Impact of measurement errors on the determination of the linear modulus of human meniscal attachments

For the development of meniscal substitutes and related finite element models it is necessary to know the mechanical properties of the meniscus and its attachments. Measurement errors can falsify the determination of material properties. Therefore the impact of metrological and geometrical measurement errors on the determination of the linear modulus of human meniscal attachments was investigated. After total differentiation the error of the force (+0.10%), attachment deformation (−0.16%), and fibre length (+0.11%) measurements almost annulled each other. The error of the cross-sectional area determination ranged from 0.00%, gathered from histological slides, up to 14.22%, obtained from digital calliper measurements. Hence, total measurement error ranged from +0.05% to −14.17%, predominantly affected by the cross-sectional area determination error. Further investigations revealed that the entire cross-section was significantly larger compared to the load-carrying collagen fibre area. This overestimation of the cross-section area led to an underestimation of the linear modulus of up to −36.7%. Additionally, the cross-sections of the collagen-fibre area of the attachments significantly varied up to +90% along their longitudinal axis. The resultant ratio between the collagen fibre area and the histologically determined cross-sectional area ranged between 0.61 for the posterolateral and 0.69 for the posteromedial ligament. The linear modulus of human meniscal attachments can be significantly underestimated due to the use of different methods and locations of cross-sectional area determination. Hence, it is suggested to assess the load carrying collagen fibre area histologically, or, alternatively, to use the correction factors proposed in this study.

The effect of standard and low-modulus cement augmentation on the stiffness, strength, and endplate pressure distribution in vertebroplasty

Vertebroplasty restores stiffness and strength of fractured vertebral bodies, but alters their stress transfer. This unwanted effect may be reduced by using more compliant cements. However, systematic experimental comparison of structural properties between standard and low-modulus augmentation needs to be done. This study investigated how standard and low-modulus cement augmentation affects apparent stiffness, strength, and endplate pressure distribution of vertebral body sections.

Properties of tooth enamel in great apes

A comparative study has been made of human and great ape molar tooth enamel. Nanoindentation techniques are used to map profiles of elastic modulus and hardness across sections from the enamel–dentin junction to the outer tooth surface. The measured data profiles overlap between species, suggesting a degree of commonality in material properties. Using established deformation and fracture relations, critical loads to produce function-threatening damage in the enamel of each species are calculated for characteristic tooth sizes and enamel thicknesses. The results suggest that differences in load-bearing capacity of molar teeth in primates are less a function of underlying material properties than of morphology.

The Young's modulus of fetal preterm and term amniotic membranes

OBJECTIVE: To examine the Young's modulus of the human amniotic membranes, as well as its relationship to gestational age. To determine whether cellular and material-related parameters affect this modulus. STUDY DESIGN: In a prospective study at the Obstetric outpatient clinic of the University Hospital Zurich Young's modulus, thickness and mesenchymal:epithelial cell ratio of amniotic membranes of preterm (N=23) and term (N=40) placentae were examined. Significance (P<0.05) was calculated with the Mann-Whitney two-sample rank sum test and Wilcoxon signed rank test, while correlations were made using the Spearman's correlation. RESULTS: The Young's modulus of preterm amniotic membranes was significantly higher than that of term membranes. It varied within the same amniotic membrane. The thickness of the amnion in both preterm and term membranes did not differ significantly. The thinner the preterm and term amniotic membranes, the higher the Young's modulus was. There was no relation to the mesenchymal:epithelial cell ratio in the amnion. CONCLUSIONS: Preterm amniotic membranes are stiffer than term amniotic membranes. Tentatively, we hypothesise that there may be a correlation between the extracellular matrix components and the elastic properties of the membrane.

Adjacent vertebral failure after vertebroplasty: a biomechanical study of low-modulus PMMA cement

PMMA is the most common bone substitute used for vertebroplasty. An increased fracture rate of the adjacent vertebrae has been observed after vertebroplasty. Decreased failure strength has been noted in a laboratory study of augmented functional spine units (FSUs), where the adjacent, non-augmented vertebral body always failed. This may provide evidence that rigid cement augmentation may facilitate the subsequent collapse of the adjacent vertebrae. The purpose of this study was to evaluate whether the decrease in failure strength of augmented FSUs can be avoided using low-modulus PMMA bone cement. In cadaveric FSUs, overall stiffness, failure strength and stiffness of the two vertebral bodies were determined under compression for both the treated and untreated specimens. Augmentation was performed on the caudal vertebrae with either regular or low-modulus PMMA. Endplate and wedge-shaped fractures occurred in the cranial and caudal vertebrae in the ratios endplate:wedge (cranial:caudal): 3:8 (5:6), 4:7 (7:4) and 10:1 (10:1) for control, low-modulus and regular cement group, respectively. The mean failure strength was 3.3 +/- 1 MPa with low-modulus cement, 2.9 +/- 1.2 MPa with regular cement and 3.6 +/- 1.3 MPa for the control group. Differences between the groups were not significant (p = 0.754 and p = 0.375, respectively, for low-modulus cement vs. control and regular cement vs. control). Overall FSU stiffness was not significantly affected by augmentation. Significant differences were observed for the stiffness differences of the cranial to the caudal vertebral body for the regular PMMA group to the other groups (p < 0.003). The individual vertebral stiffness values clearly showed the stiffening effect of the regular cement and the lesser alteration of the stiffness of the augmented vertebrae using the low-modulus PMMA compared to the control group (p = 0.999). In vitro biomechanical study and biomechanical evaluation of the hypothesis state that the failure strength of augmented functional spine units could be better preserved using low-modulus PMMA in comparison to regular PMMA cement.

Properties of an injectable low modulus PMMA bone cement for osteoporotic bone

The use of polymethylmethacrylate (PMMA) cement to reinforce fragile or broken vertebral bodies (vertebroplasty) leads to extensive bone stiffening. Fractures in the adjacent vertebrae may be the consequence of this procedure. PMMA with a reduced Young's modulus may be more suitable. The goal of this study was to produce and characterize stiffness adapted PMMA bone cements. Porous PMMA bone cements were produced by combining PMMA with various volume fractions of an aqueous sodium hyaluronate solution. Porosity, Young's modulus, yield strength, polymerization temperature, setting time, viscosity, injectability, and monomer release of those porous cements were investigated. Samples presented pores with diameters in the range of 25-260 microm and porosity up to 56%. Young's modulus and yield strength decreased from 930 to 50 MPa and from 39 to 1.3 MPa between 0 and 56% porosity, respectively. The polymerization temperature decreased from 68 degrees C (0%, regular cement) to 41 degrees C for cement having 30% aqueous fraction. Setting time decreased from 1020 s (0%, regular cement) to 720 s for the 30% composition. Viscosity of the 30% composition (145 Pa s) was higher than the ones received from regular cement and the 45% composition (100-125 Pa s). The monomer release was in the range of 4-10 mg/mL for all porosities; showing no higher release for the porous materials. The generation of pores using an aqueous gel seems to be a promising method to make the PMMA cement more compliant and lower its mechanical properties to values close to those of cancellous bone.

Photodegradation and photostabilization of weathered wood flour filled polyethylene composites

Wood plastic composites (WPCs) have gained popularity as building materials because of their usefulness in replacing solid wood in a variety of applications. These composites are promoted as being low-maintenance, high-durability products. However, it has been shown that WPCs exposed to weathering may experience a color change and/or loss in mechanical properties. An important requirement for building materials used in outdoor applications is the retention of their aesthetic qualities and mechanical properties during service life. Therefore, it is critical to understand the photodegradation mechanisms of WPCs exposed to UV radiation and to develop approaches to stabilize these composites (both unstabilized and stabilized) as well as the effect of weathering on the color fade and the retention of mechanical properties were characterized. Since different methods of manufacturing WPCs lead to different surface characteristics, which can influence weathering, the effect of manufacturing method on the photodegradation of WPCs was investigated first. Wood flour (WF) filled high-density polyethylene (HDPE) composite samples were either injection molded, extruded, or extruded and then planed. Fourier transform infrared (FTIR) spectroscopy was used to monitor the surface chemistry of the manufactured composites. The spectra showed that the surface of planed samples had more wood component than extruded and injection molded samples, respectively. After weathering, the samples were analyzed for color fade, and loss of flexural properties. The final lightness of the composites was not dependent upon the manufacturing method. However the mechanical property loss was dependent upon manufacturing method. The samples with more wood component at the surface (planed samples) experienced a larger percentage of total loss in flexural properties after weathering due to a greater effect of moisture on the samples. The change in surface chemistry of HDPE and WF/HDPE composites after weathering was studied using spectroscopic techniques. X-ray photoelectron spectroscopy (XPS) was used to characterize the occurrence of surface oxidation whereas FTIR spectroscopy was used to monitor the development of degradation products, such as carbonyl groups and vinyl groups, and to determine changes in HDPE crystallinity. Surface oxidation occurred immediately after exposure for both the neat HDPE and WF/HDPE composites. After weathering, the surface of the WF/HDPE composites was oxidized to a greater extent than the neat HDPE after weathering. This suggests that photodegradation is exacerbated by the addition of the carbonyl functional groups of the wood fibers within the HDPE atrix during composite manufacturing. While neat HDPE may undergo cross-linking in the initial stages of accelerated weathering, the WF may physically hinder the ability of the HDPE to cross-link resulting in the potential for HDPE chain scission to dominate in the initial weathering stages of the WF/HDPE composites. To determine which photostabilizers are most effective for WF/HDPE composites, factorial experimental designes were used to determine the effects of adding two hindered amine light stabilizers, an ultraviolet absorber, and a pigment on the color made and mechanical properties of both unweathered and UV weathered samples. Both the pigment and ultraviolet absorber were more effective photostabilizers for WF/HDPE composites than hinder amine light stabilizers. The ineffectiveness of hindered amine light stabilizers in protecting WPCs against UV radiation was attribuated to the acid/base reactions occurring between the WF and hindered amine light stabilizer. The efficiency of an ultraviolet absorber and/or pigment was also examined by incorporating different concentration of an ultraviolet absorber and/or pigment into WF/HDPE composites. Color change and flexural properties were determined after accelerated UV weathering. The lightness of the composite after weathering was influenced by the concentration of both the ultraviolet absorber by masking the bleaching wood component as well as blocking UV light. Flexural MOE loss was influenced by an increase in ultraviolet absorber concentration, but increasing pigment concentration from 1 to 2% had little influence on MOE loss. However, increasing both ultraviolet absorber and pigment concentration resulted in improved strength properties over the unstabilized composites after 3000 h of weather. Finally, the change in surface chemistry due to weathering of WF/HDPE composites that were either unstabilized or stabilized with an ultraviolet absorber and/or pigment was analyzed using FTIR spectroscopy. The samples were tested for loss in modulus of elasticity, carbonyl and vinyl group formation at the surface, and change in HDPE crystallinity. It was concluded that structural changes in the samples; carbonyl group formation, terminal vinyl group formation, and crystallinity changes cannot reliably be used to predict changes in modulus of elasticity using a simple linear relationship. The effect of cross-linking, chain scission, and crystallinity changes due to ultraviolet exposure as well as the interfacial degradation due to moisture exposure are inter-related factors when weathering HDPE and WF/HDPE composites.

Measuring the elastic modulus of polymers using the atomic force microscope

Testing a new method of nanoindentation using the atomic force microscope (AFM) was the purpose of this research. Nanoindentation is a useful technique to study the properties of materials on the sub-micron scale. The AFM has been used as a nanoindenter previously; however several parameters needed to obtain accurate results, including tip radius and cantilever sensitivity, can be difficult to determine. To solve this problem, a new method to determine the elastic modulus of a material using the atomic force microscope (AFM) has been proposed by Tang et al. This method models the cantilever and the sample as two springs in a series. The ratio of the cantilever spring constant (k) to diameter of the tip (2a) is treated in the model as one parameter (α=k/2a). The value of a, along with the cantilever sensitivity, are determined on two reference samples with known mechanical properties and then used to find the elastic modulus of an unknown sample. To determine the reliability and accuracy of this technique, it was tested on several polymers. Traditional depth-sensing nanoindentation was preformed for comparison. The elastic modulus values from the AFM were shown to be statistically similar to the nanoindenter results for three of the five samples tested.

Determinants of Advertising Effectiveness: The Development of an International Advertising Elasticity Database and a Meta-Analysis

Increasing demand for marketing accountability requires an efficient allocation of marketing expenditures. Managers who know the elasticity of their marketing instruments can allocate their budgets optimally. Meta-analyses offer a basis for deriving benchmark elasticities for advertising. Although they provide a variety of valuable insights, a major shortcoming of prior meta-analyses is that they report only generalized results as the disaggregated raw data are not made available. This problem is highly relevant because coding of empirical studies, at least to a certain extent, involves subjective judgment. For this reason, meta-studies would be more valuable if researchers and practitioners had access to disaggregated data allowing them to conduct further analyses of individual, e.g., product-level-specific, interests. We are the first to address this gap by providing (1) an advertising elasticity database (AED) and (2) empirical generalizations about advertising elasticities and their determinants. Our findings indicate that the average current-period advertising elasticity is 0.09, which is substantially smaller than the value 0f 0.12 that was recently reported by Sethuraman, Tellis, and Briesch (2011). Furthermore, our meta-analysis reveals a wide range of significant determinants of advertising elasticity. For example, we find that advertising elasticities are higher (i) for hedonic and experience goods than for other goods; (ii) for new than for established goods; (iii) when advertising is measured in gross rating points (GRP) instead of absolute terms; and (iv) when the lagged dependent or lagged advertising variable is omitted.

The price elasticity of demand for common stock

We study the price elasticity of demand for the common stock of an individual corporation. Despite the prevelance of assumptions that demand is perfectly elastic, there is little if any direct evidence in the literature to either support or reject that contention. Consistent with the notion of finite price elasticities, we find that the announcement of primary stock oferings by regulated firms depresses their stock prices and little if any evidence that this decline is the result of adverse information about future cash flows. Attempts to relate offer announcement effects directly to possible determinants of price elasticities, however, are inconclusive.

Modulus method and radial stretch map in the Heisenberg group

We develop a modulus method for surface families inside a domain in the Heisenberg group and we prove that the stretch map between two Heisenberg spherical rings is a minimiser for the mean distortion among the class of contact quasiconformal maps between these rings which satisfy certain boundary conditions.

Modulus and Poincaré Inequalities on Non-Self-Similar Sierpiński Carpets

A carpet is a metric space homeomorphic to the Sierpiński carpet. We characterize, within a certain class of examples, non-self-similar carpets supporting curve families of nontrivial modulus and supporting Poincaré inequalities. Our results yield new examples of compact doubling metric measure spaces supporting Poincaré inequalities: these examples have no manifold points, yet embed isometrically as subsets of Euclidean space.