Percolation theory relates corticocancellous architecture to mechanical function in vertebrae of inbred mouse strains

Effects of long-term voluntary wheel running and selective breeding for wheel running on femoral nutrient canals

The nutrient artery provides ~50%-70% of the total blood volume to long bones in mammals. Studying the functional characteristics of this artery in vivo can be difficult and expensive, so most researchers have measured the nutrient foramen, an opening on the outer surface of the bone that served as the entry point for the nutrient artery during development and bone ossification. Others have measured the nutrient canal (i.e., the passage which the nutrient artery once occupied), given that the external dimensions of the foramen do not necessarily remain uniform from the periosteal surface to the medullary cavity. The nutrient canal, as an indicator of blood flow to long bones, has been proposed to provide a link to studying organismal activity (e.g., locomotor behavior) from skeletal morphology. However, although external loading from movement and activity causes skeletal remodeling, it is unclear whether it affects the size or configuration of nutrient canals. To investigate whether nutrient canals can exhibit phenotypic plasticity in response to physical activity, we studied a mouse model in which four replicate high runner (HR) lines have been selectively bred for high voluntary wheel-running behavior. The selection criterion is the average number of wheel revolutions on days 5 and 6 of a 6-day period of wheel access as young adults (~6-8 weeks old). An additional four lines are bred without selection to serve as controls (C). For this study, 100 female mice (half HR, half C) from generation 57 were split into an active group housed with wheels and a sedentary group housed without wheels for 12 weeks starting at ~24 days of age. Femurs were collected, soft tissues were removed, and femora were micro-computed tomography scanned at a resolution of 12 μm. We then imported these scans into AMIRA and created 3D models of femoral nutrient canals. We tested for evolved differences in various nutrient canal traits between HR and C mice, plastic changes resulting from chronic exercise, and the selection history-by-exercise interaction. We found few differences between the nutrient canals of HR versus C mice, or between the active and sedentary groups. We did find an interaction between selection history and voluntary exercise for the total number of nutrient canals per femur, in which wheel access increased the number of canals in C mice but decreased it in HR mice. Our results do not match those from an earlier study, conducted at generation 11, which was prior to the HR lines reaching selection limits for wheel running. The previous study found that mice from the HR lines had significantly larger total canal cross-sectional areas compared to those from C lines. However, this discrepancy is consistent with studies of other skeletal traits, which have found differences between HR and C mice to be somewhat inconsistent across generations, including the loss of some apparent adaptations with continued selective breeding after reaching a selection limit for wheel-running behavior.

A predictive model for fracture in human ribs based on in vitro acoustic emission data

PURPOSE

The aim of this paper is to propose a fracture model for human ribs based on acoustic emission (AE) data. The accumulation of microcracking until a macroscopic crack is produced can be monitored by AE. The macrocrack propagation causes the loss of the structural integrity of the rib.

METHODS

The AE technique was used in in vitro bending tests of human ribs. The AE data obtained were used to construct a quantitative model that allows an estimation of the failure stress from the signals detected. The model predicts the ultimate stress with an error of less than 3.5% (even at stresses 15% lower than failure stress), which makes it possible to safely anticipate the failure of the rib.

RESULTS

The percolation theory was used to model crack propagation. Moreover, a quantitative probability-based model for the expected number of AE signals has been constructed, incorporating some ideas of percolation theory. The model predicts that AE signals associated with micro-failures should exhibit a vertical asymptote when stress increases. The occurrence of this vertical asymptote was attested in our experimental observations. The total number of microfailures detected prior to the failure is N ≈ 100 and the ultimate stress is σ ∞ = 197 ± 62 MPa. A significant correlation (p < 0.0001) between σ ∞ and the predicted value is found, using only the first N = 30 micro-failures (correlation improves for N higher).

CONCLUSIONS

The measurements and the shape of the curves predicted by the model fit well. In addition, the model parameters seem to explain quantitatively and qualitatively the distribution of the AE signals as the material approaches the macroscopic fracture. Moreover, some of these parameters correlate with anthropometric variables, such as age or Body Mass Index. The proposed model could be used to predict the structural failure of ribs subjected to bending.

Network models for characterization of trabecular bone

Trabecular bone is a lightweight, compliant material organized as a web of struts and rods (trabeculae) that erode with age and the onset of bone diseases like osteoporosis, leading to increased fracture risk. The traditional diagnostic marker of osteoporosis, bone mineral density (BMD), has been shown in ex vivo experiments to correlate poorly with fracture resistance when considered on its own, while structural features in conjunction with BMD can explain more of the variation in trabecular bone strength. We develop a network-based model of trabecular bone by creating graphs from micro-computed tomography images of human bone, with weighted links representing trabeculae and nodes representing branch points. These graphs enable calculation of quantitative network metrics to characterize trabecular structure. We also create finite element models of the networks in which each link is represented by a beam, facilitating analysis of the mechanical response of the bone samples to simulated loading. We examine the structural and mechanical properties of trabecular bone at the scale of individual trabeculae (of order 0.1 mm) and at the scale of selected volumes of interest (approximately a few mm), referred to as VOIs. At the VOI scale, we find significant correlations between the stiffness of VOIs and 10 different structural metrics. Individually, the volume fraction of each VOI is most strongly correlated to the stiffness of the VOI. We use multiple linear regression to identify the smallest subset of variables needed to capture the variation in stiffness. In a linear fit, we find that node degree, weighted node degree, Z-orientation, weighted Z-orientation, trabecular spacing, link length, and the number of links are the structural metrics that are most significant (p<0.05) in capturing the variation of stiffness in trabecular networks.

Strain-specific differences in the development of bone loss and incidence of osteonecrosis following glucocorticoid treatment in two different mouse strains

Objective

Glucocorticoids (GCs) are commonly prescribed as treatment for chronic inflammatory diseases. Prolonged use of GCs is a common cause of atraumatic osteonecrosis (ON) and secondary osteoporosis. Currently, there is no effective treatment for this disease; therefore, a reliable animal model would be useful to study both the pathology and novel treatment strategies for patients with the disease. The aim of this study was to establish a validated, reproducible model of GC-induced ON and bone loss in two different mouse strains (BALB/c and C57BL/6).

Methods

Seven-week-old male BALB/c (n = 32) and male C57BL/6 mice (n = 32) were randomised into placebo or GC groups and treated with daily 4 mg/L oral dexamethasone in drinking water for 90 days. Study outcome measures included histologic assessment of ON of the distal femur, bone mass and mechanical strength of tibia and lumbar vertebral body, osteoclast number, biochemical measure of bone formation and bone marrow fat quantitation.

Results

GC-induced ON lesions were observed in the distal femur in 47% of the male BALB/c mice and 25% of the male C57BL/6 mice. GC treatment decreased the trabecular bone volume and serum pro-collagen type 1N-protease (P1NP) in BALB/c mice compared with the placebo (p < 0.05) and reduced tibial bone strength in both BALB/c and C57BL/6 mice. GC-treated BALB/c mice had significantly greater marrow fat levels compared to the placebo group.

Conclusion

GC-induced ON was more prevalent in the male BALB/c mice compared to the male C57BL/6 mice. GC treatment significantly reduced bone mass, bone formation measured by P1NP, bone strength and increased marrow fat levels in male BALB/c mice. Therefore, the use of male BALB/c mice strain is recommended for both diagnostic and therapeutic studies for the prevention and treatment of ON and bone loss following prolonged treatment with GCs.

The Translational Potential of this Article

GCs are commonly used to treat patients with various chronic inflammatory diseases, and this is associated with both the development of ON and bone loss. Our study confirmed that the BALB/c mouse strain treated for 90 days with GC may be useful for developing novel treatments for ON.

Femoral Neck External Size but not aBMD Predicts Structural and Mass Changes for Women Transitioning Through Menopause

The impact of adult bone traits on changes in bone structure and mass during aging is not well understood. Having shown that intracortical remodeling correlates with external size of adult long bones led us to hypothesize that age-related changes in bone traits also depend on external bone size. We analyzed hip dual-energy X-ray absorptiometry images acquired longitudinally over 14 years for 198 midlife women transitioning through menopause. The 14-year change in bone mineral content (BMC, R²  = 0.03, p = 0.015) and bone area (R²  = 0.13, p = 0.001), but not areal bone mineral density (aBMD, R²  = 0.00, p = 0.931) correlated negatively with baseline femoral neck external size, adjusted for body size using the residuals from a linear regression between baseline bone area and height. The dependence of the 14-year changes in BMC and bone area on baseline bone area remained significant after adjusting for race/ethnicity, postmenopausal hormone use, the 14-year change in weight, and baseline aBMD, weight, height, and age. Women were sorted into tertiles using the baseline bone area-height residuals. The 14-year change in BMC (p = 0.009) and bone area (p = 0.001) but not aBMD (p = 0.788) differed across the tertiles. This suggested that women showed similar changes in aBMD for different structural and biological reasons: women with narrow femoral necks showed smaller changes in BMC but greater increases in bone area compared to women with wide femoral necks who showed greater losses in BMC but without large compensatory increases in bone area. This finding is opposite to expectations that periosteal expansion acts to mechanically offset bone loss. Thus, changes in femoral neck structure and mass during menopause vary widely among women and are predicted by baseline external bone size but not aBMD. How these different structural and mass changes affect individual strength-decline trajectories remains to be determined. © 2017 American Society for Bone and Mineral Research.

Bone structure and function in male C57BL/6 mice: Effects of a high-fat Western-style diet with or without trace minerals

PURPOSE

Osteoporosis occurs in both women and men, but most of what we know about the condition comes from studies in females. The present study examined bone structure and function over an 18-month period in male C57BL/6 mice maintained on either a rodent chow diet (AIN76A) or a high-fat, Western-style diet (HFWD). Effects of mineral supplementation were assessed in both diets.

METHODS

Trabecular and cortical bone structure in femora and vertebrae were assessed by micro-CT analysis. Following this, bone stiffness and strength measurements were made. Finally, bone levels of several cationic trace elements were quantified, and serum biomarkers of bone metabolism evaluated.

RESULTS

Bone loss occurred over time in both diets but was more rapid and extensive in mice on the HFWD. Dietary mineral supplementation reduced bone loss in both diets and increased bone stiffness in the femora and bone stiffness and strength in the vertebrae. Bone content of strontium was increased in response to mineral supplementation in both diets.

CONCLUSIONS

Bone loss was more severe in mice on the HFWD and mineral supplementation mitigated the effects of the HFWD. In comparison to previous findings with female C57BL/6 mice, the present studies indicate that males are more sensitive to diet and benefited from a healthy diet (AIN76A), while females lost as much bone on the healthy diet as on the HFWD. Male mice benefited from mineral supplementation, just as females did in the previous study.

Characterization of complex, co-adapted skeletal biomechanics phenotypes: a needed paradigm shift in the genetics of bone structure and function

The genetic architecture of skeletal biomechanical performance has tremendous potential to advance our knowledge of the biological mechanisms that drive variation in skeletal fragility and osteoporosis risk. Research using traditional approaches that focus on specific gene pathways is increasing our understanding of how and to what degree those pathways may affect population-level variation in fracture susceptibility, and shows that known pathways may affect bone fragility through unsuspected mechanisms. Non-traditional approaches that incorporate a new appreciation for the degree to which bone traits co-adapt to functional loading environments, using a wide variety of redundant compensatory mechanisms to meet both physiological and mechanical demands, represent a radical departure from the dominant reductionist paradigm and have the potential to rapidly advance our understanding of bone fragility and identification of new targets for therapeutic intervention.

The effect of scaffold macroporosity on angiogenesis and cell survival in tissue-engineered smooth muscle

Angiogenesis and survival of cells within thick scaffolds is a major concern in tissue engineering. The purpose of this study is to increase the survival of intestinal smooth muscle cells (SMCs) in implanted tissue-engineered constructs. We incorporated 250-μm pores in multi-layered, electrospun scaffolds with a macroporosity ranging from 15% to 25% to facilitate angiogenesis. The survival of green fluorescent protein (GFP)-expressing SMCs was evaluated after 2 weeks of implantation. Whereas host cellular infiltration was similar in scaffolds with different macroporosities, blood vessel development increased with increasing macroporosity. Scaffolds with 25% macropores had the most GFP-expressing SMCs, which correlated with the highest degree of angiogenesis over 1 mm away from the outermost layer. The 25% macroporous group exceeded a critical threshold of macropore connectivity, accelerating angiogenesis and improving implanted cell survival in a tissue-engineered smooth muscle construct.

Phase transitions in pancreatic islet cellular networks and implications for type-1 diabetes

In many aspects the onset of a chronic disease resembles a phase transition in a complex dynamic system: Quantitative changes accumulate largely unnoticed until a critical threshold is reached, which causes abrupt qualitative changes of the system. In this study we examine a special case, the onset of type-1 diabetes (T1D), a disease that results from loss of the insulin-producing pancreatic islet β cells. Within each islet, the β cells are electrically coupled to each other via gap-junctional channels. This intercellular coupling enables the β cells to synchronize their insulin release, thereby generating the multiscale temporal rhythms in blood insulin that are critical to maintaining blood glucose homeostasis. Using percolation theory we show how normal islet function is intrinsically linked to network connectivity. In particular, the critical amount of β-cell death at which the islet cellular network loses site percolation is consistent with laboratory and clinical observations of the threshold loss of β cells that causes islet functional failure. In addition, numerical simulations confirm that the islet cellular network needs to be percolated for β cells to synchronize. Furthermore, the interplay between site percolation and bond strength predicts the existence of a transient phase of islet functional recovery after onset of T1D and introduction of treatment, potentially explaining the honeymoon phenomenon. Based on these results, we hypothesize that the onset of T1D may be the result of a phase transition of the islet β-cell network.

Preservation of bone structure and function by Lithothamnion sp. derived minerals

Progressive bone mineral loss and increasing bone fragility are hallmarks of osteoporosis. A combination of minerals isolated from the red marine algae, Lithothamnion sp. was examined for ability to inhibit bone mineral loss in female mice maintained on either a standard rodent chow (control) diet or a high-fat western diet (HFWD) for 5, 12, and 18 months. At each time point, femora were subjected to μ-CT analysis and biomechanical testing. A subset of caudal vertebrae was also analyzed. Following this, individual elements were assessed in bones. Serum levels of the 5b isoform of tartrate-resistant acid phosphatase (TRAP) and procollagen type I propeptide (P1NP) were also measured. Trabecular bone loss occurred in both diets (evident as early as 5 months). Cortical bone increased through month 5 and then declined. Cortical bone loss was primarily in mice on the HFWD. Inclusion of the minerals in the diet reduced bone mineral loss in both diets and improved bone strength. Bone mineral density was also enhanced by these minerals. Of several cationic minerals known to be important to bone health, only strontium was significantly increased in bone tissue from animals fed the mineral diets, but the increase was large (5-10 fold). Serum levels of TRAP were consistently higher in mice receiving the minerals, but levels of P1NP were not. These data suggest that trace minerals derived from marine red algae may be used to prevent progressive bone mineral loss in conjunction with calcium. Mineral supplementation could find use as part of an osteoporosis-prevention strategy.

Heavy ion irradiation and unloading effects on mouse lumbar vertebral microarchitecture, mechanical properties and tissue stresses

Astronauts are exposed to both musculoskeletal disuse and heavy ion radiation in space. Disuse alters the magnitude and direction of forces placed upon the skeleton causing bone remodeling, while energy deposited by ionizing radiation causes free radical formation and can lead to DNA strand breaks and oxidative damage to tissues. Radiation and disuse each result in a net loss of mineralized tissue in the adult, although the combined effects, subsequent consequences for mechanical properties and potential for recovery may differ. First, we examined how a high dose (2 Gy) of heavy ion radiation ((56)Fe) causes loss of mineralized tissue in the lumbar vertebrae of skeletally mature (4 months old), male, C57BL/6 mice using microcomputed tomography and determined the influence of structural changes on mechanical properties using whole bone compression tests and finite element analyses. Next, we tested if a low dose (0.5 Gy) of heavy particle radiation prevents skeletal recovery from a 14-day period of hindlimb unloading. Irradiation with a high dose of (56)Fe (2 Gy) caused bone loss (-14%) in the cancellous-rich centrum of the fourth lumbar vertebra (L4) 1 month later, increased trabecular stresses (+27%), increased the propensity for trabecular buckling and shifted stresses to the cortex. As expected, hindlimb unloading (14 days) alone adversely affected microarchitectural and mechanical stiffness of lumbar vertebrae, although the reduction in yield force was not statistically significant (-17%). Irradiation with a low dose of (56)Fe (0.5 Gy) did not affect vertebrae in normally loaded mice, but significantly reduced compressive yield force in vertebrae of unloaded mice relative to sham-irradiated controls (-24%). Irradiation did not impair the recovery of trabecular bone volume fraction that occurs after hindlimb unloaded mice are released to ambulate normally, although microarchitectural differences persisted 28 days later (96% increase in ratio of rod- to plate-like trabeculae). In summary, (56)Fe irradiation (0.5 Gy) of unloaded mice contributed to a reduction in compressive strength and partially prevented recovery of cancellous microarchitecture from adaptive responses of lumbar vertebrae to skeletal unloading. Thus, irradiation with heavy ions may accelerate or worsen the loss of skeletal integrity triggered by musculoskeletal disuse.

Guidelines for assessment of bone microstructure in rodents using micro-computed tomography

Use of high-resolution micro-computed tomography (microCT) imaging to assess trabecular and cortical bone morphology has grown immensely. There are several commercially available microCT systems, each with different approaches to image acquisition, evaluation, and reporting of outcomes. This lack of consistency makes it difficult to interpret reported results and to compare findings across different studies. This article addresses this critical need for standardized terminology and consistent reporting of parameters related to image acquisition and analysis, and key outcome assessments, particularly with respect to ex vivo analysis of rodent specimens. Thus the guidelines herein provide recommendations regarding (1) standardized terminology and units, (2) information to be included in describing the methods for a given experiment, and (3) a minimal set of outcome variables that should be reported. Whereas the specific research objective will determine the experimental design, these guidelines are intended to ensure accurate and consistent reporting of microCT-derived bone morphometry and density measurements. In particular, the methods section for papers that present microCT-based outcomes must include details of the following scan aspects: (1) image acquisition, including the scanning medium, X-ray tube potential, and voxel size, as well as clear descriptions of the size and location of the volume of interest and the method used to delineate trabecular and cortical bone regions, and (2) image processing, including the algorithms used for image filtration and the approach used for image segmentation. Morphometric analyses should be based on 3D algorithms that do not rely on assumptions about the underlying structure whenever possible. When reporting microCT results, the minimal set of variables that should be used to describe trabecular bone morphometry includes bone volume fraction and trabecular number, thickness, and separation. The minimal set of variables that should be used to describe cortical bone morphometry includes total cross-sectional area, cortical bone area, cortical bone area fraction, and cortical thickness. Other variables also may be appropriate depending on the research question and technical quality of the scan. Standard nomenclature, outlined in this article, should be followed for reporting of results.

Cancellous bone adaptation to tibial compression is not sex dependent in growing mice

Mechanical loading can be used to increase bone mass and thus attenuate pathological bone loss. Because the skeleton's adaptive response to loading is most robust before adulthood, elucidating sex-specific responses during growth may help maximize peak bone mass. This study investigated the effect of sex on the response to controlled, in vivo mechanical loading in growing mice. Ten-week-old male and female C57Bl/6 mice underwent noninvasive compression of the left tibia. Peak loads of -11.5 N were applied, corresponding to +1,200 microepsilon at the tibial midshaft in both sexes. Cancellous bone mass, architecture, and dynamic formation in the proximal metaphysis were compared between loaded and control limbs via micro-computed tomography and histomorphometry. The strain environment of the proximal metaphysis during loading was characterized using finite element analysis. Both sexes responded to tibial compression through increased bone mass and altered architecture. Cancellous bone mass and tissue density were enhanced in loaded limbs relative to control limbs in both sexes through trabecular thickening and reduced separation. Changes in mass were due to increased cellular activity in loaded limbs compared with control limbs. Adaptation to loading increased the proportion of load transferred by the cancellous bone in the proximal metaphysis. For all cancellous measures, the response to tibial compression did not differ between male and female mice. When similar strains are engendered in males and females, the adaptive response in cancellous bone to mechanical loading does not depend on sex.

Phenotypic integration among trabecular and cortical bone traits establishes mechanical functionality of inbred mouse vertebrae

Conventional approaches to identifying quantitative trait loci (QTLs) regulating bone mass and fragility are limited because they examine cortical and trabecular traits independently. Prior work examining long bones from young adult mice and humans indicated that skeletal traits are functionally related and that compensatory interactions among morphological and compositional traits are critical for establishing mechanical function. However, it is not known whether trait covariation (i.e., phenotypic integration) also is important for establishing mechanical function in more complex, corticocancellous structures. Covariation among trabecular, cortical, and compositional bone traits was examined in the context of mechanical functionality for L(4) vertebral bodies across a panel of 16-wk-old female AXB/BXA recombinant inbred (RI) mouse strains. The unique pattern of randomization of the A/J and C57BL/6J (B6) genome among the RI panel provides a powerful tool that can be used to measure the tendency for different traits to covary and to study the biology of complex traits. We tested the hypothesis that genetic variants affecting vertebral size and mass are buffered by changes in the relative amounts of cortical and trabecular bone and overall mineralization. Despite inheriting random sets of A/J and B6 genomes, the RI strains inherited nonrandom sets of cortical and trabecular bone traits. Path analysis, which is a multivariate analysis that shows how multiple traits covary simultaneously when confounding variables like body size are taken into consideration, showed that RI strains that tended to have smaller vertebrae relative to body size achieved mechanical functionality by increasing mineralization and the relative amounts of cortical and trabecular bone. The interdependence among corticocancellous traits in the vertebral body indicated that variation in trabecular bone traits among inbred mouse strains, which is often thought to arise from genetic factors, is also determined in part by the adaptive response to variation in traits describing the cortical shell. The covariation among corticocancellous traits has important implications for genetic analyses and for interpreting the response of bone to genetic and environmental perturbations.