M.C.H. van der Meulen

Understanding bone strength: size isn’t everything

In vivo models, particularly mouse mutations, are increasingly being used to investigate the impact of the absence or overexpression of a gene product on musculoskeletal load-bearing capacity. Skeletal functional integrity can be assessed by structural strength tests that measure how well the whole bone can bear loads. Although the importance of performing these tests is well-recognized, care must be taken in designing the experiments and interpreting the data. The aim of this report is to clarify the relationship of whole bone structural strength to material and geometric properties and the interpretation of these data in the context of in vivo models, especially mice. In particular, we emphasize that there is no alternative to testing whole bone strength and that conclusions regarding bone mechanical function based solely on geometry or bone mineral content are inappropriate and likely misleading. What is a whole bone structural test and what does it measure? Different types of loads, such as bending or torsion, can be applied to whole bones in vitro to determine the structure’s stiffness and failure load (structural strength). The structural stiffness is a measure of the resistance to deformation under the applied load, and the structural strength is the load required to fail the whole bone. These two whole bone measurements are structural properties and are influenced by both the material from which the structure is composed (the tissue material properties) as well as how and where that material is distributed (the geometric form of the tissue) (Figure 1). Therefore, both material and geometric properties are required to assess the structural integrity of a long bone, and neither material nor geometry alone is sufficient to predict the structural failure load. Currently, there is no substitute for a mechanical test to measure whole bone structural behavior; no alternative parameter has been identified that is fully indicative of strength and can serve as a surrogate measure. Bone material properties are the tissue level mechanical properties that describe the constituent material and are independent of the size and shape of the bone. Material properties include the tissue ultimate stress and modulus of elasticity. These tissue properties are determined by machining precise samples from the bone of interest and testing them in a particular loading mode. The material properties are influenced by compositional measures such as mineral density, collagen content, and ash fraction. In addition to composition, factors such as collagen cross-linking, collagen fiber orientation, mineral crystal size, and the microstructural organization (e.g., lamellae, osteons) also influence material behavior. From a mechanical perspective, the composition and organization of the material clearly influence the tissue’s ability to bear loads, but most measures, except for mineral density, have not yet been related directly to the tissue properties derived from mechanical tests. When designing a structural test, the relevant material and geometric measures are determined by the loading mode applied to the whole bone to measure strength (e.g., torsion, bending, or compression) as well as the outcome parameter of interest (e.g., stiffness or failure load) (Figure 1). For example, if we test a bone to failure in torsion, then we will measure the torsional load to failure (a structural parameter). The appropriate geometric and material properties are the torsional section modulus (a geometric parameter) and the ultimate shear stress of the bone (a material parameter). The section modulus represents the geometric resistance to torsion and increases as the material lies further from the axis of rotation (Figure 2). The ultimate shear stress is the strength of the bone tissue when loaded in torsion. A biomechanics tutorial by Turner and Burr has provided a more complete presentation of mechanical assessment of whole bone and bone tissue. The contribution of structural, geometric and material analyses can be illustrated with a hypothetical example (Figure 3). Consider the case of a mutant and wild-type comparison in which animal age, gender, and weight are matched, but the bone material and geometry may be affected by the mutation. A whole bone torsion test to failure showed that both the control and mutant failed at the same torque of 8.7 Nzmm. Based on this analysis alone, we would conclude that the mutation had no effect. Additional analyses, either geometric or material, would be necessary to reveal the true effect of the mutation. On the other hand, if we only measure the geometry, we find the mutant bone to have a 21% lower section modulus than wild-type. Therefore, based on geometry alone, we might conclude that the mutant is structurally weaker than the control. However, combined with the structural information, we would know that the smaller mutant bones must have increased material properties to achieve the same structural failure load. Conversely, a tissue level material test would determine that the ultimate shear stress is 26% higher in the mutant than the wild-type. Therefore, based on material differences alone, we might conclude that the mutant is structurally stronger than the control. In each case, global conclusions based on a single analysis (structural, geometric, or material) are different, contradictory, and potentially incorrect. Ideally, all three tests would be required, but, at a minimum, combining two analyses is sufficient to understand the effect of the mutation on the structural properties of the whole bone. Address for correspondence and reprints: Marjolein C. H. van der Meulen, Ph.D., Sibley School of Mechanical and Aerospace Engineering, Cornell University, 219A Upson Hall, Ithaca, NY 14853. E-mail: mcv3@cornell.edu Bone Vol. 29, No. 2 August 2001:101–104

Mechanical factors in bone growth and development

Mechanobiologic factors strongly influence skeletal ossification and regulate changes in bone geometry and apparent density during ontogeny. We have developed computer models that implement a simple mathematical rule relating cyclic tissue stresses to bone apposition and resorption. Beginning at the fetal stages of the femoral anlage, these models successfully predict the appositional bone growth and modeling observed in the development of the diaphyseal cross section. The same basic mechanobiologic rule can also predict the architectural construction of the proximal cancellous bone formed in regions of endochondral ossification. Geometry and density changes in adult diaphyseal and cancellous bone as a result of changes in physical activity can be simulated by invoking the same rule used during development. Future clinical and experimental work is needed to provide more quantitative data for mechanobiologic rules and elucidate the interactions between chemical and mechanical factors influencing bone biology.

Mechanobiologic influences in long bone cross-sectional growth

We developed a computer model to simulate the interaction of biological and mechanobiological factors in the development of the cross-sectional morphology of long bones. The model incorporated a strong influence of biologically induced bone formation during early development. In addition, an assumed mechanical loading history during growth and development corresponding to age-related changes in body weight and muscle mass was applied. Based on the bone stress stimulus generated by the assumed loads, mechanically induced apposition and resorption rates were calculated at the periosteal and endosteal surfaces using a previously developed bone modeling theory. These methods successfully emulated the growth-related changes seen in long bone diaphyseal structure as well as changes observed in mature bones during aging. The simulations recreated the rapid increase in bone dimensions during development, stabilizing at maturity, and then the gradual, age-related subperiosteal expansion and cortical thinning. Throughout the growth, development, and aging simulations, the values of the bone radii, area, moments of inertia, and apposition rates corresponded well with measurements documented by other researchers.

Body mass is the primary determinant of midfemoral bone acquisition during adolescent growth

To study the determinants of bone mass and structure during adolescence, we analyzed the femoral mid-diaphysis of 375 healthy adolescents and young adults, ages 9-26 years, from four ethnic cohorts (African-American, Asian-American, Caucasian, and Hispanic). Whole-body dual-energy X-ray absorptiometry (DXA) scans were used to determine diaphyseal length and mid-diaphyseal diameter of the left femur, as well as linear bone mineral content (BMCL) of a region at the mid-diaphysis. Cross-sectional geometric properties were estimated and used to calculate two structural strength indicators: the section modulus and the whole bone strength index. When the relationships between the bone measurements and age, pubertal group, height, or body mass were evaluated, all cross-sectional femoral measures correlated most strongly with body mass. Multiple regressions accounting for gender and ethnicity provided little additional predictive value over the simple regressions with body mass alone. Furthermore, accounting for all developmental parameters (age, pubertal group, body mass, lean body mass, calcium intake, physical activity level) as well as ethnicity and gender in a single saturated model also did not generally significantly improve the predictive results achieved using only body mass. Our results indicate that increases in midfemoral bone mass and cross-sectional properties during adolescence are primarily related to increases in mechanical loading as reflected by body mass.

Age-related differences in cross-sectional geometry of the forearm bones in healthy women

Men exhibit age-related adaptive changes in long bone geometry, namely, endosteal resorption and periosteal apposition of bone, that help to preserve bone strength. It is not clear whether women undergo similar adaptive responses. To address this question, we assessed the bone mineral density and cross-sectional geometry of the radius and ulna at the one-third distal site by single photon absorptiometry and computed tomography (CT) in healthy young (n=21, age 20–30 years) and older (n=22, age 63–84 years) women. We used the CT data to compute the total subperiosteal, medullary, and cortical areas, as well as the maximum, minimum, and polar moments of inertia. We normalized the geometric parameters for bone length and performed comparisons using both the original and size-corrected data. Radial and ulnar bone mineral content and density were 20–30% lower in the older women (P<0.0001). Ulnar width, total area, medullary area, and maximum and polar moment of inertia were greater in the older than in the younger women. Although we observed similar trends when we examined the radius data that were corrected for bone size, age-related differences in radial geometry were less pronounced and were not significant. We conclude that women undergo endosteal resorption and periosteal apposition of the ulna with age, thereby exhibiting an adaptive pattern that helps to preserve bone strength. The different behavior of these two bones suggests that local, rather than systemic, factors underlie this adaptation.

Long bone geometry and strength in adult BMP-5 deficient mice.

Bone morphogenetic proteins (BMPs) play a critical role in early skeletal development. BMPs are also potential mediators of bone response to mechanical loading, but their role in later stages of bone growth and adaptation has yet to be studied. We characterized the postcranial skeletal defects in mature mice with BMP deficiency by measuring hind-limb muscle mass and long bone geometric, material, and torsional mechanical properties. The animals studied were 26-week-old short ear mice (n = 10) with a homozygous deletion of the BMP-5 gene and their heterozygous control litter mates (n = 15). Gender-related effects, which were found to be independent of genotype, were also examined. The femora of short ear mice were 3% shorter than in controls and had significantly lower values of many cross-sectional geometric and structural strength parameters (p < 0.05). No significant differences in ash content or material properties were detected. Lower femoral whole bone torsional strength was due to the smaller cross-sectional geometry (16% smaller section modulus) in the short ear mice. The diminished cross-sectional geometry may be commensurate with lower levels of in vivo loading, as reflected by body mass (-8%) and quadriceps mass (-11%). While no significant gender differences were found in whole bone strength or cross-sectional geometry, males had significantly greater body mass (+18%) and quadriceps mass (+15%) and lower tibio-fibular ash content (-3%). The data suggest that adult female mice have a more robust skeleton than males, relative to in vivo mechanical demands. Furthermore, although the bones of short ear mice are smaller and weaker than in control animals, they appear to be biomechanically appropriate for the in vivo mechanical loads that they experience.

The effect of systemically administered rhIGF-I/IGFBP-3 complex on cortical bone strength and structure in ovariectomized rats.

The action of systematically administered recombinant human insulinlike growth factor-I (rhIGF-I) complexed to its natural binding protein-3 (rhIGFBP-3) on cortical bone dynamic, structural, and mechanical properties was tested in previously ovariectomized (Ovx) rats. Bilateral ovariectomy or sham surgery was performed on 16-week-old female Sprague-Dawley rats. Eight weeks after surgery basal Sham and Ovx rats were killed to establish baseline cortical bone values before the initiation of treatment with rhIGF-I/IGFBP-3 complex. At that time, Ovx rats had increased body weight and body fat mass with reduced femoral BMC and BMD relative to basal Shams. Bone formation rates in Ovx rats were increased on both cortical envelopes relative to time-matched controls. The thickness of the inner lamellar bone layer and average cortical width were reduced due to increased endocortical erosion. A similar ratio between Sham and Ovx rats in body mass and composition and femoral BMC and BMD continued throughout the experiment. Sixteen weeks after surgery bone formation rates at both cortical envelopes in Ovx rats were reduced relative to Shams, but endocortical erosion remained high causing a further decrease in thickness of the inner lamellar layer. As a result of periosteal bone modeling. Ovx rats exhibited a larger femoral cross-sectional area and periosteal perimeter, as well as a thicker outer lamellar layer. Newly deposited periosteal bone increased ultimate torque values in the Ovx rats relative to Shams at 16 weeks. Treatment of Ovx rats with the rhIGF-I/IGFBP-3 complex increased body weight, lean body mass, and femoral BMC and BMD.(ABSTRACT TRUNCATED AT 250 WORDS)

Non-invasive mouse models of post-traumatic osteoarthritis

Animal models of osteoarthritis (OA) are essential tools for investigating the development of the disease on a more rapid timeline than human OA. Mice are particularly useful due to the plethora of genetically modified or inbred mouse strains available. The majority of available mouse models of OA use a joint injury or other acute insult to initiate joint degeneration, representing post-traumatic osteoarthritis (PTOA). However, no consensus exists on which injury methods are most translatable to human OA. Currently, surgical injury methods are most commonly used for studies of OA in mice; however, these methods may have confounding effects due to the surgical/invasive injury procedure itself, rather than the targeted joint injury. Non-invasive injury methods avoid this complication by mechanically inducing a joint injury externally, without breaking the skin or disrupting the joint. In this regard, non-invasive injury models may be crucial for investigating early adaptive processes initiated at the time of injury, and may be more representative of human OA in which injury is induced mechanically. A small number of non-invasive mouse models of PTOA have been described within the last few years, including intra-articular fracture of tibial subchondral bone, cyclic tibial compression loading of articular cartilage, and anterior cruciate ligament (ACL) rupture via tibial compression overload. This review describes the methods used to induce joint injury in each of these non-invasive models, and presents the findings of studies utilizing these models. Altogether, these non-invasive mouse models represent a unique and important spectrum of animal models for studying different aspects of PTOA.

MicroCT Morphometry Analysis of Mouse Cancellous Bone: Intra- and Inter-system Reproducibility

The agreement between measurements and the relative performance reproducibility among different microcomputed tomography (microCT) systems, especially at voxel sizes close to the limit of the instruments, is not known. To compare this reproducibility 3D morphometric analyses of mouse cancellous bone from distal femoral epiphyses were performed using three different ex vivo microCT systems: GE eXplore Locus SP, Scanco μCT35 and Skyscan 1172. Scans were completed in triplicate at 12 μm and 8 μm voxel sizes and morphometry measurements, from which relative values and dependence on voxel size were examined. Global and individual visually assessed thresholds were compared. Variability from repeated scans at 12 μm voxel size was also examined. Bone volume fraction and trabecular separation values were similar, while values for relative bone surface, trabecular thickness and number varied significantly across the three systems. The greatest differences were measured in trabecular thickness (up to 236%) and number (up to 218%). The relative dependence of measurements on voxel size was highly variable for the trabecular number (from 0% to 20% relative difference between measurements from 12 μm and 8 μm voxel size scans, depending on the system). The intra-system reproducibility of all trabecular measurements was also highly variable across the systems and improved for BV/TV in all the systems when a smaller voxel size was used. It improved using a smaller voxel size in all the other parameters examined for the Scanco system, but not consistently so for the GE or the Skyscan system. Our results indicate trabecular morphometry measurements should not be directly compared across microCT systems. In addition, the conditions, including voxel size, for trabecular morphometry studies in mouse bone should be chosen based on the specific microCT system and the measurements of main interest.

BMP-5 deficiency alters chondrocytic activity in the mouse proximal tibial growth plate

The role of bone morphogenetic protein-5 (BMP-5) in regulating chondrocytic activity during endochondral ossification was examined in the mouse proximal tibial growth plate. Short ear mice homozygous for the SEA/Gn point mutation in the coding region for BMP-5 (King, J. A. et al. Dev Biol 166:112122; 1994) and heterozygous long ear littermates were examined at 5 and 9 weeks of age (n = 9/group, four groups). Animals were injected with oxytetracycline to estimate the rate of growth and with bromodeoxyuridine to identify proliferative chondrocytes. Age-related changes in chondrocytic stereological and kinetic parameters were compared by image analysis of 1-microm-thick growth plate sections. The number of proliferative chondrocytes did not vary with age in either genotype, but proliferative phase duration increased significantly (approximately 67%) with age in the long ear mice, whereas no change was detected in the short ear mice. The number of hypertrophic chondrocytes increased significantly (approximately 27%) in the short ears, whereas this number decreased significantly (approximately 40%) in the long ears. There was a small, but significant, increase in hypertrophic phase duration (approximately 45%) in short ear mice, but no change was detected in the long ears. These results indicate that BMP-5 deficiency prevents age-related decelerations in chondrocytic proliferation and initiation of hypertrophic differentiation, suggesting a role of BMP-5 in inhibiting these processes.