Brief communication: Correlation between elastic modulus and radiographic density in mandibular cortical bone of colobine monkeys.

OBJECTIVES: The relationship between radiographic grayscale and elastic modulus was determined using mandibular cortical bone of colobine monkeys. Quantification of this relationship is critical for establishing absolute measures of structural rigidity of skeletal elements. MATERIALS AND METHODS: We determined the Vickers microhardness values in mandibular bone from two species of African colobine monkeys and related these values to elastic modulus through an empirically determined correlation. We also determined radiographic grayscale values from microcomputed tomographic scans of the mandible in the same regions in which microhardness was sampled. We then correlated modulus to grayscale with a power law relationship. RESULTS: We found that elastic modulus scaled with negative allometry with respect to grayscale with an exponent of 0.77. DISCUSSION: Our results suggest a single exponent can effectively capture the relationship of grayscale to elastic modulus and facilitate development of heterogeneous structural models for use in comparative and computational biomechanical studies.

The relationship between bending stress and the shape of maxillary canines in cercopithecoid monkeys.

Primate canines function in social displays but are also recruited for biting in agonistic encounters. Although the precise nature of the loads such behavior places on the canine crown is unknown, it is thought that bending is a major component of such loads. To date, modeling of canine bending strength has relied on idealized geometric representations. Accounting for the tapering of the crown as well as shape changes along an apical-basal axis provides a more realistic model for assessment of bending stress in canines. We provide such an accounting and evaluate the hypothesis that the morphology of the cercopithecoid canine represents a structural solution for maintaining constant maximum bending stress under apical or distributed loading in a parasagittal plane. This isostress hypothesis is analogous to a design criterion of minimum mass for a given structural requirement. Examining permanent maxillary canines from males and females representing eight West African cercopithecoid species, we reconstructed crown geometry from apex to base using microcomputed tomography. From reconstructed cross-sections, we determined section moduli about a buccolingual centroidal axis. We then determined what the taper should be for a variety of parasagittal loading distributions if the isostress hypothesis were true and compared these theoretical tapers to actual crown geometry. We found that a variety of loading distributions can be accommodated by the canines, particularly among males. These results suggest that our sample of canines are not optimized for resisting particular biting loads, but effectively limit stress gradients associated with a range of behaviors.

Technical note: converting durometer data into elastic modulus in biological materials.

Researchers have increasingly recognized the need to quantify the material properties of primate food items, particularly hardness (H) and stiffness (E), which is measured as elastic modulus. Assessing E in the field is particularly difficult because the typical equipment needed to perform the requisite analyses is expensive and cumbersome. Alternatively, researchers can use hand-held, relatively inexpensive, portable durometers that measure H on Shore scales. Shore-D durometers show a reliable ability to characterize H in harder-stiffer materials, and Shore-D measures in these materials can be reliably converted to E. Shore-A durometers-employed in past field studies of food properties-do not accurately characterize the properties of harder-stiffer materials, which are likely to be those materials exerting the greatest mechanical demands on primate masticatory morphology. We offer recommendations for Shore-D durometer usage in the field.

Reduced stiffness of alveolar bone in the colobine mandible.

Alveolar bone has several mechanical functions, including tooth support and accommodation of occlusal and other masticatory forces. Its unique functional-mechanical environment is reflected by its structural characteristics, but whether alveolar bone is materially distinct from bone elsewhere in the primate facial skeleton is uncertain. This uncertainty is attributable not only to a limited amount of data but also to conflicting findings among these data. We evaluated elastic modulus variation in the mandibular corpus of eight adult specimens of the monkeys Procolobus badius and Colobus polykomos via microindentation to evaluate whether alveolar bone is more compliant than basal bone and to quantify patterns of variation between sexes and species. We sampled Vickers hardness from six serial transverse sections and one coronal section from both the alveolar process and the basal corpus. Hardness values were converted to elastic modulus via regressions specific for bone tissue. Analysis of variance reveals that a plurality of variation is found on a regional scale; i.e., alveolar bone is more compliant than adjacent basal bone. Species affiliation and sex are not significant sources of variation. These findings support a hypothesis that compliance of alveolar bone represents a material solution for avoiding large stress concentrations arising from occlusal loads. Other comparative data suggest important differences between colobine and cercopithecine mandibles in terms of bone stiffness, both overall and in terms of relative stiffness of alveolar and basal cortical bone.

Spatial patterning of bone stiffness variation in the colobine alveolar process.

Alveolar bone is functionally involved with tooth support and must also be competent in accommodating masticatory forces. Data from a variety of perspectives--including observations of anatomy, metabolic activity and determination of mechanical properties--suggest that alveolar bone is more compliant than the more inferiorly situated basal bone of the mandibular corpus. The nature of stiffness variation within the alveolar process, however, remains largely unexplored. The technique of microindentation is used to estimate bone stiffness variation in the cortical alveolar bone of a sample of eight adult mandibles from two species of West African colobus monkeys. The null hypothesis under investigation is that bone stiffness variation in the alveolar process is random with respect to species, sex, and location. Alternative hypotheses are evaluated with respect to species, sex and locality effects, including those associated with cortical thickness variation and masticatory loading. Microindentation data do not indicate species or sex differences. Spatial variation in alveolar bone, however, is nonrandom. The stiffest bone is localized in the superior alveolar process, and significant differences between buccal and lingual cortical plates are found in five of eight specimens. Evidence for a superoinferior stiffness gradient is found in half the specimens but is confined to either the buccal or lingual cortical plate. Covariation between bone stiffness and bone thickness is weak. Relative compliance of the alveolar process represents a biomechanical solution for enhancing toughness of cortical bone. The relationship of the spatial patterning of bone stiffness to the masticatory loading environment is unclear.

Full-field characterization of wishboning strain in the colobine mandibular symphysis.

The masticatory loading regime of lateral transverse bending (wishboning) is hypothesized to be instrumental in the evolution of symphyseal form among primates. The biomechanics of wishboning have largely been inferred by assuming that the mandible behaves as a curved beam under this load; however, the characterization of stress and strain in the anthropoid symphysis has been interpretively challenging. This is due, in part, to both limitations of sampling strain in an in vivo context and the incongruence of beam theory assumptions on the one hand, and the anatomical complexity of mandibular morphology on the other. Utilizing three-dimensional (3D) Digital Image Correlation (DIC), we employ an in vitro approach to characterize the strain field in a sample of colobine mandibles under simulated wishboning loads in order to assess the utility of idealized curved beam models for characterizing strain gradients in symphyseal bone. Conventional theory of curved beams suggest that colobine mandibles should exhibit reduced disparity of labial and lingual stresses relative to papionin primates given differences in overall mandibular architecture. This prediction is borne out by our analysis: whereas macaques experience lingual:labial strain disparities of 3.5:1, the colobine mandibles exhibit ratios on the order of 2-3:1. However, despite the fact that wishboning loads represent a case of asymmetric bending, details of the wishboning strain field do not conform to expected stress distribution under this model.

Material property variation of mandibular symphyseal bone in colobine monkeys.

The anterior mandibular corpus of anthropoid primates is routinely subjected to masticatory loads that result in relatively high local levels of stress and strain. While structural morphological responses to these loads have been extensively explored, relatively little is known about material property variation in mandibular bone of nonhuman primates. Consequently, the role of regional and local variation in bone stiffness in conditioning stress and strain gradients is poorly understood. We sampled elastic modulus variation in the bone of the anterior mandibular corpus in two species (N = 3 each) of sympatric colobine monkeys, Procolobus badius and Colobus polykomos. These monkeys were chosen for comparison owing to their distinctive dietary regimens, as P. badius rarely includes hard objects in its diet while C. polykomos habitually processes obdurate items during feeding. Elastic modulus is determined through bone hardness data obtained via microindentation, which enables the description of stiffness variation on sub-millimeter scales. Labial bone stiffness exceeds that of lingual bone in the sample overall. Female mandibular bone is generally stiffer than that found in males, and overall Procolobus mandibular bone is stiffer than that in Colobus. These results, interpreted collectively, suggest that the material response to elevated masticatory stress is increased compliance of the affected bone.

Elastic modulus variation in mandibular bone: a microindentation study of Macaca fascicularis.

We characterized the heterogeneous anisotropic elastic properties of mandibular bone in an adult female specimen of Macaca fascicularis using the technique of microindentation. This approach used an indenter of known mass and geometry to sample bone hardness at a spatial resolution in the order of 100 mum. Hardness values were converted to elastic modulus using empirically derived regression. We determined properties in alveolar, midcorpus, and basal regions of coronal and transverse sections taken from multiple locations along the corpus and ramus. Within sections, we determined properties from endosteal, midcortical, and periosteal regions. We found regional variations in bone structure, including bands of orthotropic circumferential lamellar bone at the endosteal and periosteal corpus base, angular region, and ramus. Transversely isotropic osteonal bone characterizes the midcortices of alveolar and basal regions, with many resorption spaces in alveolar regions restricting sampling opportunities. Regional variations in elasticity include relatively compliant bone in the anterior corpus and ramus. Basal cortical bone is stiffer longitudinally than transversely or superoinferiorly, while the evidence for directional dependence in alveolar bone is equivocal. Alveolar bone appears to be relatively compliant with respect to bone found in midcorpus or basal regions. Considerable variation exists in structure and material properties on a highly localized scale, more so than is discernible through conventional approaches for determining material property variation.

Microindentation in bone: hardness variation with five independent variables.

Microindentation is an investigational tool often used to determine hardness and other derived material properties of the material bone. This study explored the variation of microindentation hardness results with five independent variables. The variables were: applied mass, dwell time, drying time, time between indentation and measurement, and distance between the center of an indentation and the edge of other indentations and pores. These variables were selected because they represented a reasonable range of specimen investigational steps. We also investigated the cross sections of typical indentation residual impressions to determine the degree of material pile-up at the edges of the impressions. We found that microindentation hardness varied with applied mass and with distance between the indentation and neighboring indentations and pores but not with the other variables. Our recommended minimum applied mass is 0.10 kg versus a previously published value of 0.05 kg. We also found no discernable material pile-up at the residual impression edges, in contrast to reports of others.

Orthotropic index for bone.

An orthotropic index (OI) is proposed to indicate the existence of a preferred material direction in each of the symmetry planes of an orthotropic material such as bone. Currently, this function is performed by the anisotropy ratio (AR) of any two Young's moduli or compressive (A(c)) and shear (A(s)) anisotropy factors comprised of complicated functions of the elastic constants. The OI incorporates the four independent engineering constants (the shear modulus and Poisson's ratio in addition to the two Young's moduli) in each symmetry plane into a single index. The OI thus improves upon the AR by reflecting orthotropy in a more holistic sense and upon the AR, A(c) and A(s) by taking on a unique value (zero) only when the material is in fact isotropic.

Change in tibial plateau angle after tibial plateau leveling osteotomy in dogs.

OBJECTIVE: To determine the change in tibial plateau angle (TPA) during healing after tibial plateau leveling osteotomy (TPLO) performed for cranial cruciate ligament insufficiency in dogs and to examine factors that may be associated with the change. STUDY DESIGN: Retrospective study. STUDY POPULATION: One hundred and forty-nine canine stifles after TPLO procedure. METHODS: Records of dogs that had TPLO were reviewed. Patient age, weight, sex, breed, pre- and postoperative TPA, recheck TPA, time to recheck, type of implant used, and radiographic evidence of healing were analyzed. RESULTS: Mean time to recheck evaluation was 46 days (range, 28-65 days). Mean difference between immediate postoperative and recheck TPA measurements was 1.5 degrees (range, -3 to 9 degrees). Recheck TPA was a significantly greater (numerically higher) than immediate postoperative TPA (P<.0001). There was no significant effect of patient weight, type of plate used, or healing status of the osteotomy at the time of recheck. No correlation between pre- or postoperative TPA angles and change in TPA angle was detected. CONCLUSIONS: TPA changes during osteotomy healing after TPLO, but factors influencing this change were not identified. CLINICAL RELEVANCE: TPA may increase during healing after TPLO despite apparently adequate osteotomy fixation. The clinical relevance of this increase is unknown but is likely minimal.

Application of an image-based weighted measure of skeletal bending stiffness to great ape mandibles.

Traditional measures of structural stiffness in the primate skeleton do not consider the heterogeneous material stiffness distribution of bone. This assumption of homogeneity introduces an unknown degree of error in estimating stiffness in skeletal elements. Measures of weighted stiffness can be developed by including heterogeneous grayscale variations evident in computed tomographic (CT) images. Since gray scale correlates with material stiffness, the distribution of bone quality and quantity can be simultaneously considered. We developed weighted measures of bending resistance and applied these to CT images at three locations along the mandibular corpus in the hominoids Gorilla, Pongo, and Pan. We calculated the traditional (unweighted) moment of inertia for comparison to our weighted measure, which weighs each pixel by its gray-scale value. This weighing results in assignment of reduced moment of inertia values to sections of reduced density. Our weighted and unweighted moments differ by up to 22%. These differences are not consistent among sections, however, such that they cannot be calculated by simple correction of unweighted moments. The effect of this result is that the rank ordering of individual sections within species changes if weighted moments are considered. These results suggest that the use of weighted moments may spur different interpretations of comparative data sets that rely on stiffness measures as estimates of biomechanical competence.

Finite-element modeling of the anthropoid mandible: the effects of altered boundary conditions.

Finite-element modeling provides a full-field method for describing the stress environment of the skull. The utility of finite-element models, however, remains uncertain given our ignorance of whether such models validly portray states of stress and strain. For example, the effects of boundary conditions that are chosen to represent the mechanical environment in vivo are largely unknown. We conducted an in vitro strain gauge experiment on a fresh, fully dentate adult mandible of Macaca fascicularis to model a simplified loading regime by finite-element analysis for purposes of model validation. Under various conditions of material and structural complexity, we constructed dentate and edentulous models to measure the effects of changing boundary conditions (force orientation and nodal constraints) on strain values predicted at the gauge location. Our results offer a prospective assessment of the difficulties encountered when attempting to validate finite-element models from in vivo strain data. Small errors in the direction of load application produce significant changes in predicted strains. An isotropic model, although convenient, shows poor agreement with experimental strains, while a heterogeneous orthotropic model predicts strains that are more congruent with these data. Most significantly, we find that an edentulous model performs better than a dentate one in recreating the experimental strains. While this result is undoubtedly tied to our failure to model the periodontal ligament, we interpret the finding to mean that in the absence of occlusal loads, teeth within alveoli do not contribute significantly to the structural stiffness of the mandible.

Effect of various distal ring-block configurations on the biomechanical properties of circular external skeletal fixators for use in dogs and cats.

OBJECTIVE: To evaluate mediolateral, axial, torsional, and craniocaudal bending behavior of 6 distal ring-block configurations commonly used to stabilize short juxta-articular bone segments in small animals. SAMPLE POPULATION: 8 circular external skeletal fixator constructs of each of 6 distal ring-block configurations. The distal ring-block configurations were composed of combinations of complete rings, incomplete rings, and drop wires. PROCEDURE: Constructs were nondestructively loaded in axial compression, craniocaudal bending, mediolateral bending, and torsional loading by use of a materials testing machine. Gap stiffness was determined by use of the resultant load displacement curve. RESULTS: Circular external skeletal fixator configurations and constructs significantly affected gap stiffness in all testing modes. Within each loading mode, gap stiffness was significantly different among most configurations. In general, complete ring configurations were significantly stiffer than similar incomplete ring configurations, and addition of a drop wire to a configuration significantly increased stiffness of that configuration. CONCLUSIONS AND CLINICAL RELEVANCE: When regional anatomic structures permit, the use of complete ring configurations is preferred over incomplete ring configurations. When incomplete ring configurations are used, the addition of a drop wire is recommended.

Load sharing in Premier and Zephir anterior cervical plates.

STUDY DESIGN: An in vitro biomechanical study using a simulated anterior cervical discectomy and interbody fusion model to compare the load sharing properties of two semiconstrained cervical (Premier and Zephir) plates. OBJECTIVES: To determine the percent load transmission through these plates and grafts under simple axial compression. SUMMARY OF BACKGROUND DATA: No published data exist as to the load transmission through these semiconstrained plates. METHODS: Cadaveric calf spines were subjected to axial compression loading while instrumented with an interbody graft and with the graft plus one of the plates. Load transmission was computed through an analysis of the load-displacement data. RESULTS: A mean load transmission of 23% was shared by the Premier plate. The Zephir, a more constrained plate but still semiconstrained, shared a mean of 32% of the load. CONCLUSIONS: The semiconstrained plates tested allow more graft loading than some previously tested constrained plates. However, there are differences between the research methods used in these studies that provide a less than satisfactory comparison.

Understanding stress concentration about a nutrient foramen.

We investigated the microstructural basis of a reduced stress concentration around the primary nutrient foramen of the equine third metacarpus. We quantified the spatial variations of compositional parameters (mineral content, volume fraction, histological architecture, and osteonal trajectories) from microradiographs and polarizing microscopic images of thin sections. These variations in composition and organization in turn cause variations in mechanical properties of cortical bone. We modeled the spatially inhomogeneous anisotropic elastic properties based on the measured compositional parameters and used the properties as inputs to a finite element model of the bone containing the foramen. This model, spatially constructed solely from the microscopic images, was subsequently validated by our mechanical test results. We found that: (1) a primary mechanism for stress concentration reduction appears to be due to an increased compliance near the foramen: the sharp discontinuity represented by the hole is softened by embedding it in a compliant region; (2) a reinforcing ring of increased stiffness exists at some distance from the foramen; and (3) a ring of lamellar bone exists along the foramen inside edge, which might serve to reduce the chance of cracks forming there. Our work is allowing us to design biomimetic structures with holes by mimicking the microstructure near the nutrient foramen.

Biomechanical comparison of a circular external skeletal fixator construct to pin and tension band wire fixation for the stabilization of olecranon osteotomies in dogs: a cadaveric study.

OBJECTIVE: To compare anatomic reduction and the biomechanical properties of a circular external skeletal fixator (CESF) construct to pin and tension band wire (PTBW) fixation for the stabilization of olecranon osteotomies in dogs. STUDY DESIGN: Cadaveric study. ANIMALS: Forelimbs from 12 skeletally mature mixed-breed dogs, weighing 23 to 28 kg. METHODS: An olecranon osteotomy was stabilized with either a CESF construct or PTBW fixation. A single distractive load to failure was applied to each specimen through the triceps tendon. Osteotomy reduction and biomechanical properties were compared between fixation groups. RESULTS: Reduction was not significantly different (gap: P =.171; malalignment: P =.558) between fixation groups. Osteotomies stabilized with the CESF had greater stiffness (P <.0001) and maximum load sustained (P <.0001) compared to PTBW fixation. There was no significant difference for yield load (P =.318) or for load at 1 mm of axial displacement (P =.997) between fixation groups. Failure of fixation occurred by bending of the intramedullary Steinmann pin and the fixation wires in the CESF specimens and by untwisting of the tension band wire knot with pullout and bending of the Kirschner wires in the PTBW specimens. CONCLUSIONS: Specimens stabilized with the CESF construct had similar reduction and yield load, greater stiffness and maximum load sustained, and less elastic deformation than specimens stabilized with PTBW fixation. CLINICAL RELEVANCE: The CESF construct may provide a biomechanically favorable alternative to PTBW fixation for stabilization of olecranon osteotomies in dogs, and its application warrants clinical investigation.

Interbody allograft in a skeletally immature spine model.

The objective of this cadaveric biomechanical study was to establish further bovine spines as models for evaluating lumbar interbody allografts and to provide guidance for their use in pediatric humans. It is unknown whether interbody allografts can be used in the pediatric spine without failure of the host vertebral bone. Allografts were placed in cow and calf spines and loaded in compression. The cow spines were much stronger and stiffer than the calf, but moderate in vivo activities were estimated to result in loads on the allograft constructs that would result in host bone failure. Bovine spines were established as suitable models for the compressive behavior of interbody allografts in the human spine, when bone density is considered. Interbody allografts should continue to be used with adjunctive instrumentation so as to preclude host bone failure.

A comparison of the accuracy and safety of vertebral body pin placement using a fluoroscopically guided versus an open surgical approach: an in vitro study.

OBJECTIVE: To compare the safety and accuracy of Steinmann pin placement in vertebral bodies T10 through L7 using either an open or closed fluoroscopic method. STUDY DESIGN: In vitro radiographic and anatomic study. ANIMALS: Ten medium-sized canine cadavers. METHODS: Cadavers were randomly assigned to 2 groups: open and closed. Steinmann pins were placed in vertebral bodies through a standard dorsal incision in the open group and percutaneously with the aid of fluoroscopy in the closed group. Pins were placed bilaterally in vertebral bodies T10 through L7 at approximately 30 degrees from horizontal and driven to a uniform depth. Necropsies were performed to examine potential pulmonary, vascular, or neurological trauma as a result of pin placement. Spines were cross-sectioned through intervertebral disc spaces, and radiographs were performed to evaluate accuracy of pin placement. Descriptive statistics were determined for pin angle, percentage of bone purchase, and penetration length. Means of interest between groups were compared using a Student t test. Complication incidence was compared using Chi;(2) analysis. Significance was P <.05. RESULTS: Mean pin insertion angle was significantly different than 30 degrees for the open group in thoracic and lumbar vertebrae and for the closed group in thoracic vertebrae. Mean pin insertion angle for all vertebrae was significantly greater than 30 degrees for the open group. Mean pin penetration distance in each vertebra was significantly different between groups with the closed group having less penetration and lower variance. Both groups were significantly different from the ideal penetration distance. The mean percentage of bone purchase was greater in the closed group for all vertebrae except T10 and T11. The complication incidence was significantly greater in the open group for thoracic vertebrae. CONCLUSION AND CLINICAL RELEVANCE: The results of this study suggest that a closed technique for placement of Steinmann pins in lumbar vertebrae for use in external skeletal fixation is a reasonable and safer alternative to the traditional open technique. Use of either technique in thoracic vertebrae should be avoided.