Passive elastic properties of the rat aorta

The passive anisotropic elastic properties of rat's aorta were studied in vitro by subjecting cylindrical segments of thoracic and abdominal aorta to a wide range of deformations. Using data on pressure, axial stretch, outer diameter, axial force and wall thickness, incremental moduli of elasticity in the circumferential, axial and radial directions were computed. Results indicate that while the elastic behavior of the aortic wall is globally anisotropic, there exists a state of deformation at which the vessel displays incremental isotropy. This state of deformation corresponds approximately to the loading conditions to which the aorta is exposed in situ. Values of the moduli, analyzed as a function of transmural pressure, show that the stiffness of the aortic wall is fairly constant at low pressures but raises steeply for pressures higher than physiological. For axial stretches as occurring in situ, the magnitudes of the circumferential and radial moduli do not differ significantly for the thoracic aorta; hence this vessel can be regarded as transversely isotropic over a wide range of pressures. The same observation is valid also for the abdominal aorta when pressures equal or smaller than physiological are considered. For both the thoracic and abdominal segments of the aorta, the circumferential and radial moduli are smaller than the axial modulus at low pressures, while the reverse is true for large pressures.     

Nanomechanical and structural properties of native cellulose under compressive stress

Cellulose is an important biopolymer with applications ranging from its use as an additive in pharmaceutical products to the development of novel smart materials. This wide applicability arises in part from its interesting mechanical properties. Here we report on the use of high pressure X-ray diffraction and Raman spectroscopy in a diamond anvil cell to determine the bulk and local elastic moduli of native cellulose. The modulus values obtained are 20 GPa for the bulk modulus and 200-355 and 15 GPa for the crystalline parts and the overall elastic (Young's) modulus, respectively. These values are consistent with those calculated from tensile measurements. Above 8 GPa, the packing of the cellulose chains within the fibers undergoes significant structural distortion, whereas the chains themselves remain largely unaffected by compression.     

Effect of long-term anemia and retransfusion on central circulation during exercise

The bulk modulus and the shear modulus describe the capacity of material to resist a change in volume and a change of shape, respectively. The values of these elastic coefficients for air-filled lung parenchyma suggest that there is a qualitative difference between the mechanisms by which the parenchyma resists expansion and shear deformation; the bulk modulus changes roughly exponentially with the transpulmonary pressure, whereas the shear modulus is nearly a constant fraction of the transpulmonary pressure for a wide range of volumes. The bulk modulus is approximately 6.5 times as large as the shear modulus. In recent microstructural modeling of lung parenchyma, these mechanisms have been pictured as being similar to the mechanisms by which an open cell liquid foam resists deformations. In this paper, we report values for the bulk moduli and the shear moduli of normal air-filled rabbit lungs and of air-filled lungs in which alveolar surface tension is maintained constant at 16 dyn/cm. Elevating surface tension above normal physiological values causes the bulk modulus to decrease and the shear modulus to increase. Furthermore, the bulk modulus is found to be sensitive to a dependence of surface tension on surface area, but the shear modulus is not. These results agree qualitatively with the predictions of the model, but there are quantitative differences between the data and the model.     

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.     

A cellular model of lung elasticity

The mechanics of the lung parenchyma is studied using models comprised of line members interconnected to form 3-D cellular structures. The mechanical properties are represented as elastic constants of a continuum. These are determined by perturbing each individual cell from a reference state by an increment in stress which is superimposed upon the uniform stretching forces initially present in the members due to the transpulmonary pressure. A force balance on the distorted structure, together with a force-deformation law for the members, leads to a calculation of the strain increments of the members. Predictions based on the analysis of the 3-D isotropic dodecahedron are in good agreement with experimental values for the Young's, shear, and bulk moduli reported in the literature. The model provides an explanation for the dependence of the elastic moduli on transpulmonary pressure, the geometrical details of the structure, and the stress-strain law of the tissue.     

How is the indentation modulus of bone tissue related to its macroscopic elastic response? A validation study

This work consists of the validation of a novel approach to estimate the local anisotropic elastic constants of the bone extracellular matrix using nanoindentation. For this purpose, nanoindentation on two planes of material symmetry were analyzed and the resulting longitudinal elastic moduli compared to the moduli measured with a macroscopic tensile test. A combined lathe and tensile system was designed that allows machining and testing of cylindrical microspecimens of approximately 4mm in length and 300 microm in diameter. Three bovine specimens were tested in tension and their outer geometry and porosity assessed by synchrotron radiation microtomography. Based on the results of the traction test and the precise outer geometry, an apparent longitudinal Young's modulus was calculated. Results between 20.3 and 27.6 GPa were found that match with previously reported values for bovine compact bone. The same specimens were then characterized by nanoindentation on a transverse and longitudinal plane. A longitudinal Young's modulus for the bone matrix was then derived using the numerical scheme proposed by Swadener and Pharr and the fabric-elasticity relationship by Zysset and Curnier. Based on the matrix modulus and a power law effective volume fraction, an apparent longitudinal Young's modulus was predicted for each microspecimen. This alternative approach provided values between 19.9 and 30.0 GPa, demonstrating differences between 2% and 13% to the values provided by the initial tensile test. This study therefore raises confidence in our nanoindentation protocol of the bone extracellular matrix and supports the underlying hypotheses used to extract the anisotropic elastic constants.     

Effects of longitudinal stretch on VSM tone and distensibility of muscular conduit arteries

With progressing age, large arteries diminish their longitudinal stretch, which in extreme cases results in tortuosity. Increased age is also associated with loss of vessel distensibility. We measured pressure-diameter curves from muscular porcine carotid arteries ex vivo at different longitudinal stretch ratios (lambda(z) = 1.4 and 1.8) and under different vascular smooth muscle (VSM) conditions (fully relaxed, normal VSM tone, and maximally contracted). Distensibility was found to be halved by decreasing longitudinal stretch from lambda(z) = 1.8 to 1.4 at physiological pressures. This counterintuitive observation is possible because highly nonlinear elastic modulus of the artery and anisotropic properties. Furthermore, a significantly larger basal VSM contraction was observed at lambda(z) = 1.8 than 1.4, although this was clearly not related to a myogenic response during inflation. This dependence of VSM tone to longitudinal stretch may have possible implications on the functional characteristics of the arterial wall.     

Reassessment of brain elasticity for analysis of biomechanisms of hydrocephalus

This paper presents results from a finite element study of the biomechanics of hydrocephalus, with special emphasis on a reassessment of the parenchyma elastic modulus. A two-dimensional finite element model of the human brain/ventricular system is developed and analysed under hydrocephalic loading conditions. It is shown that the Young's modulus of the brain parenchyma used in previous studies (3000-10000 Pa) corresponds to strain rates much higher than those present in hydrocephalic brains. Consideration of the brain's viscoelasticity leads to the derivation of a considerably lower modulus value of approximately 584 Pa.     

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.     

Effect of gravity and posture on lung mechanics.

The volume-pressure relationship of the lung was studied in six subjects on changing the gravity vector during parabolic flights and body posture. Lung recoil pressure decreased by approximately 2.7 cmH(2)O going from 1 to 0 vertical acceleration (G(z)), whereas it increased by approximately 3.5 cmH(2)O in 30 degrees tilted head-up and supine postures. No substantial change was found going from 1 to 1.8 G(z). Matching the changes in volume-pressure relationships of the lung and chest wall (previous data), results in a decrease in functional respiratory capacity of approximately 580 ml at 0 G(z) relative to 1 G(z) and of approximately 1,200 ml going to supine posture. Microgravity causes a decrease in lung and chest wall recoil pressures as it removes most of the distortion of lung parenchyma and thorax induced by changing gravity field and/or posture. Hypergravity does not greatly affect respiratory mechanics, suggesting that mechanical distortion is close to maximum already at 1 G(z). The end-expiratory volume during quiet breathing corresponds to the mechanical functional residual capacity in each condition.     

Effects of age on elastic moduli of human lungs.

The model of the lung as an elastic continuum undergoing small distortions from a uniformly inflated state has been used to describe many lung deformation problems. Lung stress-strain material properties needed for this model are described by two elastic moduli: the bulk modulus, which describes a uniform inflation, and the shear modulus, which describes an isovolume deformation. In this study we measured the bulk modulus and shear modulus of human lungs obtained at autopsy at several fixed transpulmonary pressures (Ptp). The bulk modulus was obtained from small pressure-volume perturbations on different points of the deflation pressure-volume curve. The shear modulus was obtained from indentation tests on the lung surface. The results indicated that, at a constant Ptp, both bulk and shear moduli increased with age, and the increase was greater at higher Ptp values. The micromechanical basis for these changes remains to be elucidated.     

Elastic properties of air- and liquid-filled lung parenchyma

Pressure-volume measurements and the punch indentation test are used to obtain the bulk modulus (kappa) and the shear modulus (mu) of lung parenchyma of air- and liquid-filled rabbit lungs. Plots of kappa and mu vs. transpulmonary pressure obtained from these measurements indicate that there is very little difference between the elastic behavior of the air- and liquid-filled lung, suggesting that the mechanism of resisting deformation in both cases is similar. On the other hand, from plots of kappa and mu vs. lung volume, it appears that the elastic moduli are higher in the air-filled lung than in the liquid-filled lung at the same volume. These differences, referred to as kappa gamma and mu gamma, as well as the difference in transpulmonary pressures (P gamma), are presumably due to the additional elastic recoil of the air-filled lung provided by alveolar surface tension (gamma). No conclusion could be reached about the shape of the kappa gamma vs. P gamma curve. However, the mu gamma vs. P gamma relationship appears to be approximately linear, with a slope of approximately 0.5. This result agrees qualitatively with the model (T. A. Wilson and H. Bachofen, J. Appl. Physiol. 52: 1064-1070, 1982) in which the part of the parenchyma that provides P gamma is pictured as mechanically analogous to an open cell liquid foam, having mu gamma = 0.4P gamma (J. Appl. Mech. Trans. ASME 51: 229-231, 1984), but it is statistically significant only at high lung volumes.     

离体人肺弹性增量模量的实验研究

本文就离体人肺进行实验研究和理论分析,最后求出肺在不同的膨胀程度下的弹性模量值。从压力一容积曲线的增量回滞曲线求出膨胀模量K,利用K值与凹痕实验获得的荷载-变形关系相结合,获得其它弹性模量。计算结果表明:膨胀模量K约为膨胀压力的3倍,杨氏模量E约为膨胀压力的4倍,剪切模量约为膨胀压力的1.5倍,泊松系数值约在0.3左右。最后与其它文献中所列的猫、兔、狗的各种弹性模量值进行了比较。     

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.     

A biphasic, anisotropic model of the aortic wall

A biphasic, anisotropic elastic model of the aortict wall is developed and compared to literature values of experimental measurements of vessel wall radii, thickness, and hvdraulic conductivity as a function of intraluminal pressure. The model gives good predictions using a constant wall modulus for pressures less than 60 mmHg, but requires a strain-dependent modulus for pressures greater than this. In both bovine and rabbit aorta, the tangential modulus is found to be approximately 20 times greater than the radial modulus. These moduli lead to predictions that, when perfused in a cylindrical geometry, the aortic volume and its specific hydraulic coonductivity are relatively independent of perfusion pressure, in agreement with experimental measurements. M, the parameter that relates specific hydraulic conductivy, to tissue dilation, is found to be a positive quantity correcting a previous error in the literature.     

On the calculation of the elastic modulus of a biofilm streamer

Biofilm mechanical properties are essential in quantifying the rate of microbial detachment, a key process in determining the function and structure of biofilm systems. Although properties such as biofilm elastic moduli, yield stress and cohesive strength have been studied before, a wide range of values for the biofilm Young's modulus that differ by several orders of magnitude are reported in the literature. In this article, we use experimental data reported in Stoodley et al. [Stoodley et al., Biotechnol Bioeng (1999): 65(1):83-92] and present a methodology for the calculation of Young's modulus, which partially explains the large difference between the values reported in the literature.     

Properties of lung parenchyma in distortion.

This study offers a basis for evaluating and developing models of stress-strain behavior of the lung in distortion. Tensile forces were applied along three axes to cubes of dog lung parenchyma. With axially symmetrical force-loading, expansion was reasonably symmetrical and pressure-volume relationships were reasonably conventional in range, hysteresis, and time-dependent behavior. When the force load was changed on one axis only, that axis appeared more compliant than it did during symmetrical loading and the other axes changed length in the opposite sign. Similar distortion was apparent at the alveolar level. Data for five specimens over a range of applied loads are filed with the National Auxiliary Publications Service; graphical examples are presented herein. Relationship among the compliances for symmetrical and asymmetrical loadings were consistent with elastic theory. We derived the elastic coefficients, bulk and Young's moduli, and Poisson's ratio from the data. Poison's ratio was about 0.30 in air-filled specimens, but was lower (0.16-0.24) and increases with stress in saline-filled specimens.     

An Insight into Cell Elasticity and Load-Bearing Ability. Measurement and Theory

We have studied the elasticity and load bearing ability of plant tissue at the cellular level, using onion (Allium cepa) epidermal cells. The Young's modulus and Poisson's ratio of the cells were obtained by loading a tensile force on onion epidermal peels of different turgor pressures, and measuring the elongation and the lateral contraction of the peels. The Young's moduli and the Poisson's ratios ranged from 3.5 to 8.0 MPa and 0.18 to 0.30, respectively. To determine the effects of cell elasticity and turgor pressure on the cell's ability to bear load, we loaded a small glass ball onto a cell and measured the projected contact area between the ball and the cell. Unlike previous studies, we considered the cell as a whole entity, and utilized the Boussinesq's solution to derive the relevant equations that related the elastic parameters and cell deformation. For cells with a turgor pressure > or = 0.34 MPa, the predicted contact area agreed well with the measured area. The equations could also predict cell turgor pressure with a deviation from the measured value of 0.01 MPa. This study gives strong support to ball tonometry, a new method of measuring cell turgor pressure.     

Analytical methods to determine the effective mesoscopic and macroscopic elastic properties of cortical bone

We compare theoretical predictions of the effective elastic moduli of cortical bone at both the meso- and macroscales. We consider the efficacy of three alternative approaches: the method of asymptotic homogenization, the Mori-Tanaka scheme and the Hashin-Rosen bounds. The methods concur for specific engineering moduli such as the axial Young's modulus but can vary for others. In a past study, the effect of porosity alone on mesoscopic properties of cortical bone was considered, taking the matrix to be isotropic. Here, we consider the additional influence of the transverse isotropy of the matrix. We make the point that micromechanical approaches can be used in two alternative ways to predict either the macroscopic (size of cortical bone sample) or mesoscopic (in between micro- and macroscales) effective moduli, depending upon the choice of representative volume element size. It is widely accepted that the mesoscale behaviour is an important aspect of the mechanical behaviour of bone but models incorporating its effect have started to appear only relatively recently. Before this only macroscopic behaviour was addressed. Comparisons are drawn with experimental data and simulations from the literature for macroscale predictions with particularly good agreement in the case of dry bone. Finally, we show how predictions of the effective mesoscopic elastic moduli can be made which retain dependence on the well-known porosity gradient across the thickness of cortical bone.     

The bone tissue of the canine mandible is elastically isotropic

This paper reports experimental measurements which show that canine mandibular bone tissue is elastically isotropic. Earlier work has established that human, canine and bovine cortical bone tissue of the femur, tibia and skull are elastically anisotropic and therefore the reported isotropy of mandibular tissue was unexpected. The isotropic elastic moduli of the canine mandible are represented by a Young's modulus of 7.5 GPa and a Poisson's ratio of 0.4. Earlier work gave the three orthotropic Young's moduli of the cortical one of the canine femur as 12.8 GPa, 15.6 GPa and 20.1 GPa. The experimental technique employed is elastic wave propagation at ultrasonic frequencies.