Minimum Effective Strain Research Articles

Human femur morphology and histology variation with ancestry and behaviour in an ancient sample from Vietnam

BackgroundThere is a genetic component to the minimum effective strain (MES)—a threshold which determines when bone will adapt to function—which suggests ancestry should play a role in bone (re)modelling. Further elucidating this is difficult in living human populations because of the high global genetic admixture. We examined femora from an anthropological skeletal assemblage (Mán Bạc, Vietnam) representing distinct ancestral groups. We tested whether femur morphological and histological markers of modelling and remodelling differed between ancestries despite their similar lifestyles. MethodsStatic histomorphometry data collected from subperiosteal cortical bone of the femoral midshaft, and gross morphometric measures of femur robusticity, were studied in 17 individuals from the Mán Bạc collection dated to 1906–1523 cal. BC. This assemblage represents agricultural migrants with affinity to East Asian groups, who integrated with the local hunter-gatherers with affinity to Australo-Papuan groups during the mid-Holocene. Femur robusticity and histology data were compared between groups of ‘Migrant’ (n = 8), ‘Admixed’ (n = 4), and ‘Local’ (n = 5). ResultsLocal individuals had more robust femoral diaphyses with greater secondary osteon densities, and relatively large secondary osteon and Haversian canal parameters than the migrants. The Migrant group showed gracile femoral shafts with the least dense bone made up of small secondary osteons and Haversian canals. The Admixed individuals fell between the Migrant and Local categories in terms of their femoral data. However, we also found that measures of how densely bone is remodelled per unit area were in a tight range across all three ancestries. ConclusionsBone modelling and remodelling markers varied with ancestral histories in our sample. This suggests that there is an ancestry related predisposition to bone optimising its metabolic expenditure likely in relation to the MES. Our results stress the need to incorporate population genetic history into hierarchical bone analyses. Understanding ancestry effects on bone morphology has implications for interpreting biomechanical loading history in past and modern human populations.

Influence of radial forging process on strain inhomogeneity of hollow gear shaft using finite element method and orthogonal design

Due to the current trend towards lightweight design in automotive industry, hollow stepped gear shafts for automobile and its radial forging process are widely investigated. Utilizing coupled finite element thermo-mechanical model, radial forging process of a hollow stepped gear shaft for automobile was simulated. The optimal combination of three process parameters including initial temperature, rotation rate and radial reduction was also selected using orthogonal design method. To examine the strain inhomogeneity of the forging workpiece, the strain inhomogeneity factor was introduced. The results reveal that the maximum effective strain and the minimum effective strain appeared in the outermost and innermost zones of different cross sections for the hollow stepped gear shaft, respectively. Optimal forging parameters are determined as a combination of initial temperature of 780 °C, rotation rate of 21°/stroke and radial reduction of 3 mm.

Simulation of Cold Forming of Spur Gears using DEFORM 3D

In the current study, the DEFORM3D program was used to simulation of cold forming of spur gears using lead metal. Three different forms of billets were used to forming the spur gear and the choose of the size of billets was determined according to the size of suggested gear in this study. Analyzes were performed such as effect of stress, strain, average stress, total distance and speed during the formation process. Through the results of the values ​​of the average stresses for the three billets, it was observed that the lowest value is obtained when using a solid billet. As indicated by the results of the study of the maximum stress occurs when the use of hollow billet with a diameter of 4 mm. In the study of effective stress, it was observed that there was a convergence in the stress values ​​for all work pieces; these values ​​in the age zone are greater than the center area. The results obtained from numerical modeling showed that the minimum effective strain occurs when using a hollow billet with a diameter of 4 mm and the highest value when using a solid billet. The velocity of the metal flow is proportional with the shape of the billet, it is noted that the value of the velocity in the case of hollow billets (4 mm and 6 mm) was close together and higher than the value of the metal flow velocity when using a solid billet. The speed of the metal flow is proportional with the amount of the billet cavity; in the case of the hard solid billet the speed is low. Peak load is affected during the formation of the spur gear with the shape of billet; it was observed that the peak load values ​​of the 4 mm hollow billet were less than the peak load of the other two cases.

Finite-element analysis of the mouse proximal ulna in response to elbow loading.

Bone is a mechano-sensitive tissue that alters its structure and properties in response to mechanical loading. We have previously shown that application of lateral dynamic loads to a synovial joint, such as the knee and elbow, suppresses degradation of cartilage and prevents bone loss in arthritis and postmenopausal mouse models, respectively. While loading effects on pathophysiology have been reported, mechanical effects on the loaded joint are not fully understood. Because the direction of joint loading is non-axial, not commonly observed in daily activities, strain distributions in the laterally loaded joint are of great interest. Using elbow loading, we herein characterized mechanical responses in the loaded ulna focusing on the distribution of compressive strain. In response to 1-N peak-to-peak loads, which elevate bone mineral density and bone volume in the proximal ulna in vivo, we conducted finite-element analysis and evaluated strain magnitude in three loading conditions. The results revealed that strain of ~ 1000 μstrain (equivalent to 0.1% compression) or above was observed in the limited region near the loading site, indicating that the minimum effective strain for bone formation is smaller with elbow loading than axial loading. Calcein staining indicated that elbow loading increased bone formation in the regions predicted to undergo higher strain.

Three-dimensional Numerical Simulation and Experimental Analysis of Austenite Grain Growth Behavior in Hot Forging Processes of 300M Steel Large Components

The microstructure models were integrated into finite element (FE) code, and a three-dimensional (3D) FE analysis on the entire hot forging processes of 300M steel large components was performed to predict the distributions of effective strain, temperature field and austenite grain size. The simulated results show that the finest grains distribute in the maximum effective strain region because large strain induces the occurrence of dynamic recrystallization. However, coarse macro-grains appear in the minimum effective strain region. Then, 300M steel forging test was performed to validate the results of FE simulation, and microstructure observations and quantitative analysis were implemented. The average relative difference between the calculated and experimental austenite grain size is 7.56%, implying that the present microstructure models are reasonable and can be used to analyze the hot forging processes of 300M steel.

Minimizing distortion during extrusion using adaptable dies

Warping, twisting, underfill, and/or distortion during the extrusion are challenging problems. The goal of the present paper is to develop a criterion and use an adaptable die design methodology that will allow the prediction of extrusion die shapes that produce minimum distortion in axisymmetric product. Distortion in the final extrusion product is the axial displacement experienced by an initially straight and transverse line after it has passed completely through the deformation zone. Four possible criteria for use in the die design scheme (based on deviations from ideal flow) are developed. These criteria are: (1) average axial displacement, (2) average shear strain, (3) average effective strain, and (4) volumetric effective strain rate deviation. Each of these criteria is presented in mathematical form, which can easily be incorporated into an analysis of extrusion die design. Two of the four criteria are viable and can be used to determine optimal die shapes via the adaptable design method. The average effective strain criterion can be used to minimize the effective strain distribution in the finished product. The volumetric effective strain rate deviation criterion tries to create a uniform effective strain rate field in the deformation zone, and minimizes the distortion in the final product. The extrusion die shape, which produces the minimum effective strain in the product, is different from the shape for minimum distortion. This finding is contradictory to the concept that, to minimize distortion, one should minimize redundant strain. Based on the use of the volumetric effective strain rate deviation criterion, extrusion dies, which minimize distortion, are established using the adaptable die design methodology.

Bones' adaptive response to mechanical loading is essentially linear between the low strains associated with disuse and the high strains associated with the lamellar/woven bone transition

There is a widely held view that the relationship between mechanical loading history and adult bone mass/strength includes an adapted state or “lazy zone” where the bone mass/strength remains constant over a wide range of strain magnitudes. Evidence to support this theory is circumstantial. We investigated the possibility that the “lazy zone” is an artifact and that, across the range of normal strain experience, features of bone architecture associated with strength are linearly related in size to their strain experience. Skeletally mature female C57BL/6 mice were right sciatic neurectomized to minimize natural loading in their right tibiae. From the fifth day, these tibiae were subjected to a single period of external axial loading (40, 10-second rest interrupted cycles) on alternate days for 2 weeks, with a peak dynamic load magnitude ranging from 0 to 14 N (peak strain magnitude: 0–5000 µε) and a constant loading rate of 500 N/s (maximum strain rate: 75,000 µε/s). The left tibiae were used as internal controls. Multilevel regression analyses suggest no evidence of any discontinuity in the progression of the relationships between peak dynamic load and three-dimensional measures of bone mass/strength in both cortical and cancellous regions. These are essentially linear between the low-peak locomotor strains associated with disuse (∼300 µε) and the high-peak strains derived from artificial loading and associated with the lamellar/woven bone transition (∼5000 µε). The strain:response relationship and minimum effective strain are site-specific, probably related to differences in the mismatch in strain distribution between normal and artificial loading at the locations investigated. © 2012 American Society for Bone and Mineral Research.

Knee-Loading Modality Drives Molecular Transport in Mouse Femur

Mechanical loading is well known to stimulate bone remodeling. Load-driven interstitial fluid flow and molecular transport have been postulated to play a role in the enhancement of bone formation. In order to evaluate load-driven molecular transport in a lacunocanalicular network, we conducted fluorescence recovery after photobleaching (FRAP) experiments using lacunae stained with uranine (376 Da). Loads were applied to a mouse femur ex vivo with a novel knee-loading modality, where the distal epiphysis was loaded with a sinusoidal force at 2 Hz. The lacunae in the diaphysis located 25% (approximately 4 mm) proximal to the loading site were photobleached and sequentially imaged, and a time constant for fluorescence recovery was determined both with and without knee loading. The time constant was estimated as the period to recover 63% of fluorescent intensity using a best-fit exponential curve. The results reveal that the applied loads shortened the time constant from 33 +/- 9 s with non-loading control to 25 +/- 11 s with knee loading (p = 0.0014). The strain in the measurement site was <100 microstain along the femoral midshaft, which was an order of magnitude smaller than the minimum effective strain threshold for bone remodeling. Taken together, the current study supports the notion that molecular transport in cortical bone is enhanced by the loads applied to the epiphysis without inducing significant in situ strain in the diaphysis.

Osteogenic potentials with joint-loading modality

Osteogenic potentials with a novel joint-loading modality were examined, using mouse ulnae as a model system. Load-induced deformation of rigid bone is known to generate interstitial fluid flow and stimulate osteogenesis. However, in most of the previous studies, loads were applied to cortical bone. In the current study, we addressed the question of whether deformation of the epiphysis underneath the joint would enhance bone formation in the epiphysis and the diaphysis. In order to answer the question, we applied lateral loads to a mouse elbow and conducted a bone histomorphometric analysis, as well as measurements of strains and streaming potentials. Compared to the no-loading control, the histomorphometric results showed that 0.5-N loads, applied to the elbow at 2 Hz for 3 min/day for 3 consecutive days, increased the mineralizing surface (two- to threefold), the rate of mineral apposition (three- to fivefold), and the rate of bone formation (six- to eightfold) in the ulna. Strain measurements indicated that strains of around 30 microstrain, induced with the joint-loading modality, were under the minimum effective strain of around 1000 microstrain, which is considered necessary to achieve strain-driven bone formation. To evaluate the induction of fluid flow with the joint-loading modality, streaming potentials were measured in separate experiments, using mouse femurs ex vivo. We found that the streaming potentials correlated to the magnitude of the load applied to the epiphysis (r(2) = 0.92), as well as the flow speed in the medullary cavity (r(2) = 0.93). Taken together, the findings of the current study support the idea of joint-loading driven osteogenesis, through a mechanism that involves the induction of fluid flow in cortical bone.

Osseointegration under immediate loading: biomechanical stress-strain and bone formation--resorption.

During the past 10 years, clinicians have used two-piece implants as a one-piece system for immediate loading to accomplish early recovery for function and esthetics. The statistical analysis by the Institute of Clinical Materials demonstrates high survival rates of 92.3 +/- 8.3%. Animal experiments of beagle dogs have been carried out to analyze successful conditions of immediate loading according to the dependency of bone formation--resorption upon the biomechanical stress--strain of bone. Histometric investigations clarified that the micromotion of less than 30 microns at the implant-bone interface did not interfere with the osteogenesis and new bone growth at the implant-bone interface. Bone formation and resorption are discussed from the standpoint of minimum effective strain on living bone.

Strain induced osteogenesis of the craniofacial suture upon controlled delivery of low-frequency cyclic forces.

Static forces have been used for more than a century to modulate osteogenesis of craniofacial sutures in not only laboratory research, but also clinical practice. Whether cyclic forces more effectively stimulate sutural osteogenesis than static forces is unknown. Here, the premaxillomaxillary sutures of growing rabbits received in vivo exogenous static forces with peak magnitude of 2 Newtons, or cyclic forces also at 2 Newtons but with frequencies of 0.2 Hz and 1 Hz. The static force and two cyclic forces did not evoke significant differences in the peak magnitude of static bone strain (506 microstrain 182; mean S.D.), 0.2-Hz cyclic strain (436 microstrain 191) or 1-Hz cyclic strain (461 microstrain 229). However, cyclic forces at 0.2 Hz delivered to the premaxillomaxillary suture for 10 min/d over 12 days (120 cyclic per day) induced significantly more craniofacial growth (p< 0.01), marked sutural separation, and islands of newly formed bone, in comparison with both sham controls and static force of matching peak magnitude. The bone strain threshold of approximately 500 microstrain for inducing sutural osteogenesis is lower than the minimum effective strain capable of inducing bone apposition in long bones. These data demonstrate, for the first time, that application of brief doses of cyclic forces induces sutural osteogenesis more effectively than static forces with matching peak magnitude.

Rib remodeling dynamics in a skeletal population from Kulubnarti, Nubia.

Bone remodeling variables in the rib were analyzed for a skeletal population of medieval antiquity (ca. A.D. 550-1450) from Kulubnarti, in Sudanese Nubia. The skeletal remains are naturally mummified and in an excellent state of preservation. The study sample consists of thin sections from the ribs of 80 individuals, ranging in age from 15-50+ years. Ribs were examined using a standard microscope and image analysis software. Numbers of intact osteons, fragmentary osteons, forming osteons, and resorption spaces were counted, osteon and Haversian canal areas were measured, and several variables were calculated to assess morphometric and remodeling status in the rib. Variables calculated included mean annual activation frequency, mean bone formation rate, and net osteonal remodeling. Results indicate that age changes are consistent with those observed for other archaeological and modern samples. High numbers of resorption spaces in young males may reflect slower skeletal development in boys compared to girls. Comparisons of rib data with results of a previous study on patterns of femoral bone remodeling in the same population indicate that ribs have more osteons and higher bone formation rates compared to the femur. Also, sexual differences in osteon size observed in the femur were not observed in the rib. Activation frequency and bone formation rate are low in the Kulubnarti population compared to previously published data for a modern sample, a finding consistent with reported results from other archaeological samples. Genetic factors influencing the minimum effective strain setpoint and duration of skeletal maturation, in addition to repetitive high strains at Kulubnarti, may contribute to observed differences.

Bone response to in vivo mechanical loading in C3H/HeJ mice.

Bone, being sensitive to mechanical stimulus, adapts to mechanical loads in response to bending or deformation. Although the signal/receptor mechanism for bone adaptation to deformation is still under investigation, the mechanical signal is related to the amount of bone deformation or strain. Adaptation to changes in physical activity depends on both the magnitude of increase in strain above average daily levels for maintaining current bone density and the Minimum Effective Strain (MES) for initiating adaptive bone formation. Given the variation of peak bone density that exists in any human population, it is likely that variation in levels for MES is, to a considerable degree, inherited and varies among animal species and breeds. This study showed a dose-related periosteal response to loading in C3H/HeJ mice. The extent of active formation surface, the rate of periosteal bone formation, and area of bone formation increased with increasing peak periosteal strain. In these mice, the loaded tibia consistently showed lower endocortical formation surface and mineral apposition rate than the nonloaded bones at every load level. Although periosteal expansion is the most efficient means of increasing moment of inertia in adaptation to bending, a dose response increase in endocortical formation would have been predicted. Our characterization of the mouse bone formation response to increasing bending loads will be useful in the design of experiments to study the tibial adaptive response to known loads in different mouse breeds.

An application of mechanostat theory to research design

In this paper a theoretical model for research into the area of bone health is proposed. The model is based on the mechanostat theory of bone biology, originally proposed by Harold M. Frost, and is directed toward research in the area of osteoporosis. The mechanostat theory is briefly reviewed, including the concept of changes in minimum effective strain thresholds. Each of the model's five levels is then detailed, followed by discussion of their application to research design and interpretation. The proposed research model may provide a systematic approach to research design, and thereby a method to increase the current understanding of bone biology.

Ideal forming—I. Homogeneous deformation with minimum plastic work

Ideal homogeneous deformation is defined as the path which produces a desired homogeneous deformation with minimum plastic work. Under rather broad assumptions, it is shown that this path corresponds to a path of minimum effective strain. The minimum work path is achieved when (1) the principal material lines are fixed with respect to the material during deformation, and (2) the ratio of principal true strain rates is constant. This path is unique for materials having smooth yield surfaces, such as Mises materials. For materials having pointed yield surfaces, the two conditions are only partially required and the path is not unique. For Tresca materials, an ideal path is achieved when only the major principal material line is fixed. For isotropic materials, the fixed material lines may be chosen arbitrarily; but, for anisotropic materials they are more restrictive.

Osteogenesis Irnperfecta

The minimum effective strain (MES) constitutes a threshold that separates biomechanically acceptable from unacceptable strains on growing bone and fibrous tissues. Strains above that threshold affect modeling and remodeling activities in ways that change the size and configuration of growing bones, tendons, ligaments, and fascia to fit their new mechanical usage and return their strains to the threshold level. Were that threshold set too high from birth, the effects of normal function on remodeling and modeling should lead to thin fibrous tissue structures, to slender, osteopenic diaphyses and spongiosa, and to increased fragility. Those and other predictable set point effects fit so precisely many of the known hard and soft tissue abnormalities of osteogenesis imperfecta patients, that an elevated MES set point may be a heretofore unrecognized basic pathogenetic factor in that disease.

A Determinant of Bone Architecture

Minimum effective strain (MES), a hypothesis since 1964, has achieved experimental support. The range is about 0.0008-0.002 unit bone surface strain. Strains below the MES apparently do not evoke adaptive architectural bone modeling, but those above it do. As a key property of living lamellar bone and its intermediary organization, MES offers the potential to predict exactly when and where mechanical loads will cause bone architectural adaptations. MES represents a step toward the goal of constructing a specific, predictive, and quantitative theory of the mechanical determinants of skeletal architecture.