Intrinsic mechanical properties of trabecular calcaneus determined by finite-element models using 3D synchrotron microtomography

To determine intrinsic mechanical properties (elastic and failure) of trabecular calcaneus bone, chosen as a good predictor of hip fracture, we looked for the influence of image's size on a numerical simulation. One cubic sample of cancellous bone (9 x 9 x 9 mm(3)) was removed from the body of the calcaneus (6 females, 6 males, 79+/-9 yr). These samples were tested under compressive loading. Before compressive testing, these samples were imaged at 10.13 microm resolution using a 3D microcomputed tomography (muCT) (ESRF, France). The muCT images were converted to finite-element models. Depending on the bone density values (BV/TV), we compared two different finite element models: a linear hexahedral and a linear beam finite element models. Apparent experimental Young's modulus (E(app)(exp)) and maximum apparent experimental compressive stress (sigma(max)(exp)) were significantly correlated with bone density obtained by Archimedes's test (E(app)(exp)=236+/-231 MPa [19-742 MPa], sigma(max)(exp)=2.61+/-1.97 MPa [0.28-5.81 MPa], r>0.80, p<0.001). Under threshold at 40 microm, the size of the numerical samples (5.18(3) and 6.68(3)mm(3)) seems to be an important parameter on the accuracy of the results. The numerical trabecular Young's modulus was widely higher (E(trabecular)(num)=34,182+/-22,830 MPa [9700-87,211 MPa]) for the larger numerical samples and high BV/TV than those found classically by other techniques (4700-15,000 MPa). For rod-like bone samples (BV/TV<12%, n=7), Young's modulus, using linear beam element (E(trabecular)(num-skeleton): 10,305+/-5500 MPa), were closer to the Young's modulus found by other techniques. Those results show the limitation of hexahedral finite elements at 40 microm, mostly used, for thin trabecular structures.     

The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques

Acoustic microscopy (30-60 microm resolution) and nanoindentation (1-5 microm resolution) are techniques that can be used to evaluate the elastic properties of human bone at a microstructural level. The goals of the current study were (1) to measure and compare the Young's moduli of trabecular and cortical bone tissues from a common human donor, and (2) to compare the Young's moduli of bone tissue measured using acoustic microscopy to those measured using nanoindentation. The Young's modulus of cortical bone in the longitudinal direction was about 40% greater than (p<0.01) the Young's modulus in the transverse direction. The Young's modulus of trabecular bone tissue was slightly higher than the transverse Young's modulus of cortical bone, but substantially lower than the longitudinal Young's modulus of cortical bone. These findings were consistent for both measurement methods and suggest that elasticity of trabecular tissue is within the range of that of cortical bone tissue. The calculation of Young's modulus using nanoindentation assumes that the material is elastically isotropic. The current results, i.e., the average anisotropy ratio (E(L)/E(T)) for cortical bone determined by nanoindentation was similar to that determined by the acoustic microscope, suggest that this assumption does not limit nanoindentation as a technique for measurement of Young's modulus in anisotropic bone.     

The influence of elastic modulus and thickness on the release of the soft-fouling green alga Ulva linza (syn. Enteromorpha linza) from poly(dimethylsiloxane) (PDMS) model networks

The effect of modulus and film thickness on the release of adhered spores and sporelings (young plants) of the green fouling alga Ulva (syn. Enteromorpha) was investigated. PDMS elastomers of constant thickness (100 microm) but different elastic moduli were prepared by varying cross-link density with functional silicone oligomers with degrees of polymerization ranging from 18-830. This provided a 50-fold range of modulus values between 0.2 and 9.4 MPa. Three PDMS coatings of different thicknesses were tested at constant elastic modulus (0.8 MPa). The data revealed no significant increase in percentage spore removal except at the lowest modulus of 0.2 MPa although sporelings released more readily at all but the highest modulus. The influence of coating thickness was also greater for the release of sporelings compared to spores. The release data are discussed in the light of fracture mechanics models that have been applied to hard fouling. New concepts appertaining to the release of soft fouling organisms are proposed, which take into account the deformation in the adhesive base of the adherand and deformation of the PDMS film.     

Apparent Young's modulus of vertebral cortico-cancellous bone specimens

Up to now, due to cortical thickness and imaging resolution, it is not possible to derive subject-specific mechanical properties on the 'vertebral shell' from imaging modalities applicable in vivo. As a first step, the goal of this study was to assess the apparent Young's modulus of vertebral cortico-cancellous bone specimens using an inverse method. A total of 22 cortico-cancellous specimens were harvested from 22 vertebral bodies. All specimens were tested in compression until failure. To compute the apparent Young's modulus of the specimen from the inverse method, the boundary conditions of the biomechanical experiments were faithfully reproduced in a finite element model (FEM), and an optimisation routine was used. The results showed a mean of the apparent Young's modulus of 374?±?208?MPa, ranging from 87 to 791?MPa. By computing an apparent Young's modulus of a cortico-cancellous medium, this study gives mechanical data for an FEM of an entire vertebra including an external shell combining both bone tissues.     

Release characteristics of reattached barnacles to non-toxic silicone coatings

Release mechanisms of barnacles (Amphibalanus amphitrite or Balanus amphitrite) reattached to platinum-cured silicone coatings were studied as a function of coating thickness (210-770 microm), elastic modulus (0.08-1.3 MPa), and shear rate (2-22 microm s(-1)). It was found that the shear stress of the reattached, live barnacles necessary to remove from the silicone coatings was controlled by the combined term (E/t)(0.5) of the elastic modulus (E) and thickness (t). As the ratio of the elastic modulus to coating thickness decreased, the barnacles were more readily removed from the silicone coatings, showing a similar release behavior to pseudobarnacles (epoxy glue). The barnacle mean shear stress ranged from 0.017 to 0.055 MPa whereas the pseudobarnacle mean shear stress ranged from 0.022 to 0.095 MPa.     

Synthesis and mechanical properties of quaternary salts of chitosan-based films for food application

A novel method is described to synthesize quaternary salts of chitosan with dimethylsulfate and subsequently cast films. In an attempt to improve both mechanical and hydrophobic characteristics, the chitosan was previously modified by N-alkylation, introducing 4, 8 and 12 carbons moieties into the polymeric chain. Analysis by FTIR and solid-state CP-MAS (13)C NMR spectroscopy confirmed the success of both alkylation and quaternization processes. The average degree of quaternization of these N-methylated derivatives was calculated to be 35%. DMA measurements indicated that chitosan and its derivative films are typically brittle materials, exhibiting similar non-linear viscoelastic behaviors. The films of unmodified chitosan have a very small strain (approximately 2.8%), though they were the most resistant films (Young's modulus=2283 MPa; tensile strength >44.0 MPa). In general, the alkyl-chitosan derivatives appear to be more plastic than chitosan films but less resistant, e.g., for butyl chitosan: maximum strain=13.1%; tensile strength=13.4 MPa and Young's modulus=171 MPa. Conversely the quaternization reaction increased the hardness of the parent sample, viz. for quaternary salt of dodecyl chitosan: maximum strain=2.6%; tensile strength=38.3 MPa and Young's modulus=1792 MPa.     

Jet injection into polyacrylamide gels: investigation of jet injection mechanics

Jet injectors employ high-velocity liquid jets that penetrate into human skin and deposit drugs in the dermal or subdermal region. Although jet injectors have been marketed for a number of years, relatively little is known about the interactions of high-speed jets with soft materials such as skin. Using polyacrylamide gels as a model system, the mechanics of jet penetration, including the dependence of jet penetration on mechanical properties, was studied. Jets employed in a typical commercial injector, (orifice diameter: 152 microm, velocity: 170-180 m/s) were used to inject fluid into polyacrylamide gels possessing Young's moduli in the range of 0.06-0.77 MPa and hardness values in the range of 4-70 H(OO). Motion analysis of jet entry into polyacrylamide gels revealed that jet penetration can be divided into three distinct events: erosion, stagnation, and dispersion. During the erosion phase, the jet removed the gel at the impact site and led to the formation of a distinct cylindrical hole. Cessation of erosion induced a period of jet stagnation ( approximately 600 micros) characterized by constant penetration depth. This stage was followed by dispersion of the liquid into the gel. The dispersion took place by crack propagation and was nearly symmetrical with the exception of injections into 10% acrylamide (Young's modulus of 0.06 MPa). The penetration depth of the jets as well as the rate of erosion decreased with increasing Young's modulus. The mechanics of jet penetration into polyacrylamide gels provides an important tool for understanding jet injection into skin.     

Mechanical behavior of intact and low-grade degenerated cartilage.

Young's modulus, elastic and plastic deformation, mechanical hardness and load at failure were determined for low-grade degenerated hyaline cartilage in a porcine model. Osteochondral plugs from the medial condyle of 30 female pigs were used. Cartilage defects were classified using the International Cartilage Repair Society (ICRS) protocol. Mechanical hardness was measured using a Shore A testing device. Total stiffness and plastic deformation was evaluated in the range 50-200 N using a 5-mm indenter. The load at failure was then determined. ICRS grade I specimens showed significantly lower stiffness than grade 0 specimens. ICRS grade 0 specimen showed no significant plastic deformation within the load range 25-100 N. In degenerated cartilage, plastic deformation started at a significantly lower load (50 N). The Young's modulus at 25 N in ICRS grade 0 specimens (18.8 MPa) was significantly higher than in grade I (11.1 MPa) or grade II (10.5 MPa) specimens. Intact cartilage showed significantly higher tension at failure and mechanical Shore A hardness. Young's modulus and tension at failure showed strong correlation. Cartilage degeneration is associated with a significant loss of elasticity and mechanical stress resistance. Shore hardness measurement is an adequate method for rapid biomechanical evaluation of cartilage specimens.     

Biomechanical properties of native basement membranes

Basement membranes are sheets of extracellular matrix that separate epithelia from connective tissues and outline muscle fibers and the endothelial lining of blood vessels. A major function of basement membranes is to establish and maintain stable tissue borders, exemplified by frequent vascular breaks and a disrupted pial and retinal surface in mice with mutations or deletions of basement membrane proteins. To directly measure the biomechanical properties of basement membranes, chick and mouse inner limiting membranes were examined by atomic force microscopy. The inner limiting membrane is located at the retinal-vitreal junction and its weakening due to basement membrane protein mutations leads to inner limiting membrane rupture and the invasion of retinal cells into the vitreous. Transmission electron microscopy and western blotting has shown that the inner limiting membrane has an ultrastructure and a protein composition typical for most other basement membranes and, thus, provides a suitable model for determining their biophysical properties. Atomic force microscopy measurements of native chick basement membranes revealed an increase in thickness from 137 nm at embryonic day 4 to 402 nm at embryonic day 9, several times thicker that previously determined by transmission electron microscopy. The change in basement membrane thickness was accompanied by a large increase in apparent Young's modulus from 0.95 MPa to 3.30 MPa. The apparent Young's modulus of the neonatal and adult mouse retinal basement membranes was in a similar range, with 3.81 MPa versus 4.07 MPa, respectively. These results revealed that native basement membranes are much thicker than previously determined. Their high mechanical strength explains why basement membranes are essential in stabilizing blood vessels, muscle fibers and the pial border of the central nervous system.     

Adhesion study of silicone coatings: the interaction of thickness, modulus and shear rate on adhesion force

Interactions between coating thickness, modulus and shear rate on pseudobarnacle adhesion to a platinum-cured silicone coating were studied using a statistical experimental design. A combined design method was used for two mixture components and two process variables. The two mixture components, vinyl end-terminated polydimethylsiloxanes (V21: MW=6 kg mole(-1) and V35: MW=4 9.5 kg mole(-1), Gelest Inc.) were mixed at five different levels to vary the modulus. The dry coating thickness was varied from 160 - 740 microm and shear tests were performed at four different shear rates (2, 7, 12, and 22 microm s(-1)). The results of the statistical analysis showed that the mixture components were significant factors on shear stress, showing an interaction with the process variable. For the soft silicone coating based on the high molecular weight polydimethylsiloxane (E=0.08 MPa), shear stress significantly increased as coating thickness decreased, while shear rate slightly impacted shear force especially at 160 microm coating thickness. As the modulus was increased (E=1.3 MPa), more force was required to detach the pseudobarnacle from the coatings, but thickness and rate dependence on shear stress became less important.     

Estimation of the Young's modulus of articular cartilage using an arthroscopic indentation instrument and ultrasonic measurement of tissue thickness

We evaluated whether the use of cartilage thickness measurement would improve the ability of the arthroscopic indentation technique to estimate the intrinsic stiffness of articular cartilage. First, cartilage thickness and ultrasound reflection from the surface of bovine humeral head were registered in situ using a high-frequency ultrasound probe. Subsequently, cartilage was indented in situ at the sites of the ultrasound measurements using arthroscopic instruments with plane-ended and spherical-ended indenters. Finally, full-thickness cartilage disks (n=30) were extracted from the indented sites (thickness=799-1654microm) and the equilibrium Young's modulus was determined with a material testing device in unconfined compression geometry. We applied analytical and numerical indentation models for the theoretical correction of experimental indentation measurements. An aspect-ratio (the ratio of indenter radius to cartilage thickness) correction improved the correlation of the indenter force with the equilibrium Young's modulus from r(2)=0.488 to r(2)=0.642-0.648 (n=30) for the plane-ended indenter (diameter=1.000mm, height=0.300mm) and from r(2)=0.654 to r(2)=0.684-0.692 (n=30) for the spherical-ended indenter (diameter=0.500mm, height=0.100mm), depending on the indentation model used for the correction. The linear correlation between the ultrasound reflection and the Young's modulus was r(2)=0.400 (n=30). These results suggest that with large indenters, knowledge of the cartilage thickness improves the reliability of the indentation measurements, especially in pathological situations where cartilage thickness may be significantly lower than normal. Ultrasound measurements also provide diagnostically important information about cartilage thickness as well as knowledge of the integrity of the superficial zone of cartilage.     

Development of biodegradable scaffolds based on patient-specific arterial configuration

Biodegradable scaffolds are of great value in tissue engineering. We have developed a method for fabricating patient-specific vascular scaffolds from a biocompatible and biodegradable polymer, poly(L-lactide-co-epsilon-caprolactone). This method's usefulness is due to flexibility in the choice of materials and vascular configurations. Here, we present a way to fabricate scaffolds of human carotid artery by combining processes of rapid prototyping, lost wax, dip coating, selective dissolution, and salt leaching. The result was the successful development of porous biodegradable scaffolds, with mechanical strength covering the range of human blood vessels (1-3 MPa). Human umbilical vein endothelial cells were also cultured on the scaffolds and their biocompatibility was confirmed by cell growth. The Young's modulus of scaffolds could be controlled by changing polymer concentration and porosity. The wall thickness of the tubular scaffold was also controllable by adjusting polymer concentration and pull-up velocity during dip coating. We believe that this fabrication technique can be applied to patient-specific regeneration of blood vessels.     

The underestimation of Young's modulus in compressive testing of cancellous bone specimens

In order to determine the accuracy of measurements of Young's modulus of cancellous bone by conventional compression testing, two independent strain measurements were made simultaneously during non-destructive uniaxial compression to 0.8% strain of rectangular specimens (n = 18). Strain was measured by an extensometer attached to the compression anvils close to the specimen and by an optical system covering the central half of the specimens. Mean Young's modulus determined by the extensometer technique was 689 MPa, but was 871 MPa when determined by the optical technique (mean difference = 182 MPa, SED = 50 MPa, p less than 0.002). Uneven strain distribution due to lack of support of cut vertical trabeculae at the anvil-specimen interface is believed to be causing the underestimation of Young's modulus measured by the extensometer technique. The influence of friction at the specimen-anvil interface was studied by performing a finite element analysis. It is concluded that Young's modulus of specimens of the chosen geometry on average is underestimated by about 20% by conventional compressing testing. The underestimation seems not to be dependent upon specimen density.     

The bulk elastic modulus and the reversible properties of cell walls in developing Quercus leaves

We examined the relationship between the bulk elastic modulus (epsilon) of an individual leaf obtained by the pressure-volume (P-V) technique and the mechanical properties of cell walls in the leaf. The plants used were Quercus glauca and Q. serrata, an evergreen and a deciduous broad-leaved tree species, respectively. We compared epsilon and Young's modulus of leaf specimens determined by the stretch technique at various stages of their leaf development. The results showed that epsilon increased from approximately 5 to 20 MPa during leaf development, although other potential determinants of epsilon such as the apoplastic water content in the leaf and the diameter of a palisade tissue cells remained almost constant. epsilon in these two species was similar at every developmental stages, although the apparent mechanical strength of the leaf lamina and thickness of mesophyll cell walls were greater in Q. glauca. There were significant linear relationships between Young's modulus and epsilon (P < 0.01; R (2) = 0.78 and 0.84 in Q. glauca and Q. serrata, respectively) with small y-intercepts. From these results, we conclude that epsilon is closely related to the reversible properties of the cell walls. From the estimation of epsilon based on a physical model, we suggest that the effective thickness of cell walls responsible for epsilon is smaller than the observed wall thickness.     

Design and mechanical properties of insect cuticle

Since nearly all adult insects fly, the cuticle has to provide a very efficient and lightweight skeleton. Information is available about the mechanical properties of cuticle-Young's modulus of resilin is about 1 MPa, of soft cuticles about 1 kPa to 50 MPa, of sclerotised cuticles 1-20 GPa; Vicker's Hardness of sclerotised cuticle ranges between 25 and 80 kgf mm(-2); density is 1-1.3 kg m(-3)-and one of its components, chitin nanofibres, the Young's modulus of which is more than 150 GPa. Experiments based on fracture mechanics have not been performed although the layered structure probably provides some toughening. The structural performance of wings and legs has been measured, but our understanding of the importance of buckling is lacking: it can stiffen the structure (by elastic postbuckling in wings, for example) or be a failure mode. We know nothing of fatigue properties (yet, for instance, the insect wing must undergo millions of cycles, flexing or buckling on each cycle). The remarkable mechanical performance and efficiency of cuticle can be analysed and compared with those of other materials using material property charts and material indices. Presented in this paper are four: Young's modulus-density (stiffness per unit weight), specific Young's modulus-specific strength (elastic hinges, elastic energy storage per unit weight), toughness-Young's modulus (fracture resistance under various loading conditions), and hardness (wear resistance). In conjunction with a structural analysis of cuticle these charts help to understand the relevance of microstructure (fibre orientation effects in tendons, joints and sense organs, for example) and shape (including surface structure) of this fibrous composite for a given function. With modern techniques for analysis of structure and material, and emphasis on nanocomposites and self-assembly, insect cuticle should be the archetype for composites at all levels of scale.     

Mechano-acoustic determination of Young's modulus of articular cartilage

The compressive stiffness of an elastic material is traditionally characterized by its Young's modulus. Young's modulus of articular cartilage can be directly measured using unconfined compression geometry by assuming the cartilage to be homogeneous and isotropic. In isotropic materials, Young's modulus can also be determined acoustically by the measurement of sound speed and density of the material. In the present study, acoustic and mechanical techniques, feasible for in vivo measurements, were investigated to quantify the static and dynamic compressive stiffness of bovine articular cartilage in situ. Ultrasound reflection from the cartilage surface, as well as the dynamic modulus were determined with the recently developed ultrasound indentation instrument and compared with the reference mechanical and ultrasound speed measurements in unconfined compression (n=72). In addition, the applicability of manual creep measurements with the ultrasound indentation instrument was evaluated both experimentally and numerically. Our experimental results indicated that the sound speed could predict 47% and 53% of the variation in the Young's modulus and dynamic modulus of cartilage, respectively. The dynamic modulus, as determined manually with the ultrasound indentation instrument, showed significant linear correlations with the reference Young's modulus (r(2)=0.445, p<0.01, n=70) and dynamic modulus (r(2)=0.779, p<0.01, n=70) of the cartilage. Numerical analyses indicated that the creep measurements, conducted manually with the ultrasound indentation instrument, were sensitive to changes in Young's modulus and permeability of the tissue, and were significantly influenced by the tissue thickness. We conclude that acoustic parameters, i.e. ultrasound speed and reflection, are indicative to the intrinsic mechanical properties of the articular cartilage. Ultrasound indentation instrument, when further developed, provides an applicable tool for the in vivo detection of cartilage mechano-acoustic properties. These techniques could promote the diagnostics of osteoarthrosis.     

Mechanical properties of calcified exoskeleton from the neotropical millipede, Nyssodesmus python

The calcified exoskeleton of millipedes plays a crucial role in resisting large forces developed during burrowing locomotion. I measured morphological and mechanical properties of cuticle from the neotropical forest floor millipede, Nyssodesmus python (Diplopoda: Polydesmidae), which ranges in body mass from 2 to 7 g. Scaling of thickness of the cuticle with respect to body mass followed predictions of geometric similarity. Both fracture strength and Young's modulus increased with body mass in females but not in males. In spite of their smaller size, male millipedes were still stronger, on average, than female millipedes. Mean fracture strength of millipede cuticle was 124 MPa, and Young's modulus was 17 GPa. Both of these values exceed measurements from typical insect cuticle, suggesting that calcium salts may play a role in stiffening and strengthening the millipede exoskeleton. Because of the high density of calcified millipede cuticle (1660 kg/m³), stiffness and strength relative to body weight remain comparable to values for other insect cuticles. These results corroborate a previous hypothesis that absolute not specific strength and stiffness have been selective factors in the evolution of millipede cuticle, and that bulkiness of the exoskeleton has been minimized through the deposition of calcium salts.     

Elasticity of native and cross-linked polyelectrolyte multilayer films

Mechanical properties of polyelectrolyte multilayer films were studied by nanoindentation using the atomic force microscope (AFM). Force-distance measurements using colloidal probe tips were systematically obtained for supported films of poly(L-lysine) and hyaluronan that are suited to bio-application. Both native and covalently cross-linked films were studied as a function of increasing layer number, which increases film thickness. The effective Young's modulus perpendicular to the film, Eperpendicular, was determined to be a function of film thickness, cross-linking, and sample age. Thick PEM films exhibited a lower Eperpendicular than thinner PEM, whereas the Young's modulus of cross-linked films was more than 10-fold larger than native films. Moduli range from approximately 20 kPa for native films up to approximately 800 kPa for cross-linked ones. Young's moduli increased slightly with sample age, plateauing after approximately 4 weeks. Spreading of smooth muscle cells on these substrates with pre-attached collagen proved to be highly dependent on film rigidity with stiffer films giving greater cell spreading.     

Effect of indenter size on elastic modulus of cartilage measured by indentation

Our preliminary indentation experiments showed that the equilibrium elastic modulus of murine tibial cartilage increased with decreasing indenter size: flat-ended 60 deg conical tips with end diameters of 15 microm and 90 microm gave 1.50+/-0.82 MPa (mean+/-standard deviation) and 0.55+/-0.11 MPa, respectively (p<0.01). The goal of this paper is to determine if the dependence on tip size is an inherent feature of the equilibrium elastic modulus of cartilage as measured by indentation. Since modulus values from nonindentation tests are not available for comparison for murine cartilage, bovine cartilage was used. Flat-ended conical or cylindrical tips with end diameters ranging from 5 microm to 4 mm were used to measure the equilibrium elastic modulus of bovine patellar cartilage. The same tips were used to test urethane rubber for comparison. The equilibrium modulus of the bovine patellar cartilage increased monotonically with decreasing tip size. The modulus obtained from the 2 mm and 4 mm tips (0.63+/-0.21 MPa) agreed with values reported in the literature; however, the modulus measured by the 90 microm tip was over two and a half times larger than the value obtained from the 1000 microm tip. In contrast, the elastic modulus of urethane rubber obtained using the same 5 microm-4 mm tips was independent of tip size. The equilibrium elastic modulus of bovine patellar cartilage measured by indentation depends on tip size. This appears to be an inherent feature of indentation of cartilage, perhaps due to its inhomogeneous structure.     

Viscoelastic properties of the tongue and soft palate using MR elastography

Biomechanical properties of the human tongue are needed for finite element models of the upper airway and may be important to elucidate the pathophysiology of obstructive sleep apneoa. Tongue viscoelastic properties have not been characterized previously. Magnetic resonance elastography (MRE) is an emerging imaging technique that can measure the viscoelastic properties of soft tissues in-vivo. In this study, MRE was used to measure the viscoelastic properties of the tongue and soft palate in 7 healthy volunteers during quiet breathing. Results show that the storage shear modulus of the tongue and soft palate is 2.67±0.29 and 2.53±0.31 kPa (mean ± SD), respectively. This is the first study to investigate the mechanical properties of the tongue using MRE, and it provides necessary data for future studies of patient groups with altered upper airway function.