Polar Moment Of Inertia Research Articles

Adipose Tissue Infiltration of Bone Marrow and Skeletal Muscle in Children with Mild Spastic Cerebral Palsy

Non-ambulatory children with severe cerebral palsy (CP) have a high degree of adipose tissue (AT) infiltration which could play a role in the development of insulin resistance and fractures. The objective of this study was to determine the degree of AT infiltration within the bone marrow cavity of the middle tibia and within the surrounding muscle in ambulatory children with mild spastic CP (5-11 y) compared to typically developing controls matched for age and sex (n = 8/group). The concentration of AT in the bone marrow and muscle, and the intermuscular, subfascial and subcutaneous AT volume, muscle volume, cortical bone volume and bone strength (i.e., section modulus, Z and polar moment of inertia, J) were estimated using magnetic resonance imaging. Children with CP vs. controls had a higher (P < 0.05) concentration of AT in the bone marrow (83 ± 2 % vs. 81 ± 2 %) and muscle (27 ± 7 % vs. 18 ± 5 %). Children with CP vs. controls also had higher (P < 0.05) subfascial AT (357 %), and lower muscle volume (40%), cortical bone volume (26 %), Z (31 %) and J (38 %). Although not statistically significant (P = 0.07), children with CP vs. controls also had higher intermuscular AT (391 %). Whether the high concentration of AT in bone marrow and muscle during childhood are early indicators of insulin resistance and future fracture requires further investigation. Supported by the NIH(Grant HD071397-01).

Estimation of the Reachable Set for the Problem of Vibrating Kirchhoff Plate

We consider a dynamical system with distributed parameters for the description of controlled vibrations of a Kirchhoff plate without polar moment of inertia. A class of optimal controls corresponding to finite-dimensional approximations is used to study the reachable set. Analytic estimates for the norm of these control functions are obtained depending on the boundary conditions. These estimates are used to study the reachable set for the infinite-dimensional system. For a model with incommensurable frequencies, an estimate of the reachable set is obtained under the condition of power decay of the amplitudes o generalized coordinates.

Osteoblast function and bone histomorphometry in a murine model of Rett syndrome

Rett syndrome (RTT) is an X-linked neurodevelopmental disorder due to mutations affecting the neural transcription factor MeCP2. Approximately 50% of affected females have decreased bone mass. We studied osteoblast function using a murine model of RTT. Female heterozygote (HET) and male Mecp2-null mice were compared to wild type (WT) mice. Micro-CT of tibia from 5week-old Mecp2-null mice showed significant alterations in trabecular bone including reductions in bone volume fraction (−29%), number (−19%), thickness (−9%) and connectivity density (−32%), and increases in trabecular separation (+28%) compared to WT. We also found significant reductions in cortical bone thickness (−18%) and in polar moment of inertia (−45%). In contrast, cortical and trabecular bone from 8week-old WT and HET female mice were not significantly different. However, mineral apposition rate, mineralizing surface and bone formation rate/bone surface were each decreased in HET and Mecp2-null mice compared to WT mice. Histomorphometric analysis of femurs showed decreased numbers of osteoblasts but similar numbers of osteoclasts compared to WT, altered osteoblast morphology and decreased tissue synthesis of alkaline phosphatase in Mecp2-null and HET mice. Osteoblasts cultured from Mecp2-null mice, which unlike WT osteoblasts did not express MeCP2, had increased growth rates, but reductions in mRNA expression of type I collagen, Runx2 and Osterix compared to WT osteoblasts. These results indicate that MeCP2 deficiency leads to altered bone growth. Osteoblast dysfunction was more marked in Mecp2-null male than in HET female mice, suggesting that expression of MeCP2 plays a critical role in bone development.

Irisin injected mice display increased tibial cortical mineral density and polar moment of inertia

It has been recently reported that, after physical activity, the skeletal muscle releases Irisin, the newly identified myokine able of driving transition of white adipocytes into brown [1]. This result supported the role of skeletal muscle as endocrine organ, suggesting that it could target other tissues besides adipose tissue. In our previous work, we demonstrated that conditioned media collected from primary myoblasts of exercised mice were able to increase OB differentiation and this effect was Irisinmediated [2]. Here we show that Irisin has positive effect on cortical mineral density and geometry in vivo. Young male mice were injected with r-Irisin and cortical bone adaptation was analyzed by micro-CT at tibial midshaft. Our results show that cortical tissue mineral density is significantly increased in Irisin-injected mice compared to vehicle-injected littermates (+7.15%; p<0.01). Furthermore, this higher density of calcium hydroxyapatite at cortical site is accompanied by increase in periosteal circumference (+7.5%; p<0.03) and polar moment of Inertia (pMOI +19,21%; p<0,01). A greater pMOI indicates stronger resistance of a long bone to torsion and, together with higher bone mineral density, suggests higher protection against fracture. The effect of Irisin is fully comparable to the effect of physical activity that is widely accepted method for increasing bone mineral density and bone size in healthy populations. In view of further proving the involvement of Irisin in bone metabolism, we validate its direct effect on osteoblasts in vitro. Phosphorylation of the MAP kinase ERK and the expression of Atf4 were significantly increased after Irisin treatment, as well as ALP and pro-Collagen I mRNA expression. Our data highlight a novel link in muscle-fat-bone axis demonstrating that Irisin targets bone tissue directly, driving positive effects on cortical mineral density and geometry in vivo. These findings would expand the research of exercise-mimetic drugs that might be widely used to treat osteoporotic patients who are suffering from immobilization and cannot perform physical activity.

The Steiner Formula and the Polar Moment of Inertia for the Closed Planar Homothetic Motions in Complex Plane

The Steiner area formula and the polar moment of inertia were expressed during one-parameter closed planar homothetic motions in complex plane. The Steiner point or Steiner normal concepts were described according to whether rotation number was different from zero or equal to zero, respectively. The moving pole point was given with its components and its relation between Steiner point or Steiner normal was specified. The sagittal motion of a winch was considered as an example. This motion was described by a double hinge consisting of the fixed control panel of winch and the moving arm of winch. The results obtained in the second section of this study were applied for this motion.

Twelve months of voluntary heavy alcohol consumption in male rhesus macaques suppresses intracortical bone remodeling

Chronic heavy alcohol consumption is a risk factor for cortical bone fractures in males. The increase in fracture risk may be due, in part, to reduced bone quality. Intracortical (osteonal) bone remodeling is the principle mechanism for maintaining cortical bone quality. However, it is not clear how alcohol abuse impacts intracortical bone remodeling. This study investigated the effects of long-duration heavy alcohol consumption on intracortical bone remodeling in a non-human primate model. Following a 4-month induction period, male rhesus macaques (Macaca mulatta, n=21) were allowed to voluntarily self-administer water or alcohol (4% ethanol w/v) for 22h/d, 7 d/wk for 12months. Control monkeys (n=13) received water and an isocaloric maltose-dextrin solution. Tetracycline hydrochloride was administered orally 17 and 3days prior to sacrifice for determination of active mineralization sites. Animals in the alcohol group consumed 2.7±0.2g alcohol/kg/d (mean±SE) during the 12months of self-administration, resulting in a mean daily blood alcohol concentration of 77±9mg/dl from samples taken at 7h after the start of a daily session. However, blood alcohol concentration varied widely from day to day, with peak levels exceeding 250mg/dl, modeling a binge-drinking pattern of alcohol consumption. The skeletal response to alcohol was determined by densitometry, microcomputed tomography and histomorphometry. Significant differences in tibial bone mineral content, bone mineral density, and cortical bone architecture (cross-sectional volume, cortical volume, marrow volume, cortical thickness, and polar moment of inertia) in the tibial diaphysis were not detected with treatment. However, cortical porosity was lower (1.8±0.5 % versus 0.6±0.1 %, p=0.021) and labeled osteon density was lower (0.41±0.2/mm2versus 0.04±0.01/mm2, p<0.003) in alcohol-consuming monkeys compared to controls, indicating a reduced rate of intracortical bone remodeling. In concordance, plasma CTx was lower (2.5±0.3ng/ml versus 1.7±0.1ng/ml, p=0.028) in the alcohol group. These results suggest that chronic heavy alcohol consumption may negatively impact bone health, in part, by suppressing intracortical bone remodeling.

Fractures in geriatric mice show decreased callus expansion and bone volume.

Poor fracture healing in geriatric populations is a significant source of morbidity, mortality, and cost to individuals and society; however, a fundamental biologic understanding of age-dependent healing remains elusive. The development of an aged-based fracture model system would allow for a mechanistic understanding that could guide future biologic treatments. Using a small animal model of long-bone fracture healing based on chronologic age, we asked how aging affected (1) the amount, density, and proportion of bone formed during healing; (2) the amount of cartilage produced and the progression to bone during healing; (3) the callus structure and timing of the fracture healing; and (4) the behavior of progenitor cells relative to the observed deficiencies of geriatric fracture healing. Transverse, traumatic tibial diaphyseal fractures were created in 5-month-old (n=104; young adult) and 25-month-old (n=107; which we defined as geriatric, and are approximately equivalent to 70-85 year-old humans) C57BL/6 mice. Fracture calluses were harvested at seven times from 0 to 40 days postfracture for micro-CT analysis (total volume, bone volume, bone volume fraction, connectivity density, structure model index, trabecular number, trabecular thickness, trabecular spacing, total mineral content, bone mineral content, tissue mineral density, bone mineral density, degree of anisotropy, and polar moment of inertia), histomorphometry (total callus area, cartilage area, percent of cartilage, hypertrophic cartilage area, percent of hypertrophic cartilage area, bone and osteoid area, percent of bone and osteoid area), and gene expression quantification (fold change). The geriatric mice produced a less robust healing response characterized by a pronounced decrease in callus amount (mean total volume at 20 days postfracture, 30.08±11.53 mm3 versus 43.19±18.39 mm3; p=0.009), density (mean bone mineral density at 20 days postfracture, 171.14±64.20 mg hydroxyapatite [HA]/cm3 versus 210.79±37.60 mg HA/cm3; p=0.016), and less total cartilage (mean cartilage area at 10 days postfracture, 101,279±46,755 square pixels versus 302,167±137,806 square pixels; p=0.013) and bone content (mean bone volume at 20 days postfracture, 11.68±3.18 mm3 versus 22.34±10.59 mm3; p<0.001) compared with the young adult mice. However, the amount of cartilage and bone relative to the total callus size was similar between the adult and geriatric mice (mean bone volume fraction at 25 days postfracture, 0.48±0.10 versus 0.50±0.13; p=0.793), and the relative expression of chondrogenic (mean fold change in SOX9 at 10 days postfracture, 135+25 versus 90±52; p=0.221) and osteogenic genes (mean fold change in osterix at 20 days postfracture, 22.2±5.3 versus 18.7±5.2; p=0.324) was similar. Analysis of mesenchymal cell proliferation in the geriatric mice relative to adult mice showed a decrease in proliferation (mean percent of undifferentiated mesenchymal cells staining proliferating cell nuclear antigen [PCNA] positive at 10 days postfracture, 25%±6.8% versus 42%±14.5%; p=0.047). Our findings suggest that the molecular program of fracture healing is intact in geriatric mice, as it is in geriatric humans, but callus expansion is reduced in magnitude. Our study showed altered healing capacity in a relevant animal model of geriatric fracture healing. The understanding that callus expansion and bone volume are decreased with aging can help guide the development of targeted therapeutics for these difficult to heal fractures.

Greater Polar Moment of Inertia at the Tibia in Athletes Who Develop Stress Fractures.

Background:Several previous investigations have determined potential risk factors for stress fractures in athletes and military personnel.Purpose:To determine factors associated with the development of stress fractures in female athletes.Study Design:Case-control study; Level of evidence, 3.Methods:A total of 88 female athletes (cross-country, n = 29; soccer, n = 15; swimming, n = 9; track and field, n = 14; volleyball, n = 12; and basketball, n = 9) aged 18 to 24 years were recruited to participate in a longitudinal bone study and had their left distal tibia at the 4%, 20%, and 66% sites scanned by peripheral quantitative computed tomography (pQCT). Patients included 23 athletes who developed stress fractures during the following year (cases). Whole body, hip, and spine scans were obtained using dual-energy x-ray absorptiometry (DXA). Analysis of covariance was used to determine differences in bone parameters between cases and controls after adjusting for height, lower leg length, lean mass, fat mass, and sport.Results:No differences were observed between cases and controls in any of the DXA measurements. Cases had significantly greater unadjusted trabecular bone mineral content (BMC), greater polar moment of inertia (PMI) at the 20% site, and greater cortical BMC at the 66% site; however, after adjusting for covariates, the differences became nonsignificant. When analyses were repeated using all individuals who had ever had a stress fracture as cases (n = 31) and after controlling for covariates, periosteal circumference was greater in the cases than the controls (71.1 ± 0.7 vs 69.4 ± 0.5 mm, respectively; P = .04).Conclusion:A history of stress fractures is associated with larger bones. These findings are important because larger bones were previously reported to be protective against fractures and stress fractures, but study findings indicate that may not always be true. One explanation could be that individuals who sustain stress fractures have greater loading that results in greater periosteal circumference but also results in the development of stress fractures.

Objectively measured physical activity trajectories predict adolescent bone strength: Iowa Bone Development Study

BackgroundPhysical activity improves bone strength and reduces the risk for osteoporotic fractures. However, there are substantial gaps in our knowledge as to when, how and how much activity is optimal...

D-37 Free Communication/Poster - Pulmonary Disease and Exercise

The positive association between muscle mass and bone mass is well known. However, muscle mass and areal bone mineral density are surrogate measures of the more important constructs of muscle function, muscle cross-sectional area (MCSA), and bone strength (as posited in the Mechanostat Theory). PURPOSE: We examined the relationship between lower body muscle power (a measure of muscle function), MCSA, and tibial bone strength in a healthy cohort of 303 17-year-olds. METHODS: This cross-sectional study was part of the ongoing Iowa Bone Development Study. Using peripheral quantitative computed tomography (pQCT), MCSA (66% tibia, mm2), Polar Moment of Inertia (PMI, 38% and 66% tibia, mm4), and Bone Strength Index (BSI, 4% tibia, g/cm3/mm4) were obtained during a clinical visit. Anthropometric measures (ht in cm, wt in kg) and vertical jump height (cm) were also measured. Vertical jump height and the Sayers equation were used to estimate lower body muscle power (Watts). Spearman correlations were calculated for sex-specific associations between muscle power and bone strength measures. Because MSCA is so involved in the relationship between muscle power and bone strength, mediation analysis was used to examine the effect of muscle power and MSCA on bone strength through several pathways. RESULTS: Muscle power estimates were significantly associated with bending and compression measures of bone strength. Associations were greater for bending strength (PMI 38%, 66%: females r=.70, r=.69 males r=.76, r=76) than compression strength (BSI: females r=.48 males r=.59). Mediation analysis indicated that muscle power had a significant effect on MSCA (p<.0001 at all sites), as well as on bone strength independent of MSCA (p<.0005 at all sites). CONCLUSIONS: These results showed a significant association between muscle power and bone strength even when controlling for MSCA. This is consistent with the premise that quality and use of muscle contribute over-and-above muscle size. More fully elucidating physical activity and bone health dose-response may require conceptualizing muscle power movements as a dimension of physical activity. Supported by The National Institute of Dental and Craniofacial Research (R01-DE12101 and R01-DE09551) and The National Center for Research Resources (UL1-RR024979 and M01-RR00059).

Effective stability around the Cassini state in the spin-orbit problem

We investigate the long-time stability in the neighborhood of the Cassini state in the conservative spin-orbit problem. Starting with an expansion of the Hamiltonian in the canonical Andoyer-Delaunay variables, we construct a high-order Birkhoff normal form and give an estimate of the effective stability time in the Nekhoroshev sense. By extensively using algebraic manipulations on a computer, we explicitly apply our method to the rotation of Titan. We obtain physical bounds of Titan's latitudinal and longitudinal librations, finding a stability time greatly exceeding the estimated age of the Universe. In addition, we study the dependence of the effective stability time on three relevant physical parameters: the orbital inclination, $i$, the mean precession of the ascending node of Titan orbit, $\dot\Omega$, and the polar moment of inertia, $C$.

Finite Element Based Nonlinear Normalization of Human Lumbar Intervertebral Disc Stiffness to Account for Its Morphology

Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently higher CV after normalization. Assuming that geometry and material properties affect the mechanical response, they can also compensate for one another. Therefore, the larger CV after normalization can be interpreted as a strong variability of the material properties, previously hidden by the geometry's own influence. In conclusion, a new normalization protocol for the intervertebral disc stiffness in compression, flexion, extension, bilateral torsion and bending was proposed, with the possible use of MRI and FE to acquire the discs' anatomy and determine the nonlinear relations between stiffness and morphology. Such protocol may be useful to relate the disc's mechanical properties to its degree of degeneration.

Phobos laser ranging: Numerical Geodesy experiments for Martian system science

Laser ranging is emerging as a technology for use over (inter)planetary distances, having the advantage of high (mm-cm) precision and accuracy and low mass and power consumption. We have performed numerical simulations to assess the science return in terms of geodetic observables of a hypothetical Phobos lander performing active two-way laser ranging with Earth-based stations. We focus our analysis on the estimation of Phobos and Mars gravitational, tidal and rotational parameters. We explicitly include systematic error sources in addition to uncorrelated random observation errors. This is achieved through the use of consider covariance parameters, specifically the ground station position and observation biases. Uncertainties for the consider parameters are set at 5mm and at 1mm for the Gaussian uncorrelated observation noise (for an observation integration time of 60s). We perform the analysis for a mission duration up to 5 years.It is shown that a Phobos Laser Ranging (PLR) can contribute to a better understanding of the Martian system, opening the possibility for improved determination of a variety of physical parameters of Mars and Phobos. The simulations show that the mission concept is especially suited for estimating Mars tidal deformation parameters, estimating degree 2 Love numbers with absolute uncertainties at the 10−2 to 10−4 level after 1 and 4 years, respectively and providing separate estimates for the Martian quality factors at Sun and Phobos-forced frequencies. The estimation of Phobos libration amplitudes and gravity field coefficients provides an estimate of Phobos׳ relative equatorial and polar moments of inertia with an absolute uncertainty of 10−4 and 10−7, respectively, after 1 year. The observation of Phobos tidal deformation will be able to differentiate between a rubble pile and monolithic interior within 2 years.For all parameters, systematic errors have a much stronger influence (per unit uncertainty) than the uncorrelated Gaussian observation noise. This indicates the need for the inclusion of systematic errors in simulation studies and special attention to the mitigation of these errors in mission and system design.

Effects of Chronic Heavy Alcohol Consumption and Endurance Exercise on Cancellous and Cortical Bone Microarchitecture in Adult Male Rats

Bone health is influenced by numerous lifestyle factors, including diet and exercise. Alcohol is a major nonessential constituent of diet and has dose- and context-dependent effects on bone. Endurance exercise is associated with increased risk of stress fractures. The purpose of this study was to determine the long-term independent and combined effects of chronic heavy alcohol consumption and endurance exercise (treadmill running) on bone mass and microarchitecture in young adult male Sprague-Dawley rats. Six-month-old male rats were randomized into 4 groups (9 to 13 rats/group): sedentary + control diet, sedentary + ethanol (EtOH) diet, exercise + control diet, or exercise + EtOH diet. EtOH-fed rats consumed a liquid diet (EtOH comprised 35% of caloric intake) ad libitum. Control rats were pair-fed the same diet with isocaloric substitution of EtOH with maltose-dextran. Exercise was conducted on a motorized treadmill (15% grade for 30 minutes) 5 d/wk for 16 weeks. Femur and 12th thoracic vertebra were analyzed for bone mineral content (BMC) and density (BMD) using densitometry and cortical and cancellous bone architecture using microcomputed tomography. EtOH consumption resulted in lower femur length, BMC, and BMD, and lower midshaft femur cortical volume, cortical thickness, and polar moment of inertia. In addition, trabecular thickness was lower in vertebra of EtOH-fed rats. Endurance exercise had no independent effect on any end point evaluated. A significant interaction between endurance exercise and EtOH was detected for several cancellous end points in the distal femur metaphysis. EtOH-consuming rats that exercised had lower distal femur metaphysis bone volume/tissue volume, trabecular connectivity density, and trabecular thickness compared to exercising rats that consumed control diet. The results obtained in this model suggest that chronic heavy alcohol consumption may reduce skeletal integrity by reducing bone size, mass, and density, and by negatively altering bone microarchitecture and may increase fracture risk associated with endurance exercise at weight-bearing skeletal sites.

Addenda and Erratum to: Characteristic directions of closed planar motions

In a previous paper ZAMM 92(9), 731–748 (2012), some properties of closed planar motions were investigated. The focus was on three aspects: the area enclosed by the paths of points, the polar moment of inertia and the natural average of a path. These three mathematical objects were shown to be interrelated. For reasons of completeness, the authors now add some historical references which relate the problem considered to that of mechanical integrators eg. polarplanimeter.

小卫星用反作用飞轮系统设计

According to the requirement of reaction flywheels in small satellites for small sizes, the design method for an armature size was proposed when the electrical motor was at a minimal volume, and a stator coreless reaction flywheel system was designed based on the method. To avoid the magnetic saturation, the multidisciplinary design optimization method was applied to the design of flywheel rotor and magnetic field of the motor. A optimization strategy combined with Exterior Penalty(EP) function and Sequential Quadratic Programming(SQP) was proposed to optimize the system as well. With optimization, the minimum mass and maximum air-gap magnetic flux density of the rotor were chosen as the objects, respectively, and the maximum equivalent stress, resonance frequency, the polar moment of inertia and the magnetic saturation were taken as constrains. Then, the software iSIGHT with finite element analysis (ANSYS) were integrated to achieve the optimization. Finally, a flywheel prototype was designed based on the optimal results. The results indicate that the total mass of the flywheel rotor has been decreased from 0.73 kg to 0.67 kg (reduced by 8.22%) and the flux density has been increased from 0.376 T to 0.401 T (increased by 6.65%). The optimal design method can improve the rationality of flywheel design, and will promote the progress of the miniaturization investigation of flywheel systems.

On natural flexural vibrations of a step-up rod with distributed attached mass

The paper discusses natural flexural vibrations of a step-up rod with distributed attached mass. It is shown that an increase in the step coordinate results in rising natural frequencies of the vibrations in the range of parameters under consideration. It is revealed that as the ratio of polar moments of inertia in the steps grows, the lowest two frequencies of natural flexural vibrations in the rod tend to decrease. Also, the lowest frequencies of natural flexural vibrations in the rod decrease with growing intensity of the distributed attached mass. The solution to the inverse problem makes it possible to define the step coordinate, the ratio of polar moments of inertia in the steps and the intensity of the distributed attached mass using the lowest three frequencies of free flexural vibrations in the step-up rod.

The influence of orbital dynamics, shape and tides on the obliquity of Mercury

Earth-based radar observations of the rotational dynamics of Mercury (Margot et al., 2012) combined with the determination of its gravity field by MESSENGER (Smith et al., 2012) give clues on the internal structure of Mercury, in particular its polar moment of inertia C, deduced from the obliquity (2.04±0.08)arcmin.The dynamics of the obliquity of Mercury is a very-long term motion (a few hundreds of kyrs), based on the regressional motion of Mercury’s orbital ascending node. This paper, following the study of Noyelles and D’Hoedt (2012), aims at first giving initial conditions at any time and for any values of the internal structure parameters for numerical simulations, and at using them to estimate the influence of usually neglected parameters on the obliquity, like J3, the Love number k2 and the secular variations of the orbital elements. We use, for that, averaged representations of the orbital and rotational motions of Mercury, suitable for long-term studies.We find that J3 should alter the obliquity by 250milli-arcsec, the tides by 30 milli-arcsec, and the secular variations of the orbital elements by 10 milli-arcsec over 20years. The resulting value of C could be at the most changed from 0.346mR2 to 0.345mR2.

Research on Calculation Method for Polar Moment of Inertia of Spline Shaft

This article is based on the concept and the calculation method of polar moment of inertia to derive the calculation formula for polar moment of inertia of rectangle spline shaft and involute spline shaft. Then verified the correctness of the calculation method and laid the foundation for the strength calculation of spline shaft.

Exploring the determinants of fracture risk among individuals with spinal cord injury.

In this cross-sectional study, we found that areal bone mineral density (aBMD) at the knee and specific tibia bone geometry variables are associated with fragility fractures in men and women with chronic spinal cord injury (SCI). Low aBMD of the hip and knee regions have been associated with fractures among individuals with chronic motor complete SCI; however, it is unclear whether these variables can be used to identify those at risk of fracture. In this cross-sectional study, we examined whether BMD and geometry measures are associated with lower extremity fragility fractures in individuals with chronic SCI. Adults with chronic [duration of injury ≥ 2 years] traumatic SCI (C1-L1 American Spinal Cord Injury Association Impairment Scale A-D) reported post injury lower extremity fragility fractures. Dual-energy X-ray absorptiometry (DXA) was used to measure aBMD of the hip, distal femur, and proximal tibia regions, while bone geometry at the tibia was assessed using peripheral quantitative computed tomography (pQCT). Logistic regression and univariate analyses were used to identify whether clinical characteristics or bone geometry variables were associated with fractures. Seventy individuals with SCI [mean age (standard deviation [SD]), 48.8 (11.5); 20 females] reported 19 fragility fractures. Individuals without fractures had significantly greater aBMD of the hip and knee regions and indices of bone geometry. Every SD decrease in aBMD of the distal femur and proximal tibia, trabecular volumetric bone mineral density, and polar moment of inertia was associated with fracture prevalence after adjusting for motor complete injury (odds ratio ranged from 3.2 to 6.1). Low knee aBMD and suboptimal bone geometry are significantly associated with fractures. Prospective studies are necessary to confirm the bone parameters reported to predict fracture risk in individuals with low bone mass and chronic SCI.