Prediction of Mechanical Properties of the Cancellous Bone of the Mandibular Condyle

Young's modulus of trabecular bone at the tissue level: A review

The tissue-level Young's modulus of trabecular bone is important for detailed mechanical analysis of bone and bone-implant mechanical interactions. However, the heterogeneity and small size of the trabecular struts complicate an accurate determination. Methods such as micro-mechanical testing of single trabeculae, ultrasonic testing, and nanoindentation have been used to estimate the trabecular Young's modulus. This review summarizes and classifies the trabecular Young's moduli reported in the literature. Information on species, anatomic site, and test condition of the samples has also been gathered. Advantages and disadvantages of the different methods together with recent developments are discussed, followed by some suggestions for potential improvement for future work. In summary, this review provides a thorough introduction to the approaches used for determining trabecular Young's modulus, highlights important considerations when applying these methods and summarizes the reported Young's modulus for follow-up studies on trabecular properties.

STATEMENT OF SIGNIFICANCE

The spongy trabecular bone provides mechanical support while maintaining a low weight. A correct measure of its mechanical properties at the tissue level, i.e. at a single-trabecula level, is crucial for analysis of interactions between bone and implants, necessary for understanding e.g. bone healing mechanisms. In this study, we comprehensively summarize the Young's moduli of trabecular bone estimated by currently available methods, and report their dependency on different factors. The critical review of different methods with recent updates is intended to inspire improvements in estimating trabecular Young's modulus. It is strongly suggested to report detailed information on the tested bone to enable statistical analysis in the future.

Structural and Mechanical Properties of Mandibular Condylar Bone

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.

Large-scale finite element analysis of human cancellous bone tissue micro computer tomography data: a convergence study

The complex geometry of cancellous bone tissue makes it difficult to generate finite element (FE) models. Only a few studies investigated the convergence behavior at the tissue scale using Cartesian meshes. However, these studies were not conducted according to an ideal patch test and the postelastic convergence behavior was not reported. In this study, the third principal strain and stress, and the displacement obtained from human micro finite element (microFE) models of lower resolutions were compared against the model of 19.5 μm as a reference, representing the original spatial resolution of microCT data. Uni-axial compression simulations using both linear-elastic and nonlinear constitutive equations were performed. The results showed a decrease in percentage difference in all three values as the element size decreased, with the displacement converging the fastest among the three. Simulations carried out using a nonlinear constitutive equation however, failed to show convergence for the third principal strains and stresses. It was concluded that at the tissue level, Cartesian meshes of human cancellous bone tissue were able to reach a converged solution in all three parameters investigated for linear simulation and only in displacement for nonlinear simulation. These parameters can be used as references in the future for studies in local biomechanical behavior of human cancellous bone tissues with linear simulation. The convergence behavior for human cancellous bone tissue using nonlinear constitutive equations needs further investigation.

Regional variation of bone tissue properties at the human mandibular condyle

The temporomandibular joint (TMJ) bears different types of static and dynamic loading during occlusion and mastication. As such, characteristics of mandibular condylar bone tissue play an important role in determining the mechanical stability of the TMJ under the macro-level loading. Thus, the objective of this study was to examine regional variation of the elastic, plastic, and viscoelastic mechanical properties of human mandibular condylar bone tissue using nanoindentation. Cortical and trabecular bone were dissected from mandibular condyles of human cadavers (9 males, 54-96 years). These specimens were scanned using microcomputed tomography to obtain bone tissue mineral distribution. Then, nanoindentation was conducted on the surface of the same specimens in hydration. Plastic hardness (H) at a peak load, viscoelastic creep (Creep/Pmax), viscosity (η), and tangent delta (tan δ) during a 30 second hold period, and elastic modulus (E) during unloading were obtained by a cycle of indentation at the same site of bone tissue. The tissue mineral and nanoindentation parameters were analyzed for the periosteal and endosteal cortex, and trabecular bone regions of the mandibular condyle. The more mineralized periosteal cortex had higher mean values of elastic modulus, plastic hardness, and viscosity but lower viscoelastic creep and tan δ than the less mineralized trabecular bone of the mandibular condyle. These characteristics of bone tissue suggest that the periosteal cortex tissue may have more effective properties to resist elastic, plastic, and viscoelastic deformation under static loading, and the trabecular bone tissue to absorb and dissipate time-dependent viscoelastic loading energy at the TMJ during static occlusion and dynamic mastication.

Multi-scale modelling of elastic moduli of trabecular bone

We model trabecular bone as a nanocomposite material with hierarchical structure and predict its elastic properties at different structural scales. The analysis involves a bottom-up multi-scale approach, starting with nanoscale (mineralized collagen fibril) and moving up the scales to sub-microscale (single lamella), microscale (single trabecula) and mesoscale (trabecular bone) levels. Continuum micromechanics methods, composite materials laminate theory and finite-element methods are used in the analysis. Good agreement is found between theoretical and experimental results.

Trabecular bone structure in the mandibular condyles of gouging and nongouging platyrrhine primates

The relationship between mandibular form and biomechanical function is a topic of significant interest to morphologists and paleontologists alike. Several previous studies have examined the morphology of the mandible in gouging and nongouging primates as a means of understanding the anatomical correlates of this feeding behavior. The goal of the current study was to quantify the trabecular bone structure of the mandibular condyle of gouging and nongouging primates to assess the functional morphology of the jaw in these animals. High-resolution computed tomography scan data were collected from the mandibles of five adult common marmosets (Callithrix jacchus), saddle-back tamarins (Saguinus fuscicollis), and squirrel monkeys (Saimiri sciureus), respectively, and various three-dimensional morphometric parameters were measured from the condylar trabecular bone. No significant differences were found among the taxa for most trabecular bone structural features. Importantly, no mechanically significant parameters, such as bone volume fraction and degree of anisotropy, were found to vary significantly between gouging and nongouging primates. The lack of significant differences in mechanically relevant structural parameters among these three platyrrhine taxa may suggest that gouging as a habitual dietary behavior does not involve significantly higher loads on the mandibular condyle than other masticatory behaviors. Alternatively, the similarities in trabecular architecture across these three taxa may indicate that trabecular bone is relatively unimportant mechanically in the condyle of these primates and therefore is functionally uninformative.

Effects of condylar elastic properties to temporomandibular joint stress

Mandibular condyle plays an important role in the growth and reconstruction of the temporomandibular joint (TMJ). We aimed to obtain orthotropic elastic parameters of the condyle using a continuous-wave ultrasonic technique and to observe the effects of condylar elastic parameters on stress distribution of the TMJ using finite element analysis (FEA). Using the ultrasonic technique, all nine elastic parameters were obtained, which showed that the mandibular condyle was orthotropic. With the condyle defined as orthotropic, the occlusal stress was transferred fluently and uniformly from the mandible to the TMJ. The stress distribution in the isotropic model showed stepped variation among different anatomical structures with higher stress values in the cartilage and condyle than in the orthotropic model. We conclude that anisotropy has subtle yet significant effects on stress distribution of the TMJ and could improve the reality of simulations.

Biomechanical effect of mineral heterogeneity in trabecular bone

Due to daily loading, trabecular bone is subjected to deformations (i.e., strain), which lead to stress in the bone tissue. When stress and/or strain deviate from the normal range, the remodeling process leads to adaptation of the bone architecture and its degree of mineralization to effectively withstand the sustained altered loading. As the apparent mechanical properties of bone are assumed to depend on the degree and distribution of mineralization, the goal of the present study was examine the influences of mineral heterogeneity on the biomechanical properties of trabecular bone in the human mandibular condyle. For this purpose nine right condyles from human dentate mandibles were scanned and evaluated with a microCT system. Cubic regional volumes of interest were defined, and each was transformed into two different types of finite element (FE) models, one homogeneous and one heterogeneous. In the heterogeneous models the element tissue moduli were scaled to the local degree of mineralization, which was determined using microCT. Compression and shear tests were simulated to determine the apparent elastic moduli in both model types. The incorporation of mineralization variation decreased the apparent Young's and shear moduli by maximally 21% in comparison to the homogeneous models. The heterogeneous model apparent moduli correlated significantly with bone volume fraction and degree of mineralization. It was concluded that disregarding mineral heterogeneity may lead to considerable overestimation of apparent elastic moduli in FE models.

Regional variations in mineralization and strain distributions in the cortex of the human mandibular condyle

The strain (i.e. deformation) history influences the degree of mineralization of cortical bone (DMB) as well as its osteonal microstructure. This study aimed to examine the relationships of stress and strain distributions with the variations in DMB and the osteonal orientations in the cortical bone of the human mandibular condyle. It was hypothesized that strains are inversely proportional to local DMB and that the principal strains are oriented parallel to the osteons. To test this, ten human mandibular condyles were scanned in a microCT system. Finite element models were created in order to simulate static clenching. Within each condyle, 18 volumes of interest were selected to analyze regional differences in DMB, stress and strains. Subchondral bone showed a lower equivalent strain (2652+/-612 muepsilon) as compared to the anterior (p=0.030) and posterior cortex (p=0.007) and was less mineralized. Contrary to our hypothesis, the results show that strains correlated positively with regional variations in DMB (r=0.750, p<0.001). In the anterior and the posterior cortex, the first principal strain was parallel to the cortical surface and oriented supero-inferiorly with a fan-like shape. In subchondral bone, the first and the second principal strain were parallel to the surface and oriented antero-posteriorly and medio-laterally, respectively. It was concluded that the strain distributions, by themselves, cannot explain the regional differences found in DMB. In agreement with our second hypothesis, the orientation of the osteonal network of the mandibular condyle was closely related to the strain orientations. The results of this study suggest that the subchondral and the cortical bone are structured to ensure an optimal load distribution within the mandibular condyle and have a different mechanical behaviour. Subchondral bone plays a major role in the transmission of the strains to the anterior and posterior cortex, while these ensure an optimal transmission of the strains within the condylar neck and, eventually, to the mandibular ramus.

The Influence of Mineralization on Intratrabecular Stress and Strain Distribution in Developing Trabecular Bone

The load-transfer pathway in trabecular bone is largely determined by its architecture. However, the influence of variations in mineralization is not known. The goal of this study was to examine the influence of inhomogeneously distributed degrees of mineralization (DMB) on intratrabecular stresses and strains. Cubic mandibular condylar bone specimens from fetal and newborn pigs were used. Finite element models were constructed, in which the element tissue moduli were scaled to the local DMB. Disregarding the observed distribution of mineralization was associated with an overestimation of average equivalent strain and underestimation of von Mises equivalent stress. From the surface of trabecular elements towards their core the strain decreased irrespective of tissue stiffness distribution. This indicates that the trabecular elements were bent during the compression experiment. Inhomogeneously distributed tissue stiffness resulted in a low stress at the surface that increased towards the core. In contrast, disregarding this tissue stiffness distribution resulted in high stress at the surface which decreased towards the core. It was concluded that the increased DMB, together with concurring alterations in architecture, during development leads to a structure which is able to resist increasing loads without an increase in average deformation, which may lead to damage.

Direct measurement of trabecular bone anisotropy using directional fractal dimension and principal axes of inertia

OBJECTIVE

Precise in vivo measurement of the trabecular bone's mechanical properties is very important for endosseous dental implant treatment and design in clinical practice. The fractal structure of trabecular bone shows directional anisotropy of the architecture, as is shown in most biological fractals. To analyze the anisotropy of the trabecular bone, the fractal geometry technique was applied to 2-dimensional plain radiographs.

STUDY DESIGN

The power spectrum was used to calculate the fractal dimensions (FD) of the trabecular bone. The FDs calculated as a function of orientation yielded the fractal information reflecting the spatial characteristics of the trabecular bone in each direction. A polar plot of directional FDs was defined as an ellipse of inertia. The principal loading direction in a local region of the trabecular bone was determined from the minimum moment of inertia for the ellipse of FDs. The anisotropy was calculated directly as the ratio of the 2 principal moments of inertia from the ellipse.

RESULTS

The anisotropies were measured for radiographs from the angle and incisor region of 21 human mandibles based on the principal axes of inertia and the best-fitting ellipse. The anisotropy of the angle region was significantly greater than that of the incisor region of the mandibles.

CONCLUSION

The method using directional FDs as determined by the principal axis of inertia measures the anisotropy directly, using 2-dimensional plain radiographs. It can quantify the anisotropy of trabecular bone in vivo. The investigation can be applied to the analysis of the relationships between in vivo 2-dimensional parameters and 3-dimensional mechanical properties, which enables us to predict the bone mechanical properties such as strength in vivo in various regions of the mandible.

Comparison of trabecular bone anisotropies based on fractal dimensions and mean intercept length determined by principal axes of inertia

The mechanical quality of trabecular bone depends on both its stiffness and its strength characteristics, which can be predicted indirectly by the combination of bone volume fraction and architectural anisotropy. To analyze the directional anisotropy of the trabecular bone, we applied the fractal geometry technique to plain radiographs. The anisotropy of the bone was quantified from an ellipse, based on the directional fractal dimensions (FD), by the principal axes of inertia. The anisotropies based on the FD were compared with those determined using the common method of mean intercept length (MIL). The directional FD gave the fractal information obtained from a projection along the MIL orientation. For this reason, the spatial variations associated with the bone length in any direction were manifested in a related frequency band of the power spectrum determined along the direction. The directional FD and MIL plots were highly correlated, although they originated from quite different geometries. Of the angle, premolar, and incisor regions of the human mandible, the anisotropies calculated using both FD and MIL showed the highest correlation in the trabecular bone of the angle region. The method using directional FDs as determined by the principal axis of inertia measures the anisotropy directly, using two-dimensional plain radiographs. This kind of method will be a useful to provide better estimates of bone quality in vivo compared with the density measurements alone, especially for the indirect diagnosis of jawbone quality in dental clinics.

Variations in mineralization affect the stress and strain distributions in cortical and trabecular bone

The mechanical properties of bone depend largely on its degree and distribution of mineralization. The present study analyzes the effect of an inhomogeneous distribution of mineralization on the stress and strain distributions in the human mandibular condyle during static clenching. A condyle was scanned with a micro-CT scanner to create a finite element model. For every voxel the degree of mineralization (DMB) was determined from the micro-CT scan. The Young's moduli of the elements were calculated from the DMB using constant, linear, and cubic relations, respectively. Stresses, strains, and displacements in cortical and trabecular bone, as well as the condylar deformation (extension along the antero-posterion axis) and compliance were compared. Over 90% of the bone mineral was located in the cortical bone. The DMB showed large variations in both cortical bone (mean: 884, SD: 111 mg/cm(3)) and trabecular bone (mean: 738, SD: 101 mg/cm(3)). Variations of the stresses and the strains were small in cortical bone, but large in trabecular bone. In the cortical bone an inhomogeneous mineral distribution increased the stresses and the strains. In the trabecular bone, however, it decreased the stresses and increased the strains. Furthermore, the condylar compliance remained relatively constant, but the condylar deformation doubled. It was concluded that neglect of the inhomogeneity of the mineral distribution results in a large underestimation of the stresses and strains of possibly more than 50%. The stiffness of trabecular bone strongly influences the condylar deformation. Vice versa, the condylar deformation largely determines the magnitude of the strains in the trabecular bone.

Biomechanical consequences of developmental changes in trabecular architecture and mineralization of the pig mandibular condyle

The purpose of the present study was to examine the changes in apparent mechanical properties of trabecular bone in the mandibular condyle during fetal development and to investigate the contributions of altering architecture, and degree and distribution of mineralization to this change. Three-dimensional, high-resolution micro-computed tomography (microCT) reconstructions were utilized to assess the altering architecture and mineralization during development. From the reconstructions, inhomogeneous finite element models were constructed, in which the tissue moduli were scaled to the local degree of mineralization of bone (DMB). In addition, homogeneous models were devised to study the separate influence of architectural and DMB changes on apparent mechanical properties. It was found that the bone structure became stiffer with age. Both the mechanical and structural anisotropies pointed to a rod-like structure that was predominantly oriented from anteroinferior to posterosuperior. Resistance against shear, also increasing with age, was highest in the sagittal plane. The reorganization of trabecular elements, which occurred without a change in bone volume fraction, contributed to the increase in apparent stiffness. The increase in DMB, however, contributed more dominantly. Incorporating the observed inhomogeneous distribution of mineralization decreased the apparent stiffness, but increased the mechanical anisotropy. This denotes that there might be a directional dependency of the DMB of trabecular elements, i.e. differently orientated trabecular elements might have different DMBs. In conclusion, the changes in DMB and its distribution are important to consider when studying mechanical properties during development and should be considered in other situations where differences in DMB are expected.

Degree and distribution of mineralization in the human mandibular condyle

The degree of mineralization of bone (DMB) in the mandibular condyle reflects the age and remodeling rate of the bone tissue. Quantification of DMB facilitates a better understanding of possible effects of adaptive remodeling on mineralization of the condyle and its possible consequences for its mechanical quality. We hypothesized differences in the degree and distribution of mineralization between trabecular and cortical bone and between various cortical regions. Microcomputed tomography was used to measure mineralization in 10 human mandibular condyles. Mean DMB was higher in cortical (1,045 mg hydroxyapatite/cm(3)) than in trabecular bone (857 mg/cm(3)) and differed significantly between cortical regions (anterior 987 mg/cm(3), posterior 1,028 mg/cm(3), subchondral 1,120 mg/cm(3)). The variation of DMB distribution was significantly larger in the anterior cortex than in the posterior and subchondral cortex, indicating a larger amount of heterogeneity of mineralization anteriorly. Within the cortical bone, DMB increased with the distance from the cortical canals to the periphery. Similarly, the DMB of trabecular bone increased with the distance from the surface of the trabeculae to their cores. It was concluded that the rate of remodeling differs between condylar trabecular and cortical bone and between cortical regions and that DMB is not randomly distributed across the bone. The difference in DMB between condylar cortical and trabecular bone suggests a large difference in Young's modulus.

A sensitive method for measuring spatial orientation in bone structures

OBJECTIVES

This article introduces the newly developed line frequency deviation (LFD) method for measuring the orientation of the trabecular structure and shows that it is more sensitive than the mean intercept length (MIL) method that is commonly used.

METHODS

The LFD method, which has been developed to measure the orientation of bone on two-dimensional X-ray images, was expanded to handle three-dimensional shapes. For the purpose of comparison, both the LFD and the MIL methods were applied to micro CT scans of 24 trabecular bone samples as well as to 24 simple synthetic samples. LFD and MIL values were calculated in various directions and collected in polar plots. Next, the anisotropy was quantified by calculating the coefficient of variation as well as by fitting ellipsoids through the plots.

RESULTS

The MIL method yielded smooth rather spherical ellipsoidal polar plots with almost no sensitivity for changes in structure. The LFD method yielded more slender polar plots and more sensitivity for geometrical changes. The LFD method yielded significantly more anistropy and larger variation in anisotropy.

CONCLUSIONS

The LFD method is a more sensitive descriptor of spatial orientation of bone structures than the MIL method.

Grape seed proanthocyanidins extract promotes bone formation in rat's mandibular condyle

We studied the effect of dietary supplementation with grape seed proanthocyanidins extract (GSPE) 3 mg added in 100 g high-calcium diet with a calcium content of 1697 mg 100 g(-1) on mandibular condyle bone debility, which was induced by a low-calcium diet. Forty Wistar male rats, 5 week old, were randomly divided into control (Co), low-calcium diet (LC), low-calcium/high-calcium diet (LCH), and low-calcium/high-calcium with supplementary GSPE diet (LCHG) groups for 6 wk. Bone formation of the mandibular condyle was measured using peripheral quantitative computed tomography (pQCT). Significant differences were not seen among the four groups for body weight, measured weekly. The LCHG group scored significantly higher in cortical bone density, total bone cross-sectional area, cortical bone cross-sectional area, cortical bone mineral content, total bone density, total bone mineral content, and in the stress-strain index to the reference axis x when compared with the LCH group. We concluded that a high-calcium diet combined with GSPE supplementation is more effective in reversing mandibular condyle bone debility in rats than is a low-calcium diet, standard diet, or high-calcium diet alone.