An anisotropic elastic-viscoplastic damage model for bone tissue

A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain D(κ) , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.

Specimen specific parameter identification of ovine lumbar intervertebral discs: On the influence of fibre-matrix and fibre-fibre shear interactions.

Numerical models of the intervertebral disc, which address mechanical questions commonly make use of the difference in water content between annulus and nucleus, and thus fluid and solid parts are separated. Despite this simplification, models remain complex due to the anisotropy and nonlinearity of the annulus and regional variations of the collagen fibre density. Additionally, it has been shown that cross-links make a large contribution to the stiffness of the annulus. Because of this complex composite structure, it is difficult to reproduce several sets of experimental data with one single set of material parameters. This study addresses the question to which extent the ultrastructure of the intervertebral disc should be modelled so that its moment-angle behaviour can be adequately described. Therefore, a hyperelastic constitutive law, based on continuum mechanical principles was derived, which does not only consider the anisotropy from the collagen fibres, but also interactions among the fibres and between the fibres and the ground substance. Eight ovine lumbar intervertebral discs were tested on a custom made spinal loading simulator in flexion/extension, lateral bending and axial rotation. Specimen-specific geometrical models were generated using CT images and T2 maps to distinguish between annulus fibrosus and nucleus pulposus. For the identification of the material parameters the annulus fibrosus was described with two scenarios: with and without fibre-matrix and fibre-fibre interactions. Both scenarios showed a similar behaviour on a load displacement level. Comparing model predictions to the experimental data, the mean RMS of all specimens and all load cases was 0.54±0.15° without the interaction and 0.54±0.19° when the fibre-matrix and fibre-fibre interactions were included. However, due to the increased stiffness when cross-links effects were included, this scenario showed more physiological stress-strain relations in uniaxial and biaxial stress states. Thus, the present study suggests that fibre-matrix and fibre-fibre interactions should be considered in the constitutive law when the model addresses questions concerning the stress field of the annulus fibrosus.

Continuum damage interactions between tension and compression in osteonal bone

Skeletal diseases such as osteoporosis impose a severe socio-economic burden to ageing societies. Decreasing mechanical competence causes a rise in bone fracture incidence and mortality especially after the age of 65 y. The mechanisms of how bone damage is accumulated under different loading modes and its impact on bone strength are unclear. We hypothesise that damage accumulated in one loading mode increases the fracture risk in another. This study aimed at identifying continuum damage interactions between tensile and compressive loading modes. We propose and identify the material constants of a novel piecewise 1D constitutive model capable of describing the mechanical response of bone in combined tensile and compressive loading histories. We performed several sets of loading–reloading experiments to compute stiffness, plastic strains, and stress-strain curves. For tensile overloading, a stiffness reduction (damage) of 60% at 0.65% accumulated plastic strain was detectable as stiffness reduction of 20% under compression. For compressive overloading, 60% damage at 0.75% plastic strain was detectable as a stiffness reduction of 50% in tension. Plastic strain at ultimate stress was the same in tension and compression. Compression showed softening and tension exponential hardening in the post-yield regime. The hardening behaviour in compression is unaffected by a previous overload in tension but the hardening behaviour in tension is affected by a previous overload in compression as tensile reloading strength is significantly reduced. This paper demonstrates how damage accumulated under one loading mode affects the mechanical behaviour in another loading mode. To explain this and to illustrate a possible implementation we proposed a theoretical model. Including such loading mode dependent damage and plasticity behaviour in finite element models will help to improve fracture risk analysis of whole bones and bone implant structures.

Abnormal bone geometry at the metacarpal bone shaft of rheumatoid arthritis patients with maintained muscle-bone relationship

OBJECTIVES:: Metacarpal juxta-articular bone is altered in Rheumatoid Arthritis (RA). However, a detailed analysis of disease related geometrical adaptations of the metacarpal shaft is missing. The aim of the present study was to assess the role of RA disease, forearm muscle cross-sectional area (CSA), age and sex on bone geometry at the metacarpal shaft. METHODS:: In 64 RA patients and 128 control subjects geometric properties of the third metacarpal bone mid-shaft and forearm muscle CSA were measured by peripheral quantitative computed tomography (pQCT). Linear models were performed for cortical CSA, total bone CSA, polar stress-strain Index (polar SSI, a surrogate for bone's resistance to bending and torsion), cortical thickness and Metacarpal Index (MI=cortical CSA/total CSA) with explanatory variables muscle CSA, age, RA status and sex. RESULTS:: Forearm muscle CSA was associated with cortical and total metacarpal CSA, and polar SSI. RA group status was associated with all bone parameters except cortical CSA. There was a significant interaction between RA status and age, indicating that the RA group had a greater age-related decrease in cortical CSA, cortical thickness and MI. CONCLUSIONS:: Bone geometry of the metacarpal shaft is altered in RA patients compared to healthy controls. While bone mass of the metacarpal shaft is adapted to forearm muscle mass, cortical thickness and MI are reduced but outer bone shaft circumference and polar SSI increased in RA patients. These adaptations correspond to an enhanced aging pattern in RA patients.

Overweight children have a greater proportion of fat mass relative to muscle mass in the upper limbs than in the lower limbs: implications for bone strength at the distal forearm

BACKGROUND: The influence of adiposity on upper-limb bone strength has rarely been studied in children, despite the high incidence of forearm fractures in this population. OBJECTIVE: The objective was to compare the influence of muscle and fat tissues on bone strength between the upper and lower limbs in prepubertal children. DESIGN: Bone mineral content, total bone cross-sectional area, cortical bone area (CoA), cortical thickness (CoTh) at the radius and tibia (4% and 66%, respectively), trabecular density (TrD), bone strength index (4% sites), cortical density (CoD), stress-strain index, and muscle and fat areas (66% sites) were measured by using peripheral quantitative computed tomography in 427 children (206 boys) aged 7-10 y. RESULTS: Overweight children (n = 93) had greater values for bone variables (0.3-1.3 SD; P < 0.0001) than did their normal-weight peers, except for CoD 66% and CoTh 4%. The between-group differences were 21-87% greater at the tibia than at the radius. After adjustment for muscle cross-sectional area, TrD 4%, bone mineral content, CoA, and CoTh 66% at the tibia remained greater in overweight children, whereas at the distal radius total bone cross-sectional area and CoTh were smaller in overweight children (P < 0.05). Overweight children had a greater fat-muscle ratio than did normal-weight children, particularly in the forearm (92 +/- 28% compared with 57 +/- 17%). Fat-muscle ratio correlated negatively with all bone variables, except for TrD and CoD, after adjustment for body weight (r = -0.17 to -0.54; P < 0.0001). CONCLUSIONS: Overweight children had stronger bones than did their normal-weight peers, largely because of greater muscle size. However, the overweight children had a high proportion of fat relative to muscle in the forearm, which is associated with reduced bone strength.

Numerical investigation of the mechanical loading of supporting soft tissue for partial dentures

The aim of this research was to study the impact of loading on partial dentures within the supporting soft tissue with respect to different attachment techniques. A finite element model was developed to calculate the stress and strain distribution in this tissue. The model consisted of the left half of a mandible with three remaining teeth that had suffered an atrophy in the anterior region, and a partial denture over the toothless area that was connected at the left mandibular canine using an attachment system. Resulting stress/strain distributions are presented for different load cases using a commercially available prefabricated attachment system.

Structural characterization and reliable biomechanical assessment of integrative cartilage repair

Structural and functional characterization of integrative cartilage repair in controlled model systems can play a key role in the development of innovative strategies to improve the long-term outcome of many cartilage repair procedures. In this work, we first developed a method to reproducibly generate geometrically defined disk/ring cartilage composites and to remove outgrown fibrous layers which can encapsulate cartilaginous tissues during culture. We then used the model system to test the hypothesis that such fibrous layers lead to an overestimation of biomechanical parameters of integration at the disk/ring interface. Transmission electron microscopy images of the composites after 6 weeks of culture indicated that collagen fibrils in the fibrous tissue layer were well integrated into the collagen network of the cartilage disk and ring, whereas molecular bridging between opposing disk/ring cartilage surfaces was less pronounced and restricted to regions with narrow interfacial regions (< 2 microm). Stress-strain profiles generated from mechanical push-out tests for composites with the layers removed displayed a single and distinct peak, whereas profiles for composites with the layers left intact consisted of multiple superimposed peaks. As compared to composites with removed layers, composites with intact layers had significantly higher adhesive strengths (161+/-9 vs. 71+/-11 kPa) and adhesion energies (15.0+/-0.7 vs. 2.7+/-0.4 mJ/mm2). By combining structural and functional analyses, we demonstrated that the outgrowing tissue formed during in vitro culture of cartilaginous specimens should be eliminated in order to reliably quantify biomechanical parameters related to integrative cartilage repair.

Mechanical characterization of brushite and hydroxyapatite cements

Compression, tension and torsion tests were designed and completed successfully on a brushite and a precipitated hydroxyapatite cement in moist condition. Elastic and strength properties were measured for these three loading cases. For each cement, the full set of strength data was fitted to an isotropic Tsai-Wu criterion and the associated coefficients identified. Since the compressive Young's moduli were about 10% larger than the tensile moduli, the full set of elastic data of each cement was fitted to a conewise linear elastic model. Hysteresis of the stress-strain curves was also observed, indicating dissipation mechanisms within these cement microstructures. A comparison of the measured mechanical properties with human cancellous bone confirmed the indication of brushite as a bone filling material and the potential of the hydroxyapatite cement as a structural biomaterial.

Seismic anisotropy in the Morcles nappe shear zone: Implications for seismic imaging of crustal scale shear zones

Microstructures and textures of calcite mylonites from the Morcles nappe large-scale shear zone in southwestern Switzerland develop principally as a function of 1) extrinsic physical parameters including temperature, stress, strain, strain rate and 2) intrinsic parameters, such as mineral composition. We collected rock samples at a single location from this shear zone, on which laboratory ultrasonic velocities, texture and microstructures were investigated and quantified. The samples had different concentration of secondary mineral phases (< 5 up to 40 vol.%). Measured seismic P wave anisotropy ranges from 6.5% for polyphase mylonites (~ 40 vol.%) to 18.4% in mylonites with < 5 vol.% secondary phases. Texture strength of calcite is the main factor governing the seismic P wave anisotropy. Measured S wave splitting is generally highest in the foliation plane, but its origin is more difficult to explain solely by calcite texture. Additional texture measurements were made on calcite mylonites with low concentration of secondary phases (≤ 10 vol.%) along the metamorphic gradient of the shear zone (15 km distance). A systematic increase in texture strength is observed moving from the frontal part of the shear zone (anchimetamorphism; 280 °C) to the higher temperature, basal part (greenschist facies; 350–400 °C). Calculated P wave velocities become increasingly anisotropic towards the high-strain part of the nappe, from an average of 5.8% in the frontal part to 13.2% in the root of the basal part. Secondary phases raise an additional complexity, and may act either to increase or decrease seismic anisotropy of shear zone mylonites. In light of our findings we reinterpret the origin of some seismically reflective layers in the Grône–Zweisimmen line in southwestern Switzerland (PNR20 Swiss National Research Program). We hypothesize that reflections originate in part from the lateral variation in textural and microstructural arrangement of calcite mylonites in shear zones.

Does work stress make you shorter? An ambulatory field study of daily work stressors, job control, and spinal shrinkage

Body height decreases throughout the day due to fluid loss from the intervertebral disk. This study investigated whether spinal shrinkage was greater during workdays compared with nonwork days, whether daily work stressors were positively related to spinal shrinkage, and whether job control was negatively related to spinal shrinkage. In a consecutive 2-week ambulatory field study, including 39 office employees and 512 days of observation, spinal shrinkage was measured by a stadiometer, and calculated as body height in the morning minus body height in the evening. Physical activity was monitored throughout the 14 days by accelerometry. Daily work stressors, daily job control, biomechanical workload, and recreational activities after work were measured with daily surveys. Multilevel regression analyses showed that spinal disks shrank more during workdays than during nonwork days. After adjustment for sex, age, body weight, smoking status, biomechanical work strain, and time spent on physical and low-effort activities during the day, lower levels of daily job control significantly predicted increased spinal shrinkage. Findings add to knowledge on how work redesign that increases job control may possibly contribute to preserving intervertebral disk function and preventing occupational back pain.

Estimation of the risks of thermal stress due to the microclimate for manual fruit and vegetable harvesters in central Italy

Agricultural workers are exposed to various risks, including chemical agents, noise, and many other factors. One of the most characteristic and least known risk factors is constituted by the microclimatic conditions in the different phases of work (in field, in greenhouse, etc). A typical condition is thermal stress due to high temperatures during harvesting operations in open fields or in greenhouses. In Italy, harvesting is carried out for many hours during the day, mainly in the summer, with temperatures often higher than 30 degrees C. According to ISO 7243, these conditions can be considered dangerous for workers' health. The aim of this study is to assess the risks of exposure to microclimatic conditions (heat) for fruit and vegetable harvesters in central Italy by applying methods established by international standards. In order to estimate the risk for workers, the air temperature, radiative temperature, and air speed were measured using instruments in conformity with ISO 7726. Thermodynamic parameters and two more subjective parameters, clothing and the metabolic heat production rate related to the worker's physical activity, were used to calculate the predicted heat strain (PHS) for the exposed workers in conformity with ISO 7933. Environmental and subjective parameters were also measured for greenhouse workers, according to ISO 7243, in order to calculate the wet-bulb globe temperature (WBGT). The results show a slight risk for workers during manual harvesting in the field. On the other hand, the data collected in the greenhouses show that the risk for workers must not be underestimated. The results of the study show that, for manual harvesting work in climates similar to central Italy, it is essential to provide plenty of drinking water and acclimatization for the workers in order to reduce health risks. Moreover, the study emphasizes that the possible health risks for greenhouse workers increase from the month of April through July.

Genomic differences between type strain PG1 and field strains of Mycoplasma mycoides subsp. mycoides small-colony type

The recently accomplished complete genomic sequence analysis of the type strain PG1 of Mycoplasma mycoides subsp. mycoides small-colony type revealed four large repeated segments of 24, 13, 12, and 8 kb that are flanked by insertion sequence (IS) elements. Genetic analysis of type strain PG1 and African, European, and Australian field and vaccine strains revealed that the 24-kb genetic locus is repeated only in PG1 and not in other M. mycoides subsp. mycoides SC strains. In contrast, the 13-kb genetic locus was found duplicated in some strains originating from Africa and Australia but not in strains that were isolated from the European outbreaks. The 12- and 8-kb genetic loci were found in two and three copies, respectively, in all 28 strains analyzed. The flanking IS elements are assumed to lead to these tandem duplications, thus contributing to genomic plasticity. This aspect must be considered when designing novel diagnostic approaches and recombinant vaccines.