Mechanical properties of DNA films

The Young's dynamical modulus (E) and the DNA film logarithmic decrement (theta) at frequencies from 50 Hz to 20 kHz are measured. These values are investigated as functions of the degree of hydration and temperature. Isotherms of DNA film hydration at 25 degrees C are measured. The process of film hydration changing with temperature is studied. It is shown that the Young's modulus for wet DNA films (E = 0.02-0.025 GN m-2) strongly increases with decreasing hydration and makes E = 0.5-0.7 GN m-2. Dependence of E on hydration is of a complex character. Young's modulus of denatured DNA films is larger than that of native ones. All peculiarities of changing of E and theta of native DNA films (observed at variation of hydration) vanish in the case of denatured ones. The native and denatured DNA films isotherms are different and depend on the technique of denaturation. The Young's modulus of DNA films containing greater than 1 g H2O/g dry DNA is found to decrease with increasing temperature, undergoing a number of step-like changes accompanied by changes in the film hydration. At low water content (less than 0.3 g H2O/g dry DNA), changing of E with increasing temperature takes place smoothly. The denaturation temperature is a function of the water content.     

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.     

Dynamic stiffness and crossbridge action in muscle

Small sinusoidal vibrations at 300 HZ were applied to frog sartorius muscle to measure the dynamic stiffness (Young's modulus) throughout the course of tetanus. For a peak-to-peak amplitude of 0.4% the dynamic Young's modulus increased from 1.5 X 10(5) Nm-2 in the resting state to 2 X 10(7) Nm-2 in tetanus. After correction for the external connective tissue, the dynamic Young's modulus of the muscle was almost directly proportional to the tension throughout the development of tetanus. The ratio of dynamic Young's modulus to tensile stress thus remained constant (with a value at 300 Hz of approximately 100), consistently with Huxley and Simmon's identification of the crossbridges as the source of both tension and stiffness. For a single crossbridge the ratio of stiffness to tension was 8.2 X 10(7) m-1 at 300 Hz; it is deduced from literature data that the limiting value at high frequencies is about 1.6 X 10(8) m-1. This ratio is interpreted on Harrington's (1971) model to show that crossbridge action can be explained by a helix-coil transition of about 80 out of the 260 residues in each S-2 myosin strand. It is also shown that a helix-coil model can account for the observed rapid relaxation of muscle without invoking any complex behaviour of the crossbridge head.     

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.     

Spatial orientation in bone samples and Young's modulus

Bone mass is the most important determinant of the mechanical strength of bones, and spatial structure is the second. In general, the spatial structure and mechanical properties of bones such as the breaking strength are direction dependent. The mean intercept length (MIL) and line frequency deviation (LFD) are two methods for quantifying directional aspects of the spatial structure of bone. Young's modulus is commonly used to describe the stiffness of bone, which is also a direction-dependent mechanical property. The aim of this article is to investigate the relation between MIL and LFD on one hand and Young's modulus on the other. From 11 human mandibular condyles, 44 samples were taken and scanned with high-resolution computer tomography equipment (micro-CT). For each sample the MIL and LFD were determined in 72602 directions distributed evenly in 3D space. In the same directions Young's modulus was determined by means of the stiffness tensor that had been determined for each sample by finite element analysis. To investigate the relation between the MIL and LFD on one hand and Young's modulus on the other, multiple regression was used. On average the MIL accounted for 69% of the variance in Young's modulus in the 44 samples and the LFD accounted for 72%. The average percentage of variance accounted for increased to 80% when the MIL was combined with the LFD to predict Young's modulus. Obviously MIL and LFD to some extent are complementary with respect to predicting Young's modulus. It is known that directional plots of the MIL tend to be ellipses or ellipsoids. It is speculated that ellipsoids are not always sufficient to describe Young's modulus of a bone sample and that the LFD partly compensates for this.     

Static versus dynamic gerbil tympanic membrane elasticity: derivation of the complex modulus

An accurate estimation of tympanic membrane stiffness is important for realistic modelling of middle ear mechanics. Tympanic membrane stiffness has been investigated extensively under either quasi-static or dynamic loading conditions. It is known that biological tissues are sensitive to strain rate. Therefore, in this work, the mechanical behaviour of the tympanic membrane was studied under both quasi-static and dynamic loading conditions. Experiments were performed on the pars tensa of four gerbil tympanic membranes. A custom-built indentation apparatus was used to perform in situ tissue indentations and testing was done applying both quasi-static and dynamic sinusoidal indentations up to 8.2?Hz. The unloaded shape of the tympanic membrane was measured and used to create specimen-specific finite element models to simulate the experiments. The frequency dependent Young's modulus of each specimen was then estimated by an inverse analysis in which the error between experimental and simulated indentation data was optimised for each indentation frequency separately. Using an 8?μm central region thickness, we found Young's moduli between 71 and 106?MPa (n = 4) at 0.2?Hz indentation frequency. A standard linear viscoelastic model and a viscoelastic model with a continuous relaxation spectrum were used to derive a complex modulus in the frequency domain. Due to experimental limitations, the indentation frequency upper limit was 8.2?Hz. The average relative modulus increase in this domain was 14% and the increase was the strongest below 6?Hz.     

The Growth Form of Croton pullei (Euphorbiaceae) - Functional Morphology and Biomechanics of a Neotropical Liana

Abstract: Croton pullei (Euphorbiaceae) is a woody climber of the lowland rainforest in French Guyana and Surinam. During ontogeny, a shift from a juvenile free-standing growth phase to an older supported growth phase is observed. The following biomechanical parameters were studied: structural Young's modulus, structural torsional modulus, flexural stiffness and bend to twist ratios. Changes in anatomical development were also analysed for different stages of development of C. pullei which differ significantly in their mechanical properties. Free-standing plants show a nearly constant structural Young's modulus and structural torsional modulus during ontogeny, with flexural stiffness increasing proportionally with the axial second moment of area. These patterns are typical for “semi-self-supporting plants". In contrast, supported plants show a significant decrease in structural Young's modulus in older stem parts, as well as a decrease in structural torsional modulus. Due to the decrease in structural Young's modulus, flexural stiffness does not increase proportionally with the axial second moment of area. These patterns are typical for non-self-supporting lianas. In all supported plants, a sudden transition occurs from early dense wood to a wood type with a much higher proportion of large diameter vessels. In contrast, only the dense wood type is present in all tested free-standing plants. The data are compared with results from other climbing species of the same study area and discussed with reference to observed features characterizing the growth form and life history of C. pullei.     

Sickle cell trait human erythrocytes are significantly stiffer than normal

Atomic force microscopy (AFM) allows for high-resolution topography studies of biological cells and measurement of their mechanical properties in physiological conditions. In this work, AFM was employed to measure the stiffness of abnormal human red blood cells from human subjects with the genotype for sickle cell trait. The determined Young's modulus was compared with that obtained from measurements of erythrocytes from healthy subjects. The results showed that Young's modulus of pathological erythrocytes was approximately three times higher than in normal cells. Observed differences indicate the effect of the polymerization of sickle hemoglobin as well as possible changes in the organization of the cell cytoskeleton associated with the sickle cell trait.     

Mechanical properties of the axial skeleton in gorgonians

Axial skeletons of thirteen species representing a wide range of genera of Gorgonians were investigated using Young's modulus as a measure of stiffness and Torsion modulus as a measure of resistance to shear or twist. Atomic absorption spectroscopic determination of magnesium and calcium content as measures of mineralization were done. Relative quantities of calcareous material in the axial skeletons showed a strong linear correlation with Young's modulus and suggests an important role for calcareous material in the modulation of the mechanical properties of axoskeleton. Torsion moduli also showed a mathematical but non-linear relationship to calcareous content. Axis stiffness correlated well with zonation-related water movement. Stiffest axes occur in deeper water with no wave surge, most flexible in shallower water with moderate surge and intermediate stiffness in shallow, high energy habitats. An extremely high MgCO₃ containing carbonate that may be a previously unreported biological structural material was found in the Plexauridae.     

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.     

Dynamic deformational loading results in selective application of mechanical stimulation in a layered, tissue-engineered cartilage construct

The application of dynamic physiologic loading to a bilayered chondrocyte-seeded agarose construct with a 2% (wt/vol) top layer and 3% (wt/vol) bottom layer was hypothesized to (1) improve overall construct properties and (2) result in a tissue that mimics the mechanical inhomogeneity of native cartilage. Dynamic loading over the 28 day culture period was found to significantly increase bulk mechanical and biochemical properties versus free-swelling culture. The initial depth-distribution of the compressive Young's modulus (EY) reflected the intrinsic properties of the gel in each layer and a similar trend to the native tissue, with a softer 2% gel layer and a much stiffer 3% gel layer. After 28 days in culture, free-swelling conditions maintained this general trend while loaded constructs possessed a reverse profile, with significant increases in EY observed only in the 2% gel. Histological analysis revealed preferential matrix formation in the 2% agarose layer, with matrix localized more pericellularly in the 3% agarose layer. Finite element modeling revealed that, prior to significant matrix elaboration, the 2% layer experiences increased mechanical stimuli (fluid flow and compressive strain) during loading that may enhance chondrocyte stimulation and nutrient transport in that layer, consistent with experimental observations. From these results, we conclude that due to the limitations in 3% agarose, the use of this type of bilayered construct to construct depth-dependent inhomogeneity similar to the native tissue is not likely to be successful under long-term culture conditions. Our study underscores the importance of other physical properties of the scaffold that may have a greater influence on interconnected tissue formation than intrinsic scaffold stiffness.     

Stiffness of normal and pathological erythrocytes studied by means of atomic force microscopy

During recent years, atomic force microscopy has become a powerful technique for studying the mechanical properties (such as stiffness, viscoelasticity, hardness and adhesion) of various biological materials. The unique combination of high-resolution imaging and operation in physiological environment made it useful in investigations of cell properties. In this work, the microscope was applied to measure the stiffness of human red blood cells (erythrocytes). Erythrocytes were attached to the poly-L-lysine-coated glass surface by fixation using 0.5% glutaraldehyde for 1 min. Different erythrocyte samples were studied: erythrocytes from patients with hemolytic anemias such as hereditary spherocytosis and glucose-6-phosphate-dehydrogenase deficiency patients with thalassemia, and patients with anisocytosis of various causes. The determined Young's modulus was compared with that obtained from measurements of erythrocytes from healthy subjects. The results showed that the Young's modulus of pathological erythrocytes was higher than in normal cells. Observed differences indicate possible changes in the organization of cell cytoskeleton associated with various diseases.     

Trabecular bone's mechanical properties are affected by its non-uniform mineral distribution

The bone remodeling process takes place at the surface of trabeculae and results in a non-uniform mineral distribution. This will affect the mechanical properties of cancellous bone, because the properties of bone tissue depend on its mineral content. We investigated how large this effect is by simulating several non-uniform mineral distributions in 3D finite element models of human trabecular bone and calculating the apparent stiffness of these models. In the ‘linear model’ we assumed a linear relation between mineral content and Young's modulus of the tissue. In the ‘exponential model’ we included an empirical exponential relation in the model. When the linear model was used the mineral distribution slightly changed the apparent stiffness, the difference varied between an 8% decrease and a 4% increase compared to the uniform model with the same BMD. The exponential model resulted in up to 20% increased apparent stiffness in the main load-bearing direction. A thin less mineralized surface layer (28 μm) and highly mineralized interstitial bone (mimicking mineralization resulting from anti-resorptive treatment) resulted in the highest stiffness. This could explain large reductions in fracture risk resulting from small increases in BMD. The non-uniform mineral distribution could also explain why bone tissue stiffness determined using nano-indentation is usually higher than finite element (FE)-determined stiffness. We conclude that the non-uniform mineral distribution in trabeculae does affect the mechanical properties of cancellous bone and that the tissue stiffness determined using FE-modeling could be improved by including detailed information about mineral distribution in trabeculae in the models.     

Dynamic stiffness and crossbridge action in muscle

Small sinusoidal vibrations at 300 Hz were applied to frog sartorius muscle to measure the dynamic stiffness (Young's modulus) throughout the course of tetanus. For a peak-to-peak amplitude of 0.4% the dynamic Young's modulus increased from 1.5×10⁵ Nm^–2 in the resting state to 2×10⁷ Nm^–2 in tetanus. After correction for the external connective tissue, the dynamic Young's modulus of the muscle was almost directly proportional to the tension throughout the development of tetanus. The ratio of dynamic Young's modulus to tensile stress thus remained constant (with a value at 300 Hz of approximately 100), consistently with Huxley and Simmons' identification of the crossbridges as the source of both tension and stiffness.For a single crossbridge the ratio of stiffness to tension was 8.2×10⁷ m^–1 at 300 Hz; it is deduced from literature data that the limiting value at high frequencies is about 1.6×10⁸ m^–1. This ratio is interpreted on Harrington's (1971) model to show that crossbridge action can be explained by a helix-coil transition of about 80 out of the 260 residues in each S-2 myosin strand. It is also shown that a helix-coil model can account for the observed rapid relaxation of muscle without invoking any complex behaviour of the crossbridge head.     

IL-1beta decreases the elastic modulus of human tenocytes.

Cellular responses to mechanical stimuli are regulated by interactions with the extracellular matrix, which, in turn, are strongly influenced by the degree of cell stiffness (Young's modulus). It was hypothesized that a more elastic cell could better withstand the rigors of remodeling and mechanical loading. It was further hypothesized that interleukin-1beta (IL-1beta) would modulate intracellular cytoskeleton polymerization and regulate cell stiffness. The purpose of this study was to investigate the utility of IL-1beta to alter the Young's modulus of human tenocytes. Young's modulus is the ratio of the stress to the strain, E = stress/strain = (F/A)/(deltaL/L0), where L0 is the equilibrium length, deltaL is the length change under the applied stress, F is the force applied, and A is the area over which the force is applied. Human tenocytes were incubated with 100 pM recombinant human IL-1beta for 5 days. The Young's modulus was reduced by 27-63%. Actin filaments were disrupted in >75% of IL-1beta-treated cells, resulting in a stellate shape. In contrast, immunostaining of alpha-tubulin showed increased intensity in IL-1beta-treated tenocytes. Human tenocytes in IL-1beta-treated bioartificial tendons were more tolerant to mechanical loading than were untreated counterparts. These results indicate that IL-1beta reduced the Young's modulus of human tenocytes by disrupting the cytoskeleton and/or downregulating the expression of actin and upregulating the expression of tubulins. The reduction in cell modulus may help cells to survive excessive mechanical loading that may occur in damaged or healing tendons.     

Micro-mechanical sensing platform for the characterization of the elastic properties of the ovum via uniaxial measurement

Stiffness is an important parameter in determining the physical properties of living tissue. Recently, considerable biomedical attention has centered on the mechanical properties of living tissues at the single cell level. In the present paper, the Young's modulus of zona pellucida of bovine ovum was calculated using Micro Tactile Sensor (MTS) fabricated using piezoelectric (PZT) material. The sensor consists of a needle-shaped 20-microm transduction point made using a micro-electrode puller and mounted on a micro-manipulator platform. Measurements were made under microscopic control, using a suction pipette to support the ovum in the same horizontal axis as the MTS. Young's modulus of ovum was found to be 25.3+/-7.94 kPa (n=28). This value was indirectly determined based on calibration curves relating change in resonance frequency (Deltaf(0)) of the sensor with tip displacement for gelatin at concentrations of 4%, 6%, and 8%. The regression equation between the rate of change in resonance frequency (versus sensor tip displacement), Deltaf(0)/x and Young's modulus is Deltaf(0)/x (Hz/microm)=0.2992 x Young's modulus (kPa)-1.0363. It is concluded that a reason that the stiffness of ovum measured in the present study is approximately six times larger than previously reported, may be due to the absence of large deformation present in of existing methodologies.     

Effect of freeze-drying and gamma irradiation on biomechanical properties of bovine pericardium

Freeze-drying and gamma irradiation are the techniques widely use in tissue banking for preservation and sterilization of tissue grafts respectively. However, the effect of these techniques on biomechanical properties of bovine pericardium is poorly known. A total of 300 strips of bovine pericardium each measured 4 cm × 1 cm were used in this study to evaluate the effect of freeze-drying on biomechanical properties of fresh bovine pericardium and the effect of gamma irradiation on biomechanical properties of freeze-dried bovine pericardium. The strips were divided into three equal groups, which consist of 100 strips each group. The three groups were fresh bovine pericardium, freeze-dried bovine pericardium and irradiated freeze-dried bovine pericardium. The biomechanical properties of the pericardial strips were measured by a computer controlled instron tensiometer while the strips thickness was measured by Mitutoyo thickness gauge. The results of the study revealed that freeze-drying has no significant (p > 0.05) effect on the tensile strength, Youngs modulus (stiffness) and elongation rate of fresh bovine pericardium. Irradiation with 25 kGy gamma rays caused significant decreased in the tensile strength, Youngs modulus and elongation rate of the freeze-dried pericardium. However, gamma irradiation has no significant effect on the thickness of freeze-dried bovine pericardium, while freeze-drying caused significant decreased in the thickness of the fresh bovine pericardium. The outcome of this study demonstrated that freeze-drying has no significant effect on the biomechanical properties of fresh bovine pericardium, and gamma irradiation caused significant effect on the biomechanical properties of freeze-dried bovine pericardium.     

A composites theory predicts the dependence of stiffness of cartilage culture tissues on collagen volume fraction.

The tensile stiffness of tissue grown from chondrocyte culture was both measured experimentally and predicted using a composites model theory relating tissue microstructure to macroscopic material stiffness. The tissue was altered by several treatment protocols to provide a wide range of collagen fibril volume fraction (0.015-0.15). The rate of change of tissue modulus with change in collagen volume fraction predicted by the theory was within 14% of the slope of the linear fit through the experimental data, without the use of fitting parameters for the theoretical value of the slope. Use of the model to simulate cytokine mediated tissue digestion suggests that the action of IL-1beta and retinoic acid is mainly removal of proteoglycans and some removal of collagen. The model also indicates that the matrix and collagen remaining in the tissue has the same elastic properties as the untreated tissue, and is not damaged due to the alteration. Young's modulus of the collagen fibrils is predicted to be 120 MPa, a value in the range of previous studies. This value is dependent mainly on the matrix modulus and collagen fibril volume fraction and not on Poisson's ratio of either matrix or fibril. Poisson's ratio of the tissue depends primarily on the Poisson's ratio of the matrix.     

原子力显微镜对人羊膜上皮细胞的观察

目的:在单细胞水平上分析人羊膜上皮细胞的超微结构及其机械性能(粘弹力、杨氏模量、硬度等),为进一步认识细胞结构与功能的关系奠定基础.方法:应用原子力显微镜(AFM)高分辨率、高灵敏度的特点,对人的羊膜上皮细胞进行观察.结果:人羊膜上皮细胞呈椭圆形,由原子力显微镜力位移曲线测量系统,可得粘弹力:1034.375±294.21 pN.硬度:1.1815±0.326mN/m,杨氏模量:16.44±4.67Kpa.结论:AFM能对人羊膜上皮细胞表面超微结构清晰地成像及提供更多更确切的表面信息及机械性能,从而增加对羊膜上皮细胞的认识.     

Estimation of cell Young's modulus of adherent cells probed by optical and magnetic tweezers: influence of cell thickness and bead immersion

A precise characterization of cell elastic properties is crucial for understanding the mechanisms by which cells sense mechanical stimuli and how these factors alter cellular functions. Optical and magnetic tweezers are micromanipulation techniques which are widely used for quantifying the stiffness of adherent cells from their response to an external force applied on a bead partially embedded within the cell cortex. However, the relationships between imposed external force and resulting bead translation or rotation obtained from these experimental techniques only characterize the apparent cell stiffness. Indeed, the value of the estimated apparent cell stiffness integrates the effect of different geometrical parameters, the most important being the bead embedding angle 2gamma, bead radius R, and cell height h. In this paper, a three-dimensional finite element analysis was used to compute the cell mechanical response to applied force in tweezer experiments and to explicit the correcting functions which have to be used in order to infer the intrinsic cell Young's modulus from the apparent elasticity modulus. Our analysis, performed for an extensive set of values of gamma, h, and R, shows that the most relevant parameters for computing the correcting functions are the embedding half angle gamma and the ratio h(u)/2R, where h(u) is the under bead cell thickness. This paper provides original analytical expressions of these correcting functions as well as the critical values of the cell thickness below which corrections of the apparent modulus are necessary to get an accurate value of cell Young's modulus. Moreover, considering these results and taking benefit of previous results obtained on the estimation of cell Young's modulus of adherent cells probed by magnetic twisting cytometry (MTC) (Ohayon, J., and Tracqui, P., 2005, Ann. Biomed. Eng., 33, pp. 131-141), we were able to clarify and to solve the still unexplained discrepancies reported between estimations of elasticity modulus performed on the same cell type and probed with MTC and optical tweezers (OT). More generally, this study may strengthen the applicability of optical and magnetic tweezers techniques by insuring a more precise estimation of the intrinsic cell Young's modulus (CYM).