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 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.

Computational and experimental methodology for site-matched investigations of the influence of mineral mass fraction and collagen orientation on the axial indentation modulus of lamellar bone

Relationships between mineralization, collagen orientation and indentation modulus were investigated in bone structural units from the mid-shaft of human femora using a site-matched design. Mineral mass fraction, collagen fibril angle and indentation moduli were measured in registered anatomical sites using backscattered electron imaging, polarized light microscopy and nano-indentation, respectively. Theoretical indentation moduli were calculated with a homogenization model from the quantified mineral densities and mean collagen fibril orientations. The average indentation moduli predicted based on local mineralization and collagen fibers arrangement were not significantly different from the average measured experimentally with nanoindentation (p=0.9). Surprisingly, no substantial correlation of the measured indentation moduli with tissue mineralization and/or collagen fiber arrangement was found. Nano-porosity, micro-damage, collagen cross-links, non-collagenous proteins or other parameters affect the indentation measurements. Additional testing/simulation methods need to be considered to properly understand the variability of indentation moduli, beyond the mineralization and collagen arrangement in bone structural units.

Resin composites: Modulus of elasticity and marginal quality

OBJECTIVE To investigate how the modulus of elasticity of resin composites influences marginal quality in restorations submitted to thermocyclic and mechanical loading. METHODS Charisma, Filtek Supreme XTE and Grandio were selected as they were found to possess different moduli of elasticity but quite similar polymerization contraction. MOD cavities (n=30) were prepared in extracted premolars, restored and then subjected to thermocyclic and mechanical loading. Marginal quality of the restorations before and after loading was analyzed on epoxy replicas under a scanning electron microscope. The percentage of gap-free margins and occurrence of paramarginal fractures were registered. Modulus of elasticity and polymerization contraction were analyzed with parametric and margins with nonparametric ANOVA and post hoc Tukey HSD or Wilcoxon rank-sum tests, respectively. The number of paramarginal fractures was analyzed with exact Fisher tests (α=0.05). RESULTS Grandio demonstrated significantly more gap-free enamel margins than Charisma and Filtek Supreme XTE, before and after loading (p<0.01), whereas there was no difference between Charisma and Filtek Supreme XTE (p>0.05). No significant effect of resin composite (p=0.81) on the quality of dentine margins was observed, before or after loading. Deterioration of all margins was evident after loading (p<0.0001). More paramarginal enamel fractures were observed after loading in teeth restored with Grandio when compared to Charisma (p=0.008). CONCLUSIONS The resin composite with the highest modulus of elasticity resulted in the highest number of gap-free enamel margins but with an increased incidence of paramarginal enamel fractures. CLINICAL SIGNIFICANCE The results from this study suggest that the marginal quality of restorations can be improved by the selection of a resin composite with modulus of elasticity close to that of dentine, although an increase in paramarginal enamel fractures can result as a consequence.

Relevance of In-vitro Tests of Adhesive and Composite Dental Materials. A Review in 3 Parts. Part 2: Non-standardized tests of composite materials

Summary The first part of this review examined ISO approval requirements and in vitro testing. In the second part, non-standardized test methods for composite materials are presented and discussed. Physical tests are primarily described. Analyses of surface gloss and alterations, as well as aging simulations of dental materials are presented. Again, the importance of laboratory tests in determining clinical outcomes is evaluated. Differences in the measurement protocols of the various testing institutes and how these differences can in?uence the results are also discussed. Because there is no standardization of test protocols, the values determined by different institutes cannot be directly compared. However, the ranking of the tested materials should be the same if a valid protocol is applied by different institutes. The modulus of elasticity, the expansion after water sorption, and the polishability of the material are all clinically relevant, whereas factors measured by other test protocols may have no clinical correlation. The handling properties of the materials are highly dependent on operators' preferences. Therefore, no standard values can be given.

The long-term mechanical integrity of non-reinforced PEEK-OPTIMA polymer for demanding spinal applications: experimental and finite-element analysis

Polyetheretherketone (PEEK) is a novel polymer with potential advantages for its use in demanding orthopaedic applications (e.g. intervertebral cages). However, the influence of a physiological environment on the mechanical stability of PEEK has not been reported. Furthermore, the suitability of the polymer for use in highly stressed spinal implants such as intervertebral cages has not been investigated. Therefore, a combined experimental and analytical study was performed to address these open questions. A quasi-static mechanical compression test was performed to compare the initial mechanical properties of PEEK-OPTIMA polymer in a dry, room-temperature and in an aqueous, 37 degrees C environment (n=10 per group). The creep behaviour of cylindrical PEEK polymer specimens (n=6) was measured in a simulated physiological environment at an applied stress level of 10 MPa for a loading duration of 2000 hours (12 weeks). To compare the biomechanical performance of different intervertebral cage types made from PEEK and titanium under complex loading conditions, a three-dimensional finite element model of a functional spinal unit was created. The elastic modulus of PEEK polymer specimens in a physiological environment was 1.8% lower than that of specimens tested at dry, room temperature conditions (P<0.001). The results from the creep test showed an average creep strain of less than 0.1% after 2000 hours of loading. The finite element analysis demonstrated high strain and stress concentrations at the bone/implant interface, emphasizing the importance of cage geometry for load distribution. The stress and strain maxima in the implants were well below the material strength limits of PEEK. In summary, the experimental results verified the mechanical stability of the PEEK-OPTIMA polymer in a simulated physiological environment, and over extended loading periods. Finite element analysis supported the use of PEEK-OPTIMA for load-bearing intervertebral implants.

Variation of the mechanical properties of PMMA to suit osteoporotic cancellous bone

Poly(methyl methacrylate) (PMMA) is by far the most frequently used bone substitute material for vertebroplasty. However, there are serious complications, such as cement leakage and an increased fracture rate of the adjacent vertebral bodies. The latter may be related to the mechanical properties of the augmented segment within the osteoporotic spine. A possible counter-measure is prophylactic augmentation at additional levels, but this aggravates the risk for the patient. Introduction of pores is a possible method to reduce the inherent high stiffness of PMMA. This study investigates the effect of porosity on the mechanical properties of PMMA bone cement. Different fractions of a highly viscous liquid were mixed into the PMMA during preparation. An open-porous material with adjustable mechanical properties resulted after removal of the aqueous phase. Different radiopacifiers were admixed to investigate their suitability for vertebroplasty. The final material was characterized mechanically by compressive testing, microscopically and radiologically. In addition, the monomer release subsequent to hardening was measured by means of gas chromatography. The Young's modulus in compression could be varied between 2800 +/- 70 MPa and 120 +/- 150 MPa, and the compression ultimate strength between 170 +/- 5 MPa and 8 +/- 9 MPa for aqueous fractions ranging between 0 and 50% of volume. Only a slight decrease of the Young's modulus and small changes of ultimate strength were found when the mixing time was increased. An organic hydrophilic and lipophilic radiopacifier led to a higher Young's modulus of the porous material; however, the ultimate strength was not significantly affected by adding different radiopacifiers to the porous cement. The radiopacity was lost after washing the aqueous phase out of the pores. No separation occurred between the aqueous and the PMMA phase during injection into an open porous ceramic material. The monomer released was found to increase for increasing aqueous fractions, but remained comparable in magnitude to standard PMMA. This study demonstrates that a conventional PMMA can be modified to obtain a range of mechanical properties, including those of osteoporotic bone.

Performance of vertebral cancellous bone augmented with compliant PMMA under dynamic loads

Increased fracture risk has been reported for the adjacent vertebral bodies after vertebroplasty. This increase has been partly attributed to the high Young's modulus of commonly used polymethylmethacrylate (PMMA). Therefore, a compliant bone cement of PMMA with a bulk modulus closer to the apparent modulus of cancellous bone has been produced. This compliant bone cement was achieved by introducing pores in the cement. Due to the reduced failure strength of that porous PMMA cement, cancellous bone augmented with such cement could deteriorate under dynamic loading. The aim of the present study was to assess the potential of acute failure, particle generation and mechanical properties of cancellous bone augmented with this compliant cement in comparison to regular cement. For this purpose, vertebral biopsies were augmented with porous- and regular PMMA bone cement, submitted to dynamic tests and compression to failure. Changes in Young's modulus and height due to dynamic loading were determined. Afterwards, yield strength and Young's modulus were determined by compressive tests to failure and compared to the individual composite materials. No failure occurred and no particle generation could be observed during dynamical testing for both groups. Height loss was significantly higher for the porous cement composite (0.53+/-0.21%) in comparison to the biopsies augmented with regular cement (0.16+/-0.1%). Young's modulus of biopsies augmented with porous PMMA was comparable to cancellous bone or porous cement alone (200-700 MPa). The yield strength of those biopsies (21.1+/-4.1 MPa) was around two times higher than for porous cement alone (11.6+/-3.3 MPa).

Bovine primary chondrocyte culture in synthetic matrix metalloproteinase-sensitive poly(ethylene glycol)-based hydrogels as a scaffold for cartilage repair

A poly(ethylene glycol) (PEG)-based hydrogel was used as a scaffold for chondrocyte culture. Branched PEG-vinylsulfone macromers were end-linked with thiol-bearing matrix metalloproteinase (MMP)-sensitive peptides (GCRDGPQGIWGQDRCG) to form a three-dimensional network in situ under physiologic conditions. Both four- and eight-armed PEG macromer building blocks were examined. Increasing the number of PEG arms increased the elastic modulus of the hydrogels from 4.5 to 13.5 kPa. PEG-dithiol was used to prepare hydrogels that were not sensitive to degradation by cell-derived MMPs. Primary bovine calf chondrocytes were cultured in both MMP-sensitive and MMP-insensitive hydrogels, formed from either four- or eight-armed PEG. Most (>90%) of the cells inside the gels were viable after 1 month of culture and formed cell clusters. Gel matrices with lower elastic modulus and sensitivity to MMP-based matrix remodeling demonstrated larger clusters and more diffuse, less cell surface-constrained cell-derived matrix in the chondron, as determined by light and electron microscopy. Gene expression experiments by real-time RT-PCR showed that the expression of type II collagen and aggrecan was increased in the MMP-sensitive hydrogels, whereas the expression level of MMP-13 was increased in the MMP-insensitive hydrogels. These results indicate that cellular activity can be modulated by the composition of the hydrogel. This study represents one of the first examples of chondrocyte culture in a bioactive synthetic material that can be remodeled by cellular protease activity.

Multiscale methods for shape constraints in deconvolution: Confidence statements for qualitative features

We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We investigate the moderately ill-posed setting, where the Fourier transform of the error density in the deconvolution model is of polynomial decay. For multiscale testing, we consider a calibration, motivated by the modulus of continuity of Brownian motion. We investigate the performance of our results from both the theoretical and simulation based point of view. A major consequence of our work is that the detection of qualitative features of a density in a deconvolution problem is a doable task, although the minimax rates for pointwise estimation are very slow.

The hp-adaptive FEM based on continuous Sobolev embeddings: isotropic refinements

The aim of this paper is to present a new class of smoothness testing strategies in the context of hp-adaptive refinements based on continuous Sobolev embeddings. In addition to deriving a modified form of the 1d smoothness indicators introduced in [26], they will be extended and applied to a higher dimensional framework. A few numerical experiments in the context of the hp-adaptive FEM for a linear elliptic PDE will be performed.

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.

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.