Polar Moment Of Inertia Research Articles

Genetic loci affecting bone structure and strength in inbred COP and DA rats

Previous studies have shown that the Copenhagen 2331 (COP) and Dark Agouti (DA) rats have significant differences in bone structure and strength despite their similar body mass. Thus, these inbred rat strains may provide a unique resource to identify the genetics underlying the phenotypic variation in bone fragility. A sample of 828 (405 males and 423 females) COP×DA F2 progeny had extensive phenotyping for bone structure measures including cortical bone area and polar moment of inertia at the femur midshaft and total, cortical and trabecular bone areas, for the lumbar vertebra 5 (L5). Bone strength phenotypes included ultimate force, stiffness and work to failure of femur and L5. These skeletal phenotypes were measured using peripheral quantitative computed tomography (pQCT) and mechanical testing. A whole-genome screen was conducted in the F2 rats, using microsatellite markers spaced at approximately 20 cM intervals. Genetic marker maps were generated from the F2 data and used for genome-wide linkage analyses to detect linkage to the bone structure and strength phenotypes. Permutation testing was employed to obtain the thresholds for genome-wide significance ( p < 0.01). Significant QTL for femur structure and strength were identified on chromosome (Chr) 1 with a maximum LOD score of 33.5; evidence of linkage was found in both the male and female rats. In addition, Chrs 6, 7, 10, 13, 15 and 18 were linked to femur midshaft structure. QTL linked to femur strength were identified on Chrs 5 and 10. For L5 vertebrae, Chrs 2, 16, and 18 harbored QTL for cortical structure and trabecular structure for L5 was linked to Chrs 1, 7, 12, and 18. One female-specific QTL for femur ultimate force was identified on Chr 5, and two male-specific QTL for L5 cortical area were found on Chrs 2 and 18. Our study demonstrates strong evidence of linkage for bone structure and strength to multiple rat chromosomes.

Loss of Sex-Specific Difference in Femoral Bone Parameters in Male Leptin Knockout Mice

Sex-dependent differences were identified in the femoral bone parameters of male and female ob/ob (leptin knockout) mice compared with their C57BL/6 wild-type background strain. Total fat, lean weight and body weight were not different between adult male and female leptin knockout mice. However, leptin knockout males exhibited lower lean weights than C57BL/6 males. Peripheral quantitative computerized tomographic measurements at the femoral midshaft revealed that the normal differences in the periosteal circumference, endosteal circumference, total bone mineral content, and polar moment of inertia normally observed between adult male and female wild-type mice were lost between adult male and female ob/ob mice. Significant reductions in these bone parameters were seen in male ob/ob mice compared to male wild-type mice but not in female ob/ob mice compared to female wild-type mice. In prepubertal mice, there were no differences in phenotype and femoral bone parameters between males and females within any strain, suggesting sex hormone functions. Serum free testosterone levels were 5.6-fold higher in adult male ob/ob mice than in adult male C57BL/6 wild-type mice, and serum estradiol levels were 1.8- and 1.3-fold greater in adult male and female ob/ob mice, respectively, than in their wild-type counterparts. Androgen receptor gene expression was not different in femur-derived bone cells of male ob/ob mice compared with wild-type mice. The loss of sex-related differences in these bone parameters in adult male ob/ob mice might result from deficient signaling in the androgen signaling pathway and the fact that leptin functions are permissive for androgen effects on bone development.

Novel Role of Y1 Receptors in the Coordinated Regulation of Bone and Energy Homeostasis

The importance of neuropeptide Y (NPY) and Y2 receptors in the regulation of bone and energy homeostasis has recently been demonstrated. However, the contributions of the other Y receptors are less clear. Here we show that Y1 receptors are expressed on osteoblastic cells. Moreover, bone and adipose tissue mass are elevated in Y1(-/-) mice with a generalized increase in bone formation on cortical and cancellous surfaces. Importantly, the inhibitory effects of NPY on bone marrow stromal cells in vitro are absent in cells derived from Y1(-/-) mice, indicating a direct action of NPY on bone cells via this Y receptor. Interestingly, in contrast to Y2 receptor or germ line Y1 receptor deletion, conditional deletion of hypothalamic Y1 receptors in adult mice did not alter bone homeostasis, food intake, or adiposity. Furthermore, deletion of both Y1 and Y2 receptors did not produce additive effects in bone or adiposity. Thus Y1 receptor pathways act powerfully to inhibit bone production and adiposity by nonhypothalamic pathways, with potentially direct effects on bone tissue through a single pathway with Y2 receptors.

Evaluation of the Muscle-Bone Relationship in Children Using Magnetic Resonance Imaging

PURPOSE: To examine the relationship between muscle mass in the midthigh and bone structure in the femur in 8 to 12 year-old children. METHODS: Twenty children (8 boys and 12 girls) 8 to 12 years of age and within the 10th and 90thage-based percentiles for height and weight participated in the study. Pubertal development was assessed by Tanner staging. Height and weight were determined using standard procedures. Magnetic resonance imaging (GE, 1.5 T) was used to determine muscle mass, cortical bone volume, cross-sectional moment of inertia (CSMI), section modulus (Z) and polar moment of inertia (J) at the level of the middle third of the femur (TR = 750, TE = 14, FOV = 16, 1 cm thick separated by 0.5 cm, 512x512 imaging matrix) and trabecular bone microarchitecture in the lateral half of the distal femur (TR = 30, TE = 4.5, FOV = 9 cm, 0.7 cm thick, 512 × 512 imaging matrix). RESULTS: Children were prepubertal (Tanner stage I; n = 18) or early pubertal (Tanner stage II; n = 2) and not different from the 50th percentile for height (48 ±21 %) and weight (48 ± 24 %). Midthigh muscle mass was strongly related to midfemur cortical bone volume, CSMI, J and Z (r = 0.91, 0.87, 0.88 and 0.89, respectively, P < 0.05). Midthigh muscle mass was not related to apparent trabecular number or separation in the distal femur (P > 0.05), however, it was moderately related to apparent trabecular bone volume and trabecular thickness (appTb.Th; r = 0.58 and 0.80, respectively, P < 0.05). When height and weight were taken into account, midfemur cortical bone volume, CSMI, J and Z and distal femur appTb.Th were still related to midthigh muscle mass (partial r = 0.68, 0.58, 0.59, 0.63 and 0.65, respectively, P < 0.05). CONCLUSION: Midthigh muscle mass is related to cortical and trabecular bone structure in the femur of children, however, the relationship to cortical bone structure is stronger. Supported by the National Osteoporosis Foundation.

A novel solution for pressure drop in singly connected microchannels of arbitrary cross-section

This paper outlines a novel approximate solution for determining the pressure drop of fully developed, laminar, single-phase flow in singly connected microchannels of arbitrary cross-section. Using a “bottom-up” approach, it is shown that for constant fluid properties and flow rate in fixed cross-section channels, the Poiseuille number is only a function of geometrical parameters of the cross-section, i.e., perimeter, area, and polar moment of inertia. The proposed model is validated with experimental data for rectangular, trapezoidal, and triangular microchannels. The model is also compared against numerical results for a wide variety of channel cross-sections including: hyperellipse, trapezoid, sine, square duct with two adjacent round corners, rhombic, circular sector, circular segment, annular sector, rectangular with semi-circular ends, and moon-shaped channels. The model predicts the pressure drop for the cross-sections listed within 8% of the values published.

Impaired geometric properties of tibia in older women with hip fracture history

This study evaluated side-to-side differences in tibial mineral mass and geometry in women with previous hip fracture sustained on average 3.5 years earlier. Both tibial mineral mass and geometry were found to be reduced in the fractured leg. The purpose of this study was to evaluate side-to-side differences in tibial mineral mass and geometry after hip fracture and to assess the determinants of such differences. Thirty-eight 60- to 85-year-old women with a previous hip fracture and 22 same-aged control women without fractures participated in the study. Bone characteristics of the distal tibia and tibial shaft of both legs were assessed using pQCT in order to compare the side-to-side differences of tibias between the two groups. The subjects with fracture history had significantly (p < OR = 0.05, analysis of covariance) larger side-to-side differences than the controls in tibial shaft BMC (-4.9% vs. -0.5%), cortical area (-5.2% vs. 0.1%) and polar moment of inertia (I(polar)) (-5.6% vs. -0.8%) and in distal tibia BMC (-5.1% vs. -1.4%) and I(polar) (-7.5% vs. -2.4%). In the fracture patients, the side-to-side differences in muscle characteristics explained 23 to 44% of the variances in the side-to-side differences in bone mass and geometry. Hip fracture results in reduced bone mass and impaired bone geometry in the tibia of the affected limb in older women. Muscle-induced loading may have a considerable role in the recovery of bone mineral mass and geometry after hip fracture.

A model for the twist distribution in the slub‐yarn

PurposeThis paper seeks to build a mathematical model to deduct the twists distribution in the slub‐yarn.Design/methodology/approachThe model, considering the shearing modulus and polar moment of inertia of the yarn, influenced by the yarn density, is established based on the bar torsion model. The twists distribution in the slub‐yarn is concluded based on the analysis of the results. The rules were verified via an indirect method, by testing the breaking strength of the slub‐yarn.FindingsThe results of the analysis showed that twists in every section of the slub‐yarn are in inverse proportion to the square of the line density of the corresponding section. Slub length is a key factor to the twist in the base yarn, and the increase of the slub length will increase the twist; while the multiple is the key factor to the slub twist, and the enhancement of the multiple will decrease the twist significantly.Research limitations/implicationsThe analysis cannot be verified via a direct method. A new, more conceivable direct method should be utilized to test the result.Originality/valueThe paper builds a base for the research of the mechanical properties of slub‐yarn and gives directions to the slub‐yarn production.

Using Solid Mechanics to Evaluate the Capillary and Viscous Behavior of Noncircular Tube Shapes

The similarity between torsion-solid mechanics and incompressible-viscous tube flow is investigated by finite element solutions of the governing partial differential equations. After the numerical solutions are validated against several well-known analytical functions for noncircular shapes, a method is presented to illustrate how hydraulic resistance factors may be computed from the polar moment of inertia. Since the results are scaleable, the macroscopic solid mechanics information can be used to predict the viscous pressure loss term for micro-machined flow features. The numerical technique is then further developed to estimate the Laplace pressure jump across the main terminal meniscus in noncircular capillaries. The solid mechanics based numerical technique is demonstrated on several special cases involving horizontal and vertical capillary flow in noncircular regimes. The numerical technique compares well to published experimental results. Then a nozzle shape figure of merit is derived, and applied to a variety of noncircular shapes. Finally, the numerical methods are merged into the LXK droplet simulation model where their effectiveness is demonstrated against lab data from a wide experimental space for thermal inkjet.

Structural Bone Allograft Combined with Genetically Engineered Mesenchymal Stem Cells as a Novel Platform for Bone Tissue Engineering

The presence of live periosteal progenitor cells on the surface of bone autografts confers better healing than devitalized allograft. We have previously demonstrated in a murine 4 mm segmental femoral bone-grafting model that live periosteum produces robust endochondral and intramembraneous bone formation that is essential for effective healing and neovascularization of structural bone grafts. To the end of engineering a live pseudo-periosteum that could induce a similar response onto devitalized bone allograft, we seeded a mesenchymal stem cell line stably transfected with human bone morphogenic protein-2/beta-galactosidase (C9) onto devitalized bone allografts or onto a membranous small intestinal submucosa scaffold that was wrapped around the allograft. Histology showed that C9-coated allografts displayed early cartilaginous tissue formation at day 7. By 6 and 9 weeks, a new cortical shell was found bridging the segmental defect that united the host bones. Biomechanical testing showed that C9-coated allografts displayed torsional strength and stiffness equivalent to intact femurs at 6 weeks and superior to live isografts at 9 weeks. Volumetric and histomorphometric micro-computed tomography analyses demonstrated a 2-fold increase in new bone formation around C9-coated allografts, which resulted in a substantial increase in polar moment of inertia (pMOI) due to the formation of new cortical shell around the allografts. Positive correlations between biomechanics and new bone volume and pMOI were found, suggesting that the biomechanical function of the grafted femur relates to both morphological parameters. C9-coated allograft also exhibited slower resorption of the graft cortex at 9 weeks than live isograft. Both new bone formation and the persistent allograft likely contributed to the improved biomechanics of C9-coated allograft. Taken together, we propose a novel strategy to combine structural bone allograft with genetically engineered mesenchymal stem cells as a novel platform for bone tissue engineering.

Models, figures, and gravitational moments of Jupiter’s satellites Io and Europa

Two types of trial three-layer models have been constructed for the satellites Io and Europa. In the models of the first type (Io1 and E1), the cores are assumed to consist of eutectic Fe-FeS melt with the densities ρ1 = 5.15 g cm−3 (Io1) and 5.2 g cm−3 (E1). In the models of the second type (Io3 and E3), the cores consist of FeS with an admixture of nickel and have the density ρ1 = 4.6 g cm−3. The approach used here differs from that used previously both in chosen model chemical composition of these satellites and in boundary conditions imposed on the models. The most important question to be answered by modeling the internal structure of the Galilean satellites is that of the condensate composition at the formation epoch of Jupiter’s system. Jupiter’s core and the Galilean satellites were formed from the condensate. Ganymede and Callisto were formed fairly far from Jupiter in zones with temperatures below the water condensation temperature, water was entirely incorporated into their bodies, and their modeling showed the mass ratio of the icy (I) component to the rock (R) component in them to be I/R ∼ 1. The R composition must be clarified by modeling Io and Europa. The models of the second type (Io3 and E3), in which the satellite cores consist of FeS, yield 25.2 (Io3) and 22.8 (E3) for the core masses (in weight %). In discussing the R composition, we note that, theoretically, the material of which the FeS+Ni core can consist in the R accounts for ∼25.4% of the satellite mass. In this case, such an important parameter as the mantle silicate iron saturation is Fe# = 0.265. The Io3 and E3 models agree well with this theoretical prediction. The models of the first and second types differ markedly in core radius; thus, in principle, the R composition in the formation zone of Jupiter’s system can be clarified by geophysical studies. Another problem studied here is that of the error made in modeling Io and Europa using the Radau-Darvin formula when passing from the Love number k2 to the nondimensional polar moment of inertia \(\bar C\). For Io, the Radau-Darvin formula underestimates the true value of \(\bar C\) by one and a half units in the third decimal digit. For Europa, this effect is approximately a factor of 3 smaller, which roughly corresponds to a ratio of the small parameters for the satellites under consideration αIo/αEuropa ∼ 3.4. In modeling the internal structure of the satellites, the core radius depends strongly on both the mean moment of inertia I* and k2. Therefore, the above discrepancy in \(\bar C\) for Io is appreciable.

Long-term effects of calcium–vitamin-D 3-fortified milk on bone geometry and strength in older men

The long-term effects of calcium and vitamin D supplementation on bone material and structural properties in older men are not known. The aim of this study was to examine the effects of high calcium (1000 mg/day)- and vitamin-D 3 (800 IU/day)-fortified milk on cortical and trabecular volumetric BMD (vBMD) and bone geometry at the axial and appendicular skeleton in men aged over 50 years. One hundred and eleven men who were part of a larger 2-year randomized controlled trial had QCT scans of the mid-femur and lumbar spine (L 1–L 3) to assess vBMD, bone geometry and indices of bone strength [polar moment of inertia ( I polar)]. After 2 years, there were no significant differences between the milk supplementation and control group for the change in any mid-femur or L 1–L 3 bone parameters for all men aged over 50 years. However, the mid-femur skeletal responses to the fortified milk varied according to age, with a split of ≤ 62 versus > 62 years being the most significant for discriminating the changes between the two groups. Subsequent analysis revealed that, in the older men (> 62 years), the expansion in mid-femur medullary area was 2.8% ( P < 0.01) less in the milk supplementation compared to control group, which helped to preserve cortical area in the milk supplementation group (between group difference 1.1%, P < 0.01). Similarly, for mid-femur cortical vBMD and I polar, the net loss was 2.3 and 2.8% less in the milk supplementation compared to control group ( P < 0.01 and < 0.001, respectively). In conclusion, calcium–vitamin-D 3-fortified milk may represent an effective strategy to maintain bone strength by preventing endocortical bone loss and slowing the loss in cortical vBMD in elderly men.

Lifetime sport and leisure activity participation is associated with greater bone size, quality and strength in older men

It remains uncertain whether long-term participation in regular weight-bearing exercise confers an advantage to bone structure and strength in old age. The aim of this study was to investigate the relationship between lifetime sport and leisure activity participation on bone material and structural properties at the axial and appendicular skeleton in older men (>50 years). We used dual-energy X-ray absorptiometry (DXA) to assess hip, spine and ultradistal (UD) radius areal bone mineral density (aBMD) (n=161), quantitative ultrasound (QUS) to measure heel bone quality (n=161), and quantitative computed tomography (QCT) to assess volumetric BMD, bone geometry and strength at the spine (L(1)-L(3)) and mid-femur (n=111). Current (>50+ years) and past hours of sport and leisure activity participation during adolescence (13-18 years) and adulthood (19-50 years) were assessed by questionnaire. This information was used to calculate the total time (min) spent participating in sport and leisure activities and an osteogenic index (OI) score for each participant, which provides a measure of participation in weight-bearing activities. Regression analysis revealed that a greater lifetime (13-50+ years) and mid-adulthood (19-50 years) OI, but not total time (min), was associated with a greater mid-femur total and cortical area, cortical bone mineral content (BMC), and the polar moment of inertia (I (p)) and heel VOS (p ranging from <0.05 to <0.01). These results were independent of age, height (or femoral length) and weight (or muscle cross-sectional area). Adolescent OI scores were not found to be significant predictors of bone structure or strength. Furthermore, no significant relationships were detected with areal or volumetric BMD at any site. Subjects were then categorized into either a high (H) or low/non-impact (L) group during adolescence (13-18 years) and adulthood (19-50+ years) according to their OI scores during each of these periods. Three groups were subsequently formed to reflect weight-bearing impact categories during adolescence and then adulthood: LL, HL and HH. Compared to the LL group, mid-femur total and cortical area, cortical BMC and I (p) were 6.5-14.2% higher in the HH group. No differences were detected between the LL and HL groups. In conclusion, these findings indicate that long-term regular participation in sport and leisure activities categorized according to an osteogenic index [but not the total time (min) spent participating in all sport and leisure activities] was an important determinant of bone size, quality and strength, but not BMD, at loaded sites in older men. Furthermore, continued participation in weight-bearing exercise in early to mid-adulthood appears to be important for reducing the risk of low bone strength in old age.

Homogenization of a Micro-Periodic Helix with Parabolic or Hyperbolic Heat Conduction

ABSTRACT Based on a recent model for vibration of an elastic helix [6], a thermoelastic heterogeneous helix is studied by the asymptotic homogenization method. The objective of the study is the determination of the averaged equation of motion and of the effective coefficients of a one-dimensional micro-periodic thermoelastic helix. The results are valid in the case of waves much longer than the length of the periodic unit cell, and for any finite number of phases for within that cell. Also perfect contact conditions between phases are considered. Generally, the constitutive coefficients are harmonic averages, while the mass density and polar moment of inertia are arithmetic averages.

Identification of a quantitative trait locus on rat chromosome 4 that is strongly linked to femoral neck structure and strength

Risk factors for osteoporotic hip fracture include reduced bone mineral density and poor structure of the femoral neck, both of which are heritable traits. Previously, we showed that despite similar body size, Fischer 344 (F344) rats have significantly different skeletal traits compared with Lewis (LEW) rats. To identify a gene or genes regulating fracture risk at the femoral neck, we mapped quantitative trait loci (QTL) for femoral neck density and structure phenotypes using a 595 F2 progeny derived from the inbred F344 and LEW strains of rats. Femoral neck phenotypes included volumetric bone mineral density (vBMD), neck width, femoral neck cross-sectional area and polar moment of inertia ( Ip). A 20-cM genome-wide scan was performed using 118 microsatellite markers and linkage analysis was conducted to identify chromosomal regions harbor QTL for femoral neck phenotypes. Strong evidence of linkage ( P < 0.01) to femoral neck vBMD was observed on chromosomes (Chrs) 1, 2, 4, 5, 7, 10 and 15. QTL affecting femoral neck structure and biomechanical properties were detected only on Chr 4 where the F344 alleles were shown to improve femoral neck structure, whereas these alleles had no effect on bone measurements at the lumbar spine and only modest effects at the femoral midshaft. In contrast, QTL on Chrs 1, 2 and 10 affected multiple skeletal sites. Several QTL regions in this study are homologous to human chromosomal regions, where linkage to femoral neck and related phenotypes has been reported previously. These findings represent an important first step in localizing and identifying genes that influence hip fragility.

Pressure Drop of Fully-Developed, Laminar Flow in Microchannels of Arbitrary Cross-Section

Abstract The pressure drop of fully developed, laminar, incompressible flow in smooth mini- and microchannels of arbitrary cross-section is investigated. A compact approximate model is proposed that predicts the pressure drop for a wide variety of shapes. The model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The proposed model is compared with analytical and numerical solutions for several shapes. Also, the comparison of the model with experimental data, collected by several researchers, shows good agreement.

Compact and cancellous bone behave as a “bimaterial beam model” of constant strength

A mechanical model of bone should describe stress and strain distributions according to minimum/maximum laws. At the macrolevel the shape of the bone enables the support of significant loads if these are applied in physiological directions. With this concept in mind we have examined the geometric distributions of compact and cancellous bone and compared these to variations of V in the shear diagram and M in the bending moment diagram respectively. Two types of analytical methods have been used: (i) basic mechanical models of cylindrical and fusiform tube shapes with different thicknesses of tube plates, all compared with bone and presented as FEM models ; (ii) FEM models of human long bones obtained from CT data. Preprocessing was carried out using CATIA V5R14, and ABAQUS/Standard was used for subsequent analysis. In this analysis FEM simulation of different bending tests was performed in all samples. It was observed that there were: (a) variations of V in the shear diagram and M in the bending moment diagram according to the shape, (b) variations of the cortical thickness of different cross sections of bone shafts according to the polar moment of inertia and (c) variations of the CT densities of bone tissue and Young's modulus of elasticity distribution according to previously published data. The results from these models indicate that the local compact bone volume mainly correlates with the bending moment stresses and cancellous bone volume correlates with the shear stresses. Bone avoids higher local stresses by distributing the internal forces and bone volume according to a minimum/maximum law which continuously optimises the bone shape to one with constant strength.

Geophysical constraints on the composition and structure of the Martian interior

Most recent Martian interior structure models are based on the planet's polar moment of inertia C, although the mean moment of inertia I is required for constructing spherically symmetric models of planetary interiors. Using the improved value of C/MpRp2 recently obtained from a combined reanalysis of the entire set of radio science data collected during the last three decades and accounting for the rotationally and topographically induced shape of the planet's gravitational field, we find a mean moment‐of‐inertia factor of I/MpRp2 = 0.3635 ± 0.0012. The new lower value suggests a core radius several tens of kilometers larger if other parameters like core density, crust density, and crust thickness are fixed. It further implies that the Martian crust is several tens of kilometers thicker than previously thought if crust and mantle densities and core size are given. Moreover, the Martian mantle may be less dense, about several tens of kg m−3, with a smaller iron content than previously thought if crust thickness and core size are specified. The mantle density of Mars is relatively well determined by the planet's moment of inertia factor if crust thickness and density are specified.

Homogenization of a micro-periodic helix

Equations of motion governing the dynamics of helix are studied in the situation when the microstructure is micro-periodic. Using the asymptotic homogenization method, we derive these equations in the case of waves much longer than the length scale of a periodic unit cell and for any finite number of phases in the cell. The procedure of constructing a formal asymptotic expansion solution is derived. Generally, the constitutive coefficients are harmonic averages, while the mass density and polar moment of inertia are arithmetic averages. These results are illustrated numerically on the case of a two-phase helix.

The use of micro-CT to evaluate cortical bone geometry and strength in nude rats: Correlation with mechanical testing, pQCT and DXA

In both clinical and experimental settings, access to quantitative methods enabling the objective evaluation of cortical bone mass, structure, geometry and strength are essential for the assessment of efficacy and safety of different treatments aimed to improve bone strength. The ability of non-invasive methodologies (DXA, pQCT and micro-CT) to assess and quantify cortical bone mass and geometry was tested in a nude rat model in which bone loss was induced by surgical castration. Treatment with a bone antiresorptive (alendronate) or a bone forming (PTH) drug was used to: (A) validate the nude rat model in terms of bone metabolism, (B) test the ability of each technology to detect change in cortical bone geometry and (C) correlate cortical bone geometry with bone strength data obtained by 3-point bending method. Our observations regarding effect of castration and treatment with PTH and alendronate on cortical bone parameters in nude rats is in general agreement with previously published data obtained in immunocompetent male rats under similar experimental conditions. Data presented here support the hypothesis that nude rats have similar bone physiology and response to known bone therapies to that observed in normal rats and therefore could be effectively used to predict skeletal response in humans. All three technologies deployed in this study (DXA, pQCT and micro-CT) proved useful in describing cancellous and/or cortical bone parameters and positive correlations were demonstrated between data obtained by different methods. The cross-sectional area of a bone structure is crucial for resisting loads in bending or torsion and is described as “areal moment of inertia” for bending, and as “polar moment of inertia” in torsion. Novel, three-dimensional micro-CT methodology used in this study to assess geometry of cortical bone provides data that accurately describes cortical bone geometry and parallels cortical bone strength results obtained by the 3-point bending method. Our micro-CT data meet the criteria of providing quick, reproducible and accurate answers regarding cortical bone geometry as a predictor of cortical bone strength.

Effect of Activity and Age on Long Bones Using a New Densitometric Technique

Long bone structural parameters such as cross-sectional area or area moments of inertia are useful measures of long bone mechanical properties. We implemented a three-scan densitometric method to measure structural parameters in long bones of the lower leg in vivo. The validated method was applied to investigate the relationship between activity level, age, and long bone structural parameters in women. An aluminum phantom was used to estimate in vivo setup accuracy. In vivo precision was determined by same-day repeated measures on human subjects. For the activity study, women were recruited in two age groups (25-35, 60+yr) and two activity levels (recreational runners, nonrunners). Scans were taken of the middle third of the lower right leg; structural parameters for the tibia and fibula were determined at each scan line, averaged over the section, and adjusted by factors accounting for body size variations. Aluminum phantom cross-sectional area was underestimated by 4-6%, principal moments were underestimated by <5%, and principal angles were within +/-1.2 degrees. In vivo precision results (lower energy, scans spanning 60 degrees) indicated coefficients of variation for cross-sectional area (A), principal moments of inertia (Imax, Imin), and polar moment of inertia (J) of 0.52, 5.87, 2.22, and 3.82%, respectively. The activity study showed mean adjusted tibial A, Imax, Imin, and J were significantly higher in runners compared with nonrunners. There was no dependence on age. A three-scan densitometric method for measuring cross-sectional structural parameters in long bones in vivo was validated; accuracy and precision measurements establishes confidence limits. From the activity study results, we postulate that higher loads associated with running lead to increased cross-sectional parameters to support axial loads, bending, and torsion in the tibia.