Mechanics of cranial sutures during simulated cyclic loading

Previous computational and experimental analyses revealed that cranial sutures, fibrous joints between the bones, can reduce the strain experienced by the surrounding skull bones during mastication. This damping effect reflects the importance of including sutures in finite element (FE) analyses of the skull. Using the FE method, the behaviour of three suture morphologies of increasing complexity (butt-ended, moderate interdigitated, and complex interdigitated) during static loading was recently investigated, and the sutures were assumed to have linear elastic properties. In the current study, viscoelastic properties, derived from published experimental results of the nasofrontal suture of young pigs (Sus scrofa), are applied to the three idealised bone-suture models. The effects of suture viscoelasticity on the stress, strain, and strain energy in the models were computed for three different frequencies (corresponding to periods of 1, 10, and 100s) and compared to the results of a static, linear elastic analysis. The range of applied frequencies broadly represents different physiological activities, with the highest frequency simulating mastication and the lowest frequency simulating growth and pressure of the surrounding tissues. Comparing across all three suture morphologies, strain energy and strain in the suture decreased with the increase in suture complexity. For each suture model, the magnitude of strain decreased with an increase in frequency, and the magnitudes were similar for both the elastic and 1s frequency analyses. In addition, a viscous response is less apparent in the higher frequency analyses, indicating that viscous properties are less important to the behaviour of the suture during those analyses. The FE results suggest that implementation of viscoelastic properties may not be necessary for computational studies of skull behaviour during masticatory loading but instead might be more relevant for studies examining lower frequency physiological activities.     

Strain accommodation in the zygomatic arch of the pig: A validation study using digital speckle pattern interferometry and finite element analysis

It has been repeatedly suggested that mammalian cranial sutures act not only to allow growth but also to reduce the levels of strain experienced by the skull during feeding. However, because of the added complexity they introduce, sutures are rarely included in finite element (FE) models, despite their potential to influence strain results. Because sutures present different morphologies and with differing degrees of internal fusion, many different methods of modeling may be necessary to accurately measure strain environments. Alternatively, these variables may exert very little influence on the scale of a whole‐skull model. To validate suture modeling methods, four alternative ways of including a suture in 3D FE models of the pig zygomatic arch were considered and compared with ex vivo experimental data from digital speckle pattern interferometry (DSPI). The use of DSPI rather than traditional strain gauge techniques allows strain gradients around the suture as well as the motions of the two bones to be observed. Results show that the introduction of 3D elements assigned more compliant material properties than the surrounding bone, is the most effective way of modeling both morphologies of suture, both in tension and compression. However, models containing no suture are almost indistinguishable from these compliant suture models, beyond the high strain gradient immediately adjacent to the suture. Conversely, modeling the suture as an open break in the mesh, or with spring elements assigned suture properties, fails to reproduce the experiment. Thus, although a solid but flexible model of sutures is preferred, the similarity between these models and those without sutures tentatively suggests that such extra detail may be unnecessary in pigs if the behavior of the whole skull is of interest. J. Morphol., 2011. © 2011 Wiley‐Liss, Inc.     

A finite element analysis of masticatory stress hypotheses

Understanding how the skull transmits and dissipates forces during feeding provides insights into the selective pressures that may have driven the evolution of primate skull morphology. Traditionally, researchers have interpreted masticatory biomechanics in terms of simple global loading regimes applied to simple shapes (i.e., bending in sagittal and frontal planes, dorsoventral shear, and torsion of beams and cylinders). This study uses finite element analysis to examine the extent to which these geometric models provide accurate strain predictions in the face and evaluate whether simple global loading regimes predict strains that approximate the craniofacial deformation pattern observed during mastication. Loading regimes, including those simulating peak loads during molar chewing and those approximating the global loading regimes, were applied to a previously validated finite element model (FEM) of a macaque (Macaca fascicularis) skull, and the resulting strain patterns were compared. When simple global loading regimes are applied to the FEM, the resulting strains do not match those predicted by simple geometric models, suggesting that these models fail to generate accurate predictions of facial strain. Of the four loading regimes tested, bending in the frontal plane most closely approximates strain patterns in the circumorbital region and lateral face, apparently due to masseter muscle forces acting on the zygomatic arches. However, these results indicate that no single simple global loading regime satisfactorily accounts for the strain pattern found in the validated FEM. Instead, we propose that FE models replace simple cranial models when interpreting bone strain data and formulating hypotheses about craniofacial biomechanics.     

Improving the validation of finite element models with quantitative full-field strain comparisons

The techniques used to validate finite element (FE) models against experimental results have changed little during the last decades, even though the traditional approach of using single point measurements from strain gauges has major limitations: the strain distribution across the surface is not captured and the accurate determination of strain gauge positions on the model surface is difficult if the 3D surface topography of the bone surface is not measured. The full-field strain measurement technique of digital speckle pattern interferometry (DSPI) can overcome these problems, but the potential of this technique has not yet been fully exploited in validation studies. Here we explore new ways of quantifying and visualising the variation in strain magnitudes and orientations within and between repeated DSPI measurements as well as between the DSPI measurements and FEA results. We show that our approach provides a much more comprehensive and accurate validation than traditional methods. The measurement repeatability and the correspondence between measured and predicted strains vary to a great degree within and between measurement areas. The two models used in this study predict the measured strain directions and magnitudes surprisingly well considering that homogeneous and isotropic mechanical properties were assigned to the models. However, the full-field comparisons also reveal some discrepancies between measured and predicted strains that are most probably caused by inaccuracies in the models' geometries and the degree of simplification of the modelled material properties.     

Development of a Finite Element Model of Decompressive Craniectomy

Decompressive craniectomy (DC), an operation whereby part of the skull is removed, is used in the management of patients with brain swelling. While the aim of DC is to reduce intracranial pressure, there is the risk that brain deformation and mechanical strain associated with the operation could damage the brain tissue. The nature and extent of the resulting strain regime is poorly understood at present. Finite element (FE) models of DC can provide insight into this applied strain and hence assist in deciding on the best surgical procedures. However there is uncertainty about how well these models match experimental data, which are difficult to obtain clinically. Hence there is a need to validate any modelling approach outside the clinical setting. This paper develops an axisymmetric FE model of an idealised DC to assess the key features of such an FE model which are needed for an accurate simulation of DC. The FE models are compared with an experimental model using gelatin hydrogel, which has similar poro-viscoelastic material property characteristics to brain tissue. Strain on a central plane of the FE model and the front face of the experimental model, deformation and load relaxation curves are compared between experiment and FE. Results show good agreement between the FE and experimental models, providing confidence in applying the proposed FE modelling approach to DC. Such a model should use material properties appropriate for brain tissue and include a more realistic whole head geometry.     

Subject-specific finite element model of the pelvis: development, validation and sensitivity studies

A better understanding of the three-dimensional mechanics of the pelvis, at the patient-specific level, may lead to improved treatment modalities. Although finite element (FE) models of the pelvis have been developed, validation by direct comparison with subject-specific strains has not been performed, and previous models used simplifying assumptions regarding geometry and material properties. The objectives of this study were to develop and validate a realistic FE model of the pelvis using subject-specific estimates of bone geometry, location-dependent cortical thickness and trabecular bone elastic modulus, and to assess the sensitivity of FE strain predictions to assumptions regarding cortical bone thickness as well as bone and cartilage material properties. A FE model of a cadaveric pelvis was created using subject-specific computed tomography image data. Acetabular loading was applied to the same pelvis using a prosthetic femoral stem in a fashion that could be easily duplicated in the computational model. Cortical bone strains were monitored with rosette strain gauges in ten locations on the left hemipelvis. FE strain predictions were compared directly with experimental results for validation. Overall, baseline FE predictions were strongly correlated with experimental results (r2=0.824), with a best-fit line that was not statistically different than the line y=x (experimental strains = FE predicted strains). Changes to cortical bone thickness and elastic modulus had the largest effect on cortical bone strains. The FE model was less sensitive to changes in all other parameters. The methods developed and validated in this study will be useful for creating and analyzing patient-specific FE models to better understand the biomechanics of the pelvis.     

Assessment of the role of sutures in a lizard skull: a computer modelling study

Sutures form an integral part of the functioning skull, but their role has long been debated among vertebrate morphologists and palaeontologists. Furthermore, the relationship between typical skull sutures, and those involved in cranial kinesis, is poorly understood. In a series of computational modelling studies, complex loading conditions obtained through multibody dynamics analysis were imposed on a finite element model of the skull of Uromastyx hardwickii, an akinetic herbivorous lizard. A finite element analysis (FEA) of a skull with no sutures revealed higher patterns of strain in regions where cranial sutures are located in the skull. From these findings, FEAs were performed on skulls with sutures (individual and groups of sutures) to investigate their role and function more thoroughly. Our results showed that individual sutures relieved strain locally, but only at the expense of elevated strain in other regions of the skull. These findings provide an insight into the behaviour of sutures and show how they are adapted to work together to distribute strain around the skull. Premature fusion of one suture could therefore lead to increased abnormal loading on other regions of the skull causing irregular bone growth and deformities. This detailed investigation also revealed that the frontal-parietal suture of the Uromastyx skull played a substantial role in relieving strain compared with the other sutures. This raises questions about the original role of mesokinesis in squamate evolution.     

Characterization of craniofacial sutures using the finite element method

Characterizing the biomechanical behavior of sutures in the human craniofacial skeleton (CFS) is essential to understand the global impact of these articulations on load transmission, but is challenging due to the complexity of their interdigitated morphology, the multidirectional loading they are exposed to and the lack of well-defined suture material properties. This study aimed to quantify the impact of morphological features, direction of loading and suture material properties on the mechanical behavior of sutures and surrounding bone in the CFS. Thirty-six idealized finite element (FE) models were developed. One additional specimen-specific FE model was developed based on the morphology obtained from a µCT scan to represent the morphological complexity inherent in CFS sutures. Outcome variables of strain energy (SE) and von Mises stress (σ_vm) were evaluated to characterize the sutures’ biomechanical behavior. Loading direction was found to impact the relationship between SE and interdigitation index and yielded varied patterns of σ_vm in both the suture and surrounding bone. Adding bone connectivity reduced suture strain energy and altered the σ_vm distribution. Incorporating transversely isotropic material properties was found to reduce SE, but had little impact on stress patterns. High-resolution µCT scanning of the suture revealed a complex morphology with areas of high and low interdigitations. The specimen specific suture model results were reflective of SE absorption and σ_vm distribution patterns consistent with the simplified FE results. Suture mechanical behavior is impacted by morphologic factors (interdigitation and connectivity), which may be optimized for regional loading within the CFS.     

The effects of the periodontal ligament on mandibular stiffness: a study combining finite element analysis and geometric morphometrics

It is generally accepted that the periodontal ligament (PDL) plays a crucial role in transferring occlusal forces from the teeth to the alveolar bone. Studies using finite element analysis (FEA) have helped to better understand this role and show that the stresses and strains in the alveolar bone are influenced by whether and how PDL is included in FE models. However, when the overall distribution of stresses and strains in crania and mandibles are of interest, PDL is often not included in FE models, although little is known about how this affects the results. Here we study the effect of representing PDL as a layer of solid material with isotropic homogeneous properties in an FE model of a human mandible using a novel application of geometric morphometrics. The results show that the modelling of the PDL affects the deformation and thus strain magnitudes not only of the alveolar bone around the biting tooth, but that the whole mandible deforms differently under load. As a result, the strain in the mandibular corpus is significantly increased when PDL is included, while the strain in the bone beneath the biting tooth is reduced. These results indicate the importance of the PDL in FE studies. Thus we recommend that the PDL should be included in FE models of the masticatory apparatus, with tests to assess the sensitivity of the results to changes in the Young's modulus of the PDL material.     

Comparison of strain measurement in the mouse forearm using subject-specific finite element models,strain gaging,and digital image correlation

Mechanical loading in bone leads to the activation of bone-forming pathways that are most likely associated with a minimum strain threshold being experienced by the osteocyte. To investigate the correlation between cellular response and mechanical stimuli, researchers must develop accurate ways to measure/compute strain both externally on the bone surface and internally at the osteocyte level. This study investigates the use of finite element (FE) models to compute bone surface strains on the mouse forearm. Strains from three FE models were compared to data collected experimentally through strain gaging and digital image correlation (DIC). Each FE model was assigned subject-specific bone properties and consisted of one-dimensional springs representing the interosseous membrane. After three-point bending was performed on the ulnae and radii, moment of inertia was determined from microCT analysis of the bone region between the supports and then used along with standard beam analyses to calculate the Young’s modulus. Non-contact strain measurements from DIC were determined to be more suitable for validating numerical results than experimental data obtained through conventional strain gaging. When comparing strain responses in the three ulnae, we observed a 3–14% difference between numerical and DIC strains while the strain gage values were 37–56% lower than numerical values. This study demonstrates a computational approach for capturing bone surface strains in the mouse forearm. Ultimately, strains from these macroscale models can be used as inputs for microscale and nanoscale FE models designed to analyze strains directly in the osteocyte lacunae.     

The importance of nonlinear tissue modelling in finite element simulations of infant head impacts

Despite recent efforts on the development of finite element (FE) head models of infants, a model capable of capturing head responses under various impact scenarios has not been reported. This is hypothesized partially attributed to the use of simplified linear elastic models for soft tissues of suture, scalp and dura. Orthotropic elastic constants are yet to be determined to incorporate the direction-specific material properties of infant cranial bone due to grain fibres radiating from the ossification centres. We report here on our efforts in advancing the above-mentioned aspects in material modelling in infant head and further incorporate them into subject-specific FE head models of a newborn, 5- and 9-month-old infant. Each model is subjected to five impact tests (forehead, occiput, vertex, right and left parietal impacts) and two compression tests. The predicted global head impact responses of the acceleration–time impact curves and the force–deflection compression curves for different age groups agree well with the experimental data reported in the literature. In particular, the newly developed Ogden hyperelastic model for suture, together with the nonlinear modelling of scalp and dura mater, enables the models to achieve more realistic impact performance compared with linear elastic models. The proposed approach for obtaining age-dependent skull bone orthotropic material constants counts both an increase in stiffness and decrease in anisotropy in the skull bone—two essential biological growth parameters during early infancy. The profound deformation of infant head causes a large stretch at the interfaces between the skull bones and the suture, suggesting that infant skull fractures are likely to initiate from the interfaces; the impact angle has a profound influence on global head impact responses and the skull injury metrics for certain impact locations, especially true for a parietal impact.     

Finite element analysis of ramming in Ovis canadensis

The energy produced during the ramming of bighorn sheep (Ovis canadensis) would be expected to result in undesirable stresses in their frontal skull, which in turn would cause brain injury; yet, this animal seems to suffer no ill effects. In general, horn is made of an α-keratin sheath covering a bone. Despite volumes of data on the ramming behavior of Ovis canadensis, the extent to which structural components of horn and horn-associated structure or tissue absorb the impact energy generated by the ramming event is still unknown. This study investigates the hypothesis that there is a mechanical relationship present among the ramming event, the structural constituents of the horn, and the horn-associated structure. The three-dimensional complex structure of the bighorn sheep horn was successfully constructed and modeled using a computed tomography (CT) scan and finite element (FE) method, respectively. Three different three-dimensional quasi-static models, including a horn model with trabecular bone, a horn model with compact bone that instead of trabecular bone, and a horn model with trabecular bone as well as frontal sinuses, were studied. FE simulations were used to compare distributions of principal stress in the horn and the frontal sinuses and the strain energy under quasi-static loading conditions. It was noticed that strain energy due to elastic deformation of the complex structure of horn modeled with trabecular bone and with trabecular bone and frontal sinus was different. In addition, trabecular bone in the horn distributes the stresses over a larger volume, suggesting a mechanical link between the structural constituents and the ramming event. This phenomenon was elucidated through the principal stress distribution in the structure. This study will help designers in choosing appropriate material combinations for the successful design of protective structures against a similar impact.     

3D characterization of bone strains in the rat tibia loading model

Bone strain is considered one of the factors inducing bone tissue response to loading. Nevertheless, where animal studies can provide detailed data on bone response, they only offer limited information on experimental bone strains. Including micro-CT-based finite element (micro FE) models in the analysis represents a potent methodology for quantifying strains in bone. Therefore, the main objective of this study was to develop and validate specimen-specific micro FE models for the assessment of bone strains in the rat tibia compression model. Eight rat limbs were subjected to axial compression loading; strain at the medio-proximal site of the tibiae was measured by means of strain gauges. Specimen-specific micro FE models were created and analyzed. Repeated measurements on each limb indicated that the effect of limb positioning was small (COV?= 6.45 ± 2.27 %). Instead, the difference in the measured strains between the animals was high (54.2%). The computational strains calculated at the strain gauge site highly correlated to the measured strains (R ²?=?0.95). Maximum peak strains calculated at exactly 25% of the tibia length for all specimens were equal to 435.11 ± 77.88 microstrains (COV?=?17.19%). In conclusion, we showed that strain gauge measurements are very sensitive to the exact strain gauge location on the bone; hence, the use of strain gauge data only is not recommended for studies that address at identifying reliable relationships between tissue response and local strains. Instead, specimen-specific micro FE models of rat tibiae provide accurate estimates of tissue-level strains.     

Finite element and experimental cortex strains of the intact and implanted tibia

Finite Element (FE) models for the simulation of intact and implanted bone find their main purpose in accurately reproducing the associated mechanical behavior. FE models can be used for preclinical testing of joint replacement implants, where some biomechanical aspects are difficult, if not possible, to simulate and investigate in vitro. To predict mechanical failure or damage, the models should accurately predict stresses and strains. Commercially available synthetic femur models have been extensively used to validate finite element models, but despite the vast literature available on the characteristics of synthetic tibia, numerical and experimental validation of the intact and implant assemblies of tibia are very limited or lacking. In the current study, four FE models of synthetic tibia, intact and reconstructed, were compared against experimental bone strain data, and an overall agreement within 10% between experimental and FE strains was obtained. Finite element and experimental (strain gauge) models of intact and implanted synthetic tibia were validated based on the comparison of cortex bone strains. The study also includes the analysis carried out on standard tibial components with cemented and noncemented stems of the P.F.C Sigma Modular Knee System. The overall agreement within 10% previously established was achieved, indicating that FE models could be successfully validated. The obtained results include a statistical analysis where the root-mean-square-error values were always <10%. FE models can successfully reproduce bone strains under most relevant acting loads upon the condylar surface of the tibia. Moreover, FE models, once properly validated, can be used for preclinical testing of tibial knee replacement, including misalignment of the implants in the proximal tibia after surgery, simulation of long-term failure according to the damage accumulation failure scenario, and other related biomechanical aspects.     

Comparison of micro-level and continuum-level voxel models of the proximal femur

Continuum-level finite element (FE) models became standard computational tools for the evaluation of bone mechanical behavior from in vivo computed tomography scans. Such scans do not account for the anisotropy of the bone. Instead, local mechanical properties in the continuum-level FE models are assumed isotropic and are derived from bone density, using statistical relationships. Micro-FE models, on the other hand, incorporate the anisotropic structure in detail. This study aimed to quantify the effects of assumed isotropy, by comparing continuum-level voxel models of a healthy and a severely osteoporotic proximal femur with recently analyzed micro-FE models of the same bones. The micro-model element size was coarsened to generate continuum FE models with two different element sizes (0.64 and 3.04 mm) and two different density–modulus relationships found in the literature for wet and ash density. All FE models were subjected to the same boundary conditions that simulated a fall to the side, and the stress and strain distributions, model stiffness and yield load were compared. The results indicated that the stress and strain distributions could be reproduced well with the continuum models. The smallest differences between the continuum-level model and micro-level model predictions of the stiffness and yield load were obtained with the coarsest element size. Better results were obtained for both continuum-element sizes when isotropic moduli were based on ash density rather than wet density.     

Influences of geometrical and mechanical properties of bone tissues in mandible behaviour – experimental and numerical predictions

The properties and geometry of bone in the mandible play a key role in mandible behaviour during a person’s lifetime, and attention needs to be paid to the influence of bone properties. We analysed the effect of bone geometry, size and bone properties in mandible behaviour, experimenting on cadaveric mandibles and FE models. The study was developed using the geometry of a cadaveric mandible without teeth. Three models of cadaveric condyles were experimentally tested with instrumented with four rosettes, and a condyle reaction of 300 N. Four finite element models were considered to validate the experiments and analyse mandible behaviour. One numeric model was simulated with 10 muscles in a quasi-static condition. The experimental results present different condyle stiffness’s, of 448, 215 and 254 N/mm. The values presented in the rosettes are influenced by bone geometry and bone thickness; maximum value was ?600 με in rosette #4, and the maximum strain difference between mandibles was 111%. The numerical results show that bone density decreases and strain distribution increases in the thinner mandible regions. Nevertheless, the global behaviour of the structure remains similar, but presents different strain magnitudes. The study shows the need to take into account bone characteristics and their evolutions in order to improve implant design and fixation throughout the patient life. The change in bone stiffness promotes a change in maximum strain distribution with same global behaviour.     

Three-dimensional model of the human craniofacial skeleton: method and preliminary results using finite element analysis

The purpose of this study was to develop a three-dimensional finite element model of the craniofacial skeleton using a dry human skull. The model consisted of 2918 nodes and 1776 solid elements, and was used to investigate the biomechanical effect of a distally directed orthopaedic force on the craniofacial complex. The force was applied at the level of the maxillary first molar. The results indicated that in response to the force system applied: the nasomaxillary complex displaces in a backward and downward direction and rotates in clockwise sense; the nasomaxillary complex, including the zygomatic bone, experiences high stress levels in comparison with those at the remaining bones; the stress distribution in the maxillary basal bone area is relatively uniform; and the stress distribution across the opposing surface of the bony margins of the sutures is non-uniform.     

Development of a finite element model of the tibia for short-duration high-force axial impact loading

Finite element (FE) models can allow computer simulations of impact loading, providing a useful companion to cadaveric testing. These models allow injury evaluations to be conducted under a variety of conditions, but must be validated against experimental data. An FE model of a cadaveric tibia was developed using geometry from CT scans, and the quality of the mesh was evaluated. Loading and boundary conditions from experimental tests were simulated, and the model was optimised to best represent the response of natural bone to impacts. The model was shown to have good agreement for impact force, duration, impulse and strain during simulation of three non-injurious and one injurious axial impact when compared with experimental test data for the specimen. Failure criteria were evaluated for their ability to predict fracture. This model of the tibia can be used for future injury prediction assessment studies.     

In vivo and in vitro bone strain in the owl monkey circumorbital region and the function of the postorbital septum

Anthropoids and tarsiers are the only vertebrates possessing a postorbital septum. This septum, formed by the frontal, alisphenoid, and zygomatic bones, separates the orbital contents from the temporal muscles. Three hypotheses suggest that the postorbital septum evolved to resist stresses acting on the skull during mastication or incision. The facial-torsion hypothesis posits that the septum resists twisting of the face about a rostrocaudal axis during unilateral mastication; the transverse-bending hypothesis argues that the septum resists caudally directed forces acting at the lateral orbital margin during mastication or incision; and the tension hypothesis suggests that the septum resists ventrally directed components of masseter muscle force during mastication and incision. This study evaluates these hypotheses using in vitro and in vivo bone strain data recorded from the circumorbital region of owl monkeys. Incisor loading of an owl monkey skull in vitro bends the face upward in the sagittal plane, compressing the interorbital region rostrocaudally and “buckling” the lateral orbital walls. Unilateral loading of the toothrow in vitro also bends the face in the sagittal plane, compressing the interorbital region rostrocaudally and buckling the working side lateral orbital wall. When the lateral orbital wall is partially cut, so as to reduce the width of its attachment to the braincase, the following changes in circumorbital bone strain patterns occur. During loading of the incisors, lower bone strain magnitudes are recorded in the interorbital region and lateral orbital walls. In contrast, during unilateral loading of the P³, higher bone strain magnitudes are observed in the interorbital region, and generally lower bone strain magnitudes are observed in the lateral orbital walls. During unilateral loading of the M², higher bone strain magnitudes are observed in both the interorbital region and in the lateral orbital wall ipsilateral to the loaded molar. Comparisons of the in vitro results with data gathered in vivo suggest that, during incision and unilateral mastication, the face is subjected to upward bending in the sagittal plane resulting in rostrocaudal compression of the interorbital region. Modeling the lateral orbital walls as curved plates suggests that during mastication the working side wall is buckled due to the dorsally directed component of the maxillary force which causes upward bending of the face in the sagittal plane. The balancing side lateral orbital wall may also be buckled due to upward bending of the face in the sagittal plane as well as being twisted by the caudoventrally directed components of the superficial masseter muscle force. The in vivo data do not exclude the possibility that the postorbital septum functions to improve the structural integrity of the postorbital bar during mastication. However, there is no reason to believe that a more robust postorbital bar could not also perform this function. Hypotheses stating that the postorbital septum originally evolved to reinforce the skull against routine masticatory loads must explain why, rather than evolving a postorbital septum, the stem anthropoids did not simply enlarge their postorbital bars. © 1996 Wiley-Liss, Inc.     

Determination of orthotropic bone elastic constants using FEA and modal analysis

Finite element models have been widely employed in an effort to quantify the stress and strain distribution around implanted prostheses and to explore the influence of these distributions on their long-term stability. In order to provide meaningful predictions, such models must contain an appropriate reflection of mechanical properties. Detailed geometrical and density information is now readily available from CT scanning. However, despite the use of phantoms, a method of determining mechanical properties (or elastic constants) from bone density has yet to be made available in a usable form.In this study, a cadaveric bone was CT scanned and its natural frequencies were measured using modal analysis. Using the geometry obtained from the CT scan data, a finite element mesh was created with the distribution of density established by matching the mass of the FE bone model with the mass of the cadaveric bone. The maximum values of the orthotropic elastic constants were then established by matching the predictions from FE modal analyses to the experimental natural frequencies, giving a maximum error of 7.8% over 4 modes of vibration. Finally, the elastic constants of the bone derived from the analyses were compared with those measured using ultrasound techniques. This produced a difference of <1% for both the maximum density and axial Young's Modulus. This study has thereby produced an orthotropic finite element model of a human femur. More importantly, however, is the implication that it is possible to create a valid FE model by simply comparing the FE results with the measured resonant frequency of the CT scanned bone.