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Structural and Mechanical Properties of Mandibular Condylar BoneDepartment of Functional Anatomy, Academic Centre for Dentistry Amsterdam (ACTA), Universiteit van Amsterdam and Vrije Universiteit, Meibergdreef 15, 1105 AZ Amsterdam, The Netherlands Correspondence: * corresponding author, t.m.vaneijden{at}amc.uva.nl
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
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.
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  ).
Micro-CT To obtain a three-dimensional representation of the bone structure, we used micro-CT (µCT 40, Scanco Medical AG, Bassersdorf, Switzerland). For an extensive description of the method, we refer to earlier work (Giesen and Van Eijden, 2000; Van Ruijven et al., 2002). The condyles were scanned at a resolution of 34 µm. Bone and marrow were separated by a fixed threshold.
Rectangular volumes of interest, containing trabecular bone, were selected in the 4 quadrants of each condyle: superolateral, superomedial, inferolateral, and inferomedial (Fig. 1
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 (DAMIL) 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
Finite Element Model
Statistical Analysis
Both structural and mechanical parameters showed a large variation (Table ). The structure of the trabecular bone in the condyle was anisotropic (H1/H3; DAMIL > 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.
The degree of mechanical anisotropy was significantly (p < 0.05) larger and showed a larger variation (E1/E3; DAE, range 4.65–10.83) than the degree of structural anisotropy (H1/H3; DAMIL, range 2.0–2.2). The Young’s moduli in the first principal direction (E1, range 415–685 MPa) were about 100–200 MPa larger than those in the second principal direction (E2, range 300–471 MPa), while they were relatively small in the third principal direction (E3, range 90–207 MPa).
The first and second principal mechanical directions were in a plane that deviated slightly (
The relationship between the density and orientation of the bone and the various moduli and their principal directions is shown in Fig. 3
This is the first study to report on the magnitudes and principal mechanical directions of Young’s and shear moduli of the trabecular bone in the human mandibular condyle. These moduli were anisotropic and depended on the location, confirming the hypothesis that the trabecular bone of the condyle is mechanically anisotropic and heterogeneous. We also found that the magnitude of the moduli increased with the bone volume fraction, and the amount of increase differed between the principal directions (Fig. 3A  ), confirming the hypothesis that the magnitude of the moduli depended on trabecular density and direction. Finally, we could confirm that the principal mechanical directions coincided with the principal structural directions (Fig. 3B), supporting the suggestion that principal mechanical directions are closely aligned to the direction of the trabecular structure.
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 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 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.
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 for publication April 28, 2005. Revision received September 2, 2005. Accepted for publication September 16, 2005.
Journal of Dental Research, Vol. 85, No. 1,
33-37 (2006)
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