cost of $250 million [5]. The search for effective treatments and preventive strategies continues. Clinical evidence indicates that individual risk for vertebral fracture increases as vertebral bone mineral density (BMD) declines [6–8]. This risk may be related to the mechanical characteristics of bone, with an altered trabecular micro-architecture (specifically, with fewer transverse trabeculae) in osteoporosis [9], which leads to an uneven load distribution. Song et al . [10] * Corresponding author. Tel.: +82 33 760 2942; fax: +82 33 760 2913. E-mail addresses: [email protected] (D.G. Woo), [email protected] (H.S. Kim). 1567-1739/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cap.2009.07.021
related a reduction in fracture threshold to a corresponding deficit in bone mass to compare damage from distinct architectural changes in bone. Newitt et al. [11] assessed bone strength and fracture risk with high-resolution magnetic resonance (MR) imaging. Investigators have also used experimental and simulated compression tests, based on micro-finite element (lFE) analysis, to evaluate the mechanical characteristics of human trabecular bone. Ulrich et al. [12] used three-dimensional (3D) micro-computed tomography (lCT)-based FE models at various voxel resolutions (28– 168 lm). Frank et al. [13,14] tested the effects of specimen geometry on the mechanical characteristics of trabecular bone specimens and proposed a cubic specimen with a side length of 6.5 mm as a standard specimen for experimental tests of trabecular bone. Here we report our findings on the plastic characteristics of trabecular bone obtained through the assessment of bone strength, which is a correlate of fracture risk. Osteoporosis is multi-factorial in origin, and the resulting loss of bone mass cannot completely explain fracture risk. An analysis of physiological loads imposed on the spine may identify additional risk components [15], such as a loss of bone strength that lowers fracture threshold. A previous study showed that abrupt mechanical action (e.g., forward flexion or lifting) upon an abnormal load may trigger vertebral fracture in
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D.G. Woo et al. / Current Applied Physics 10 (2010) 729–733
osteoporotic bone [16]. In line with this biomechanical viewpoint, we performed experimental and simulated tests of the plastic mechanical characteristics of osteoporotic trabecular bone using models produced by rapid prototyped (RP) technology and FE analysis, based on lCT data. These non-destructive methods reproduce, in solid and numerical forms, the specific scaffold architectures revealed in 3D images (in this study, by micro-CT) of real bone specimens. We performed the experimental compression test and the analysis of mechanical plasticity in vertebral trabecular bone with the RP models (in place of ‘real bone specimens’), and verified the results in simulated compression tests with models based on FE analysis. 2. Materials and methods 2.1. Bone specimens acquisition and lCT imaging To generate RP and FE models, specimens of second lumbar vertebral bodies (L2) were taken from the cadavers of three females, aged 70, 75, and 85 years. The vertebral bodies had no radiographic evidence of tumors, gross kyphosis, scoliosis, or previous surgery. Trabecular cylinders of 11 mm diameter were obtained by coring the central part of L2. Two types of specimens were prepared: (a) a 6.5 mm cube, and (b) a cylinder 7 mm in diameter and 5 mm long, as recommended for testing compression [14] and dynamic mechanical properties [17] of trabecular bone, respectively. Bone specimens were scanned with high-resolution lCT (Skyscan1076, Skyscan, Belguim), at 21 lm resolution. All lCT images were captured by BIONIX (CANTiBio Co., Korea) and converted to 3D voxel images using a mass-compensated thresholding technique [12]. In the mass-compensated hexahedron meshing technique, a unique threshold value was selected for each of the three images of different voxel resolution to match the relative bone volume fraction (BV/TV) of the specimen obtained using lCT (Table 1). 2.2. Classification of osteoporotic bones: morphological study The morphological study was performed to identify the extent of osteoporosis for trabecular bones used in our compression tests. The relative BV/TV of osteoporotic vertebral trabecular bone was obtained from the morphological parameters of real bone samples that were measured by lCT. The tissue volume (TV, mm3) and the trabecular bone volume (BV, mm3) were measured by the direct method available with lCT, and the BV/TV was calculated. Trabecular thickness (Tb.Th, mm), trabecular separation (Tb.Sp, mm), and trabecular number (Tb.N) were measured directly on 3D image data. The plate–rod characteristic of the bone structure can be measured using the structure model index (SMI) value, which is 0 for an ideal plate, and 3 for an ideal rod. The degree of anisotropy (DOA), a relative measure of orientation within the trabecular bones, varies from 0 to 1. The higher the DOA, the more closely the bone is aligned in the principal direction (on-axis direction) relative to other directions. For the morphological analysis of trabecular bone, each outcome parameter of bone microstructure showed similar values for samples from all three cadavers (ages 70, 75, and 85 years) (Table 1). Target size range was adjusted as recommended in previous studies of osteoporotic bone [11]. The
same 3D lCT image data were used to generate both the solid (3D) RP and numerical FE models for the experimental and simulated compression tests, respectively. 2.3. Compression tests 2.3.1. Experimental tests Using data obtained from computer-aided design (CAD) systems, RP technology can rapidly produce highly complex 3D objects. This rapid-prototyping and manufacturing (RP&M) process represents a group of innovative manufacturing methods to build a solid model, layer by layer (layer thickness = 0.254 mm), using RP techniques of fused deposition modeling (FDM) and 3D-printed stereo lithography (STL format file). The most common format is the STL used by most 3D rendering and modeling software programs. The 3D, segmented, vertebral trabecular micro-CT data were imported into a commercial FE pre-processor (Altair HyperMesh 7.0, Altair Engineering, Detroit, Michigan, USA) to generate the STL format files for the manufacture of RP models in a fused deposition modeling system (FDM TITAN, Stratasys, Eden Prairie, USA). A variety of high performance engineering materials are available for this purpose, including polycarbonate [18] and acrylonitrile–butadiene–styrene (ABS) copolymerizing plastic [19]. Based on the widespread use of ABS in FDM–RP&M processes [19–21], we selected ABS plastic to produce a realistic functional model of human vertebral trabecular bone for experimental compression tests. In previous work [22], we determined the material properties of ABS copolymer in three-point bending tests performed with an INSTRON testing machine (8874 series, Instron, UK) (Table 2). Trabecular bone specimens of actual size were too small to reproduce by RP–FDM modeling; therefore, we first scaled up the architectural replicas by a factor of 20 [22]. Two types of RP-FDM specimen were produced [(a) a cubic specimen with sides of 6.5 mm; and (b) a cylindrical specimen 7 mm in diameter and 5 mm long], using lCT data obtained at two different voxel resolutions (42 lm and 84 lm) for each specimen type. The ABS plastic models were compressed beyond failure in the INSTRON testing machine, and the compressive strength of the models was recorded. 2.3.2. Simulation (RP) A simulated compression test was also performed using microFE models with ABS material properties. This analysis examined the effect of lCT image resolution on the plastic mechanical characteristics of lFE models. The 3D lFE models were generated from lCT gray-scale images using two different voxel resolutions (42 lm and 84 lm). For the images at each resolution, lFE models with the same BV/TV were built by converting each bone voxel to a hexahedral element. The 42 lm voxel resolution consisted of 2 2 2 voxels in 21 lm voxel resolutions, and the 84 lm voxel resolution consisted of 4 4 4 voxels. Table 2 shows the values we used for Young’s modulus, strength, and Poisson’s ratio [12,22]. The trabecular material in this FE analysis was assumed to be isotropic and perfectly elastic plastic. Displacement boundary conditions were applied to the specimens to simulate a uniaxial compression test. To derive the plastic mechanical component of this analysis, a compressive displacement was applied, and reaction force and compressive strength were measured. All FE analy-
Table 1 Micro-structural parameters for vertebral trabecular bones.
Age 70 Age 75 Age 85
Tb.Th (mm)
Tb.Sp (mm)
Volume (mm3)
Surface (mm2)
BV/TV (%)
DOA
SMI
Tb.N (mm
0.156 0.145 0.194
0.934 0.928 0.789
5.319 4.638 6.939
136.695 128.366 107.616
8.239 7.652 10.662
0.121 0.133 0.112
1.910 1.856 2.315
0.528 0.465 1.017
1
)
D.G. Woo et al. / Current Applied Physics 10 (2010) 729–733 Table 2 Material properties of trabecular bones and acrylonitrile–butadiene–styrene (ABS) copolymer ([12,22]). Property
Value: trabecular bone
Value: ABS
Young’s modulus (E) Compressive strength (r) Poisson’s ratio (t)
10 GPa 136 MPa 0.3
1.1 GPa 108 MPa 0.3
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post hoc multiple comparisons was used to identify significant changes of the results in a three-way validation of compression tests of osteoporotic vertebral trabecular bone using experimental models with ABS material properties; and FE models with material properties of ABS copolymer and human vertebral trabecular bone. The significance levels for all statistical tests were set at 0.05. 3. Results
ses were performed using a commercial FE software package (ABAQUS 6.4, HKS Inc., USA). The results (reaction force and compressive strength) of these simulated compression tests were compared with those of the experimental compression tests on the ABS models of trabecular bone as an indirect method of validation. The simulated compression test with FE analysis could also provide important insights into the failure pattern of internal bone structures which could not be exactly investigated in experimental test. 2.3.3. Simulation (Bone) For the simulated compression tests of trabecular bone, the same two geometric specimens as those used in the experimental tests with ABS material properties were reconstructed in FE models based on lCT gray-scale images taken at two different voxel resolutions (42 lm and 84 lm). The trabecular material in this FE analysis was assumed to be isotropic and perfectly elastic. Table 2 shows the values used for Young’s modulus, strength, and Poisson’s ratio. To evaluate plastic mechanical characteristics, the reaction force and compressive strength of specimens were measured during a compressive displacement. A commercial FE software package (ABAQUS 6.4, HKS Inc., USA) was used to perform all FE analysis. 2.4. Comparison of compression test results Experimental compression tests were performed with an INSTRON testing machine using ABS plastic models of osteoporotic vertebral trabecular bones reproduced by RP&M from micro-CT images of real bone specimens (Fig. 1a). Simulated compression tests were performed using lFE models with the properties of either ABS or trabecular bone material (Fig. 1b). Replicate models of each type were generated from micro-CT images taken at 42 lm and 84 lm resolution. The normalized data from the compression tests were compared for an indirect validation of the experimental test values. A one-way ANOVA test with Tukey’s-b
Based on assumptions of the plastic strength of living tissue, the plastic characteristics of osteoporotic trabecular bone can be estimated from experimental and simulated tests performed with RP models and FE analysis. As compared to healthy vertebral bones, we found the trabeculae of osteoporotic bones to be fewer in number, thinner, farther apart, and more axial in orientation, at the expense of the transverse direction. The morphological parameters of the trabecular bone did not differ significantly among the specimens obtained from donors aged 70, 75, and 85 years (Table 1), based on a target range appropriate for osteoporotic bone [11]. We performed a three-way validation of compression tests of osteoporotic vertebral trabecular bone using experimental models with ABS material properties; and FE models with material properties of ABS copolymer and human vertebral trabecular bone (Fig. 1). For the experimental tests, we generated plastic 3D models from original micro-CT data using RP and FDM technology, and measured effects of compression with an INSTRON testing machine. We have previously reported that the ‘mass-compensated voxel meshing techniques’ suggested by Ulrich et al. [12] are effective for FE analysis of models based on lCT scans, up to an 84 lm resolution, of specimens with the geometries used here [23]. For this study, we therefore selected only two different voxel levels (42 lm and 84 lm) for our original lCT data set. In the experimental and simulated compression tests, the plastic mechanical characteristics were determined from the maximum values in the stress–strain curves obtained during nonlinear simulations. As shown in Fig. 2, the results did not differ significantly for experimental and simulated compression tests in models with the same geometry, based on lCT images of the same resolution (p > 0.05). Results are presented as relative values (r*/rS), normalized by the values for the material property. The compressive strength of the 42 lm resolution models agreed closely with results for the 84 lm resolution models in the experimental and simulated tests, respectively. The results of the simulated compression test therefore support those of the experimental test. The simu-
Fig. 1. Experimental and simulated compression tests in representative cubic specimens.
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D.G. Woo et al. / Current Applied Physics 10 (2010) 729–733
(a)
Exp_RP
FE_ABS
FE_trabecular
3 2.5
σ σS
∗
2 1.5 1 0.5 0 42 µm
(b)
Exp_RP
Resolutions
FE_ABS
8 4 µm
FE_trabecular
3.5 3
σ∗ σS
2.5 2 1.5 1 0.5 0 42 µm
Resolutions
8 4 µm
Fig. 2. Results for compression tests with experimental and simulated models with material properties of ABS polymer and trabecular bone. (EXP_RP: experimental test with RP models, FE_ABS: FE analysis with ABS material properties, FE_trabecular: FE analysis with trabecular bone material properties). (a) Cubic specimens (side length 6.5 mm), (b) cylindrical specimens (diameter = 7 mm, length = 5 mm). r*: compressive strength, rS: strength of material property.
lated compression test with FE analysis also provided important insights into the failure pattern of internal bone structures which could not be exactly investigated in experimental test (Fig. 1b); we found that thin central area of trabeculae was destroyed before everything else in stress distribution. 4. Discussion and conclusions In this study, we applied the non-destructive methods of RP technology and FE analysis, based on 3D lCT images of biological specimens, to explore the plastic mechanical characteristics of osteoporotic vertebral trabecular bone. The parameters of the experimental RP models agree closely with corresponding values for micro-FE element models given the material properties of ABS plastic or vertebral trabecular bones; the three arms of the study were thus mutually supportive. Although osteoporotic compression fracture is associated with the plastic mechanical properties of bone, few researchers have explored this relationship with the methodology used in this study. We expected osteoporotic vertebral bone to display a suboptimal architecture that could result in uneven load distribution [16]. Previous work suggested a relationship between osteoporotic architecture and mechanical properties that determine resistance to loading in normal activities. In principle, a fracture may occur through either a reduction in structural strength of the vertebra or overload of the normal structure. The longer and thinner trabeculae of osteoporotic bones may succumb more readily to buckling, and osteoclasts may resorb thin trabeculae more easily than longer ones [24]. High stress applied to the plastic mechanical resistance of bone increases the trabecular tendency to buckle, which may explain the decreased compression strength we measured in the
osteoporotic vertebral bones. This implies that vertebral fractures may be caused by higher than normal loading in certain dimensions of bone strength [16]. Accordingly, we investigated the plastic mechanical characteristics of osteoporotic trabecular bones to better understand vertebral fractures caused by overload. Vertebral compression fractures alter vertebral biomechanics by decreasing stiffness in both compression and bending. Occupational bending and lifting with heavy weights presents one risk factor in osteoporotic fracture. These activities induce compression overloads, in addition to large rotations in the direction of forward flexion. To protect the osteoporotic person from fracture, the resulting pain, deformity, and incapacitation, it is important to stabilize the spine against compression overload. To clarify the structural basis for compression fracture, we combined three powerful technologies: lCT imaging, RP&M, and FE analysis. Micro-CT scanning produces digitalized 3D images of entire human or animal bones at resolutions of about 21 lm. From 2D sections of these images, we can reconstruct 3D high-resolution models of trabecular bones, and from these, generate solid RP models providing visual and tactile information. The coupling of imaging technology to RP&M has revolutionized anatomical and biomechanical analyses. Human organ models produced in this way assist in diagnosis and preparation for complex surgeries. Scaffold structures patterned on native tissue morphology may serve as matrices for the culture of living tissue implants to heal serious injuries and conditions. In research, RP models may relieve limitations encountered in the use of animals and biological tissues. Advantages include true-to-life-accuracy (assuming optimal parameters for scanning, reconstruction, thresholding, and model-building), reproducibility, experimental control, and high sample capacity. The methodology may also reduce expense, variability, and ethical concern, particularly in the use of cadavers. We find in this technology an effective alternative to real bone specimens, yielding valuable insight into mechanisms of failure in trabecular bone. Mechanisms we identified in RP models were similar to those in real bone specimens, although the models consisted of an isotropic, homogeneous material. This suggests that geometrical, or architectural flaws, rather than cellular or tissue-level defects, may largely determine how and where the failure occurs [25]. The study extends a previous one in which we performed compression tests on RP replicas of trabecular specimens from human vertebrae [22]. We found a close correlation between the structural pattern for the RP replicas and those for the real bone specimens, as well as striking similarities in the mechanical point of view. Our previous research showed that RP models realistically represented elastic mechanical characteristics of trabecular bone. Importantly, RP&M technology can generate bone replicas patterned on the architecture of healthy, authentic bone, but with varying levels of bone loss introduced. Intrinsic structural parameters, such as the volume fraction (BV/TV), can also be controlled in the production of RP models. A third innovation, FE analysis, is gaining rapidly in power through development of analytical codes that can handle up to 106 elements of information. Although high cost in terms of computer time, these new codes enable the analysis of osteoporotic vertebral trabecular bone at very high resolutions, and as we showed in our simulated compression tests, micro-FE models provide a valuable indirect validation of results from experimental compression tests with RP models. Researchers have historically obtained bone specimens from cadavers and/or animals for use in destructive tests of compression under load or displacement with a mechanical testing machine [26–28]. Our new combination of RP technology with FE analysis may eventually replace, at least in part, the use of biological specimens.
D.G. Woo et al. / Current Applied Physics 10 (2010) 729–733
Our methods and findings face several limitations. While the Young’s modulus of material properties is appropriate for normal vertebral trabecular bone, it may not represent the properties of aging bone. Our models consist of a relatively homogenous material, and are therefore more isotropic than real bone, and our FE model may not accurately replicate bone’s viscoelastic properties. We tested only a small number of models in this study; however, because they were all based on high-resolution lCT data, and we could closely replicate the intrinsic architecture of the same trabecular specimens in both RP and FE models, we feel that our data accurately represent the plastic mechanical characteristics of osteoporotic bones. Overall, our findings support the use of RP technology with FE analysis as a non-destructive method to investigate the properties of bone and, possibly, to test emergent therapies. References [1] M.J. Silva, L.J. Gibson, Bone 21 (1997) 191. [2] J. Kabel, A. Odgaard, B.V. Rietbergen, R. Huiskes, Bone 24 (1999) 115. [3] F. Phillips, A. Turner, H. Seim, M. Jennifer, C. Toth, A. Pierce, D. Wheeler, Spine J. 6 (2006) 500. [4] R.D. Wasnich, Epidemiology of osteoporosis, in: M.J. Favus (Ed.), Primer on the Metabolic Bone Diseases and Disorders of Minal Metabolism, Lippincott/ Williams and Wilkins, 1999. Chapter 46. [5] C. Kim, A. Mahar, A. Perry, J. Massie, L. Lu, B. Currier, M.J. Yaszemski, J. Spinal Disord. Technol. 20 (2007) 604. [6] P.D. Ross, J.W. Davis, R.S. Epstein, R.D. Wasnich, Ann. Intern. Med. 114 (1991) 919. [7] C.C. Johnson, L.J. Melton, in: B.L. Riggs, L.J. Melton (Eds.), Osteoporosis: Etiology, Diagnosis, Management, Lippincott-Raven, Philadelphia, 1995, p. 275.
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Contents lists available at ScienceDirect
Current Applied Physics journal homepage: www.elsevier.com/locate/cap
Experimental and simulated studies on the plastic mechanical characteristics of osteoporotic vertebral trabecular bone D.G. Woo a, C.H. Kim a, D. Lim b, H.S. Kim a,* a b
Department of Biomedical Engineering, Yonsei University, Wonju, Gangwon-Do 220-710, Republic of Korea Silver Technology Center, Korea Institute of Industry Technology, Chenan, Chungnam-Do 331-825, Republic of Korea
a r t i c l e
i n f o
Article history: Received 29 May 2009 Accepted 24 July 2009 Available online 6 August 2009 Keywords: Rapid prototyped technology Finite element method Plastic mechanical characteristics Micro-computed tomography Vertebral trabecular bone
a b s t r a c t Osteoporotic vertebral fractures present a major health care burden worldwide, thereby prompting vigorous investigation of the mechanical properties of vertebral bone. Because most vertebral fractures occur gradually and asymptomatically, they are thought to result from loading in daily activities rather than traumatic events. Hence, with respect to stress resistance, the elastic properties of osteoporotic vertebral trabecular bone have generated many studies. A large part of this data describes the linear elastic properties of the bone, with relatively less focus on the plastic mechanical characteristics which may be closely associated with load-induced fracture. We performed experimental and simulated studies of the plastic mechanical characteristics of osteoporotic trabecular bone using non-destructive technologies, rapid-prototyping (RP), and finite element (FE) analysis to build models based on high-resolution micro-computed tomography (micro-CT) data. Two-dimensional geometries for RP and FE models were derived from micro-CT scans of specimens from the central part of the lumbar vertebrae of aged female donors. A cubic specimen (6.5 mm) and a cylindrical specimen (7 mm in diameter and 5 mm long) were generated for the RP and FE models and analysed in place of real bone specimens. We performed simulated compression tests with the FE models to indirectly validate results of the experimental compression tests. To a remarkable degree, results obtained from experimental and simulated compression tests with the RP and FE models concurred. The results of this study support the use of RP technology and FE analysis in the non-destructive evaluation of the plastic mechanical characteristics of osteoporotic bone. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction A large body of research attempts to quantify the effects of agerelated bone loss in trabecular bone [1–3]. Osteoporosis is defined as a systemic skeletal disease caused by low bone mass and microstructural deterioration of the bone. Although bone mass increases during growth, it begins to decrease after approximately 30.5 years of age [4]. About 16% of postmenopausal women and 20% of people over 70 years of age show signs of osteoporotic vertebral fractures in the world, at an estimated annual cost of $250 million [5]. The search for effective treatments and preventive strategies continues. Clinical evidence indicates that individual risk for vertebral fracture increases as vertebral bone mineral density (BMD) declines [6–8]. This risk may be related to the mechanical characteristics of bone, with an altered trabecular micro-architecture (specifically, with fewer transverse trabeculae) in osteoporosis [9], which leads to an uneven load distribution. Song et al . [10] * Corresponding author. Tel.: +82 33 760 2942; fax: +82 33 760 2913. E-mail addresses: [email protected] (D.G. Woo), [email protected] (H.S. Kim). 1567-1739/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cap.2009.07.021
related a reduction in fracture threshold to a corresponding deficit in bone mass to compare damage from distinct architectural changes in bone. Newitt et al. [11] assessed bone strength and fracture risk with high-resolution magnetic resonance (MR) imaging. Investigators have also used experimental and simulated compression tests, based on micro-finite element (lFE) analysis, to evaluate the mechanical characteristics of human trabecular bone. Ulrich et al. [12] used three-dimensional (3D) micro-computed tomography (lCT)-based FE models at various voxel resolutions (28– 168 lm). Frank et al. [13,14] tested the effects of specimen geometry on the mechanical characteristics of trabecular bone specimens and proposed a cubic specimen with a side length of 6.5 mm as a standard specimen for experimental tests of trabecular bone. Here we report our findings on the plastic characteristics of trabecular bone obtained through the assessment of bone strength, which is a correlate of fracture risk. Osteoporosis is multi-factorial in origin, and the resulting loss of bone mass cannot completely explain fracture risk. An analysis of physiological loads imposed on the spine may identify additional risk components [15], such as a loss of bone strength that lowers fracture threshold. A previous study showed that abrupt mechanical action (e.g., forward flexion or lifting) upon an abnormal load may trigger vertebral fracture in
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osteoporotic bone [16]. In line with this biomechanical viewpoint, we performed experimental and simulated tests of the plastic mechanical characteristics of osteoporotic trabecular bone using models produced by rapid prototyped (RP) technology and FE analysis, based on lCT data. These non-destructive methods reproduce, in solid and numerical forms, the specific scaffold architectures revealed in 3D images (in this study, by micro-CT) of real bone specimens. We performed the experimental compression test and the analysis of mechanical plasticity in vertebral trabecular bone with the RP models (in place of ‘real bone specimens’), and verified the results in simulated compression tests with models based on FE analysis. 2. Materials and methods 2.1. Bone specimens acquisition and lCT imaging To generate RP and FE models, specimens of second lumbar vertebral bodies (L2) were taken from the cadavers of three females, aged 70, 75, and 85 years. The vertebral bodies had no radiographic evidence of tumors, gross kyphosis, scoliosis, or previous surgery. Trabecular cylinders of 11 mm diameter were obtained by coring the central part of L2. Two types of specimens were prepared: (a) a 6.5 mm cube, and (b) a cylinder 7 mm in diameter and 5 mm long, as recommended for testing compression [14] and dynamic mechanical properties [17] of trabecular bone, respectively. Bone specimens were scanned with high-resolution lCT (Skyscan1076, Skyscan, Belguim), at 21 lm resolution. All lCT images were captured by BIONIX (CANTiBio Co., Korea) and converted to 3D voxel images using a mass-compensated thresholding technique [12]. In the mass-compensated hexahedron meshing technique, a unique threshold value was selected for each of the three images of different voxel resolution to match the relative bone volume fraction (BV/TV) of the specimen obtained using lCT (Table 1). 2.2. Classification of osteoporotic bones: morphological study The morphological study was performed to identify the extent of osteoporosis for trabecular bones used in our compression tests. The relative BV/TV of osteoporotic vertebral trabecular bone was obtained from the morphological parameters of real bone samples that were measured by lCT. The tissue volume (TV, mm3) and the trabecular bone volume (BV, mm3) were measured by the direct method available with lCT, and the BV/TV was calculated. Trabecular thickness (Tb.Th, mm), trabecular separation (Tb.Sp, mm), and trabecular number (Tb.N) were measured directly on 3D image data. The plate–rod characteristic of the bone structure can be measured using the structure model index (SMI) value, which is 0 for an ideal plate, and 3 for an ideal rod. The degree of anisotropy (DOA), a relative measure of orientation within the trabecular bones, varies from 0 to 1. The higher the DOA, the more closely the bone is aligned in the principal direction (on-axis direction) relative to other directions. For the morphological analysis of trabecular bone, each outcome parameter of bone microstructure showed similar values for samples from all three cadavers (ages 70, 75, and 85 years) (Table 1). Target size range was adjusted as recommended in previous studies of osteoporotic bone [11]. The
same 3D lCT image data were used to generate both the solid (3D) RP and numerical FE models for the experimental and simulated compression tests, respectively. 2.3. Compression tests 2.3.1. Experimental tests Using data obtained from computer-aided design (CAD) systems, RP technology can rapidly produce highly complex 3D objects. This rapid-prototyping and manufacturing (RP&M) process represents a group of innovative manufacturing methods to build a solid model, layer by layer (layer thickness = 0.254 mm), using RP techniques of fused deposition modeling (FDM) and 3D-printed stereo lithography (STL format file). The most common format is the STL used by most 3D rendering and modeling software programs. The 3D, segmented, vertebral trabecular micro-CT data were imported into a commercial FE pre-processor (Altair HyperMesh 7.0, Altair Engineering, Detroit, Michigan, USA) to generate the STL format files for the manufacture of RP models in a fused deposition modeling system (FDM TITAN, Stratasys, Eden Prairie, USA). A variety of high performance engineering materials are available for this purpose, including polycarbonate [18] and acrylonitrile–butadiene–styrene (ABS) copolymerizing plastic [19]. Based on the widespread use of ABS in FDM–RP&M processes [19–21], we selected ABS plastic to produce a realistic functional model of human vertebral trabecular bone for experimental compression tests. In previous work [22], we determined the material properties of ABS copolymer in three-point bending tests performed with an INSTRON testing machine (8874 series, Instron, UK) (Table 2). Trabecular bone specimens of actual size were too small to reproduce by RP–FDM modeling; therefore, we first scaled up the architectural replicas by a factor of 20 [22]. Two types of RP-FDM specimen were produced [(a) a cubic specimen with sides of 6.5 mm; and (b) a cylindrical specimen 7 mm in diameter and 5 mm long], using lCT data obtained at two different voxel resolutions (42 lm and 84 lm) for each specimen type. The ABS plastic models were compressed beyond failure in the INSTRON testing machine, and the compressive strength of the models was recorded. 2.3.2. Simulation (RP) A simulated compression test was also performed using microFE models with ABS material properties. This analysis examined the effect of lCT image resolution on the plastic mechanical characteristics of lFE models. The 3D lFE models were generated from lCT gray-scale images using two different voxel resolutions (42 lm and 84 lm). For the images at each resolution, lFE models with the same BV/TV were built by converting each bone voxel to a hexahedral element. The 42 lm voxel resolution consisted of 2 2 2 voxels in 21 lm voxel resolutions, and the 84 lm voxel resolution consisted of 4 4 4 voxels. Table 2 shows the values we used for Young’s modulus, strength, and Poisson’s ratio [12,22]. The trabecular material in this FE analysis was assumed to be isotropic and perfectly elastic plastic. Displacement boundary conditions were applied to the specimens to simulate a uniaxial compression test. To derive the plastic mechanical component of this analysis, a compressive displacement was applied, and reaction force and compressive strength were measured. All FE analy-
Table 1 Micro-structural parameters for vertebral trabecular bones.
Age 70 Age 75 Age 85
Tb.Th (mm)
Tb.Sp (mm)
Volume (mm3)
Surface (mm2)
BV/TV (%)
DOA
SMI
Tb.N (mm
0.156 0.145 0.194
0.934 0.928 0.789
5.319 4.638 6.939
136.695 128.366 107.616
8.239 7.652 10.662
0.121 0.133 0.112
1.910 1.856 2.315
0.528 0.465 1.017
1
)
D.G. Woo et al. / Current Applied Physics 10 (2010) 729–733 Table 2 Material properties of trabecular bones and acrylonitrile–butadiene–styrene (ABS) copolymer ([12,22]). Property
Value: trabecular bone
Value: ABS
Young’s modulus (E) Compressive strength (r) Poisson’s ratio (t)
10 GPa 136 MPa 0.3
1.1 GPa 108 MPa 0.3
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post hoc multiple comparisons was used to identify significant changes of the results in a three-way validation of compression tests of osteoporotic vertebral trabecular bone using experimental models with ABS material properties; and FE models with material properties of ABS copolymer and human vertebral trabecular bone. The significance levels for all statistical tests were set at 0.05. 3. Results
ses were performed using a commercial FE software package (ABAQUS 6.4, HKS Inc., USA). The results (reaction force and compressive strength) of these simulated compression tests were compared with those of the experimental compression tests on the ABS models of trabecular bone as an indirect method of validation. The simulated compression test with FE analysis could also provide important insights into the failure pattern of internal bone structures which could not be exactly investigated in experimental test. 2.3.3. Simulation (Bone) For the simulated compression tests of trabecular bone, the same two geometric specimens as those used in the experimental tests with ABS material properties were reconstructed in FE models based on lCT gray-scale images taken at two different voxel resolutions (42 lm and 84 lm). The trabecular material in this FE analysis was assumed to be isotropic and perfectly elastic. Table 2 shows the values used for Young’s modulus, strength, and Poisson’s ratio. To evaluate plastic mechanical characteristics, the reaction force and compressive strength of specimens were measured during a compressive displacement. A commercial FE software package (ABAQUS 6.4, HKS Inc., USA) was used to perform all FE analysis. 2.4. Comparison of compression test results Experimental compression tests were performed with an INSTRON testing machine using ABS plastic models of osteoporotic vertebral trabecular bones reproduced by RP&M from micro-CT images of real bone specimens (Fig. 1a). Simulated compression tests were performed using lFE models with the properties of either ABS or trabecular bone material (Fig. 1b). Replicate models of each type were generated from micro-CT images taken at 42 lm and 84 lm resolution. The normalized data from the compression tests were compared for an indirect validation of the experimental test values. A one-way ANOVA test with Tukey’s-b
Based on assumptions of the plastic strength of living tissue, the plastic characteristics of osteoporotic trabecular bone can be estimated from experimental and simulated tests performed with RP models and FE analysis. As compared to healthy vertebral bones, we found the trabeculae of osteoporotic bones to be fewer in number, thinner, farther apart, and more axial in orientation, at the expense of the transverse direction. The morphological parameters of the trabecular bone did not differ significantly among the specimens obtained from donors aged 70, 75, and 85 years (Table 1), based on a target range appropriate for osteoporotic bone [11]. We performed a three-way validation of compression tests of osteoporotic vertebral trabecular bone using experimental models with ABS material properties; and FE models with material properties of ABS copolymer and human vertebral trabecular bone (Fig. 1). For the experimental tests, we generated plastic 3D models from original micro-CT data using RP and FDM technology, and measured effects of compression with an INSTRON testing machine. We have previously reported that the ‘mass-compensated voxel meshing techniques’ suggested by Ulrich et al. [12] are effective for FE analysis of models based on lCT scans, up to an 84 lm resolution, of specimens with the geometries used here [23]. For this study, we therefore selected only two different voxel levels (42 lm and 84 lm) for our original lCT data set. In the experimental and simulated compression tests, the plastic mechanical characteristics were determined from the maximum values in the stress–strain curves obtained during nonlinear simulations. As shown in Fig. 2, the results did not differ significantly for experimental and simulated compression tests in models with the same geometry, based on lCT images of the same resolution (p > 0.05). Results are presented as relative values (r*/rS), normalized by the values for the material property. The compressive strength of the 42 lm resolution models agreed closely with results for the 84 lm resolution models in the experimental and simulated tests, respectively. The results of the simulated compression test therefore support those of the experimental test. The simu-
Fig. 1. Experimental and simulated compression tests in representative cubic specimens.
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D.G. Woo et al. / Current Applied Physics 10 (2010) 729–733
(a)
Exp_RP
FE_ABS
FE_trabecular
3 2.5
σ σS
∗
2 1.5 1 0.5 0 42 µm
(b)
Exp_RP
Resolutions
FE_ABS
8 4 µm
FE_trabecular
3.5 3
σ∗ σS
2.5 2 1.5 1 0.5 0 42 µm
Resolutions
8 4 µm
Fig. 2. Results for compression tests with experimental and simulated models with material properties of ABS polymer and trabecular bone. (EXP_RP: experimental test with RP models, FE_ABS: FE analysis with ABS material properties, FE_trabecular: FE analysis with trabecular bone material properties). (a) Cubic specimens (side length 6.5 mm), (b) cylindrical specimens (diameter = 7 mm, length = 5 mm). r*: compressive strength, rS: strength of material property.
lated compression test with FE analysis also provided important insights into the failure pattern of internal bone structures which could not be exactly investigated in experimental test (Fig. 1b); we found that thin central area of trabeculae was destroyed before everything else in stress distribution. 4. Discussion and conclusions In this study, we applied the non-destructive methods of RP technology and FE analysis, based on 3D lCT images of biological specimens, to explore the plastic mechanical characteristics of osteoporotic vertebral trabecular bone. The parameters of the experimental RP models agree closely with corresponding values for micro-FE element models given the material properties of ABS plastic or vertebral trabecular bones; the three arms of the study were thus mutually supportive. Although osteoporotic compression fracture is associated with the plastic mechanical properties of bone, few researchers have explored this relationship with the methodology used in this study. We expected osteoporotic vertebral bone to display a suboptimal architecture that could result in uneven load distribution [16]. Previous work suggested a relationship between osteoporotic architecture and mechanical properties that determine resistance to loading in normal activities. In principle, a fracture may occur through either a reduction in structural strength of the vertebra or overload of the normal structure. The longer and thinner trabeculae of osteoporotic bones may succumb more readily to buckling, and osteoclasts may resorb thin trabeculae more easily than longer ones [24]. High stress applied to the plastic mechanical resistance of bone increases the trabecular tendency to buckle, which may explain the decreased compression strength we measured in the
osteoporotic vertebral bones. This implies that vertebral fractures may be caused by higher than normal loading in certain dimensions of bone strength [16]. Accordingly, we investigated the plastic mechanical characteristics of osteoporotic trabecular bones to better understand vertebral fractures caused by overload. Vertebral compression fractures alter vertebral biomechanics by decreasing stiffness in both compression and bending. Occupational bending and lifting with heavy weights presents one risk factor in osteoporotic fracture. These activities induce compression overloads, in addition to large rotations in the direction of forward flexion. To protect the osteoporotic person from fracture, the resulting pain, deformity, and incapacitation, it is important to stabilize the spine against compression overload. To clarify the structural basis for compression fracture, we combined three powerful technologies: lCT imaging, RP&M, and FE analysis. Micro-CT scanning produces digitalized 3D images of entire human or animal bones at resolutions of about 21 lm. From 2D sections of these images, we can reconstruct 3D high-resolution models of trabecular bones, and from these, generate solid RP models providing visual and tactile information. The coupling of imaging technology to RP&M has revolutionized anatomical and biomechanical analyses. Human organ models produced in this way assist in diagnosis and preparation for complex surgeries. Scaffold structures patterned on native tissue morphology may serve as matrices for the culture of living tissue implants to heal serious injuries and conditions. In research, RP models may relieve limitations encountered in the use of animals and biological tissues. Advantages include true-to-life-accuracy (assuming optimal parameters for scanning, reconstruction, thresholding, and model-building), reproducibility, experimental control, and high sample capacity. The methodology may also reduce expense, variability, and ethical concern, particularly in the use of cadavers. We find in this technology an effective alternative to real bone specimens, yielding valuable insight into mechanisms of failure in trabecular bone. Mechanisms we identified in RP models were similar to those in real bone specimens, although the models consisted of an isotropic, homogeneous material. This suggests that geometrical, or architectural flaws, rather than cellular or tissue-level defects, may largely determine how and where the failure occurs [25]. The study extends a previous one in which we performed compression tests on RP replicas of trabecular specimens from human vertebrae [22]. We found a close correlation between the structural pattern for the RP replicas and those for the real bone specimens, as well as striking similarities in the mechanical point of view. Our previous research showed that RP models realistically represented elastic mechanical characteristics of trabecular bone. Importantly, RP&M technology can generate bone replicas patterned on the architecture of healthy, authentic bone, but with varying levels of bone loss introduced. Intrinsic structural parameters, such as the volume fraction (BV/TV), can also be controlled in the production of RP models. A third innovation, FE analysis, is gaining rapidly in power through development of analytical codes that can handle up to 106 elements of information. Although high cost in terms of computer time, these new codes enable the analysis of osteoporotic vertebral trabecular bone at very high resolutions, and as we showed in our simulated compression tests, micro-FE models provide a valuable indirect validation of results from experimental compression tests with RP models. Researchers have historically obtained bone specimens from cadavers and/or animals for use in destructive tests of compression under load or displacement with a mechanical testing machine [26–28]. Our new combination of RP technology with FE analysis may eventually replace, at least in part, the use of biological specimens.
D.G. Woo et al. / Current Applied Physics 10 (2010) 729–733
Our methods and findings face several limitations. While the Young’s modulus of material properties is appropriate for normal vertebral trabecular bone, it may not represent the properties of aging bone. Our models consist of a relatively homogenous material, and are therefore more isotropic than real bone, and our FE model may not accurately replicate bone’s viscoelastic properties. We tested only a small number of models in this study; however, because they were all based on high-resolution lCT data, and we could closely replicate the intrinsic architecture of the same trabecular specimens in both RP and FE models, we feel that our data accurately represent the plastic mechanical characteristics of osteoporotic bones. Overall, our findings support the use of RP technology with FE analysis as a non-destructive method to investigate the properties of bone and, possibly, to test emergent therapies. References [1] M.J. Silva, L.J. Gibson, Bone 21 (1997) 191. [2] J. Kabel, A. Odgaard, B.V. Rietbergen, R. Huiskes, Bone 24 (1999) 115. [3] F. Phillips, A. Turner, H. Seim, M. Jennifer, C. Toth, A. Pierce, D. Wheeler, Spine J. 6 (2006) 500. [4] R.D. Wasnich, Epidemiology of osteoporosis, in: M.J. Favus (Ed.), Primer on the Metabolic Bone Diseases and Disorders of Minal Metabolism, Lippincott/ Williams and Wilkins, 1999. Chapter 46. [5] C. Kim, A. Mahar, A. Perry, J. Massie, L. Lu, B. Currier, M.J. Yaszemski, J. Spinal Disord. Technol. 20 (2007) 604. [6] P.D. Ross, J.W. Davis, R.S. Epstein, R.D. Wasnich, Ann. Intern. Med. 114 (1991) 919. [7] C.C. Johnson, L.J. Melton, in: B.L. Riggs, L.J. Melton (Eds.), Osteoporosis: Etiology, Diagnosis, Management, Lippincott-Raven, Philadelphia, 1995, p. 275.
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