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Structural and Mechanical Properties of Mandibular Condylar Bone

Department of Functional Anatomy, Academic Centre for Dentistry Amsterdam (ACTA), Universiteit van Amsterdam and Vrije Universiteit, Meibergdreef 15, 1105 AZ Amsterdam, The Netherlands

^* corresponding author, t.m.vaneijden{at}amc.uva.nl

	ABSTRACT

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The trabecular bone of the mandibular condyle is structurally anisotropic and heterogeneous. We hypothesized that its apparent elastic moduli are also anisotropic and heterogeneous, and depend on trabecular density and orientation. Eleven condyles were scanned with a micro-CT system. Volumes of interest were selected for the construction of finite element models. We simulated compressive and shear tests to determine the principal mechanical directions and the apparent elastic moduli. Compressive moduli were relatively large in directions acting in the sagittal plane, and small in the mediolateral direction. The degree of mechanical anisotropy ranged from 4.7 to 10.8. Shear moduli were largest in the sagittal plane and smallest in the transverse plane. The magnitudes of the moduli varied with the condylar region and were proportional to the bone volume fraction. Furthermore, principal mechanical direction correlated significantly with principal structural direction. It was concluded that variation in trabecular structure coincides with variation in apparent mechanical properties.

KEY WORDS: mandible • condyle • trabecular bone • finite element analysis • stiffness

	INTRODUCTION

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The trabecular bone of the mandibular condyle is structurally anisotropic and heterogeneous. It is composed of sagittally oriented plate-like trabeculae, and the three-dimensional arrangement of trabeculae varies regionally within the condyle (Giesen and Van Eijden, 2000). The architecture of the trabecular bone (i.e., the density and direction of the trabeculae), in combination with the material properties of the bone tissue, determines its apparent mechanical properties (e.g., stiffness and strength) and, consequently, the stresses and strains occurring during loading.

Because of the anisotropic and heterogeneous structure of bone, it can be expected that its apparent mechanical properties are also anisotropic and heterogeneous. For the Young’s moduli, such an anisotropy has indeed been found by experimental compression tests (Giesen et al., 2001; Van Ruijven et al., 2003). However, these measurements have limitiations. For example, it is impossible to harvest specimens of adequate sizes at various locations.

Since the introduction of modern imaging techniques, such as microcomputed tomography (micro-CT), detailed three-dimensional reconstructions of the trabecular structure can be made. These reconstructions can be converted into micromechanical finite element models. By simulating different loading situations, one can calculate all elastic properties and principal mechanical directions (Van Rietbergen et al., 1996) of the reconstructed bone specimens (Hollister et al., 1994; Van Rietbergen et al., 1995). The finite element method thus provides a powerful tool for the examination of elastic properties throughout the condyle.

Thus far, no information is available on the magnitudes and principal mechanical directions of the apparent Young’s and shear moduli of the trabecular bone in the mandibular condyle. In addition, no information is available on how these magnitudes and directions depend on gross trabecular structure (density and direction), and the extent to which they differ between and among various regions of the condyle. Previous investigations of mechanical properties have focused on the compressive moduli, measured in supero-inferior and mediolateral directions (Giesen et al., 2001, 2003; Van Eijden et al., 2004). No information could be obtained about the principal directions of the moduli relative to the entire condyle. In addition, these measurements allowed for a comparison only between the medial and lateral halves of the condyle, and not between superior and inferior regions.

In the present study, we hypothesized that compressive and shear moduli in the trabecular bone of the condyle are anisotropic and heterogeneous. It was also hypothesized that compressive and shear moduli depend primarily on trabecular density and orientation. To test these hypotheses, we: (1) determined principal directions and magnitudes of moduli and compared these directions and magnitudes between various mediolateral and supero-inferior regions of the condyle; and (2) examined how these directions and magnitudes were related to, respectively, the direction and density of the trabecular structure.

	MATERIALS & METHODS

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Condyle Preparation
Eleven mandibular condyles (7 left, 4 right) were obtained from embalmed human cadavers (three male, eight female; mean age ± SD, 72.6 ± 11.2 yrs; range, 56 to 89 yrs). The numbers of teeth were (in the upper jaw) 9.6 ± 3.5 and (in the lower jaw) 11.9 ± 2.8. The use of the condyles conformed to a written protocol that was reviewed and approved by the Department of Anatomy and Embryology of the Academic Medical Center of the University of Amsterdam. The preparation of condyles and the definition of their position relative to a skull-related Cartesian coordinate system have been extensively described in previous work (Van Eijden et al., 1997; Giesen and Van Eijden, 2000). The y-axis of the coordinate system was perpendicular to the Frankfort horizontal plane; the x- and z-axes were parallel to this plane (Fig. 1).

View larger version (89K): [in this window] [in a new window]   Figure 1. A schematic overview of the different steps in the analysis. A condyle is separated from a human mandible. The condyle was scanned in a micro-CT system, after which 4 volumes of interest were selected and used for the construction of finite element models.

Rectangular volumes of interest, containing trabecular bone, were selected in the 4 quadrants of each condyle: superolateral, superomedial, inferolateral, and inferomedial (Fig. 1). The average volume size was 105 x 104 x 101 voxels.

Bone architectural parameters were calculated for each volume of interest (Hildebrand and Rüegsegger, 1997). To determine the direction and structural anisotropy of the trabecular structure, we applied the mean intercept length method (Harrigan and Mann, 1984). With these measurements, the 3 principal directions of the trabecular structure (H₁, H₂, and H₃) can be obtained and fitted to an ellipsoid with axis lengths H₁ > H₂ > H₃. The method assumes orthogonality for these axes. The degree of structural anisotropy (DA_MIL) was defined by H₁/H₃, H₁/H₂, and H₂/H₃. To determine the direction of the trabecular structure, we used the projections of H₁ on the sagittal xy-plane and frontal yz-plane (Fig. 1) to calculate angles _MIL and _MIL, respectively, relative to the y-axis. The bone architectural parameters were calculated with morphometric software (Software Version 3.2, Scanco Medical AG, Bassersdorf, Switzerland).

Finite Element Model
The apparent linear elastic properties of the trabecular structure in the volumes of interest were calculated by means of a finite element program (Van Rietbergen et al., 1995). Each volume was represented by a finite element model (Fig. 1) with its voxels meshed to 8-noded brick elements (size, 34 µm). The average number of elements in the models was 160,000. The bone tissue was assumed to be isotropic, with a stiffness of 10 GPa and a Poisson ratio of 0.3 (Van Rietbergen et al., 1995; Van Ruijven et al., 2003). Six FE analyses were performed for each volume of interest, 3 compressive tests and 3 shear tests. From the results of these analyses, the complete elastic stiffness matrix was calculated (Hollister et al., 1994; Van Rietbergen et al., 1996). Using a numerical optimization procedure, we calculated the principal mechanical directions (Van Rietbergen et al., 1996), and the Young’s moduli (E_1,2,3) and shear moduli (G_12,23,31) were calculated relative to these directions. We verified that deviations from orthogonality were negligible. The indices 1, 2, and 3 refer to the principal mechanical directions. Together, these directions constitute an orthogonal coordinate system. The Young’s moduli E_1,2,3 define the resistance against compression in the 1-, 2-, and 3-directions. The shear moduli G_12,23,31 define the resistance against shearing in planes through the 1- and 2-axes, the 2- and 3-axes, and the 3- and 1-axes, respectively. Indices were sorted such that E₁ >E₂ > E₃. The degree of mechanical anisotropy (DA_E) was defined by E₁/E₃, E₁/E₂, and E₂/E₃. To determine the orientation of the principal mechanical directions relative to the coordinate system of the condyle, we projected the first principal direction on the sagittal and frontal plane to calculate angles _E and _E, respectively, relative to the y-axis. The simulations were performed with finite element software (Software Revision v1.02, Scanco Medical AG, Zürich, Switzerland).

Statistical Analysis
We used analyses of variance for repeated measures to test for regional differences. When ANOVA indicated a significant difference, we carried out post hoc tests to establish between which pairs of regions significant differences were present. All tests were conducted by means of the General Linear Model for repeated measures. We conducted regression analyses to determine the relationships between bone volume fraction (bone volume/total volume) and Young’s and shear moduli for each of the principal mechanical directions. For this purpose, we used power functions to fit, for all volumes of interest, the moduli vs. bone volume fraction. We used linear regression analyses to determine the relationship between the orientation of the principal mechanical direction and the orientation of the principal structural direction; for this purpose, angles _E vs. _MIL and _E vs. _MIL were compared. We used SPSS 11.0 software (SSPS Inc.) to perform the statistical analyses. Since SPPS has no methods for calculating means and standard deviations for angular data, we used custom-made software for this purpose.

	RESULTS

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Both structural and mechanical parameters showed a large variation (Table). The structure of the trabecular bone in the condyle was anisotropic (H₁/H₃; DA_MIL > 2), as illustrated by the mean-intercept-length ellipsoids constructed from the principal structural directions (Fig. 2). The first principal direction (H₁) deviated slightly from the vertical axis (_MIL < 11°, _MIL < 5°). In the medial and lateral superior regions, they were diverging to the medial and lateral sides of the condyle, respectively; in the two inferior regions, they were more vertical and parallel to each other (Fig. 2). The second (H₂) and third (H₃) principal directions pointed anteroposteriorly and mediolaterally, respectively. There was also a marked structural heterogeneity. For example, in the superolateral region, bone volume fraction was significantly larger than in the inferomedial region, which was due to more and thicker trabeculae and a smaller separation between these trabeculae (data not shown). Furthermore, inferiorly in the condyle, structural anisotropy was larger than superiorly.

View larger version (28K): [in this window] [in a new window]   Figure 2. Anterior (upper panels) and lateral (lower panels) views of plots of ellipsoids of mean intercept lengths and Young’s moduli. The axes of the ellipsoids correspond to 3 principal directions. The distance from the surface to the center of the ellipsoid depicts the magnitude of mean intercept length or Young’s modulus. The three-dimensional orientation of the ellipsoids is emphasized by the meridians. Ellipsoids were constructed with the average H1, H2, and H3, and the average E1, E2, and E3 (n = 11; see Table for means and SD values). Differences in the magnitude of the mechanical ellipsoids are primarily related to differences in bone volume fractions (compare superolateral and inferomedial regions). Differences in the magnitudes of the principal directions are related to the amount of structural and mechanical anisotropy. Since the mechanical anisotropy (E1/E3) is larger than the structural anisotropy (H1/H3), the Young’s moduli ellipsoids are flatter than the mean intercept length ellipsoids.

The first and second principal mechanical directions were in a plane that deviated slightly (_E < 5°) from the sagittal plane (Fig. 2, frontal view). The flat shape (frontal view) of the ellipsoids of the Young’s moduli indicates that resistance against compression was relatively small in the mediolateral direction. The round shape (lateral view) indicates that resistance was relatively large along directions acting in the sagittal plane. Resistance against shear was also the largest in the sagittal plane (G₁₂, range 178–260 MPa), and was relatively small in the transverse (G₂₃, range 82–136) and frontal planes (G₁₃, range 91–165). The magnitudes of the Young’s and shear moduli varied significantly with the condylar region. The largest moduli were found in the superolateral region of the condyle, and the smallest ones in the inferomedial region. The degree of mechanical anisotropy (E₁/E₃) was significantly larger (p < 0.05) in the inferior than in the superior region. The orientations of the principal mechanical directions in the various regions showed a remarkable resemblance and correlated significantly with those of the principal structural directions (Fig. 2).

The relationship between the density and orientation of the bone and the various moduli and their principal directions is shown in Fig. 3. The stiffnesses correlated significantly (adjusted R² > 0.8, p < 0.001) with the bone volume fraction (Fig. 3A). This dependency differed for the various principal directions. Consequently, the degree of anisotropy depended on the bone density, i.e., it decreased with an increase in bone density. The orientation of the trabecular structure correlated significantly (angle —adjusted R² = 0.67, p < 0.001; angle —adjusted R² = 0.94, p < 0.001) with the principal mechanical direction (Fig. 3B).

View larger version (28K): [in this window] [in a new window]   Figure 3. Relationships between density and orientation of the trabecular structure and the magnitudes of the various moduli and their principal mechanical directions. (A) Relation between bone volume fraction (BV/TV) and Young’s (E1,2,3) and shear moduli (G12,23,31) relative to the 3 principal mechanical directions. (B) Relation between principal structural direction (angles MIL and MIL) and principal mechanical direction (angles E and E). For each graph, n = 44.

	DISCUSSION

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The first and second principal mechanical directions were in the sagittal plane, while the third principal mechanical direction was oriented mediolaterally. E₁ and E₂ were relatively large compared with E₃. This difference is reflected by the flat shape of the ellipsoids of the Young’s moduli (Fig. 2). The rounded shape of the ellipsoids in the sagittal plane was due to the relatively small difference between E₁ and E₂, and to the fact that they were not always pointing in the same direction (see large SD value of angle _E). This shape implies that, on average, the trabecular bone of the condyle tends to be mechanically transversely isotropic. Obviously, this is due to the structure of the bone, with plates and rods that are oriented sagittally and mediolaterally, respectively (Giesen and Van Eijden, 2000). It should be realized that, within these plates, there is variation in the orientation of the principal directions.

It must be emphasized that the present study concerns the apparent moduli and structural anisotropy of gross volumes of trabeculae and does not reveal anything about the properties of the bone tissue within individual trabeculae. The results of a recent study (Van Eijden et al., 2004) suggest that the bone tissue stiffness of the mediolaterally oriented rods is about 15% larger than that of the sagitally oriented plates. In the present study, the bone tissue stiffness was assumed to be isotropic. If differences in tissue stiffness would have been taken into account, the apparent mechanical anisotropy would have been slightly smaller than those predicted in the present study.

The plate-like trabecular structure can be considered to be optimal to sustain the majority of joint forces applied to the condyle during jaw movements (Koolstra and Van Eijden, 2005). The small Young’s moduli (E₃) found in the mediolateral direction are probably related to the relatively small stresses that occur in the mediolateral direction during loading of the condyle (Van Ruijven et al., 2002). This anisotropy also implies that the trabecular structure is less capable of sustaining loads in the mediolateral direction than in the supero-inferior and anteroposterior directions. This is supported by the relatively high resistance against shear that was found for the sagittal plane.

The degree of structural anisotropy (H₁/H₃) was larger in the inferior than in the superior region, indicating that, in the inferior regions of the condyle, relatively fewer trabeculae have a mediolateral direction. The same supero-inferior difference was found for the degree of mechanical anisotropy (E₁/E₃). We also found a higher bone density in the superior regions than in the inferior regions, and, concomitantly, the stiffnesses were higher there. These higher stiffnesses might be required, since it is conceivable that these superior regions play a more prominent role in transferring and distributing the loads acting on the subchondral cortical bone, below the joint surface, to the cortical envelope of the mandibular neck. Similarly, the principal mechanical directions in the superomedial and superolateral regions of the condyle might be optimal, since they were directed in slightly medial and lateral directions, respectively, which is more or less perpendicular to the articular joint surface. The thin articular surface seems to be supported by trabeculae oriented perpendicular to this surface (Giesen and Van Eijden, 2000).

The moduli increased significantly with bone volume fraction (Fig. 3A). In addition, the amount of increase differed between the principal directions. As a consequence, the degree of anisotropy (E₁/E₃) increased with a decrease in bone density. This implies that bone loss has a lesser effect on the "strength" of the sagittally oriented plates than on the more mediolaterally oriented rod-like trabeculae. In a previous study (Van Ruijven et al., 2005), it was found that bone loss coincided with a deterioration of these plates.

We conclude that variation in structure of the trabecular bone in the condyle coincides with variation in mechanical properties. The magnitudes and directions of elastic moduli seem to be an optimal adaptation in sustaining and transferring loads that act on the condyle.

	ACKNOWLEDGMENTS

 
We are grateful to Irene Aartman for statistical advice, and to Jan Harm Koolstra and Geerling Langenbach for their comments on the manuscript. This work was sponsored by the National Computing Facilities Foundation (NCF) for the use of supercomputing facilities. This research was institutionally supported by the Inter-University Research School of Dentistry, through the Academic Centre for Dentistry Amsterdam. We thank the Academic Computer Services Amsterdam for the use of their technical support.

Received April 28, 2005; Last revision September 2, 2005; Accepted September 16, 2005

	REFERENCES

TOP ABSTRACT INTRODUCTION MATERIALS & METHODS RESULTS DISCUSSION REFERENCES

 
Giesen EB, van Eijden TM (2000). The three-dimensional cancellous bone architecture of the human mandibular condyle. J Dent Res 79:957–963.[Abstract/Free Full Text]

Giesen EB, Ding M, Dalstra M, van Eijden TM (2001). Mechanical properties of cancellous bone in the human mandibular condyle are anisotropic. J Biomech 34:799–803.[ISI][Medline]

Giesen EB, Ding M, Dalstra M, van Eijden TM (2003). Architectural measures of the cancellous bone of the mandibular condyle identified by principal components analysis. Calcif Tissue Int 73:225–231.[ISI][Medline]

Harrigan TP, Mann RW (1984). Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. J Mater Sci 19:761–767.

Hildebrand T, Rüegsegger P (1997). A new method for the model-independent assessment of thickness in three-dimensional images. J Microsc 185:67–75.

Hollister SJ, Brennan JM, Kikuchi N (1994). A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stress. J Biomech 27:433–444.[ISI][Medline]

Koolstra JH, van Eijden TMGJ (2005). Combined finite-element and rigid-body analysis of human jaw joint dynamics. J Biomech 38:2431–2439.[ISI][Medline]

van Eijden TM, Korfage JA, Brugman P (1997). Architecture of the human jaw-closing and jaw-opening muscles. Anat Rec 248:464–474.[Medline]

van Eijden TM, van Ruijven LJ, Giesen EB (2004). Bone tissue stiffness in the mandibular condyle is dependent on the direction and density of the cancellous structure. Calcif Tissue Int 75:502–508.[ISI][Medline]

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 28:69–81.[ISI][Medline]

van Rietbergen B, Odgaard A, Kabel J, Huiskes R (1996). Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture. J Biomech 29:1653–1657.[ISI][Medline]

van Ruijven LJ, Giesen EB, van Eijden TM (2002). Mechanical significance of the trabecular microstructure of the human mandibular condyle. J Dent Res 81:706–710.[Abstract/Free Full Text]

van Ruijven LJ, Giesen EB, Farella M, van Eijden TM (2003). Prediction of mechanical properties of the cancellous bone of the mandibular condyle. J Dent Res 82:819–823.[Abstract/Free Full Text]

van Ruijven LJ, Giesen EB, Mulder L, Farella M, van Eijden TM (2005). The effect of bone loss on rod-like and plate-like trabeculae in the cancellous bone of the mandibular condyle. Bone 36:1078–1085.[Medline]

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