Effects of specimen load-bearing and free surface layers on the compressive mechanical properties of cellular materials

A graph model to describe the network connectivity of trabecular plates and rods

Introduction: The trabecular network is perceived as a collection of interconnected plate- (P) and rod-like (R) elements. Previous research has highlighted how these elements and their connectivity influence the mechanical properties of bone, yet further work is required to elucidate better the deeply interconnected nature of the trabecular network with distinct element formations conducting forces per their mechanical boundary conditions. Within this network, forces act through elements: a rod or plate with force applied to one end will transmit this force to a component connected to the other end, defining the boundary conditions for the loading of each element. To that end, this study has two aims: First, to investigate the connectivity of individually segmented elements of trabecular bone with respect to their local boundary conditions as defined by the surrounding trabecular network and linking them directly to the bone's overall mechanical response during loading using a mathematical graph model of the plate and rod (PR) Network. Second, we use this model to quantify side artifacts, a known artifact when testing an excised specimen of trabecular bone, where vertical trabeculae lose their load-bearing capacity due to a loss of connectivity, ultimately resulting in a change of the trabecular network topology. Resuts: Connected elements derived from our model predicted apparent elastic modulus by fitting a linear regression (R 2 = 0.81). In comparison, prediction using conventional bone volume fraction results in a lower accuracy (R 2 = 0.72), demonstrating the ability of the PR Network to estimate compressive elastic modulus independent of specimen size or loading boundary condition. Discussion: PR Network models are a novel approach to describing connectivity within the trabecular network and incorporating mechanical boundary conditions within the morphological analysis, thus enabling the study of intrinsic material properties of trabecular bone. Ultimately, PR Network models may be an early predictor or provide further insights into osteo-degenerative diseases.

Compressive mechanical properties of dry antler cortical bone cylinders from different cervidae species

Antlers are bony structures composed predominantly of primary osteons with unique mechanical properties due to their specific use by deer as weapon and shield. Antler bone fracture resistance has attracted prior scrutiny through experimental tests and theoretical models. To characterize antler mechanical properties, compression of cubes, or bending or tensioning of rectangular bars have been performed in the literature with variations in the protocols precluding comparisons of the data. Compression testing is a widely used experimental technique for determining the mechanical properties of specimens excised from cortical or cancellous regions of bone. However, the recommended geometry for compression tests is the cylinder, being more representative of the real performances of the material. The purpose of research was to report data for compressive strength and stiffness of antler cortical bone following current guidelines. Cylinders (n = 296) of dry antler cortical bone from either the main beam or the tines of Cervus elaphus, Rangifer tarandus, Cervus nippon and Damadama were tested. This study highlights the fact that compression of antler cortical bone cylinders following current guidelines is feasible but not applicable in all species. Standardization of the testing protocols could help to compare data from the literature. This study also confirms that sample localization has no effect on the mechanical properties, that sample density has a significant impact and allows enriching the knowledge of the mechanical properties of dry antler cortical bone.

Evaluating a theoretical and an empirical model of "side effects" in cancellous bone

Accurate measurement of cancellous bone's apparent elastic modulus, E, is confounded by the experimental artefacts created when trabeculae are severed during specimen preparation. Although standardized axial testing protocols have been developed to deal with the so-called "end effects" caused by severed trabeculae at the loading surfaces, much less attention has been given to the "side effects" around the periphery and the specimen size dependence they create. Two models (one theoretical, one empirical) have been proposed in the literature to predict the reduction in E with decreasing specimen diameter. The current study used finite element method (FEM) modelling to analyze bovine cancellous bone from five different anatomic sites and quantify the changes in E that occurred with specimen diameter. The two models were adapted so that they could predict E based on diameter and architectural parameters (BV/TV, DA, Tb.Sp) alone, without requiring that a "true" modulus be known a priori. Both models fit the data equally well; however, the empirical model gives simpler estimations as a function of trabecular separation (Tb.Sp). A minimum diameter of 5-8 Tb.Sp is recommended.

Standardizing compression testing for measuring the stiffness of human bone

Objectives

The ability to determine human bone stiffness is of clinical relevance in many fields, including bone quality assessment and orthopaedic prosthesis design. Stiffness can be measured using compression testing, an experimental technique commonly used to test bone specimens in vitro. This systematic review aims to determine how best to perform compression testing of human bone.

Methods

A keyword search of all English language articles up until December 2017 of compression testing of bone was undertaken in Medline, Embase, PubMed, and Scopus databases. Studies using bulk tissue, animal tissue, whole bone, or testing techniques other than compression testing were excluded.

Results

A total of 4712 abstracts were retrieved, with 177 papers included in the analysis; 20 studies directly analyzed the compression testing technique to improve the accuracy of testing. Several influencing factors should be considered when testing bone samples in compression. These include the method of data analysis, specimen storage, specimen preparation, testing configuration, and loading protocol.

Conclusion

Compression testing is a widely used technique for measuring the stiffness of bone but there is a great deal of inter-study variation in experimental techniques across the literature. Based on best evidence from the literature, suggestions for bone compression testing are made in this review, although further studies are needed to establish standardized bone testing techniques in order to increase the comparability and reliability of bone stiffness studies.

Cite this article: S. Zhao, M. Arnold, S. Ma, R. L. Abel, J. P. Cobb, U. Hansen, O. Boughton. Standardizing compression testing for measuring the stiffness of human bone. Bone Joint Res 2018;7:524–538. DOI: 10.1302/2046-3758.78.BJR-2018-0025.R1.

The different distribution of enzymatic collagen cross-links found in adult and children bone result in different mechanical behavior of collagen

Enzymatic collagen cross-linking has been shown to play an important role in the macroscopic elastic and plastic deformation of bone across ages. However, its direct contribution to collagen fibril deformation is unknown. The aim of this study is to determine how covalent intermolecular connections from enzymatic collagen cross-links contribute to collagen fibril elastic and plastic deformation of adults and children's bone matrix. We used ex vivo data previously obtained from biochemical analysis of children and adults bone samples (n = 14; n = 8, respectively) to create 22 sample-specific computational models of cross-linked collagen fibrils. By simulating a tensile test for each fibril, we computed the modulus of elasticity (E), ultimate tensile and yield stress (σ_u and σ_y), and elastic, plastic and total work (W_e, W_p and W_tot) for each collagen fibril. We present a novel difference between children and adult bone in the deformation of the collagen phase and suggest a link between collagen fibril scale and macroscale for elastic behavior in children bone under the influence of immature enzymatic cross-links. We show a parametric linear correlation between W_e and immature enzymatic collagen cross-links at the collagen fibril scale in the children population that is similar to the one we found at the macroscale in our previous study. Finally, we suggest the key role of covalent intermolecular connections to stiffness parameters (e.g. elastic modulus and W_e) in children's collagen fibril and to toughness parameters in adult's collagen fibril, respectively.

Current concepts on structure-function relationships in the menisci

The menisci are intricately organized structures that perform many tasks in the knee. We review their structure and function and introduce new data about their tibial and femoral surfaces. As the femur and tibia approach each other when the knee is bearing load, circumferential tension develops in the menisci, enabling the transmission of compressive load between the femoral and tibial cartilage layers. A low shear modulus is necessary for the tissue to adapt its shape to the changing radius of the femur as that bone moves relative to the tibia during joint articulation. The organization of the meniscus facilitates its functions. In the outer region of the menisci, intertwined collagen fibrils, fibers, and fascicles with predominantly circumferential orientation are prevalent; these structures are held together by radial tie fibers and sheets. Toward the inner portion of the menisci, there is more proteoglycan and the structure becomes more cartilage-like. The transition between these structural forms is gradual and seamless. The flexible roots, required for rigid body motion of the menisci, meld with both the tibia and the outer portion of the menisci to maintain continuity for resistance to the circumferential tension. Our new data demonstrate that the femoral and tibial surfaces of the menisci are structurally analogous to the surfaces of articular cartilage, enabling consistent modes of lubrication and load transfer to occur at the interfacing surfaces throughout motion. The structure and function of the menisci are thus shown to be strongly related to one another: form clearly complements function.

Comparison of Different Fixation Types Used in Unilateral Mandibular Condylar Fractures: An In Vivo Study With New Biomechanical Model

INTRODUCTION

The aim of this in vivo study is to compare the single-titanium, double-titanium mini plate, and single resorbable plate systems used in internal rigid fixation of the unilateral mandibular condylar fractures on new design biomechanical model.

METHODS

Thirty synthetic polyurethane models were used for biomechanical testing. Fracture lines were created for each model. Fragments were fixed with single-titanium plates in Group A (n = 10), double-titanium plates in Group B (n = 10), and single biodegradable plate (PPLA) in Group C (n = 10). Masticatory forces were applied to the models and the biomechanical properties of the titanium plate and screws, resorbable plate, and screws were evaluated.

RESULTS

The average failure force for Group A, Group B, and Group C is 199, 324, 177N and the average bone displacement for Group A, Group B, Group C is 1.9, 0.3, 2.1 mm, respectively.

DISCUSSION

Double titanium plates showed the most acceptable results in the fixation of unilateral subcondylar fractures where the single titanium and biodegradable plate systems failed to provide enough stability in unilateral subcondylar fracture fixation. Biodegradable plate systems are still not an alternative in fixation of unilateral condylar fractures.

Ratio between mature and immature enzymatic cross-links correlates with post-yield cortical bone behavior: An insight into greenstick fractures of the child fibula

As a determinant of skeletal fragility, the organic matrix is responsible for the post-yield and creep behavior of bone and for its toughness, while the mineral apatite acts on stiffness. Specific to the fibula and ulna in children, greenstick fractures show a plastic in vivo mechanical behavior before bone fracture. During growth, the immature form of collagen enzymatic cross-links gradually decreases, to be replaced by the mature form until adolescence, subsequently remaining constant throughout adult life. However, the link between the cortical bone organic matrix and greenstick fractures in children remains to be explored. Here, we sought to determine: 1) whether plastic bending fractures can occur in vitro, by testing cortical bone samples from children's fibula and 2) whether the post-yield behavior (ωp plastic energy) of cortical bone before fracture is related to total quantity of the collagen matrix, or to the quantity of mature and immature enzymatic cross-links and the quantity of non-enzymatic cross-links. We used a two-step approach; first, a 3-point microbending device tested 22 fibula machined bone samples from 7 children and 3 elderly adults until fracture. Second, biochemical analysis by HPLC was performed on the sample fragments. When pooling two groups of donors, children and elderly adults, results show a rank correlation between total energy dissipated before fracture and age and a linear correlation between plastic energy dissipated before fracture and ratio of immature/mature cross-links. A collagen matrix with more immature cross-links (i.e. a higher immature/mature cross-link ratio) is more likely to plastically deform before fracture. We conclude that this ratio in the sub-nanostructure of the organic matrix in cortical bone from the fibula may go some way towards explaining the variance in post-yield behavior. From a clinical point of view, therefore, our results provide a potential explanation of the presence of greenstick fractures in children.

Human perivascular stem cell-based bone graft substitute induces rat spinal fusion

Adipose tissue is an attractive source of mesenchymal stem cells (MSCs) because of its abundance and accessibility. We have previously defined a population of native MSCs termed perivascular stem cells (PSCs), purified from diverse human tissues, including adipose tissue. Human PSCs (hPSCs) are a bipartite cell population composed of pericytes (CD146+CD34-CD45-) and adventitial cells (CD146-CD34+CD45-), isolated by fluorescence-activated cell sorting and with properties identical to those of culture identified MSCs. Our previous studies showed that hPSCs exhibit improved bone formation compared with a sample-matched unpurified population (termed stromal vascular fraction); however, it is not known whether hPSCs would be efficacious in a spinal fusion model. To investigate, we evaluated the osteogenic potential of freshly sorted hPSCs without culture expansion and differentiation in a rat model of posterolateral lumbar spinal fusion. We compared increasing dosages of implanted hPSCs to assess for dose-dependent efficacy. All hPSC treatment groups induced successful spinal fusion, assessed by manual palpation and microcomputed tomography. Computerized biomechanical simulation (finite element analysis) further demonstrated bone fusion with hPSC treatment. Histological analyses showed robust endochondral ossification in hPSC-treated samples. Finally, we confirmed that implanted hPSCs indeed differentiated into osteoblasts and osteocytes; however, the majority of the new bone formation was of host origin. These results suggest that implanted hPSCs positively regulate bone formation via direct and paracrine mechanisms. In summary, hPSCs are a readily available MSC population that effectively forms bone without requirements for culture or predifferentiation. Thus, hPSC-based products show promise for future efforts in clinical bone regeneration and repair.

Scale and boundary conditions effects on the apparent elastic moduli of trabecular bone modeled as a periodic cellular solid

We study apparent elastic moduli of trabecular bone, which is represented, for simplicity, by a two- or three-dimensional periodic cellular network. The term "apparent" refers to the case when the region used in calculations (or specimen size) is smaller than a representative volume element and the moduli depend on the size of that region and boundary conditions. Both the bone tissue forming the network and the pores (represented by a very soft material) are assumed, for simplicity, as homogeneous, linear elastic, and isotropic. In order to investigate the effects of scale and boundary conditions on the moduli of these networks we vary the specimen size and apply four different boundary conditions: displacement, traction, mixed, and periodic. The analysis using periodic boundary conditions gives the effective moduli, while the displacement, traction, and mixed boundary conditions give apparent moduli. The apparent moduli calculated using displacement and traction boundary conditions bound the effective moduli from above and below, respectively. The larger is the size of the region used in our calculations, the closer are the bounds. Our choice of mixed boundary conditions gives results that are very close to those obtained using periodic boundary conditions. We conduct this analysis computationally using a finite element method. We also investigate the effect of mismatch in elastic moduli of bone tissue and soft fill, trabecular bone structure geometry, and bone tissue volume fraction on the apparent elastic moduli of idealized periodic models of trabecular bone. This study gives guidance on how the size of the specimen and boundary conditions (used in experiments or simulations) influence elastic moduli of cellular materials. This approach is applicable to heterogeneous materials in general.

Specimen diameter and "side artifacts" in cancellous bone evaluated using end-constrained elastic tension

In cancellous bone testing of cored samples, side artifacts are the underestimation of the true (i.e. in situ) mechanical properties due to the severing of the trabecular network during specimen preparation. Although other researchers have suggested correction factors derived from finite element method (FEM) models, it is proposed that side effects can be minimized by increasing the specimen diameter. Six different diameter specimens (3.1-10.6 mm), from two different anatomic sites (bovine femoral condyle and bovine lumbar vertebrae), were mechanically tested in elastic tension using an epoxy endcap protocol to eliminate end artifacts. Elastic modulus was found to be significantly affected by diameter in both sites. For example, the 5.1 mm samples underestimated the elastic modulus of the 10.6 mm samples by an average of roughly 20%. Yet no statistical difference was detected between the 8.3 and 10.6 mm samples in either anatomic site, suggesting that 8.3 mm diameter specimens were sufficiently large to avoid side artifacts. FEM models created from micro-CT images reveal that modulus approaches an asymptotic value with increasing diameter, and demonstrate an architecture-dependent drop in modulus at decreasing diameters. These results confirm, both experimentally and numerically, that side effects can be ignored given a suitably large specimen diameter and that this minimum diameter will be dependent on the cancellous architecture. An important implication of the latter result is that specimen diameters must be chosen appropriately when comparing test groups with different architectures (e.g. normal versus osteoporotic) to ensure that the magnitude of side artifacts does not confound the true differences between the groups.

Pullout strength of suture anchors: effect of mechanical properties of trabecular bone

This study investigated the relationships between trabecular microstructure and elastic modulus, compressive strength, and suture anchor pullout strength. Twelve fresh-frozen humeri underwent mechanical testing followed by micro-computed tomography (microCT). Either compression testing of cylindrical bone samples or pullout testing using an Arthrex 5mm Corkscrew was performed in synthetic sawbone or at specific locations in the humerus such as the greater tuberosity, lesser tuberosity, and humeral head. Synthetic sawbone underwent identical mechanical testing and microCT analysis. Bone volume fraction (BVF), structural model index (SMI), trabecular thickness (TbTh), trabecular spacing (TbSp), trabecular number (TbN), and connectivity density were compared against modulus, compressive strength, and pullout strength in both materials. In cadaveric bone, modulus showed correlations to all of the microstructural properties, while compressive and pullout strength were only correlated to BVF, SMI, and TbSp. The microstructure of synthetic bone differed from cadaveric bone as SMI and TbTh showed little variation across the densities tested. Therefore, SMI and TbTh were the only microstructural properties that did not show correlations to the mechanical properties tested in synthetic bone. This study helps identify key microstructure-property relationships in cadaveric and synthetic bone as well as illustrate the similarities and differences between cadaveric and synthetic bone as biomechanical test materials.

Assessment of bone quality using finite element analysis based upon micro-CT images

Background

To evaluate the feasibility of a micro-image based finite element model to determine the efficacy of sequential treatments on the bone quality in a rat osteoporosis model.

Methods

Rat osteoporosis and treated osteoporosis models were established with the bone loss, restore and maintain concept. Thirty Sprague-Dawley rats were used in this study. A sham operation or ovariectomy was performed at 20 weeks after birth, which was followed by the respective sequential trials as follows: (1) sham-operation only, (2) ovariectomy only, (3) ovariectomized rats with parathyroid hormone maintenance, (4) ovariectomized rats treated with PTH for 5 weeks and then withdrawal, (5) ovariectomized rats treated with PTH for 5 weeks and then with 17 beta-estradiol, and (6) ovariectomized rats treated with parathyroid hormone for 5 weeks and then treated with zoledronate. The histomorphometry indices were determined using the micro-images from a micro-computed tomogram. Finite element analysis was carried out to determine the mechanical properties (Stiffness and Young's modulus) of the vertebra bodies. The differences in properties between the groups were compared using ANOVA and a Bonferroni's multiple group comparison procedure.

Results

The histomorphometry and mechanical properties were significantly better in groups (3) and (6) than in the groups (1) and (2) (p < 0.05). The stiffness (σ_s) and Young's modulus (E) was highest in group (3) following by group (6).

Conclusions

Finite element analysis based on micro-images provides a useful tool that reflects the changes in micro-structural and mechanical properties of a rat vertebral body with the bone loss, restore and maintain concept.

Mechanical properties of open-cell foam synthetic thoracic vertebrae

This study presents comprehensive morphological and mechanical properties (static, dynamic) of open-cell rigid foams (Pacific Research Laboratories Inc. Vashon, WA) and a synthetic vertebral body derived from each of the foams. Synthetic vertebrae were comprised of a cylindrical open-cell foam core enclosed by a fiberglass resin cortex. The open-cell rigid foam was shown to have similar morphology and porosity as human vertebral cancellous bone, and exhibited a crush or fracture consolidation band typical of open-celled materials and cancellous bone. However, the foam material density was 40% lower than natural cancellous bone resulting in a lower compressive apparent strength and apparent modulus in comparison to human bone. During cyclic, mean compression fatigue tests, the synthetic vertebrae exhibited an initial apparent modulus, progressive modulus reduction, strain accumulation and S-N curve behaviour similar to human and animal vertebral cancellous bone. Synthetic open-cell foam vertebrae offer researchers an alternative to human vertebral bone for static and dynamic biomechanical experiments, including studies examining the effects of cement injection.

Side-artifact errors in yield strength and elastic modulus for human trabecular bone and their dependence on bone volume fraction and anatomic site

In the context of reconciling the mechanical properties of trabecular bone measured from in vitro mechanical testing with the true in situ behavior, recent attention has focused on the "side-artifact" which results from interruption of the trabecular network along the sides of machined specimens. The objective of this study was to compare the magnitude of the side-artifact error for measurements of elastic modulus vs. yield stress and to determine the dependence of these errors on anatomic site and trabecular micro-architecture. Using a series of parametric variations on micro-CT-based finite element models of trabecular bone from the human vertebral body (n=24) and femoral neck (n=10), side-artifact correction factors were quantified as the ratio of the side-artifact-free apparent mechanical property to the corresponding property measured in a typical experiment. The mean (+/-SD) correction factors for yield stress were 1.32+/-0.17 vs. 1.20+/-0.11 for the vertebral body and femoral neck (p<0.05), respectively, and the corresponding factors for modulus were 1.24+/-0.09 vs. 1.10+/-0.04 (p<0.0001). Correction factors were greater for yield stress than modulus (p<0.003), but no anatomic site effect was detected (p>0.29) after accounting for variations in bone volume fraction (BV/TV). Approximately 30-55% of the variation in the correction factors for modulus and yield stress could be accounted for by BV/TV or micro-architecture, representing an appreciable systematic component of the error. Although some scatter in the correction factor-BV/TV relationships may confound accurate correction of modulus and yield stress for individual specimens, side-artifact correction is nonetheless essential for obtaining accurate mean estimates of modulus and yield stress for a cohort of specimens. We conclude that appreciation and correction for the differential effects of the side-artifact in modulus vs. yield stress and their dependence on BV/TV may improve the interpretation of measured elastic and failure properties for trabecular bone.

The role of fabric in the quasi-static compressive mechanical properties of human trabecular bone from various anatomical locations

Osteoporosis leads to an increased risk of bone fracture. While bone density and architecture can be assessed in vivo with increasing accuracy using CT and MRI, their relationship with the critical mechanical properties at various anatomical sites remain unclear. The objective of this study was to quantify the quasi-static compressive mechanical properties of human trabecular bone among different skeletal sites and compare their relationships with bone volume fraction and a measure of microstructural anisotropy called fabric. Over 600 trabecular bone samples from six skeletal sites were assessed by microCT and tested in uniaxial compression. Bone volume fraction correlated positively with elastic modulus, yield stress, ultimate stress, and the relationships depended strongly on skeletal site. The account of fabric improved these correlations substantially, especially when the data of all sites were pooled together, but the fabric-mechanical property relationships remained somewhat distinct among the anatomical sites. The study confirms that, beyond volume fraction, fabric plays an important role in determining the mechanical properties of trabecular bone and should be exploited in mechanical analysis of clinically relevant sites of the human skeleton.

The effects of side-artifacts on the elastic modulus of trabecular bone

Determining accurate density-mechanical property relationships for trabecular bone is critical for correct characterization of this important structure-function relation. When testing any excised specimen of trabecular bone, an unavoidable experimental artifact originates from the sides of the specimen where peripheral trabeculae lose their vertical load-bearing capacity due to interruption of connectivity, a phenomenon denoted here as the 'side-artifact'. We sought in this study to quantify the magnitude of such side-artifact errors in modulus measurement and to do so as a function of the trabecular architecture and specimen size. Using parametric computational analysis of high-resolution micro-CT-based finite-element models of cores of elderly human vertebral trabecular bone, a specimen-specific correction factor for the side-artifact was quantified as the ratio of the side-artifact-free apparent modulus (Etrue) to the apparent modulus that would be measured in a typical experiment (Emeasured). We found that the width over which the peripheral trabeculae were mostly unloaded was between 0.19 and 0.58 mm. The side-artifact led to an underestimation error in Etrue of over 50% in some specimens, having a mean (+/-SD) of 27+/-11%. There was a trend for the correction factor to linearly increase as volume fraction decreased (p=0.001) and as mean trabecular separation increased (p<0.001). Further analysis indicated that the error increased substantially as specimen size decreased. Two methods used for correcting for the side-artifact were both successful in bringing Emeasured into statistical agreement with Etrue. These findings have important implications for the interpretation of almost all literature data on trabecular bone mechanical properties since they indicate that such properties need to be adjusted to eliminate the substantial effects of side-artifacts in order to provide more accurate estimates of in situ behavior.

Creep Does Not Contribute to Fatigue in Bovine Trabecular Bone

In both cortical and trabecular bone loaded in fatigue, the stress-strain loops translate along the strain axis. Previous studies have suggested that this translation is the result of creep associated with the mean stress applied in the fatigue test. In this study, we measured the residual strain (corresponding to the translation of the stress-strain loops) in fatigue tests on bovine trabecular bone and compared it to an upper bound estimate of the creep strain in each test. Our results indicate that the contribution of creep to the translation of the stress-strain loops is negligible in bovine trabecular bone. These results, combined with models for fatigue in lower density bone, suggest that that creep does not contribute to the fatigue of normal human bone. Creep may make a significant contribution to fatigue in low-density osteoporotic bone in which trabeculae have resorbed, reducing the connectivity of the trabecular structure.

Quantitative computed tomography estimates of the mechanical properties of human vertebral trabecular bone

The objective of this study was to report our quantitative computed tomography (QCT) density-mechanical property regressions for trabecular bone for use in biomechanical modelling of the human spine. Cylindrical specimens of human vertebral trabecular bone (from T10 to L4) were cored from 32 cadavers (mean +/- SD age = 70.1 +/- 16.8; 13 females, 19 males) and scanned using QCT. Mechanical tests were conducted using a protocol that minimized end-artifacts over the apparent density range tested (0.09-0.38 g/cm3). To account for the presence of multiple specimens per donor in this data set, donor was treated as a random effect in the regression model. Mean modulus (319 +/- 189 MPa) was higher and mean yield strain (0.78 +/- 0.06%) was lower than typical values reported previously due to minimization of the end-artifact errors. QCT density showed a strong positive correlation with modulus (n = 76) and yield stress (r2 = 0.90-0.95, n = 53, p < 0.001). There was a weak positive linear correlation with yield strain (r2 = 0.58, n = 53, p = 0.07). Prediction errors, incurred when estimating modulus or strength for specimens from a new donor, were 30-36% of the mean values of these properties. Direct QCT density-mechanical property regressions gave more precise predictions of mechanical properties than if physically measured wet apparent density was used as an intermediate variable to predict mechanical properties from QCT density. Use of these QCT density-mechanical property regressions should improve the fidelity of QCT-based biomechanical models of the human spine for whole bone and bone-implant analyses.

A biomechanical evaluation of mandibular condyle fracture plating techniques

OBJECTIVES

The purpose of this investigation was to evaluate the biomechanical behavior of various rigid internal fixation techniques for mandibular condylar process fractures.

MATERIALS AND METHODS

Synthetic mandible replicas (Synbone, Landquart, Switzerland) were used to evaluate a control, and four monocortical mandibular condyle plating techniques. Each group was subjected to linear loading in lateral to medial, medial to lateral and posterior to anterior directions by an Instron 1331 (Instron, Canton, MA) servohydraulic mechanical testing unit. Yield load, yield displacement, and stiffness were measured. In addition, each group was subjected to torsional loading using an Instron 8521 (Instron). Yield torque, yield rotation, and stiffness were measured. Five samples were tested for each group and method of loading (n = 100). Means and standard deviations were derived and compared for statistical significance using a 1-way analysis variance (P <.05). Third-order polynomial best-fit curves were also created for each group to further evaluate and compare the mechanical behavior.

RESULTS

Statistically significant differences were noted between fixation groups for the different mechanical measures evaluated under the different conditions of linear loading. Statistically significant differences were noted between groups for yield rotation during torsional loading. Although different in magnitude, similar patterns of mechanical behavior were observed in the third-order polynomial best-fit curves for lateral to medial loading, medial to lateral loading and torsional loading. For posterior to anterior loading, different patterns of mechanical behavior were noted between the experimental groups, but similar behavior was noted between the control and mini dynamic compression plate

CONCLUSIONS

While differences were noted between each of the fixation systems in their abilities to resist loads under the conditions tested, the mini dynamic compression plate provided the most favorable mechanical behavior. Based on the presumed clinical parameters, we can suggest that none of the systems evaluated were ideal for the treatment of mandibular condyle fractures, but that the mini dynamic compression plate is the closest to an effective means for reconstruction.

Finite element calculated uniaxial apparent stiffness is a consistent predictor of uniaxial apparent strength in human vertebral cancellous bone tested with different boundary conditions

Strong correspondence between the uniaxial apparent strength and stiffness of cancellous bone allows the use of stiffness as a predictor of bone strength. Measured values of mechanical properties in cancellous bone can be different between experiments due to different experimental conditions. In the current study, bone volume fraction, experimentally determined and finite element (FE) predicted stiffness were examined as predictors of cancellous bone ultimate strength in two different groups each of which was tested using a different end constraint. It is demonstrated that, although always significant, the relationships of strength with bone volume fraction and experimentally determined stiffness are different between test groups. Apparent stiffness, estimated by FE modeling, predicts the ultimate strength of human cancellous bone consistently for all examined experimental protocols.

The influence of bone volume fraction and ash fraction on bone strength and modulus

Although bone strength and modulus are known to be influenced by both volume fraction and mineral content (ash fraction), the relative influence of these two parameters remains unknown. Single-parameter power law functions are used widely to relate bone volume or ash fraction to bone strength and elastic modulus. In this study we evaluate the potential for predicting bone mechanical properties with two-parameter power law functions of bone volume fraction (BV/TV) and ash fraction (alpha) of the form y = a(BV/TV)(b) alpha(c) (where y is either ultimate strength or elastic modulus). We derived an expression for bone volume fraction as a function of apparent density and ash fraction to perform a new analysis of data presented by Keller in 1994. Exponents b and c for the prediction of bone strength were found to be 1.92 +/- 0.02 and 2.79 +/- 0.09 (mean +/- SE), respectively, with r(2) = 0.97. The value of b was found to be consistent with that found previously, whereas the value of c was lower than values previously reported. For the prediction of elastic modulus we found b and c to be 2.58 +/- 0.02 and 2.74 +/- 0.13, respectively, with r(2) = 0.97. The exponent related to ash fraction was typically larger than that associated with bone volume fraction, suggesting that a change in mineral content will, in general, generate a larger change in bone strength and stiffness than a similar change in bone volume fraction. These findings are important for interpreting the results of antiresorptive drug treatments that can cause changes in both ash and bone volume fraction.

Poroelastic properties of bovine vertebral trabecular bone

The theory of poroelasticity has been used to study bone mechanics without directly measuring poroelastic properties. In this study, we developed an experimental protocol and measured the poroelastic properties of bovine vertebral trabecular bone. Mean (+/-SD) values for drained shear modulus, drained Poisson's ratio, undrained Poisson's ratio, Skempton's coefficient, and permeability coefficient were, respectively, 90.85 (+/-59.59) MPa and 0.242 (+/-0.099), 0.399 (+/-0.083), 0.851 (+/-0.144), and 16.31 (+/-8.02) x 10(-8) m2/Pa/sec, respectively. The experimental protocol can be used generally for the measurement of poroelastic properties of bone when cylindrical specimens are available. Measured poroelastic properties can be used directly or converted to Biot's coefficient and modulus, without assuming the incompressibility of solid and fluid constituents, for the poroelastic modeling of bone.

Speed of sound reflects Young's modulus as assessed by microstructural finite element analysis

We analyzed the ability of the quantitative ultrasound (QUS) parameter, speed of sound (SOS), and bone mineral density (BMD), as measured by dual-energy X-ray absorptiometry (DXA), to predict Young's modulus, as assessed by microstructural finite element analysis (muFEA) from microcomputed tomography (muCT) reconstructions. With muFEA simulation, all bone elements in the model can be assigned the same isotropic Young's modulus; therefore, in contrast to mechanical tests, only the trabecular structure plays a role in the determination of the elastic properties of the specimen. SOS, BMD, and microCT measurements were performed in 15 cubes of pure trabecular bovine bone in three orthogonal directions: anteroposterior (AP); mediolateral (ML); and craniocaudal (CC). The anisotropy of the architecture was determined using mean intercept length (MIL) measurements. SOS, MIL, and Young's modulus (E) values were significantly different in all three directions (p < 0.001), with the highest values in the CC direction. There was a strong linear relationship between E and SOS in each of the three orthogonal directions, with r(2) being 0.88, 0.92, and 0.84 (all p < 0.0001) for the CC, ML, and AP directions, respectively. The relationship between E and BMD was less strong, with r(2) being between 0.66 and 0.85 (all p < 0.0001) in the different directions. There was also a significant, positive correlation between SOS and BMD in each of the three axes (r(2) being 0.81, 0.42, and 0.92 in the CC, ML, and AP directions, respectively; p < 0.0001). After correction for BMD, the correlations between SOS and E in each of the three directions remained highly significant (r(2) = 0.77, p < 0. 0001 for the AP direction; r(2) = 0.48, p < 0.001 for the CC direction; r(2) = 0.52, p < 0.005 for the ML direction). After correction for SOS, BMD remained significantly correlated with Young's modulus in the AP and CC directions (r(2) = 0.52, p < 0.005; r(2) = 0.30, p < 0.05, respectively), but the correlation in the ML direction was no longer statistically significant. In a stepwise regression model, E was best predicted by SOS in each of the orthogonal directions. These observations illustrate the ability of the SOS technique to assess the architectural mechanical quality of trabecular bone.

Elastic and physicochemical relationships within cortical bone

The purpose of this study was to examine the relationships that exist between the elastic properties and the physicochemical properties of cortical bone in two groups of experimental animals. The animal model was the immature mutant dwarf rat, and the groups consisted of rats treated and not treated with recombinant human growth hormone (rhGH). The objective was to establish and broaden the quantifiable link between the three-dimensional form and function of bone beyond the typical unidirectional measures. This study was based on previously reported work that refined the ultrasonic elasticity technique for use with small specimens (<1.0 mm) and determined that the administration of rhGH can counter the degenerative effects produced by hormone-suppressed downregulation on the elastic and physicochemical characteristics of cortical bone. Ultrasonic wave propagation and density measurements were used previously to determine the three-dimensional (orthotropic) material properties of rat femoral cortical bone. X-ray powder diffraction, microscopic, morphometric, and biochemical analysis techniques have been used to describe physicochemical properties, including mineral crystal size, cortical porosity, mineral and nonmineral content, and microstructural characteristics. In this study, mathematical relationships between the local physicochemical (independent variable) and elastic (dependent variable) properties were formulated via linear and nonlinear regression analyses. In general, apparent density was found to have the highest level of correlation with most of the longitudinal and shear moduli (R(2) = 0.300 to 0.800). Concomitantly, mineral crystal width and cortical porosity offered the best correlations with the Poisson's ratios (R(2) up to 0.600). Wilcoxon t tests verified a significant decrease in the elastic properties in dwarf rat cortical bone after rhGH treatments (p < 0.05). Physicochemical measures of bone quality (density, crystal size) generally decreased while measures of bone quantity (cortical area, moments of inertia) generally increased (p < 0.05) after rhGH treatments. Some mineral and nonmineral properties were unchanged. This study presents a quantifiable link between cortical bone elasticity and its composite construction as measured across two dramatically different experimental groups.

The role of an effective isotropic tissue modulus in the elastic properties of cancellous bone

Conceptually, the elastic characteristics of cancellous bone could be predicted directly from the trabecular morphology--or architecture--and by the elastic properties of the tissue itself. Although hardly any experimental evidence exists, it is often implicitly assumed that tissue anisotropy has a negligible effect on the apparent elastic properties of cancellous bone. The question addressed in this paper is whether this is actually true. If it is, then micromechanical finite element analysis (micro-FEA) models, representing trabecular architecture, using an 'effective isotropic tissue modulus' should be able to predict apparent elastic properties of cancellous bone. To test this, accurate multi-axial compressive mechanical tests of 29 whale bone specimens were simulated with specimen-specific micro-FEA computer models built from true three-dimensional reconstructions. By scaling the micro-FEA predictions by a constant tissue modulus, 92% of the variation of Young's moduli determined experimentally could be explained. The correlation even increased to 95% when the micro-FEA moduli were scaled to the isotropic tissue moduli of individual specimens. Excellent agreement was also found in the elastic symmetry axes and anisotropy ratios. The prediction of Poisson's ratios was somewhat less precise at 85% correlation. The results support the hypothesis; for practical purposes, the concept of an 'effective isotropic tissue modulus' concept is a viable one. They also suggest that the value of such a modulus for individual cases might be inferred from the average tissue density, hence the degree of mineralization. Future studies must clarify how specific the tissue modulus should be for different types of bone if adequate predictions of elastic behavior are to be made in this way.

Measurement of strain distributions within vertebral body sections by texture correlation

STUDY DESIGN

A high-resolution strain measurement technique was applied to axially loaded parasagittal sections from thoracic spinal segments.

OBJECTIVES

To establish a new experimental technique, develop data analysis procedures, characterize intrasample shear strain distributions, and measure intersample variability within a group of morphologically diverse samples.

SUMMARY OF BACKGROUND DATA

Compression of intact vertebral bodies yields structural stiffness and strength, but not strain patterns within the trabecular bone. Finite element models yield trabecular strains but require uncertain boundary conditions and material properties.

METHODS

Six spinal segments (T8-T10) were sliced in parasagittal sections 6-mm thick. Axial compression was applied in 25-N increments up to sample failure, then the load was removed. Contact radiographs of the samples were made at each loading level. Strain distributions within the central vertebral body were measured from the contact radiographs by an image correlation procedure.

RESULTS

Intrasample shear strain probability distributions were log-normal at all load levels. Shear strains were concentrated directly inferior to the superior end-plate and adjacent to the anterior cortex, in regions where fractures are commonly seen clinically. Load removal restored overall sample shape, but measurable residual strains remained.

CONCLUSIONS

This experimental model is a suitable means of studying low-energy vertebral fractures. The methods of data interpretation are consistent and reliable, and strain patterns correlate with clinical fracture patterns. Quantification of intersample variability provides guidelines for the design of future experiments, and the strain patterns form a basis for validation of finite element models. The results imply that strain uniformity is an important criterion in assessing risk of vertebral failure.

A global relationship between trabecular bone morphology and homogenized elastic properties

An alternative concept of the relationship between morphological and elastic properties of trabecular bone is presented and applied to human tissue from several anatomical locations using a digital approach. The three-dimensional morphology of trabecular bone was assessed with a microcomputed tomography system and the method of directed secants as well as the star volume procedure were used to compute mean intercept length (MIL) and average bone length (ABL) of 4 mm cubic specimens. Assuming isotropic elastic properties for the trabecular tissue, the general elastic tensors of the bone specimens were determined using the homogenization method and the closest orthotropic tensors were calculated with an optimization algorithm. The assumption of orthotropy for trabecular bone was found to improve with specimen size and hold within 6.1 percent for a 4 mm cube size. A strong global relationship (r2 = 0.95) was obtained between fabric and the orthotropic elastic tensor with a minimal set of five constants. Mean intercept length and average bone length provided an equivalent power of prediction. These results support the hypothesis that the elastic properties of human trabecular bone from an arbitrary anatomical location can be estimated from an approximation of the anisotropic morphology and a prior knowledge of tissue properties.

Relationships between bone morphology and bone elastic properties can be accurately quantified using high-resolution computer reconstructions

It would be advantageous if the mechanical properties of trabecular bone could be directly inferred from stereomorphometric parameters. For that purpose, apparent density and mean intercept length, as measures of bone mass and directionality (fabric), are commonly correlated with the elastic characteristics of bone samples, as determined in compression tests. However, complete and accurate relationships have not yet been established in this way. This may be due not only to the occurrence of artifacts in both the stereomorphometric and the mechanical assessments but also to an inherent inadequacy of mean intercept length in characterizing the full mechanical significance of bone architecture or nonhomogeneities in trabecular tissue properties not accounted for in stereomorphometry. In this study, we introduce a computer modeling approach allowing these biases to be eliminated. With use of high-resolution three-dimensional computer reconstructions of trabecular bone specimens for stereomorphometry and for microstructural finite element models to simulate mechanical tests, unbiased comparisons become feasible. The purpose was to investigate if accurate and complete relationships can be established in this way. Four different fabric measures were considered: mean intercept length and three volume-based ones. Compliance matrices were calculated from fabric tensors, with use of the mathematical relationship proposed by Cowin for 29 vertebral whale-bone specimens. These were correlated with the compliance constants determined directly from the microstructural finite element model simulation. The nine orthotropic elastic constants of all 29 specimens were well predicted from their stereomorphometric fabric and volume fraction values, with correlation coefficients ranging from R2adj = 0.9934 to 0.9963. When individual compliance components were considered (1/Ei, 1/Gij, or -v[ij]/Ei), correlation coefficients ranged from R2adj = 0.924 to 0.982. All four fabric measures performed equally well. It is concluded that volume fraction and fabric measures correlate highly with the apparent elastic properties of bone samples, provided that anisotropy and nonhomogeneity in the elastic properties of the trabecular tissue itself have negligible effects on the apparent properties. Whether this is true for bone in general remains to be seen, as only a subset was analyzed here. These methods, however, can be valuable in similar assessments of other subsets.

Time analysis for screw application: traditional lag technique versus self-tapping lag technique

A study was conducted to compare the procedural time of a 2.7-mm. fully threaded cortical screw versus a self-tapping, 2.4-mm. lag screw, which is reported to eliminate the need for overdrilling and tapping. The screws were applied by four board-certified podiatric and orthopedic physicians and four second-year podiatric and orthopedic residents. Each screw was placed through two 8-mm. layers of Last-a-foam, and the participants were timed for length of application of four screws from each system per week. The trials were repeated weekly for 4 weeks. The results showed a statistically significant difference between the length of time for insertion between a traditional cortical screw and a self-tapping lag screw, regardless of physician experience.

Three-dimensional methods for quantification of cancellous bone architecture

Recent development in three-dimensional (3-D) imaging of cancellous bone has made possible true 3-D quantification of trabecular architecture. This provides a significant improvement of the tools available for studying and understanding the mechanical functions of cancellous bone. This article reviews the different techniques for 3-D imaging, which include serial sectioning, X-ray tomographic methods, and NMR scanning. Basic architectural features of cancellous bone are discussed, and it is argued that connectivity and architectural anisotropy (fabric) are of special interest in mechanics-architecture relations. A full characterization of elastic mechanical properties is, with traditional mechanical testing, virtually impossible, but 3-D reconstruction in combination with newly developed methods for large-scale finite element analysis allow calculations of all elastic properties at the cancellous bone continuum level. Connectivity has traditionally been approached by various 2-D methods, but none of these methods have any known relation to 3-D connectivity. A topological approach allows unbiased quantification of connectivity, and this further allows expressions of the mean size of individual trabeculae, which has previously also been approached by a number of uncertain 2-D methods. Anisotropy may be quantified by fundamentally different methods. The well-known mean intercept length method is an interface-based method, whereas the volume orientation method is representative of volume-based methods. Recent studies indicate that volume-based methods are at least as good as interface-based methods in predicting mechanical anisotropy. Any other architectural property may be quantified from 3-D reconstructions of cancellous bone specimens as long as an explicit definition of the property can be given. This challenges intuitive and vaguely defined architectural properties and forces bone scientists toward 3-D thinking.

Systematic and random errors in compression testing of trabecular bone

We sought to quantify the systematic and random errors associated with end-artifacts in the platens compression test for trabecular bone. Our hypothesis was that while errors may depend on anatomic site, they do not depend on apparent density and therefore have substantial random components. Trabecular bone specimens were first tested nondestructively using newly developed accurate protocols and then were tested again using the platens compression test. Percentage differences in modulus between the techniques (bovine proximal tibia [n = 18] and humerus [n = 17] and human lumbar spine, [n = 9]) were in the range of 4-86%. These differences did not depend on anatomic site (p = 0.21) and were only weakly dependent on apparent density and specimen aspect ratio (r2 < 0.10). The mean percentage difference in modulus was 32.6%, representing the systematic component of the end-artifact error. Neglecting the minor variations explained by density and specimen size (approximately 10%), an upper bound on the random error from end-artifacts in this experiment was taken as the SD of the modulus difference (+/-18.2%). Based on a synthesis of data taken from this study and from the literature, we concluded that the systematic underestimation error in the platens compression test can be only approximated and is in the range of 20-40%; the substantial random error (+/-12.5%) confounds correction, particularly when the sample size is small. These errors should be considered when interpreting results from the platens test, and more accurate testing techniques should be used when such errors are not acceptable.