Structure and mechanics of water-holding feathers of Namaqua sandgrouse (Pterocles namaqua).

Desert sandgrouse, such as the Namaqua sandgrouse, nest up to 30 km away from watering holes. Adult male desert sandgrouse have specially adapted feathers on their bellies that hold water, even during flight, allowing the birds to transport water back to the chicks at the nest. The structure of the belly feathers and aspects of the mechanism by which they hold water was first described by Cade and Maclean (Cade, Maclean 1967 Condor 69, 323-343 (doi:10.2307/1366197)). Here, we use scanning electron microscopy and micro-computed tomography as well as videography to characterize the geometry of different components of the belly feathers and to show how differences in their bending stiffnesses contribute to the water-holding mechanism. The results of this study will be used in a companion paper to model computationally water uptake by the feather.

3D printed structures for modeling the Young's modulus of bamboo parenchyma.

Bamboo is a sustainable, lightweight material that is widely used in structural applications. To fully develop micromechanical models for plants, such as bamboo, the mechanical properties of each individual type of tissue are needed. However, separating individual tissues and testing them mechanically is challenging. Here, we report an alternative approach in which micro X-ray computed tomography (µ-CT) is used to image moso bamboo (Phyllostachys pubescens). The acquired images, which correspond to the 3D structure of the parenchyma, are then transformed into physical, albeit larger scale, structures by 3D printing, and their mechanical properties are characterized. The normalized longitudinal Young's moduli of the fabricated structures depend on relative density raised to a power between 2 and 3, suggesting that elastic deformation of the parenchyma cellular structure involves considerable cell wall bending. The mechanical behavior of other biological tissues may also be elucidated using this approach. STATEMENT OF SIGNIFICANCE: Bamboo is a lightweight, sustainable engineering material widely used in structural applications. By combining micro X-ray computed tomography and 3D printing, we have produced bamboo parenchyma mimics and characterized their stiffness. Using this approach, we gained insight into bamboo parenchyma tissue mechanics, specifically the cellular geometry's role in longitudinal elasticity.

Prevalence of infertility and help seeking among 15 000 women and men.

STUDY QUESTION: What is the prevalence of infertility and of help seeking among women and men in Britain? SUMMARY ANSWER: One in eight women and one in ten men aged 16-74 years had experienced infertility, defined by unsuccessfully attempting pregnancy for a year or longer, and little more than half of these people sought medical or professional help. WHAT IS KNOWN ALREADY: Estimates of infertility and help seeking in Britain vary widely and are not easily comparable because of different definitions and study populations. STUDY DESIGN, SIZE, DURATION: A cross-sectional population survey was conducted between 2010 and 2012 with a sample of 15 162 women and men aged 16-74 years. PARTICIPANTS/MATERIALS, SETTING, METHODS: Participants completed the Natsal-3 questionnaire, using computer-assisted personal interviewing (CAPI) and computer-assisted self-interview (CASI). MAIN RESULTS AND THE ROLE OF CHANCE: The reported prevalence of infertility was 12.5% (CI 95% 11.7-13.3) among women and 10.1% (CI 95% 9.2-11.1) among men. Increased prevalence was associated with later cohabitation with a partner, higher socio-economic status and, for those who had a child, becoming parents at older ages. The reported prevalence of help seeking was 57.3% (CI 95% 53.6-61.0) among women and 53.2% (CI 95% 48.1-58.1) among men. Help seekers were more likely to be better educated and in higher status occupations and, among those who had a child, to have become parents later in life. LIMITATIONS, REASONS FOR CAUTION: These data are cross-sectional so it is not possible to establish temporality or infer causality. Self-reported data may be subject to recall bias. WIDER IMPLICATIONS OF THE FINDINGS: The study provides estimates of infertility and help seeking in Britain and the results indicate that the prevalence of infertility is higher among those delaying parenthood. Those with higher educational qualifications and occupational status are more likely to consult with medical professionals for fertility problems than others and these inequalities in help seeking should be considered by clinical practice and public health. STUDY FUNDING/COMPETING INTERESTS: Funding was provided by grants from the Medical Research Council and the Wellcome Trust, with support from the Economic and Social Research Council and the Department of Health. AMJ is a Governor of the Wellcome Trust. Other authors have no competing interests.

Stress concentration around an atelectatic region: a finite element model.

Lung parenchyma surrounding an atelectatic region is thought to be subjected to increased stress compared with the rest of the lung. Using 37 hexagonal cells made of linear springs, Mead et al. (1970) measured a stress concentration greater than 30% in the springs surrounding a stiffer central cell. We re-examine the problem using a 2D finite element model of 500 cells made of thin filaments with a non-linear stress-strain relationship. We study the consequences of increasing the central stiff region from one to nine contiguous cells in regular hexagonal honeycombs and random Voronoi honeycombs. The honeycomb structures were uniformly expanded with strains of 15%, 30%, 45% and 55% above their resting, non-deformed geometry. The curve of biaxial stress vs. fractional area change has a similar shape to that of the pressure-volume curve of the lung, showing an initial regime with relatively flat slope and a final regime with decreasing slope, tending toward an asymptote. Regular honeycombs had little variability in the maximum stress in radially oriented filaments adjacent to the central stiff region. In contrast, some filaments in random Voronoi honeycombs were subjected to stress concentration approximately 16 times the average stress concentration in the radially oriented filaments adjacent to the stiff region. These results may have implications in selecting the appropriate strategy for mechanical ventilation in ARDS and defining a "safe" level of alveolar pressure for ventilating atelectatic lungs.

The structure and mechanics of Moso bamboo material.

Although bamboo has been used structurally for millennia, there is currently increasing interest in the development of renewable and sustainable structural bamboo products (SBPs). These SBPs are analogous to wood products such as plywood, oriented strand board and glue-laminated wood. In this study, the properties of natural Moso bamboo (Phyllostachys pubescens) are investigated to further enable the processing and design of SBPs. The radial and longitudinal density gradients in bamboo give rise to variations in the mechanical properties. Here, we measure the flexural properties of Moso bamboo in the axial direction, along with the compressive strengths in the axial and transverse directions. Based on the microstructural variations (observed with scanning electron microscopy) and extrapolated solid cell wall properties of bamboo, we develop models, which describe the experimental results well. Compared to common North American construction woods loaded along the axial direction, Moso bamboo is approximately as stiff and substantially stronger, in both flexure and compression but denser. This work contributes to critical knowledge surrounding the microstructure and mechanical properties of bamboo, which are vital to the engineering and design of sustainable SBPs.

Aromatase inhibitors for treatment of advanced breast cancer in postmenopausal women.

BACKGROUND: Hormonal treatments for advanced or metastatic breast cancer, such as tamoxifen and the progestins megestrol acetate and medroxyprogesterone acetate, have been in use for many years. Aromatase inhibitors (AIs) are a class of compounds that systemically inhibit oestrogen synthesis in the peripheral tissues. Aminoglutethimide was the first AI in clinical use (first generation) and had a similar tumour-regressing effect to other endocrine treatments, which showed the potential of this alternative type of therapy. Other AIs have since been developed and the third generation AIs anastrozole, exemestane and letrozole are in current use. Randomised evidence on response rates and side effects of these drugs is still limited. OBJECTIVES: To compare aromatase inhibitors to other endocrine therapy in the treatment of advanced breast cancer in postmenopausal women. SEARCH STRATEGY: The Cochrane Breast Cancer Group Specialised Register was searched on 3 December 2004 using the codes for "advanced" and "endocrine therapy". Details of the search strategy applied to create the Register and the procedure used to code references are described in the Cochrane Breast Cancer Group module on The Cochrane Library. The search was updated to 30 September 2005 and additional publications were included. Experts were consulted to determine that no relevant studies had been excluded. SELECTION CRITERIA: Randomised trials comparing the effects of any aromatase inhibitor versus other endocrine therapy, no endocrine therapy or a different aromatase inhibitor in the treatment of advanced (metastatic) breast cancer. DATA COLLECTION AND ANALYSIS: Data from published trials were extracted by two independent review authors. A third independent author then carried out a further cross check for accuracy and consistency. Hazard ratios (HR) were derived for analysis of time-to-event outcomes (overall and progression-free). Odds ratios (OR) were derived for objective response and clinical benefit (both analysed as dichotomous variables). Toxicity data were extracted where present and treatments were compared using odds ratios. All but one of the studies included data on one or more of the following outcomes: overall survival, progression-free survival, clinical benefit and objective response. MAIN RESULTS: Thirty studies were identified, twenty five of which were included in the main analysis of any AI versus any other treatment (9416 women). The pooled estimate showed a significant survival benefit for treatment with an AI over other endocrine therapies (HR 0.89, 95%CI 0.82 to 0.96). A subgroup analysis of the three commonly prescribed AIs (anastrozole, exemestane, letrozole) also showed a similar survival benefit (HR 0.88, 95%CI 0.80 to 0.96). The results for progression-free survival, clinical benefit and objective response were not statistically significant and there was statistically significant heterogeneity across types of AI. There were very limited data to compare one AI with a different AI, but these suggested an advantage for letrozole over anastrozole. All the trials of AIs used exclusively as first-line therapy were against tamoxifen. There was an advantage to treatment with AIs in terms of progression-free survival (HR 0.78, 95% CI 0.70 to 0.86) and clinical benefit (OR 0.70, 95% CI 0.51 to 0.97) but not overall survival or objective response. There was considerable heterogeneity across studies when considering clinical benefit (P = 0.001). Use of an AI as second-line therapy showed a significant benefit in terms of overall survival (HR 0.80, 95% CI 0.66 to 0.96) but not for progression-free survival (HR 1.08, 95% CI 0.89 to 1.31), clinical benefit (OR 1.00, 95% CI 0.87 to 1.14) or objective response (OR 0.96, 95% CI 0.81 to 1.14). This is difficult to interpret due to the extreme heterogeneity across AIs for progression-free survival but not the other endpoints.AIs have a different toxicity profile to other endocrine therapies. For all AIs combined, they had similar levels of hot flushes (especially when compared to tamoxifen) and arthralgia, increased risks of nausea, diarrhoea and vomiting, but a decreased risk of vaginal bleeding and thromboembolic events compared with other endocrine therapies. A similar pattern of risks and benefits was still seen when analyses were limited to the currently most-prescribed third generation AIs. AUTHORS' CONCLUSIONS: In women with advanced (metastatic) breast cancer, aromatase inhibitors including those in current clinical use show a survival benefit when compared to other endocrine therapy.

The effect of pore size on cell adhesion in collagen-GAG scaffolds.

The biological activity of scaffolds used in tissue engineering applications hypothetically depends on the density of available ligands, scaffold sites at which specific cell binding occurs. Ligand density is characterized by the composition of the scaffold, which defines the surface density of ligands, and by the specific surface area of the scaffold, which defines the total surface of the structure exposed to the cells. It has been previously shown that collagen-glycosaminoglycan (CG) scaffolds used for studies of skin regeneration were inactive when the mean pore size was either lower than 20 microm or higher than 120 microm (Proc. Natl. Acad. Sci., USA 86(3) (1989) 933). To study the relationship between cell attachment and viability in scaffolds and the scaffold structure, CG scaffolds with a constant composition and solid volume fraction (0.005), but with four different pore sizes corresponding to four levels of specific surface area were manufactured using a lyophilization technique. MC3T3-E1 mouse clonal osteogenic cells were seeded onto the four scaffold types and maintained in culture. At the experimental end point (24 or 48 h), the remaining viable cells were counted to determine the percent cell attachment. A significant difference in viable cell attachment was observed in scaffolds with different mean pore sizes after 24 and 48 h; however, there was no significant change in cell attachment between 24 and 48 h for any group. The fraction of viable cells attached to the CG scaffold decreased with increasing mean pore size, increasing linearly (R2 = 0.95, 0.91 at 24 and 48 h, respectively) with the specific surface area of the scaffold. The strong correlation between the scaffold specific surface area and cell attachment indicates that cell attachment and viability are primarily influenced by scaffold specific surface area over this range (95.9-150.5 microm) of pore sizes for MC3T3 cells.

A phenomenological model for predicting fatigue life in bovine trabecular bone.

Cyclic loading of bone during daily activities can lead to fatigue degradation and increased risk of fracture in both the young and elderly population. Damage processes under cyclic loading in trabecular bone result in the reduction of the elastic modulus and accumulation of residual strain. These effects increase with increasing stress levels, leading to a progressive reduction in fatigue life. The present work analyzes the effect of stress and strain variation on the above damage processes in bovine trabecular bone, and develops a phenomenological model relating fatigue life to the imposed stress level. The elastic modulus reduction of the bone specimens was observed to depend on the maximum compressive strain, while the rate of residual strain accumulation was a function of the stress level. A model was developed for the upper and lower bounds of bone elastic modulus reduction with increasing number of cycles, at each stress range. The experimental observations were described well by the model. The model predicted the bounds of the fatigue life with change in fatigue stress. The decrease in the fatigue life with increasing stress was related to corresponding increases in the residual strain accumulation rates at the elevated stress levels. The model shows the validity of fatigue predictions from relatively few cyclic experiments, by combining trends observed in the monotonic and the cyclic tests. The model also presents a relatively simple procedure for predicting the endurance limit for bovine trabecular bone specimens.

Creep does not contribute to fatigue in bovine trabecular bone.

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

Expression of alpha-smooth muscle actin by and contraction of cells derived from synovium.

Cells derived from synovium have drawn interest as donor cells for articular cartilage tissue engineering because they have been implicated in certain cartilage repair processes in vivo and the chondrogenic potential of the cells has been demonstrated in vitro. Studies have demonstrated that several other types of musculoskeletal connective tissue cells--including chondrocytes, fibrochondrocytes, ligament fibroblasts and osteoblasts, and mesenchymal stem cells can express the gene for the contractile actin isoform, alpha-smooth muscle actin (SMA), and can contract analogs of extracellular matrix in vitro. Although the physiological roles of SMA-enabled contraction of these cells have yet to be established, cell-mediated contraction of scaffolds employed for tissue engineering can alter the pore diameter of the matrix and distort its overall shape, and thus needs to be addressed. Toward this goal, the objective of this study was to investigate the expression of SMA by synovial cells and to evaluate their contraction of collagen-glycosaminoglycan (GAG) scaffolds. Synovial membranes obtained from the knees (stifle joints) of six adult dogs were evaluated for the presence of SMA by immunohistochemistry. Cells isolated from the synovial tissue were expanded through seven passages in monolayer culture, with samples from each passage allocated for Western blot analysis of SMA. Cells from passage 4 were seeded into porous type I collagen-GAG matrices and cultured for 4 weeks. Synovial cell-mediated contraction of the scaffolds was determined by measuring the diameters of the cell-seeded scaffolds and nonseeded controls every other day. Synovium-derived cells cultured as micropellets or in collagen-GAG matrices were incubated in chondrogenic medium with and without fetal bovine serum and evaluated for chondrogenesis by type II collagen immunohistochemistry. Immunohistochemistry revealed the presence of SMA in some cells (less than 10% of the cells) in the intimal layer of synovium from four of the five animals analyzed. Western blot analysis demonstrated a regular increase in the amount of SMA in the synovium-derived cells with passage number. Synovial cell-mediated contraction of the collagen-GAG scaffolds reached a value of 43% of the original diameter after 4 weeks, comparable to that found with other musculoskeletal cell types. Incubation of micropellet cultures of synovium-derived cells with chondrogenic medium revealed trace amounts of type II collagen production by immunohistochemistry. The findings of this study indicate that control of SMA-enabled contraction may be important when employing synovial cells for cartilage repair procedures, and warrant further investigation into the physiological role of SMA expression in synovial cells.

Degradation of a collagen-chondroitin-6-sulfate matrix by collagenase and by chondroitinase.

Highly porous, type I collagen-chondroitin-6-sulfate (collagen-GAG) scaffolds, produced by freeze-drying techniques, have proven to be of value as implants to facilitate the regeneration of certain tissues. The objective of this project was to evaluate changes in the microstructure and mechanical properties of selected collagen-GAG scaffolds as they degrade in an in vitro model system. Environmental scanning electron microscopy and video imaging demonstrated that collagenase degradation caused strut erosion through the creation of 1-3 microm diameter micropits within a 2-h period, leading to eventual removal of strut material and strut breakage. Loss of microstructural topography may have been due to gelatinization when collagen was cleaved by collagenase. Chondroitinase degradation of GAG resulted in swelling of the struts, causing the pores to become smaller and rounder. The compressive modulus of the collagen-GAG matrix decreased when degraded by collagenase, but remained unchanged when degraded by chondroitinase. Carbodiimide-cross-linked matrices were found to have a higher cross-link density, a higher compressive stiffness and a greater resistance to collagenase and chondroitinase, compared to non-cross-linked controls and matrices that were cross-linked by the dehydrothermal process. This investigation provides information that can be used to design collagen-GAG scaffolds with desired compressive stiffness and degradation rate to collagenase and chondroitinase.

Analysis of crack growth in a 3D Voronoi structure: a model for fatigue in low density trabecular bone.

Both creep and crack growth contribute to the reduction in modulus associated with fatigue loading in bone. Here we simulate crack growth and subsequent strut failure in fatigue in an open-cell, three-dimensional Voronoi structure which is similar to that of low density, osteoporotic bone. The model indicates that sequential failure of struts leads to a precipitous drop in modulus: the failure of 1% of the struts leads to about a 10% decrease in modulus. A parametric study is performed to assess the influence of normalized stress range, relative density, initial crack size, crack shape and cell geometry on the fatigue life. The fatigue life is most sensitive to the relative density and the initial crack length. The results lead to a quantitative expression for the fatigue life associated with crack growth. Data for the fatigue life of trabecular bone are compared with the crack growth model described in this paper as well as with a previous model for creep of a three-dimensional Voronoi structure. In our models, creep dominates the fatigue behavior in low cycle fatigue while crack growth dominates in high cycle fatigue, consistent with previous observations on cortical bone. The large scatter in the trabecular bone fatigue data make it impossible to identify a transition between creep dominated fatigue and crack growth dominated fatigue. The parametric study of the crack growth model indicates that variations in relative density among specimens, initial crack size within trabeculae and crack shape could easily produce such variability in the test results.

A kinetoplast DNA minicircle probe (B18) specific for the Leishmania subgenus Viannia.

This paper reports the development, sequence and specificity of probe B18, which hybridizes only to the kinetoplast deoxyribonucleic acid (kDNA) minicircle of Leishmania species of the subgenus Viannia. This probe was developed in 1985 and has been used extensively since, on whole kDNA, Leishmania dot-blots and kDNA minicircles amplified by the polymerase chain reaction.

Microdamage accumulation in bovine trabecular bone in uniaxial compression.

In this study we investigated how microdamage accumulated with increasing compressive strain in bovine trabecular bone. We found that little damage is created in the linear elastic region, up to -0.4 percent strain. At an average strain of -0.76 percent +/-0.25 percent, the stress-strain curve became nonlinear, and peaked at -1.91 percent +/-0.55 percent strain. Microdamage increases rapidly during the peak of the stress-strain curve, and a localized band of damage formed. At strains beyond the ultimate strain, the damaged band widened and the density of damage within the band increased. Microdamage occurred as groupings of cracks; the majority of damage occurred as regions of cross-hatching. All microdamage parameters increased with increasing maximum compressive strain. We also observed exponential relationships between crack numerical density and damage (1(o) - (o)Esec/E0) and between crack length density and damage.

Fibroblast contractile force is independent of the stiffness which resists the contraction.

Using a device named the cell force monitor, the contractile force developed by fibroblasts has been studied by measuring the macroscopic contraction of porous collagen-glycosaminoglycan (GAG) matrices over the first 24 h following cell attachment. In this paper, the effect of a variation in the stiffness that resists matrix contraction by cells on the contractile force generated by the cells was determined. Data from these experiments revealed that the contractile force generated by the fibroblasts was independent of the stiffness of the resistance within the range tested (0.7-10.7 N/m). These results suggest that during the time when fibroblasts are attaching to and spreading on collagen-GAG matrices the contractile forces they generate are force limited, not displacement limited. Therefore, the cytoskeletal mechanism of force generation, corresponding with cell elongation, is capable of increasing the displacement of adhesion sites in order to develop the same level of force. Although a detailed understanding of how the passive mechanical signals provided by substrate materials affect cell processes is still unavailable, in vitro modeling of cell-mediated contraction continues to provide useful information.

Growth factor regulation of smooth muscle actin expression and contraction of human articular chondrocytes and meniscal cells in a collagen-GAG matrix.

Recent work has demonstrated that human articular chondrocytes and meniscus cells can express the gene for a contractile actin isoform, alpha-smooth muscle actin (SMA), in vivo. The objective of the present study was to evaluate the effects of two growth factors, transforming growth factor (TGF)-beta1 and platelet-derived growth factor (PDGF)-BB, on the SMA content of these cells and their contraction of a collagen-glycosaminoglycan (GAG) analog of extracellular matrix in vitro. TGF-beta1 was found to markedly increase SMA content of the cells and PDGF-BB decreased SMA expression, with both findings achieving statistical significance. A notable finding was the increased contraction of the collagen-GAG matrix induced by TGF-beta1 and the decrease in contraction resulting from PDGF-BB treatment, indicating a causal relationship between expression of SMA and the contractility of the cells. A novel cell force monitor, employed to estimate the force exerted per cell, demonstrated a higher force exerted by the TGF-beta1-treated cells. The findings demonstrate that the expression of SMA by articular chondrocytes and meniscal cells and their associated contractile behavior can be regulated by selected growth factors. This work provides a foundation for the rational investigation of the mechanisms underlying SMA-enabled contraction of these cell types and the control of this behavior in tissue engineering.

Fibroblast contraction of a collagen-GAG matrix.

Contractile cells, found in wounded or diseased tissues, are associated with the formation of scar tissue. The complexity of contraction in vivo has led to the development of models of contraction by cells in vitro. In this work, a device was developed which quantitatively measured the contractile force developed by fibroblasts seeded into a collagen-glycosaminoglycan porous matrix in vitro. This device differed from most of those previously described in that it directly transferred cellular contractile force to the force transducer (a cantilever beam) and that it used a porous matrix rather than a collagen gel. The data for the increase in contractile force with time were fit to a mathematical equation using two fitting parameters. Data were then compared using the fitting parameters and the cell density. A study of the effect of cell density on the contractile force resulted in a linearly proportional relationship. Subsequent normalization of force by cell density or number resulted in a value of contractile force per cell, 1 nN, that was independent of cell density. The time for the contractile force to develop was also independent of cell density. These results suggest that, in this system, cells develop contractile force individually, irrespective of the force generated by surrounding cells.

Micromechanics of fibroblast contraction of a collagen-GAG matrix.

The contractile force developed by fibroblasts has been studied by measuring the macroscopic contraction of porous collagen-GAG matrices over time. We have identified the microscopic deformations developed by individual fibroblasts which lead to the observed macroscopic matrix contraction. Observation of live cells attached to the matrix revealed that matrix deformation occurred as a result of cell elongation. The time dependence of the increase in average fibroblast aspect ratio over time corresponded with macroscopic matrix contraction, further linking cell elongation and matrix contraction. The time dependence of average fibroblast aspect ratio and macroscopic matrix contraction was found to be the result of the stochastic nature of cell elongation initiation and of the time required for cells to reach a final morphology (2-4 h). The proposed micromechanics associated with observed buckling or bending of individual struts of the matrix by cells may, in part, explain the observation of a force plateau during macroscopic contraction. These findings indicate that the macroscopic matrix contraction measured immediately following cell attachment is related to the extracellular force necessary to support cell elongation, and that macroscopic time dependence is not directly related to microscopic deformation events.

Modeling modulus reduction in bovine trabecular bone damaged in compression.

Loading bone beyond its yield point creates microdamage, leading to reduction in stiffness. Previously, we related microdamage accumulation to changes in mechanical properties. Here, we develop a model that predicts stiffness loss based on the presence of microdamage. Modeling is done at three levels: (1) a single trabecula, (2) a cellular solid consisting of intact, damaged, and fractured trabeculae, and (3) a specimen with a localized damage band. Predictions of a reduced modulus agree well with experimental measured modulus reductions of post-yield compression of bovine trabecular bone. The predicted reduced modulus is relatively insensitive to changes in the input parameters.

A cellular solid model for modulus reduction due to resorption of trabeculae in bone.

In osteoporotic trabecular bone, bone loss occurs by thinning and subsequent resorption of the trabeculae. In this study, we compare the effects of density reductions from uniform thinning of struts or from removal of struts in a random, open-cell, three-dimensional Voronoi structure. The results of this study, combined with those previous studies on other regular and random structures, suggest that the modulus and strength of trabecular bone are reduced more dramatically by density losses from resorption of trabeculae than by those from uniform thinning of trabeculae.