Geometrical and material parameters to assess the macroscopic mechanical behaviour of fresh cranial bone samples

The present study aims at providing quantitative data for the personalisation of geometrical and mechanical characteristics of the adult cranial bone to be applied to head FE models. A set of 351 cranial bone samples, harvested from 21 human skulls, were submitted to three-point bending tests at 10 mm/min. For each of them, an apparent elastic modulus was calculated using the beam's theory and a density-dependant beam inertia. Thicknesses, apparent densities and percentage of ash weight were also measured. Distributions of characteristics among the different skull bones show their symmetry and their significant differences between skull areas. A data analysis was performed to analyse potential relationship between thicknesses, densities and the apparent elastic modulus. A specific regression was pointed out to estimate apparent elastic modulus from the product of thickness by apparent density. These results offer quantitative tools in view of personalising head FE models and thus improve definition of local injury criteria for this body part.     

The mechanical properties of cranial bone: The effect of loading rate and cranial sampling position

Linear and depressed skull fractures are frequent mechanisms of head injury and are often associated with traumatic brain injury. Accurate knowledge of the fracture of cranial bone can provide insight into the prevention of skull fracture injuries and help aid the design of energy absorbing head protection systems and safety helmets. Cranial bone is a complex material comprising of a three-layered structure: external layers consist of compact, high-density cortical bone and the central layer consists of a low-density, irregularly porous bone structure.In this study, cranial bone specimens were extracted from 8 fresh-frozen cadavers (F=4, M=4; 81±11 years old). 63 specimens were obtained from the parietal and frontal cranial bones. Prior to testing, all specimens were scanned using a μCT scanner at a resolution of 56.9 μm. The specimens were tested in a three-point bend set-up at different dynamic speeds (0.5, 1 and 2.5 m/s). The associated mechanical properties that were calculated for each specimen include the 2nd moment of inertia, the sectional elastic modulus, the maximum force at failure, the energy absorbed until failure and the maximum bending stress. Additionally, the morphological parameters of each specimen and their correlation with the resulting mechanical parameters were examined.It was found that testing speed, strain rate, cranial sampling position and intercranial variation all have a significant effect on some or all of the computed mechanical parameters. A modest correlation was also found between percent bone volume and both the elastic modulus and the maximum bending stress.     

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.     

Some mechanical properties of goose femoral cortical bone

The ultimate compressive strength and modulus of elasticity of femoral cortical bone from adult geese (Anser anser), were determined by sex and by quadrant by compressing small right circular cylinders which were 2.4 mm in height and 0.8 mm in diameter. The average ultimate compressive strength was 183 +/- 29 MPa. The average modulus of elasticity was 13.2 +/- 3.4 GPa. The bending strength and bending modulus of elasticity were determined by a three point bend test on rectangular prisms which had the approximate dimensions 0.75 mm X 0.75 mm X 25 mm. The average bending strength was 263 +/- 44 MPa while the average bending modulus was 19.6 +/- 3.1 GPa. The calcium content was determined by atomic absorption spectrophotometry and no correlation was found with the mechanical properties. The histology of the cortical bone was examined both quantitatively and qualitatively. A unique type of Haversian bone is described. Goose bone was found to be morphologically similar to adolescent human bone and to have mechanical properties similar to those of adult human bone.     

Elastic moduli, yield stress, and ultimate stress of cancellous bone in the canine proximal femur

Elastic moduli, yield stress and ultimate compressive stress were determined for cancellous bone from the femoral head and neck regions of the canine femur. Unconfined compression tests were performed on 5 mm cubic samples which were cut from two femurs. Elastic moduli were measured in three orthogonal directions, and the yield stress and ultimate stress were measured along the proximal-distal axis. The results from this investigation support previous assumptions that the mechanical behavior of canine cancellous bone is qualitatively similar to human cancellous bone. The canine cancellous bone was observed to be anisotropic in elastic modulus. For two thirds of the cubic specimens tested, the elastic modulus was largest in the load-bearing, proximal-distal direction. A linear relationship between yield stress and elastic modulus was observed for canine bone, as is typical of human bone. A similar linear relationship between ultimate stress and elastic modulus was observed. Thus, for canine bone as well as for human bone, failure appears to be governed by a strain level which is position independent. The yield strain of 0.0259 and ultimate strain of 0.0288 for canine bone were both less than the yield strain of 0.0395 reported for human bone.     

Systematic review and meta-analysis of the biomechanical properties of the human dura mater applicable in computational human head models

Accurate biomechanical properties of the human dura mater are required for computational models and to fabricate artificial substitutes for transplantation and surgical training purposes. Here, a systematic literature review was performed to summarize the biomechanical properties of the human dura mater that are reported in the literature. Furthermore, anthropometric data, information regarding the mechanically tested samples, and specifications with respect to the used mechanical testing setup were extracted. A meta-analysis was performed to obtain the pooled mean estimate for the elastic modulus, ultimate tensile strength, and strain at maximum force. A total of 17 studies were deemed eligible, which focused on human cranial and spinal dura mater in 13 and 4 cases, respectively. Pooled mean estimates for the elastic modulus (n?=?448), the ultimate tensile strength (n?=?448), and the strain at maximum force (n?=?431) of 68.1 MPa, 7.3 MPa and 14.4% were observed for native cranial dura mater. Gaps in the literature related to the extracted data were identified and future directions for mechanical characterizations of human dura mater were formulated. The main conclusion is that the most commonly used elastic modulus value of 31.5 MPa for the simulation of the human cranial dura mater in computational head models is likely an underestimation and an oversimplification given the morphological diversity of the tissue in different brain regions. Based on the here provided meta-analysis, a stiffer linear elastic modulus of 68 MPa was observed instead. However, further experimental data are essential to confirm its validity.

     

Mechanical properties of cranial sutures

Many bones in mammalian skulls are linked together by cranial sutures, connective tissue joints that are morphologically variable and show different levels of interdigitation among and within species. The goal of this investigation was to determine whether sections of skull with cranial sutures have different mechanical properties than adjacent sections without sutures, and if these properties are enhanced with increased interdigitation. To test these hypotheses, bending strength and impact energy absorption were measured for samples of goat (Capra hircus) cranial bone without sutures and with sutures of different degrees of interdigitation. Bending strength was measured under both dynamic (9.7 mm displacement s-1) and relatively static (0.8 mm s-1) conditions, and at either speed, increased sutural interdigitation provided increased strength during three-point bending. However, except for very highly interdigitated sutures loaded slowly, sutures were not as strong in bending as bone. In contrast, sutures absorbed from 16% to 100% more energy per unit volume during impact loading than did bone. This five-fold increase in energy absorption by the sutures was significantly correlated with increased sutural interdigitation.     

Biomechanical properties of bones from rats treated with sevelamer

Sevelamer hydrochloride is used for ten years in patients on dialysis as a phosphate binder. We have previously shown that oral application of sevelamer prevents the bone loss and increases the bone volume in ovariectomized rats. In this study we further analysed the biomechanical properties of bones from rats treated with sevelamer utilizing a threepoint bending test to determine the mechanical properties of the cortical bone of the mid-shaft femur, while the indentation test was used to determine the mechanical properties of cancellous bone in the marrow cavity of the distal femoral metaphysis. Parameters analyzed included: maximum load (F(u)), stiffness (S), energy absorbed (W), toughness (T) and ultimate strength (sigma). The intrinsic properties, stress, elastic modulus and toughness were determined from measured maximum load, strains, stiffness, energy absorbed, outer and inner diameters, and calculated bone cross-sectional moment of inertia. Sevelamer was given to rats for 25 weeks with a content of 3% of sevelamer in a standard diet, starting immediately following ovariectomy (OVX). Animals were divided to the following groups: (1) Sham; (2) Sham + sevelamer 3%; (3) OVX; (4) OVX + sevelamer 3%. Our results showed that sevelamer particularly influenced the rat trabecular bone by increasing the maximum load for 26.2%, energy absorbed for 24.2% and the ultimate strength for 26.2% in sham animals treated with sevelamer 3%, as compared to sham rats. Sevelamer 3% in OVX rats also increased the maximum load for 71.4%, stiffness for 70.7%, energy absorbed for 55.9% and the ultimate strength for 71.3% as compared to OVX controls. In the three bending test sevelamer had a very little effect on preventing loss of bone strenght in the cortical bone. These results collectively suggest that sevelamer improves bone biomechanical properties, mainly affecting trabecular bone quality in both normal and ovariectomized rats.     

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.     

Viscoelastic behaviour and failure of bovine cancellous bone under constant strain rate

A programme has been established to characterize the long-term behaviour of cancellous bone. Fresh bovine cancellous specimens of dimensions 10 x 10 x 10 mm3 and 10 x 40 x 3.6 mm3 were manufactured and used within the testing programme. Results published in the literature indicate that the long-term behaviour of cancellous bone is well described by a power law, which is a very similar response of typical polymers. So far, dynamic mechanical tests (DMA) in three-point bending, under frequencies between 0.01 and 100 Hz at room temperature, confirmed the published results in a qualitative way. Nevertheless, the measured dimensionless damping, tan delta, was slightly higher than the values reported in the literature for the compact bone. The relaxation curves were obtained from dynamic tests and confirmed that bone relaxation modulus can be described by a power law function of time. Tests under constant compression strain rate were performed at four different strain rates: 0.15/s, 0.015/s, 0.0015/s and 0.00015/s and strain rate dependent behaviour was observed. An average elastic bending modulus of 300 MPa was obtained.     

The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus

The elastic moduli of human subchondral, trabecular, and cortical bone tissue from a proximal tibia were experimentally determined using three-point bending tests on a microstructural level. The mean modulus of subchondral specimens was 1.15 GPa, and those of trabecular and cortical specimens was 4.59 GPa and 5.44 GPa respectively. Significant differences were found in the modulus values between bone tissues, which may have mainly resulted from the differences in the microstructures of each bone tissue rather than in the mineral density. Furthermore, the size-dependency of the modulus was examined using eight different sizes of cortical specimens (heights h = 100-1000 microns). While the modulus values for relatively large specimens (h greater than 500 microns) remained fairly constant (approximately 15 GPa), the values decreased as the specimens became smaller. A significant correlation was found between the modulus and specimen size. The surface area to volume ratio proved to be a key variable to explain the size-dependency.     

The effect of chemical cleansing procedures combined with peracetic acid-ethanol sterilization on biomechanical properties of cortical bone.

Peracetic acid-ethanol sterilization (PES) with a preceding delipidation step is an effective sterilization method for allograft bone, but its influence on biomechanical properties of bone has not been studied. The aim of this study was to evaluate the effects of different incubation times of water, hydrogen peroxide and alcohol cleansing procedures combined with PES on biomechanical properties of freeze-dried cortical bone. These effects were studied by performing three-point bending tests on cortical samples. The lyophilized cortical samples were rehydrated prior to mechanical testing. The bending strength and the absorbed energy of the processed cortical samples were increased slightly but the Young's modulus was decreased compared to unprocessed samples. However, when the residual moisture content of the processed cortical samples was reduced from <5% to 0% all the biomechanical properties studied were significantly decreased. Hexane elution was used to determine the residual fat content of the processed cortical bone. Reducing the incubation time in cleansing had no effect on the residual fat content of the bone samples. Our in vitro study indicates that the cleansing procedure proposed combined with PES affects the biomechanical properties of cortical bone only on a limited scale.     

A Statistical Skull Geometry Model for Children 0-3 Years Old

Head injury is the leading cause of fatality and long-term disability for children. Pediatric heads change rapidly in both size and shape during growth, especially for children under 3 years old (YO). To accurately assess the head injury risks for children, it is necessary to understand the geometry of the pediatric head and how morphologic features influence injury causation within the 0–3 YO population. In this study, head CT scans from fifty-six 0–3 YO children were used to develop a statistical model of pediatric skull geometry. Geometric features important for injury prediction, including skull size and shape, skull thickness and suture width, along with their variations among the sample population, were quantified through a series of image and statistical analyses. The size and shape of the pediatric skull change significantly with age and head circumference. The skull thickness and suture width vary with age, head circumference and location, which will have important effects on skull stiffness and injury prediction. The statistical geometry model developed in this study can provide a geometrical basis for future development of child anthropomorphic test devices and pediatric head finite element models.     

Mechanical Properties of Calvarial Bones in a Mouse Model for Craniosynostosis

The mammalian cranial vault largely consists of five flat bones that are joined together along their edges by soft fibrous tissues called sutures. Premature closure of the cranial sutures, craniosynostosis, can lead to serious clinical pathology unless there is surgical intervention. Research into the genetic basis of the disease has led to the development of various animal models that display this condition, e.g. mutant type Fgfr2^C342Y/+ mice which display early fusion of the coronal suture (joining the parietal and frontal bones). However, whether the biomechanical properties of the mutant and wild type bones are affected has not been investigated before. Therefore, nanoindentation was used to compare the elastic modulus of cranial bone and sutures in wild type (WT) and Fgfr2^C342Y/+mutant type (MT) mice during their postnatal development. Further, the variations in properties with indentation position and plane were assessed. No difference was observed in the elastic modulus of parietal bone between the WT and MT mice at postnatal (P) day 10 and 20. However, the modulus of frontal bone in the MT group was lower than the WT group at both P10 (1.39±0.30 vs. 5.32±0.68 GPa; p<0.05) and P20 (5.57±0.33 vs. 7.14±0.79 GPa; p<0.05). A wide range of values was measured along the coronal sutures for both the WT and MT samples, with no significant difference between the two groups. Findings of this study suggest that the inherent mechanical properties of the frontal bone in the mutant mice were different to the wild type mice from the same genetic background. These differences may reflect variations in the degree of biomechanical adaptation during skull growth, which could have implications for the surgical management of craniosynostosis patients.     

The elastic and ultimate properties of compact bone tissue

The use of a tranversely isotropic model is tested for the elastic behavior of bovine and human bone and the five independent constants of this model are determined. The accuracy of the model is tested for eight cases by comparing the off-axis modulus predicted by a rotation of stiffness matrix with an experimentally determined off-axis modulus.

Ultimate properties are presented for bovine and human bone for tension, compression, and torsional loads. A Hankinson type failure criterion is proposed for off-axis ultimate stress and this predicted value compared with experimental values for nine cases.     

Cranial Osteogenesis and Suture Morphology in Xenopus laevis: A Unique Model System for Studying Craniofacial Development

Background

The tremendous diversity in vertebrate skull formation illustrates the range of forms and functions generated by varying genetic programs. Understanding the molecular basis for this variety may provide us with insights into mechanisms underlying human craniofacial anomalies. In this study, we provide evidence that the anuran Xenopus laevis can be developed as a simplified model system for the study of cranial ossification and suture patterning. The head structures of Xenopus undergo dramatic remodelling during metamorphosis; as a result, tadpole morphology differs greatly from the adult bony skull. Because of the extended larval period in Xenopus, the molecular basis of these alterations has not been well studied.

Methodology/Principal Findings

We examined late larval, metamorphosing, and post-metamorphosis froglet stages in intact and sectioned animals. Using micro-computed tomography (μCT) and tissue staining of the frontoparietal bone and surrounding cartilage, we observed that bone formation initiates from lateral ossification centers, proceeding from posterior-to-anterior. Histological analyses revealed midline abutting and posterior overlapping sutures. To determine the mechanisms underlying the large-scale cranial changes, we examined proliferation, apoptosis, and proteinase activity during remodelling of the skull roof. We found that tissue turnover during metamorphosis could be accounted for by abundant matrix metalloproteinase (MMP) activity, at least in part by MMP-1 and -13.

Conclusion

A better understanding of the dramatic transformation from cartilaginous head structures to bony skull during Xenopus metamorphosis may provide insights into tissue remodelling and regeneration in other systems. Our studies provide some new molecular insights into this process.     

Elastic properties of human supraorbital and mandibular bone

Elastic constants, including the elastic modulus, the shear modulus, and Poisson's ratio, were measured on human craniofacial bone specimens obtained from the supraorbital region and the buccal surfaces of the mandibles of unembalmed cadavers. Constants were determined using an ultrasonic wave technique in three directions relative to the surface of each sample: 1) normal, 2) tangential, and 3) longitudinal. Statistical analysis of these elastic constants indicated that significant differences in the relative proportions of elastic properties existed between the regions. Bone from the mandible along its longitudinal axis was stiffer than bone from the supraorbital region. Directional differences in both locations demonstrated that cranial bone was not elastically isotropic. It is suggested that differences in elastic properties correspond to regional differences in function. © 1993 Wiley-Liss, Inc.     

Effects of freeze–thaw and micro-computed tomography irradiation on structure–property relations of porcine trabecular bone

We study the effects of freeze–thaw and irradiation on structure–property relations of trabecular bone. We measure the porosity, apparent density, mineral content, trabecular orientation, trabecular thickness, fractal dimension, surface area, and connectivity of trabecular bone using micro-computed tomography (micro-CT) and relate them to Young?s modulus and ultimate strength measured by uniaxial compression testing. The analysis is done on six-month porcine trabecular bone from femoral heads. The effects of freeze–thaw are studied by using bones from three different groups: fresh bone and bones frozen for one and five years. We find that the porosity and apparent density have most dominant influence on the elastic modulus and strength of fresh bone. Also, five years of freezing lowers both Young?s modulus and ultimate strength of trabecular bone. Additionally, the effects of radiation are investigated by comparing Young?s modulus before and after micro-CT exposure. We find that the micro-CT irradiation has a negligible effect on the Young?s modulus of trabecular bone. These findings provide insights on the effects of tissue preservation and imaging on properties of trabecular bone.     

Phenotypic integration of neurocranium and brain

Evolutionary history of Mammalia provides strong evidence that the morphology of skull and brain change jointly in evolution. Formation and development of brain and skull co-occur and are dependent upon a series of morphogenetic and patterning processes driven by genes and their regulatory programs. Our current concept of skull and brain as separate tissues results in distinct analyses of these tissues by most researchers. In this study, we use 3D computed tomography and magnetic resonance images of pediatric individuals diagnosed with premature closure of cranial sutures (craniosynostosis) to investigate phenotypic relationships between the brain and skull. It has been demonstrated previously that the skull and brain acquire characteristic dysmorphologies in isolated craniosynostosis, but relatively little is known of the developmental interactions that produce these anomalies. Our comparative analysis of phenotypic integration of brain and skull in premature closure of the sagittal and the right coronal sutures demonstrates that brain and skull are strongly integrated and that the significant differences in patterns of association do not occur local to the prematurely closed suture. We posit that the current focus on the suture as the basis for this condition may identify a proximate, but not the ultimate cause for these conditions. Given that premature suture closure reduces the number of cranial bones, and that a persistent loss of skull bones is demonstrated over the approximately 150 million years of synapsid evolution, craniosynostosis may serve as an informative model for evolution of the mammalian skull.     

Long-term effects of tissue expansion on cranial and skeletal bone development in neonatal miniature swine: clinical findings and histomorphometric correlates

Progressive tissue expansion induces significant gross, histologic, and bony changes in skulls and long bones of neonatal miniature swine. These bony changes consist of erosion underlying tissue expanders, with bony lipping and bone deposition at the periphery of the expander. Cranial suture lines underneath expanders appear effaced and convoluted. Serial CT scans reveal decreased bone thickness and volume (p less than 0.02) but identical bone density (p = 0.60) beneath expanders. Increased bone volume and thickness occur at the periphery of expanders (p less than 0.02). Bone density (CT number) is unaffected by tissue expansion in both cranial and long bones. These findings have histomorphometric correlates: Osteoclastic bone resorption occurs underneath expanders with periosteal reaction at the periphery of expanders. Cranial sutures are similarly affected, but no cranial synostosis results. No changes to the inner table of the skull or stigmata of increased intracranial pressure were observed either in CT scans or in behavioral changes in long-term animals. The pathophysiology of bony changes is a remodeling effect, not one of simple pressure deformation. Increased bone resorption and complete inhibition of bone formation occur until the pressure is removed. Cranial bone is significantly more affected than long bone. After removal of the expanders, reparative bone remodeling begins within 5 days and nearly complete healing of the cranial defects occurs within 2 months (p less than 0.02). No plagiocephaly results despite early coronal suture changes. On the basis of this study, we conclude that tissue expansion causes significant but reversible effects, readily monitored by high-resolution CT scans, on neonatal and infant cranial and long bones.