Borjana Mikic

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

GDF-5 deficiency in mice delays Achilles tendon healing

The aim of this study was to examine the role of one of the growth/differentiation factors, GDF‐5, in the process of tendon healing. Specifically, we tested the hypothesis that GDF‐5 deficiency in mice would result in delayed Achilles tendon repair. Using histologic, biochemical, and ultrastructural analyses, we demonstrate that Achilles tendons from 8‐week‐old male GDF‐5 –/– mice exhibit a short‐term delay of 1–2 weeks in the healing process compared to phenotypically normal control littermates. Mutant animals took longer to achieve peak cell density, glycosaminoglycan content, and collagen content in the repair tissue, and the time course of changes in collagen fibril size was also delayed. Revascularization was delayed in the mutant mice by 1 week. GDF‐5 deficient Achilles tendons also contained significantly more fat within the repair tissue at all time points examined, and was significantly weaker than control tissue at 5 weeks after surgery, but strength differences were no longer detectable by 12‐weeks. Together, these data support the hypothesis that GDF‐5 may play an important role in modulating tendon repair, and are consistent with previously posited roles for GDF‐5 in cell recruitment, migration/adhesion, differentiation, proliferation, and angiogenesis.

Multiple Effects of GDF-5 Deficiency on Skeletal Tissues: Implications for Therapeutic Bioengineering

The growth/differentiation factors (GDFs) are a subfamily of the highly conserved group of bone morphogenetic protein (BMP) signaling molecules known to play a diverse set of roles in the skeletal system. GDFs 5, 6, and 7 in particular have been grouped together on the basis of the high degree of amino acid sequence homology in the C-terminal signaling region of these proteins. The existence of several naturally occurring and engineered mouse models with functional null mutations in these GDFs has led to a variety of investigations into the effects of GDF deficiency on skeletal tissues and processes. The best characterized of these models to date is the GDF-5-deficient brachypod (bp) mouse. In this paper, a comprehensive review of the studies performed on the bp mouse is provided in an effort to elucidate implications for potential therapeutic bioengineering applications using GDF-5. On the basis of the available evidence to date, GDF-5 may hold promise as a possible therapeutic agent for applications involving tendon/ligament repair as well as perhaps intervertebral disk degeneration, cartilage repair, and bone augmentation, although further detailed interventional studies will be required to investigate these potential applications.

Bone strain gage data and theoretical models of functional adaptation

The in vivo implantation of strain gages on the surface of bones has proven to be a very useful technique for studying the relationship between in vivo loading and bone growth and adaptation. However, data from such experiments have yet to be well incorporated within the context of theoretical models of bone adaptation. Methods for analyzing bone rosette strain gage recordings within the framework of strain energy density-based computational modeling/remodeling theories are presented. A new strain energy density based parameter, energy equivalent strain, is proposed as a single scalar measure of cyclic strain magnitudes and the concept of a daily strain stimulus is also introduced. As an illustrative example, the approach is applied to analyze previously reported in vivo data from the anteromedial human tibia (Lanyon et al., 1975, Acta orthop. Scand. 46, 256-268).

GDF-5 Deficiency in Mice Leads to Disruption of Tail Tendon Form and Function

Although the biological factors which regulate tendon homeostasis are poorly understood, recent evidence suggests that Growth and Differentiation Factor-5 (GDF-5) may play a role in this important process. The purpose of this study was to investigate the effect of GDF-5 deficiency on mouse tail tendon using the brachypodism mouse model. We hypothesized that GDF-5 deficient tail tendon would exhibit altered composition, ultrastructure, and biome-chanical behavior when compared to heterozygous control littermates. Mutant tail tendons did not display any compositional differences in sulfated glycosaminoglycans (GAG/DNA), collagen (hydroxyproline/DNA), or levels of fibromodulin, decorin, or lumican. However, GDF-5 deficiency did result in a 17% increase in the proportion of medium diameter (100–225 nm) collagen fibrils in tail tendon (at the expense of larger fibrils) when compared to controls (p < 0.05). Also, mutants exhibited a trend toward an increase in irregularly-shaped polymorphic fibrils (33% more, p > 0.05). While GDF-5 deficient tendon fascicles did not demonstrate any significant differences in quasistatic biomechanical properties, mutant fascicles relaxed 11 % more slowly than control tendons during time-dependent stress-relaxation tests (p < 0.05). We hypothesize that this subtle alteration in time-dependent mechanical behavior is most-likely due to the increased prevalence of irregularly shaped type I collagen fibrils in the mutant tail tendons. These findings provide additional evidence to support the conclusion that GDF-5 may play a role in tendon homeostasis in mice.

Mechanical modulation of cartilage structure and function during embryogenesis in the chick.

The mechanical behavior of cartilage is intimately related to its biochemical composition, and tissue composition is known to be influenced by its local mechanical loading environment. Although this phenomenon has been well-studied in adult cartilage, few investigations have examined such structure–function relationships in embryonic cartilage. The goal of this work was to elucidate the role of mechanical loading on the development of cartilage composition during embryogenesis. Using an embryonic chick model, cartilage from the tibiofemoral joints of immobilized embryos was compared to that of controls. The normal time course of changes in glycosaminoglycan/DNA and hydroxyproline/DNA were significantly influenced by loading history, with the most pronounced effects observed between days 9 and 14 during the period of most rapid increase in motility in control embryos. Stress-relaxation tests conducted on samples from day 14 indicate that the effects of embryonic immobilization on cartilage matrix composition have direct consequences for the mechanical behavior of the tissue, resulting in compromised material properties (e.g. 50% reduction in Einst). Because embryogenesis provides a unique model for identifying key factors which influence the establishment of functional biomechanical tissues in the skeleton, these data suggest that treating mechanical loading as an in vitro culture variable for tissue engineering approaches to cartilage repair is likely to be a sound approach.

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 growth/differentiation factor-5 deficiency on femoral composition and mechanical behavior in mice

A subclass of the bone morphogenetic proteins (BMPs), known as growth/differentiation factors (GDFs) 5, 6, and 7, have been shown to affect several skeletal processes, including endochondral ossification, synovial joint formation, and tendon and ligament repair. Mice deficient in GDF-5 have also been shown to exhibit biomechanical abnormalities in tendon that may be associated with altered type I collagen. The purpose of this study was to investigate the effect of GDF-5 deficiency on another type I collagen-rich tissue: cortical bone. Analyses were performed on femora from 8-week-old GDF-5-deficient male brachypodism mice. We hypothesized that GDF-5-deficient bones would exhibit altered geometric, structural, and material properties compared with control littermates. Mutant animals were significantly smaller in body mass than controls (-21%). Geometrically, mutant long bones were significantly shorter (-25%), had a lower polar moment of inertia (-34%), and a lower geometric strength indicator (analogous to the section modulus of a circular section) (-30%). When normalized by body mass, however, geometric differences were no longer significant. Structurally, GDF-5-deficient femora were weaker (-31%) and more compliant (-57%) than controls when tested to failure in torsion. Lower bone structural stiffness in the mutants was not completely explained by the smaller bone geometry, because mutant bones exhibited a significantly lower effective shear modulus (-36%). Although body mass did not fully explain the reduced structural strength in mutant bones, strength differences were adequately explained by bone cross-sectional geometry; maximum effective shear stress was not significantly different between mutants and controls, despite a statistically significant 6% lower ash fraction in mutant femora. No significant difference was detected in collagen content, as indicated by hydroxyproline per dry mass.

Ultrastructural Determinants of Murine Achilles Tendon Strength During Healing

The mechanisms by which tendon strength is established during growth and development and restored following injury are not completely understood and are likely to be complex, multifactorial processes. Several studies examining the relationship between mechanical behavior and ultrastructural characteristics of tendons and ligaments during growth and maturation suggest that collagen fibril diameter is strongly correlated with tendon strength. Because of the similarities between development and repair processes of musculoskeletal tissues, increases in tendon strength during healing may be related to increases in fibril ultrastructural parameters such as fibril size, numerical density, and area fraction. In this study, we compared murine Achilles tendons at various time points after tenotomy with sham-operated controls in tensile tests to failure and examined tendons using electron microscopy to assess collagen fibril ultrastructure. We found that in the 6-week period following Achilles tenotomy, fibril mean diameter remained significantly smaller than sham-side diameter by a factor of 2–3. Despite the persistently small fibril size, increasing numerical density resulted in a gradual increase in fibril area fraction. Biomechanical strength did not reach that of intact tendons until some time between 5 and 7 weeks, approximately the same time period when fibril area fraction began to approach sham values. These data suggest that parameters other than collagen fibril size are most responsible for increased tendon strength during healing.

Sexual dimorphism in the effect of GDF-6 deficiency on murine tendon.

Three members of the growth/differentiation factor (GDF) subfamily of bone morphogenetic proteins (BMPs), GDFs‐5, ‐6, and ‐7, have demonstrated the potential to augment tendon and ligament repair. To gain further insight into the in vivo role of these molecules, previous studies have characterized intact and healing tendons in mice with functional null mutations in GDF‐5 and ‐7. The primary goal of the present study was to perform a detailed characterization of the intact tendon phenotype in 4‐ and 16‐week‐old male and female GDF6−/− mice and their +/+ littermates. The results demonstrate that GDF6 deficiency was associated with an altered tendon phenotype that persisted into adulthood. Among males, GDF6−/− tail tendon fascicles had significantly less collagen and glycosaminoglycan content, and these compositional differences were associated with compromised material properties. The effect of GDF6 deficiency on tendon was sexually dimorphic, however, for among female GDF6−/− mice, neither differences in tendon composition nor in material properties were detected. The tendon phenotype that was observed in males appeared to be stronger in the tail site than in the Achilles tendon site, where some compositional differences were present, but no material property differences were detected. These data support existing in vitro studies, which suggest a potential role for BMP‐13 (the human homologue to GDF‐6) in tendon matrix modeling and/or remodeling.