Determination of the axial and circumferential mechanical properties of the skin tissue using experimental testing and constitutive modeling

The skin, being a multi-layered material, is responsible for protecting the human body from the mechanical, bacterial, and viral insults. The skin tissue may display different mechanical properties according to the anatomical locations of a body. However, these mechanical properties in different anatomical regions and at different loading directions (axial and circumferential) of the mice body to date have not been determined. In this study, the axial and circumferential loads were imposed on the mice skin samples. The elastic modulus and maximum stress of the skin tissues were measured before the failure occurred. The nonlinear mechanical behavior of the skin tissues was also computationally investigated through a suitable constitutive equation. Hyperelastic material model was calibrated using the experimental data. Regardless of the anatomic locations of the mice body, the results revealed significantly different mechanical properties in the axial and circumferential directions and, consequently, the mice skin tissue behaves like a pure anisotropic material. The highest elastic modulus was observed in the back skin under the circumferential direction (6.67 MPa), while the lowest one was seen in the abdomen skin under circumferential loading (0.80 MPa). The Ogden material model was narrowly captured the nonlinear mechanical response of the skin at different loading directions. The results help to understand the isotropic/anisotropic mechanical behavior of the skin tissue at different anatomical locations. They also have implications for a diversity of disciplines, i.e., dermatology, cosmetics industry, clinical decision making, and clinical intervention.     

Hyperelastic properties of human meniscal attachments

Meniscal attachments are ligamentous tissues anchoring the menisci to the underlying subchondral bone. Currently little is known about the behavior of meniscal attachments, with only a few studies quantitatively documenting their properties. The objective of this study was to quantify and compare the tensile mechanical properties of human meniscal attachments in the transverse direction, curve fit experimental Cauchy stress-stretch data to evaluate the hyperelastic behavior, and couple these results with previously obtained longitudinal data to generate a more complete constitutive model. Meniscal attachment specimens were tested using a uniaxial tension test with the collagen fibers oriented perpendicular to the loading axis. Tests were run until failure and load-optical displacement data was recorded for each test. The medial posterior attachment was shown to have a significantly greater elastic modulus (6.42±0.78 MPa) and ultimate stress (1.73±0.32 MPa) when compared to the other three attachments. The Mooney-Rivlin material model was selected as the best fit for the transverse data and used in conjunction with the longitudinal data. A novel computational approach to determining the transition point between the toe and linear regions is presented for the hyperelastic stress-stretch curves. Results from piece-wise non-linear longitudinal curve fitting correlate well with previous linear elastic and SEM findings. These data can be used to advance the design of meniscal replacements and improve knee joint finite element models.     

Molecular modeling of the axial and circumferential elastic moduli of tubulin

Microtubules play a number of important mechanical roles in almost all cell types in nearly all major phylogenetic trees. We have used a molecular mechanics approach to perform tensile tests on individual tubulin monomers and determined values for the axial and circumferential moduli for all currently known complete sequences. The axial elastic moduli, in vacuo, were found to be 1.25 GPa and 1.34 GPa for α- and β-bovine tubulin monomers. In the circumferential direction, these moduli were 378 MPa for α- and 460 MPa for β-structures. Using bovine tubulin as a template, 269 homologous tubulin structures were also subjected to simulated tensile loads yielding an average axial elastic modulus of 1.10 ± 0.14 GPa for α-tubulin structures and 1.39 ± 0.68 GPa for β-tubulin. Circumferentially the α- and β-moduli were 936 ± 216 MPa and 658 ± 134 MPa, respectively. Our primary finding is that that the axial elastic modulus of tubulin diminishes as the length of the monomer increases. However, in the circumferential direction, no correlation exists. These predicted anisotropies and scale dependencies may assist in interpreting the macroscale behavior of microtubules during mitosis or cell growth. Additionally, an intergenomic approach to investigating the mechanical properties of proteins may provide a way to elucidate the evolutionary mechanical constraints imposed by nature upon individual subcellular components.     

Pipette aspiration technique for the measurement of nonlinear and anisotropic mechanical properties of blood vessel walls under biaxial stretch

A pipette aspiration technique was proposed for the measurement of nonlinear mechanical properties of arteries under biaxial stretching. A cross-shaped specimen of porcine thoracic aorta whose principal axes corresponded with the axial and circumferential directions of the aortic walls was excised. The intraluminal surface of the specimen was aspirated with a circular cross-sectioned glass pipette while the specimen was stretching in the axial and circumferential directions in 10% increments. The elastic modulus agreed with the incremental elastic modulus obtained through a conventional pressure-diameter test of the same specimen to within an error of 30% at a circumferential stretch ratio below 1.3 and an axial stretch ratio of 1.0, 1.1 or 1.2, which represent lower range of physiological stretch ratios for the porcine aorta. A rectangular cross-sectioned pipette was utilized to measure anisotropic properties of the specimen under biaxial stretching. When aspirated with such a pipette, the specimens' elastic properties along the length of the rectangular pipette cross section can be neglected. The elastic modulus was found to increase rapidly when the specimen was stretched in the direction of the pipette's width. Thus, pipette aspiration should have many advantages such as well measurement of the local nonlinear and anisotropic mechanical properties of blood vessel walls.     

Determining the mechanical properties of yeast cell walls

The intrinsic cell wall mechanical properties of Baker's yeast (Saccharomyces cerevisiae) cells were determined. Force-deformation data from compression of individual cells up to failure were recorded, and these data were fitted by an analytical model to extract the elastic modulus of the cell wall and the initial stretch ratio of the cell. The cell wall was assumed to be homogeneous, isotropic, and incompressible. A linear elastic constitutive equation was assumed based on Hencky strains to accommodate the large stretches of the cell wall. Because of the high compression speed, water loss during compression could be assumed to be negligible. It was then possible to treat the initial stretch ratio and elastic modulus as adjustable parameters within the analytical model. As the experimental data fitted numerical simulations well up to the point of cell rupture, it was also possible to extract cell wall failure criteria. The mean cell wall properties for resuspended dried Baker's yeast were as follows: elastic modulus 185 ± 15 MPa, initial stretch ratio 1.039 ± 0.006, circumferential stress at failure 115 ± 5 MPa, circumferential strain at failure 0.46 ± 0.03, and strain energy per unit volume at failure 30 ± 3 MPa. Data on yeast cells obtained by this method and model should be useful in the design and optimization of cell disruption equipment for yeast cell processing.     

The role of fabric in the large strain compressive behavior of human trabecular bone

Osteoporosis-related vertebral body fractures involve large compressive strains of trabecular bone. The small strain mechanical properties of the trabecular bone such as the elastic modulus or ultimate strength can be estimated using the volume fraction and a second order fabric tensor, but it remains unclear if similar estimations may be extended to large strain properties. Accordingly, the aim of this work is to identify the role of volume fraction and especially fabric in the large strain compressive behavior of human trabecular bone from various anatomical locations. Trabecular bone biopsies were extracted from human T12 vertebrae (n=31), distal radii (n=43), femoral head (n=44), and calcanei (n=30), scanned using microcomputed tomography to quantify bone volume fraction (BV/TV) and the fabric tensor (M), and tested either in unconfined or confined compression up to very large strains (～70%). The mechanical parameters of the resulting stress-strain curves were analyzed using regression models to examine the respective influence of BV/TV and fabric eigenvalues. The compressive stress-strain curves demonstrated linear elasticity, yielding with hardening up to an ultimate stress, softening toward a minimum stress, and a steady rehardening followed by a rapid densification. For the pooled experiments, the average minimum stress was 1.89 ± 1.77 MPa, while the corresponding mean strain was 7.15 ± 1.84%. The minimum stress showed a weaker dependence with fabric as the elastic modulus or ultimate strength. For the confined experiments, the stress at a logarithmic strain of 1.2 was 8.08 ± 7.91 MPa, and the dissipated energy density was 5.67 ± 4.42 MPa. The latter variable was strongly related to the volume fraction (R(2)=0.83) but the correlation improved only marginally with the inclusion of fabric (R(2)=0.84). The influence of fabric on the mechanical properties of human trabecular bone decreases with increasing strain, while the role of volume fraction remains important. In particular, the ratio of the minimum versus the maximum stress, i.e., the relative amount of softening, decreases strongly with fabric, while the dissipated energy density is dominated by the volume fraction. The collected results will prove to be useful for modeling the softening and densification of the trabecular bone using the finite element method.     

Determination of homeostatic elastic moduli in two layers of the esophagus

The function of the esophagus is mechanical. To understand the function, it is necessary to know how the stress and strain in the esophagus can be computed, and how to determine the stress-strain relationship of the wall materials. The present article is devoted to the issue of determining the incremental elastic moduli in the layers of the esophagus under homeostatic conditions. The esophagus is treated as a two-layered structure consisting of an inner collagen-rich submucosa layer and an outer muscle layer. We adopt a theory based on small perturbation experiments at homeostatic conditions for determination of incremental moduli in circumferential, axial, and cross directions in the two layers. The experiments are inflation, axial stretching, circumferential bending, and axial bending. The analysis takes advantage of knowing the esophageal zero-stress state (an open sector with an opening angle of 59.4 +/- 13.2 deg). The neutral axis was located 27% +/- 1.9%away from the mucosal surface. It is demonstrated that under homeostatic conditions, the incremental moduli are layer and direction dependent. The incremental modulus is the highest in the axial direction. Furthermore, the axial moduli for the two layers are similar, whereas in the circumferential direction, the incremental modulus is a factor of 6 higher in the mucosa-submucosa layer compared to the muscle layer. Hence, the esophagus has to be treated as a composite, anisotropic body. With this additional information, we can then look forward to a vision of truly understanding the mechanical events of the esophagus.     

Anisotropic and inhomogeneous mechanical characteristics of the retina

We studied contribution of blood vessels to the mechanical properties of retina. Previous studies revealed anisotropic and inhomogeneous retinal mechanical characteristics. To examine different vessel types and sizes, 3 strips of retinal samples were dissected in each of 5 pig eyes. One strip contained the superior-temporal vein in the axial direction, one strip contained the superior-temporal artery in the axial direction, and one strip did not contain any visible vessel. To examine different vessel orientations, 2 strips of retinal samples were dissected in each of 5 other pig eyes. One strip contained the superior-temporal vein in the axial direction, and one strip contained the superior-temporal vein in the circumferential direction. Tensile testing was performed on the samples. The venous and arterial samples were found to be significantly stiffer than the no-visible-vessel samples. No significant difference was observed neither between the venous and arterial samples, nor between the venous samples in the axial versus circumferential directions. We therefore conclude that the blood vessels contribute significantly to the stiffness of the retina, and the vessel size is the only determining factor that governs the anisotropic and inhomogeneous characteristics of the retina.     

Mechanical anisotropy of inflated elastic tissue from the pig aorta

Uniaxial and biaxial mechanical properties of purified elastic tissue from the proximal thoracic aorta were studied to understand physiological load distributions within the arterial wall. Stress–strain behaviour was non-linear in uniaxial and inflation tests. Elastic tissue was 40% stiffer in the circumferential direction compared to axial in uniaxial tests and～100% stiffer in vessels at an axial stretch ratio of 1.2 or 1.3 and inflated to physiological pressure. Poisson’s ratio v_θz averaged 0.2 and v_zθ increased with circumferential stretch from ～0.2 to ～0.4. Axial stretch had little impact on circumferential behaviour. In intact (unpurified) vessels at constant length, axial forces decreased with pressure at low axial stretches but remained constant at higher stretches. Such a constant axial force is characteristic of incrementally isotropic arteries at their in vivo dimensions. In purified elastic tissue, force decreased with pressure at all axial strains, showing no trend towards isotropy. Analysis of the force–length–pressure data indicated a vessel with v_θz≈0.2 would stretch axially 2–4% with the cardiac pulse yet maintain constant axial force. We compared the ability of 4 mathematical models to predict the pressure-circumferential stretch behaviour of tethered, purified elastic tissue. Models that assumed isotropy could not predict the stretch at zero pressure. The neo-Hookean model overestimated the non-linearity of the response and two non-linear models underestimated it. A model incorporating contributions from orthogonal fibres captured the non-linearity but not the zero-pressure response. Models incorporating anisotropy and non-linearity should better predict the mechanical behaviour of elastic tissue of the proximal thoracic aorta.     

Periosteal biaxial residual strains correlate with bone specific growth rates in chick embryos

It has been proposed that periosteal residual tensile strains influence periosteal bone apposition and endochondral ossification. The role of bone growth rates on the development of residual strains is not well known. This study examined the relationships between specific growth rate and residual strains in chick tibiotarsi. We measured length and circumference during embryonic days 11-20 using microCT. Bones grew faster in length, with longitudinal and circumferential specific growth rates decreasing from 17 to 9% and 14 to 8% per day, respectively. To calculate residual strains, opening dimensions of incisions through the periosteum were analysed using finite element techniques. Results indicate that Poisson's ratio for an isotropic material model is between 0 and 0.04. For the model with Poisson's ratio 0.03, longitudinal and circumferential residual strains decreased from 46.2 to 29.3% and 10.6 to 3.9%, respectively, during embryonic days 14-20. Specific growth rates and residual strains were positively correlated (p<0.05).     

Elastic modulus variation in mandibular bone: a microindentation study of Macaca fascicularis

We characterized the heterogeneous anisotropic elastic properties of mandibular bone in an adult female specimen of Macaca fascicularis using the technique of microindentation. This approach used an indenter of known mass and geometry to sample bone hardness at a spatial resolution in the order of 100 mum. Hardness values were converted to elastic modulus using empirically derived regression. We determined properties in alveolar, midcorpus, and basal regions of coronal and transverse sections taken from multiple locations along the corpus and ramus. Within sections, we determined properties from endosteal, midcortical, and periosteal regions. We found regional variations in bone structure, including bands of orthotropic circumferential lamellar bone at the endosteal and periosteal corpus base, angular region, and ramus. Transversely isotropic osteonal bone characterizes the midcortices of alveolar and basal regions, with many resorption spaces in alveolar regions restricting sampling opportunities. Regional variations in elasticity include relatively compliant bone in the anterior corpus and ramus. Basal cortical bone is stiffer longitudinally than transversely or superoinferiorly, while the evidence for directional dependence in alveolar bone is equivocal. Alveolar bone appears to be relatively compliant with respect to bone found in midcorpus or basal regions. Considerable variation exists in structure and material properties on a highly localized scale, more so than is discernible through conventional approaches for determining material property variation.     

A model for passive elastic properties of rat vena cava

A two-dimensional model for the elastic properties of vena cava abdominalis under orthotropic deformation is introduced and tested against the experimental data obtained from six specimen of rat venae cavae by pressurization experiments. The model is based on membrane approximation and suited for vessels where most of the elastic elements are oriented axially, while circumferential contraction is exerted by redirecting axial stress by some network of oblique fibers. For the experimental data considered in this paper, the ratio between axial and circumferential stress depends almost exclusively on the circumferential extension ratio. As a consequence, the mechanical system can be formally decomposed in a kinematic system reacting by axial contraction on circumferential extension without any loss or storage of energy, serially connected to a hyperelastic system acting only in axial direction. Both systems are modeled separately by equations obtained by a purely phenomenological approach with two parameters for each system. This leads to reasonable reproduction of the experimental data. Introducing a correction parameter, which takes into account that the model assumption on the decomposition does not hold exactly, we get better reproduction of data. However, this is paid for by loss of physical rigor and in particular by departing from the assumption of hyperelasticity.     

Morphology and stress-strain properties along the small intestine in the rat

The stress-strain relationship is determined by the inherent mechanical properties of the intestinal wall, the geometric configurations, the loading conditions and the zero-stress state of the segment. The purpose of this project was to provide morphometric and biomechanical data for rat duodenum, jejunum and ileum. The circumferential strains were referenced to the zero-stress state. Large morphometric variations were found along the small intestine with an increase in the outer circumferential length and luminal area and a decrease in wall thickness in distal direction. The serosal residual strain was tensile and decreased in distal direction (P < 0.05). The mucosal residual strain was compressive and the absolute value decreased in distal direction (P < 0.001). The stress-strain experiments showed that the duodenum was stiffest. All segments were stiffest in longitudinal direction (P < 0.05). In conclusion, axial variation in morphometric and biomechanical properties was found in the small intestine. The zero-stress state must be considered in future biomechanical studies in the gastrointestinal tract.     

Effect of fiber orientation and strain rate on the nonlinear uniaxial tensile material properties of tendon

Tendons are exposed to complex loading scenarios that can only be quantified by mathematical models, requiring a full knowledge of tendon mechanical properties. This study measured the anisotropic, nonlinear, elastic material properties of tendon. Previous studies have primarily used constant strain-rate tensile tests to determine elastic modulus in the fiber direction. Data for Poisson's ratio aligned with the fiber direction and all material properties transverse to the fiber direction are sparse. Additionally, it is not known whether quasi-static constant strain-rate tests represent equilibrium elastic tissue behavior. Incremental stress-relaxation and constant strain-rate tensile tests were performed on sheep flexor tendon samples aligned with the tendon fiber direction or transverse to the fiber direction to determine the anisotropic properties of toe-region modulus (E0), linear-region modulus (E), and Poisson's ratio (v). Among the modulus values calculated, only fiber-aligned linear-region modulus (E1) was found to be strain-rate dependent. The E1 calculated from the constant strain-rate tests were significantly greater than the value calculated from incremental stress-relaxation testing. Fiber-aligned toe-region modulus (E(1)0 = 10.5 +/- 4.7 MPa) and linear-region modulus (E1 = 34.0 +/- 15.5 MPa) were consistently 2 orders of magnitude greater than transverse moduli (E(2)0 = 0.055 +/- 0.044 MPa, E2 = 0.157 +/- 0.154 MPa). Poisson's ratio values were not found to be rate-dependent in either the fiber-aligned (v12 = 2.98 +/- 2.59, n = 24) or transverse (v21 = 0.488 +/- 0.653, n = 22) directions, and average Poisson's ratio values in the fiber-aligned direction were six times greater than in the transverse direction. The lack of strain-rate dependence of transverse properties demonstrates that slow constant strain-rate tests represent elastic properties in the transverse direction. However, the strain-rate dependence demonstrated by the fiber-aligned linear-region modulus suggests that incremental stress-relaxation tests are necessary to determine the equilibrium elastic properties of tendon, and may be more appropriate for determining the properties to be used in elastic mathematical models.     

Comparison of nonlinear mechanical properties of bovine articular cartilage and meniscus

Nonlinear, linear and failure properties of articular cartilage and meniscus in opposing contact surfaces are poorly known in tension. Relationships between the tensile properties of articular cartilage and meniscus in contact with each other within knee joints are also not known. In the present study, rectangular samples were prepared from the superficial lateral femoral condyle cartilage and lateral meniscus of bovine knee joints. Tensile tests were carried out with a loading rate of 5 mm/min until the tissue rupture. Nonlinear properties of the toe region, linear properties in larger strains, and failure properties of both tissues were analysed. The strain-dependent tensile modulus of the toe region, Young's modulus of the linear region, ultimate tensile stress and toughness were on average 98.2, 8.3, 4.0 and 1.9 times greater (p<0.05) for meniscus than for articular cartilage. In contrast, the toe region strain, yield strain and failure strain were on average 9.4, 3.1 and 2.3 times greater (p<0.05) for cartilage than for meniscus. There was a significant negative correlation between the strain-dependent tensile moduli of meniscus and articular cartilage samples within the same joints (r=−0.690, p=0.014). In conclusion, the meniscus possesses higher nonlinear and linear elastic stiffness and energy absorption capability before rupture than contacting articular cartilage, while cartilage has longer nonlinear region and can withstand greater strains before failure. These findings point out different load carrying demands that both articular cartilage and meniscus have to fulfil during normal physiological loading activities of knee joints.     

The use of a temporal osteoperiosteal flap for the reconstruction of malar hypoplasia in Treacher Collins syndrome

The clinical use of a temporal periosteal bone flap for the reconstruction of a malar bone in a patient with the Treacher Collins syndrome is presented. The temporal muscle functions as an axial carrier of the periosteum that induces osteogenesis in young children, whereas the bone segments may serve as a nucleus for further bone formation from the periosteum. Correction of the eyelid coloboma was obtained by the rotation and advancement of a temporopalpebral flap.     

Anisotropic and inhomogeneous tensile behavior of the human anulus fibrosus: experimental measurement and material model predictions

The anulus fibrosus (AF) of the intervertebral disc exhibits spatial variations in structure and composition that give rise to both anisotropy and inhomogeneity in its material behaviors in tension. In this study, the tensile moduli and Poisson's ratios were measured in samples of human AF along circumferential, axial, and radial directions at inner and outer sites. There was evidence of significant inhomogeneity in the linear-region circumferential tensile modulus (17.4+/-14.3 MPa versus 5.6+/-4.7 MPa, outer versus inner sites) and the Poisson's ratio v21 (0.67+/-0.22 versus 1.6+/-0.7, outer versus inner), but not in the axial modulus (0.8+/-0.9 MPa) or the Poisson's ratios V12 (1.8+/-1.4) or v13 (0.6+/-0.7). These properties were implemented in a linear an isotropic material model of the AF to determine a complete set of model properties and to predict material behaviors for the AF under idealized kinematic states. These predictions demonstrate that interactions between fiber populations in the multilamellae AF significantly contribute to the material behavior, suggesting that a model for th     

Anatomical variation of orthotropic elastic moduli of the proximal human tibia

The anatomical variation of orthotropic elastic moduli of the cancellous bone from three human proximal tibiae was investigated using an ultrasonic technique. With this technique, it was possible to measure three orthogonal elastic moduli and three shear moduli from cubic specimens of cancellous bone as small as 8 mm per side. Correlation with mechanical tensile testing has shown this technique to offer a precise measure of cancellous modulus (Eten = 0.94Eult + 144.6 MPa, r2 = 0.96, n = 34). The cancellous bone of the proximal tibia was found to be very inhomogeneous, with the axial modulus ranging between 340 and 3350 MPa. A course map is presented, showing measured Young's moduli as a function of anatomical position. The anisotropy of the cancellous bone, determined by the relative differences between the three orthogonal moduli, was shown to be relatively constant over the entire range of cancellous densities tested. The relationship between the axial elastic modulus and the apparent density was found to be approximately linear, as reported by others for proximal tibial cancellous bone.     

Polymer-based composite hip prostheses

A composite hip prosthesis (CHP) made from poly(ether-imide) reinforced with carbon and glass fibres was manufactured and characterized. The main objective of the study was to evaluate the effect of fibre organization on the mechanical properties of the composite femoral implant and compare with the bone. A stacking sequence of drop-off plies of carbon/glass fibres reinforcing poly(ether-imide) (PEI) constitutes a symmetrical and balanced CHP. The hip was manufactured according to the finite element modelling (FEM) design and using the compression moulding and water-jet technologies. The measured stress-strain data according to tensile, flexural and torsional tests showed agreement with the numerical calculation. Young's modulus and the strength in tension are uniform along the stem axis (40 GPa and 600 MPa, respectively) while the elastic modulus in bending varies from 10 to 60 GPa in the tip-head direction. The composite stem showed a linear load-displacement relation up to 4500 N without breaking. Mechanical behaviour of the CHP is compared to that of a canine femur. Comparison with metal prostheses has also been undertaken. CHPs control stress-strain distributions, and hence the mechanical signals to bone, through a material-structure design.     

Circumferential variations of mechanical behavior of the porcine thoracic aorta during the inflation test

We developed an extension-inflation experimental apparatus with a stereo vision system and a stress-strain analysis method to determine the regional mechanical properties of a blood vessel. Seven proximal descending thoracic aortas were investigated during the inflation test at a fixed longitudinal stretch ratio of 1.35 over a transmural pressure range from 1.33 to 21.33 kPa. Four circumferential regions of each aorta were designated as the anterior (A), left lateral (L), posterior (P), and right lateral (R) regions, and the inflation test was repeated for each region of the aortas. We used continuous functions to approximate the surfaces of the regional aortic wall in the reference configuration and the deformed configuration. Circumferential stretch and stress at the four circumferential regions of the aorta were computed. Circumferential stiffness, defined as the tangent of the stress-stretch curve, and physiological aortic stiffness, named pressure-strain elastic modulus, were also computed for each region. In the low pressure range, the stress increased linearly with increased stretch, but the mechanical response became progressively stiffer in the high-pressure range above a transition point. At a transmural pressure of 12.00 kPa, mean values of stiffness were 416±104 kPa (A), 523±99 kPa (L), 634±91 kPa (P), and 489±82 kPa (R). The stiffness of the posterior region was significantly higher than that of the anterior region, but no significant difference was found in pressure-strain elastic modulus.