Elastic and physicochemical relationships within cortical bone

A stochastic model validated with human test data causally associating target vehicle Delta V, occupant cervicocranial biomechanics, and injury during rear-impact crashes

Even at low to moderate-speeds, rear-end motor vehicle crashes have been strongly associated with occupant cervicocranial biomechanics that lead to head and neck injury. In this paper, we present the development of an analytic mechanics model of occupant head and neck motion as associated with modeled target vehicle Delta V during rear-end vehicular crashes. The inclusion of stochastic mechanical input variables further developed the model beyond the deterministic framework by reflecting aspects of the random nature of real-world crashes and the resulting injuries. This approach led to the characterization of 1000 crash simulations, quantifying Delta V and the resulting probabilistic occupant biomechanics. The model was validated through the direct comparison with 86 published human subject crash tests. Overall, the model slightly underestimated by -2.6% the magnitude of peak head accelerations identified in the literature. The utility of the model allows a forensic biomechanical investigator to customize some of the fundamental input crash parameters and appropriately explore the resulting vehicular mechanics and their direct influence on injury biomechanics.

A temporospatial histomorphometric analysis of bone density adjacent to acid-etched self-tapping dental implants with an external hexagon connection in the female baboon

OBJECTIVE

To characterize osseointegration as the percent of bone-implant contact (%BIC) along the surface (0.0 mm) as well as at surface profiles 0.5 mm and 1.0 mm lateral to the implant, determining any differences between early occlusally loaded and non-loaded implants.

MATERIAL AND METHODS

In ten adult female baboons, 120 dental implants were randomly placed in opposing mandibular and maxillary locations. Eighty sites had two groups of healing (no load) of either 1 (n = 40) or 2 (n = 40) months leading to 3 months of functional loading. These sites received full acid-etched surface implants. The 40 control implants represented healing only periods (no load) for 1 (n = 10), 2 (n = 10), 4 (n = 10), and 5 (n = 10) months. These implants were of a vertically split surface texture design (acid-etched and machined). Block sections and photomicrographs were obtained. Blinded histometric analyses determined the %BIC via a superimposed template.

RESULTS

The unloaded groups (1, 2, and 4 months) had higher %BIC compared to the 5-month group (p < 0.0001). The loaded groups exhibited mean bone densities of 59.2% and 55.5% (1-month healing at 0.5 mm and 1.0 mm, respectively) and 61.0% and 57.1% (2-month healing at 0.5 mm and 1.0 mm, respectively) with no significant difference between healing time (p = 0.4118).

CONCLUSION

There was a lateral increase in %BIC in the loaded compared to unloaded groups.

CLINICAL RELEVANCE

The decrease in bone densities at the 5-month unloaded group suggests that there is a critical earlier time period when dental implants should be placed into functional load.

Application of flexural and membrane stress analysis to distinguish tensile and compressive moduli of biologic materials

Three-point bending is often used during the mechanical determination of tissue material properties. When taken to failure, the test samples often experience high deformations. The objective of this study was to present beam and plate theories as analytical tools for determining tensile and compressive elastic moduli during the transition from flexure to membrane stress states. Samples of cartilage, a highly flexible connective tissue having differing tensile and compressive moduli, were tested. Three-point bending tests were conducted on auricular (ear) and costal (rib) cartilage harvested from pigs. The influence of span length variation and Poisson's ratio assumptions were statistically assessed. Tensile elastic moduli of the ear (3.886 MPa) and rib (6.131 MPa) were derived from high-deformation bending tests. The functional assessment described here can be applied as a design input approach for tissue reconstruction and tissue engineering, considering both hard and soft tissue applications.

Experimental study of time response of bending deformation of bone cantilevers in an electric field

Bone is a complex composite material with hierarchical structures and anisotropic mechanical properties. Bone also processes electromechanical properties, such as piezoelectricity and streaming potentials, which termed as stress generated potentials. Furthermore, the electrostrictive effect and flexoelectric effect can also affect electromechanical properties of the bone. In the present work, time responses of bending deflections of bone cantilever in an external electric field are measured experimentally to investigate bone's electromechanical behavior. It is found that, when subjected to a square waveform electric field, a bone cantilever specimen begins to bend and its deflection increases gradually to a peak value. Then, the deflection begins to decrease gradually during the period of constant voltage. To analyze the reasons of the bending response of bone, additional experiments were performed. Experimental results obtained show the following two features. The first one is that the electric polarization, induced in bone by an electric field, is due to the Maxwell-Wagner polarization mechanism that the polarization rate is relatively slow, which leads to the electric field force acted on a bone specimen increase gradually and then its bending deflections increase gradually. The second one is that the flexoelectric polarization effect that resists the electric force to decrease and then leads to the bending deflection of a bone cantilever decrease gradually. It is concluded that the first aspect refers to the organic collagens decreasing the electric polarization rate of the bone, and the second one to the inorganic component influencing the bone's polarization intensity.

An improved interfacial bonding model for material interface modeling

An improved interfacial bonding model was proposed from potential function point of view to investigate interfacial interactions in polycrystalline materials. It characterizes both attractive and repulsive interfacial interactions and can be applied to model different material interfaces. The path dependence of work-of-separation study indicates that the transformation of separation work is smooth in normal and tangential direction and the proposed model guarantees the consistency of the cohesive constitutive model. The improved interfacial bonding model was verified through a simple compression test in a standard hexagonal structure. The error between analytical solutions and numerical results from the proposed model is reasonable in linear elastic region. Ultimately, we investigated the mechanical behavior of extrafibrillar matrix in bone and the simulation results agreed well with experimental observations of bone fracture.

Towards new material biomarkers for fracture risk

Osteoporosis is a prevalent bone condition, characterised by low bone mass and increased fracture risk. Currently, the gold standard for identifying osteoporosis and increased fracture risk is through quantification of bone mineral density (BMD) using dual energy X-ray absorption (DEXA). However, the risk of osteoporotic fracture is determined collectively by bone mass, architecture and physicochemistry of the mineral composite building blocks. Thus DEXA scans alone inevitably fail to fully discriminate individuals who will suffer a fragility fracture. This study examines trabecular bone at both ultrastructure and microarchitectural levels to provide a detailed material view of bone, and therefore provides a more comprehensive explanation of osteoporotic fracture risk. Physicochemical characterisation obtained through X-ray diffraction and infrared analysis indicated significant differences in apatite crystal chemistry and nanostructure between fracture and non-fracture groups. Further, this study, through considering the potential correlations between the chemical biomarkers and microarchitectural properties of trabecular bone, has investigated the relationship between bone mechanical properties (e.g. fragility) and physicochemical material features.

Classification of fracture and non-fracture groups by analysis of coherent X-ray scatter

Osteoporotic fractures present a significant social and economic burden, which is set to rise commensurately with the aging population. Greater understanding of the physicochemical differences between osteoporotic and normal conditions will facilitate the development of diagnostic technologies with increased performance and treatments with increased efficacy. Using coherent X-ray scattering we have evaluated a population of 108 ex vivo human bone samples comprised of non-fracture and fracture groups. Principal component fed linear discriminant analysis was used to develop a classification model to discern each condition resulting in a sensitivity and specificity of 93% and 91%, respectively. Evaluating the coherent X-ray scatter differences from each condition supports the hypothesis that a causal physicochemical change has occurred in the fracture group. This work is a critical step along the path towards developing an in vivo diagnostic tool for fracture risk prediction.

Discordant recovery of bone mass and mechanical properties during prolonged recovery from disuse

Profound bone loss at weight bearing sites is a primary effect of long-duration spaceflight. Moreover, a significant increase in estimated fracture risk remains even 1 year after returning to Earth; hence, it is important to define how quickly bone integrity can recover following prolonged disuse. This study characterized the loss and recovery dynamics of bone following a period of rodent hindlimb unloading in three anatomic sites. We hypothesized that the rat femoral neck would exhibit a discordant recovery dynamic most similar to that observed in astronauts' proximal femur; that is, bone mineral content (absolute mass) at this site would recover faster and more completely than would bone density and cortical area, and they will all recover before bone strength does. We characterized loss and long-term recovery of densitometric properties at the femoral neck, proximal tibia metaphysis, and tibia diaphysis, and also mechanical properties at the femoral neck and tibia diaphysis for which mechanical testing is amenable. We assessed the relationship between calculated strength indices and measured mechanical properties. Adult male Sprague-Dawley rats (6 months) were assigned to baseline, age-matched control (AC), and hindlimb unloaded (HU) groups. The HU group was unloaded for 28 days and then returned to normal cage activity for 84 days of weight bearing recovery (3 times the duration of HU). Fifteen animals were euthanized from each of the HU and AC groups on days 28, 56, 84, and 112 of the study. At baseline and then every 28 days in vivo longitudinal pQCT scans were taken at proximal tibia metaphysis (PTM) and tibia diaphysis (TD); ex vivo pQCT scans were taken later at the femoral neck (FN). TD and FN were tested to failure to measure mechanical properties. The hypothesis that the femoral neck in rats will exhibit a discordant recovery dynamic most similar to that observed in astronauts' proximal femurs was not supported by our data. At the femoral neck, densitometric and geometric variables (total BMC, total vBMD, cancellous vBMD, and cortical area) recovered to age-matched control levels after a recovery period twice the duration of unloading. Contrary to our hypothesis, changes in densitometric variables at the PTM provided a better model for changes in the human femoral neck with prolonged weightlessness. Following 28 days of HU, PTM total BMC recovered to age-matched control levels after roughly two times the duration of unloading; however, total vBMD did not recover even after three recovery periods. Cortical thinning occurred at the PTM following HU likely due to inhibition of periosteal growth; cortical shell thickness did not recover even after three recovery periods. Calculated strength indices suggested a loss in strength at the tibial diaphysis, which was not confirmed with direct testing of mechanical properties. HU had no effect on maximum fracture force at mid-tibia diaphysis; however, femoral neck experienced a significant loss of maximum force due to unloading that fully recovered after 28 days. Estimated strength indices for the femoral neck suggested a recovery period of 56 days in contrast to the 28-day recovery that was observed with mechanical testing. However, the inaccuracy of strength indices vs. directly measured mechanical properties highlights the continued importance of ground based animal models and mechanical testing. Our results demonstrate that the PTM in the rat better matches loss and recovery dynamics observed in astronauts' proximal femur than does the rat FN, at least in terms of densitometric variables. More complete utility of the rat PTM as a model in this case, however, depends upon meaningful characterization of changes in mechanical properties as well.

An experimental and theoretical composite model of the human mandible

The purpose is to design and manufacture a composite mandible replicate suitable for testing the influence of prosthetic materials on the stress distribution of bone. Composite mandibles made of a poly(methylmethacrylate) core and a glass reinforced outer shell are manufactured and characterised through mechanical tests assisted by the finite element analysis. The mandible replicate has been conveniently equipped with strain gauges, moreover a video extensometer has also been used in order to measure the arch width change during loading. A close agreement is found between the experimental data and the theoretical predictions. By laterally loading the mandibles the maximum values of stress and strain take place in the premolar-incisal region. By varying technological parameters such as the fiber volume fraction and orientation, it is easy to replicate the behaviour of mandibles having different stiffnesses. The results obtained by laterally loading the composite mandibles through the condyles or through the gonion regions are consistent with literature data relative to the arch width decrease of natural jaws during opening and closing. This novel synthetic system coupled with the Finite Element model constitutes an experimental-theoretical model suitable to investigate the biomechanical effects of oral rehabilitations on mandibular bone.

Novel experimental effects on bone material properties and the pre- and postyield behavior of bones may be independent of bone mineralization

In this article, we summarize the results of six different tomographic/biomechanical rat studies involving hypophysectomy (Hx), ovariectomy, treatment with rhGH, olpadronate, alendronate, and toxic doses of aluminum and the development of a genetic diabetes in the eSS strain. All these conditions induced some interesting and rarely reported effects on postyield bone strength. These effects were generally related neither to the degree of mineralization or the elastic modulus of the bone tissue nor to the preyield behavior of the bones. In two particular cases (Hx, eSS), the elastic modulus of bone tissue varied independently of its degree of mineralization. These results suggest the involvement of some microstructural factor(s) of bone tissue resistance to crack progression (a postyield feature of bone behavior), rather than to crack initiation (the yield-determining factor) in the corresponding mechanism. Changes in collagen or crystal structure may play that role. These changes are relevant to the mechanism of fracture production during plastic deformation, a feature of bone strength that might be independent from mineralization. Therefore, these changes might help to explain some effects of novel treatments on bone strength unrelated to bone mineralization. This questions the belief that the remaining bone mass in metabolic osteopenias is biologically and mechanically normal.

Effects of hypophysectomy and recombinant human growth hormone on material and geometric properties and the pre- and post-yield behavior of femurs in young rats

To study the musculoskeletal effects of hypophysectomy (Hx) and a partial replacement treatment with recombinant human growth hormone (rhGH) in rats, we determined the stiffness (elastic modulus, E) and volumetric BMD (vBMD) of cortical bone; the periosteal and endosteal perimeters, area and bending moment of inertia (xCSMI) of the cross sections, and the structural stiffness and pre- and post-yield strength of the femur diaphyses by pQCT and mechanical tests, and the gastrocnemius weight of rats that were either intact (n = 9) or Hx at 15 days of age (20). The latter were otherwise untreated (Hx controls, 4) or given 0.4 (8) or 2.0 (8) IU kg(-1) day(-1), s.c., of rhGH for 45 days starting 15 days after surgery. Hx delayed musculoskeletal development (gastrocnemius weight, bone geometric properties), thus affecting the diaphyseal stiffness and strength. It also reduced the cortical vBMD through an undefined mechanism, and increased the elastic modulus of cortical bone. The Hx also affected the correlation between bone geometric and material properties (xCSMI vs. E), suggesting an antianabolic interaction with the biomechanical control of bone modeling in response to strains caused by mechanical usage. As a result, Hx reduced the stiffness, post-yield, and ultimate strength of the diaphyses. These effects should reflect changes in bone tissue microstructure, perhaps associated with crack generation and progress, but unrelated to bone mineral mass. They are compatible with the induction of a delay in collagen turnover with associated increases in fibers' diameter and crystals' size that may have resulted from the suppression of some other hormones, such as thyroid, prolactin, or other hormones regulated by ACTH. The above doses of rhGH significantly but incompletely prevented the negative Hx effects on bone and muscle development (bone geometric properties, muscle mass). However, rhGH treatment failed to prevent the demineralizing and stiffening effect of Hx on bone tissue and the unusual effects on the post-yield strength (less clearly related to muscle development than the former). Consequently, rhGH treatment tended to preserve the natural relationship between muscle function and bone geometry but not bone strength. The effects of larger rhGH doses and the interaction of other hormones with the described effects remain to be investigated. Nevertheless, these findings would deserve special attention because they challenge the prevailing view that in endocrine-metabolic bone-weakening diseases the bone matrix always has a normal composition.

Infrared analysis of the mineral and matrix in bones of osteonectin-null mice and their wildtype controls

Osteonectin function in bone was investigated by infrared analysis of bones from osteonectin-null (KO) and wildtype mice (four each at 11, 17, and 36 weeks). An increase in mineral content and crystallinity in newly formed KO bone and collagen maturity at all sites was found using FTIR microspectroscopy and imaging; consistent with osteonectin's postulated role in regulating bone formation and remodeling. Mineral and matrix properties of tibias of osteonectin-null mice and their age- and background-matched wildtype controls were compared using Fourier-transform infrared microspectroscopy (FTIRM) and infrared imaging (FTIRI) at 10- and 7-mm spatial resolution, respectively. The bones came from animals that were 11, 17, and 36 weeks of age. Individual FTIRM spectra were acquired from 20 x 20 microm areas, whereas 4096 simultaneous FTIRI spectra were acquired from 400 x 400 microm areas. The FTIRM data for mineral-to-matrix, mineral crystallinity, and collagen maturity were highly correlated with the FTIRI data in similar regions. In general, the osteonectin-null mice bones had higher mineral contents and greater crystallinity (crystal size and perfection) than the age-matched wildtype controls. Specifically, the mineral content of the newly forming periosteal bone was increased in the osteonectin-null mice; the crystallinity of the cortical bone was decreased in all but the oldest animals, relative to the wildtype. The most significant finding, however, was increased collagen maturity in both the cortical and trabecular bone of the osteonectin-null mice. These spectroscopic data are consistent with a mechanism of decreased bone formation and remodeling.

Mechanical and chemical characteristics of mineral produced by basic fibroblast growth factor-treated bone marrow stromal cells in vitro

It has been shown that various organ and cell cultures exhibit increased mineral formation with the addition of basic fibroblast growth factor (bFGF) and phosphate ions in the medium. However, to date there has been no attempt to relate the chemical composition of mineral formed in vitro to a measure of its mechanical properties. This information is important for understanding the in vivo mineralization process, the development of in vitro models, and the design of tissue-engineered bone substitutes. In this study we examined the reduced modulus; hardness; and mineral-to-matrix, crystallinity, carbonate-to-mineral, and calcium-to-phosphorus ratios of mineral formed by bFGF-treated rat-derived bone marrow stromal cells in vitro. The cells were treated with 1 or 3 mM beta-glycerophosphate for 3 and 4 weeks. Both mechanical parameters, reduced modulus and hardness, increased with increasing beta-glycerophosphate concentration. The only chemical measure of the mineral composition that exhibited the same dependency was the mineral-to-matrix ratio. The values of crystallinity and carbonate fraction were similar to those for intact cortical bone, but the calcium-to-phosphorus ratio was substantially lower than that of normal bone. These data indicate that the mineral formed by bFGF-treated bone cells is mechanically and chemically different from naturally formed lamellar bone tissue after 4 weeks in culture. These results can be used to improve in vitro models of mineral formation as well as enhance the design of tissue-engineered bone substitutes.

Linear poroelastic cancellous bone anisotropy: trabecular solid elastic and fluid transport properties

The mechanical performance of cancellous bone is characterized using experiments which apply linear poroelasticity theory. It is hypothesized that the anisotropic organization of the solid and pore volumes of cancellous bone can be physically characterized separately (no deformable boundary interactive effects) within the same bone sample. Due to its spongy construction, the in vivo mechanical function of cancellous or trabecular bone is dependent upon fluid and solid materials which may interact in a hydraulic, convective fashion during functional loading. This project provides insight into the organization of the tissue, ie., the trabecular connectivity, by defining the separate nature of this biphasic performance. Previous fluid flow experiments [Kohles et al., 2001, Journal of Biomechanics, 34(11), pp. 1197-1202] describe the pore space via orthotropic permeability. Ultrasonic wave propagation through the trabecular network is used to describe the solid component via orthotropic elastic moduli and material stiffness coefficients. The linear poroelastic nature of the tissue is further described by relating transport (fluid flow) and elasticity (trabecular load transmission) during regression analysis. In addition, an empirical relationship between permeability and porosity is applied to the collected data. Mean parameters in the superior-inferior (SI) orientation of cubic samples (n=20) harvested from a single bovine distal femur were the largest (p<0.05) in comparison to medial-lateral (ML) and anterior-posterior (AP) orientations: Apparent elastic modulus (2,139 MPa), permeability (4.65x10(-10) m2), and material stiffness coefficient (13.6 GPa). A negative correlation between permeability as a predictor of structural elastic modulus supported a parametric relationship in the ML (R2=0.4793), AP (R2=0.3018), and SI (R2=0.6445) directions (p<0.05).

Direct perfusion measurements of cancellous bone anisotropic permeability

More extensive characterization of trabecular connectivity and intertrabecular space will be instrumental in understanding disease states and designing engineered bone. This project presents an experimental protocol to define the directional dependence of transport properties as measured from healthy cancellous bone when considered as a biologic, porous medium. In the initial design phases, mature bovine bone was harvested from the femoral neck (n=6 cylinders) and distal condyle (n=4 cubes) regions and used for "proof of concept" experimentation. A power study on those results led to the presented work on 20 cubic samples (mean volume=4.09cm(3)) harvested from a single bovine distal femur. Anisotropic intrinsic permeabilities (k(i)) were quantified along the orthogonal anatomic axes (i=medial-lateral, anterior-posterior, and superior-inferior) from each individual cubic bone sample. Using direct perfusion measurements, permeability was calculated based upon Darcy's Law describing flow through porous media. The maximum mean value was associated with the superior-inferior orientation (4.65x10(-10)m(2)) in comparison with the mean anterior-posterior (4.52x10(-10)m(2)) and medial-lateral (2.33x10(-10)m(2)) direction values. The results demonstrate the anisotropic (p=0.0143) and heterogeneous (p=0.0002) nature of the tissue and encourage the ongoing quantification of parameters within the established poroelastic models.