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.     

Mechanical properties and chemical composition of avian long bones

We have studied the mechanical behaviour of avian long bones as whole structures, by calculating mechanical parameters such as maximum load, stiffness, bending strength and flexural Young's modulus; bones were always tested in three-point bending. Furthermore composition in several chemical elements and amino acids related to collagen content was also analysed. Correlations were established between body mass, mechanical parameters and chemical contents. Both bending strength and Young's modulus were negatively correlated to body mass. Significant correlations were found between nitrogen content and both strength and Young's modulus, with negative slopes in both cases. Magnesium and phosphorus appear to be the most important inorganic elements to the understanding of the mechanical behaviour of avian long bones.     

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.     

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.     

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.     

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.     

The Use of Free Vibrations to Measure Peduncle Stiffness in Triticale

The possibility of using the period of free vibrations to determineelastic modulus and flexural rigidity of plant material withcontrasting elasticity to viscosity ratios was tested. A simple,easy-to-operate method is described. Both the mature sectionsof Triticale peduncle as well as those sampled from the meristematiczone were found to behave like a lightly damped linear oscillator,providing that the excitements were of a very small amplitude.Elastic modulus calculated from the period of free vibrationsfor the meristematic zone was consistent with most data reportedin the literature for other growing tissues investigated bythe resonance technique. A high gradient of elastic modulus,from 33 MPa to 2·89 GPa per 8 cm was found within thezone of differentiation and development of strengthening tissues.The applicability of the free vibration technique to study plantrigidity as compared to other methods is discussed. Key words: Triticosecale, free vibrations, peduncle, stiffness measurement, Young's modulus     

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.     

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.     

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.     

Bicarbonate,the most important factor inducing iron chlorosis in vine grapes on calcareous soil

Summary In pot experiments grape vine was grown on a calcareous and on a non calcareous soil with a low and with a high water saturation. During the growing period soil solution samples were collected and analyzed for their pH and for HCO ₃ ⁻ , phosphate, Fe, and Ca. High water saturation resulted in a pH increase and in an increase of the HCO ₃ ⁻ concentration in both soils. The level in pH and HCO ₃ ⁻ , however, was much higher in the calcareous soil than in the non calcareous soil. The Fe concentration varied much throughout the experimental period, but there was no major differences between soils and water saturation treatments. The Ca concentration of the soil solution increased with time in the calcareous soil; for the non calcareous soil rather the reverse was true. The phosphate level in the soil solution of the non calcareous soil was about 10 times higher than in the calcareous soil. After 3 weeks growth all plants of the calcareous soil with the high water saturation showed first symptoms of Fe deficiency. These became more intense from day to day. Plants of the other treatments did not show any chlorotic symptoms. In the treatment with the chlorotic plants the HCO ₃ ⁻ concentration of the soil solution was the highest, the phosphate concentration the lowest from all treatments. It is therefore concluded that HCO ₃ ⁻ and not phosphate is the primary cause for lime induced Fe chlorosis. Despite the low phosphate concentration in the soil solution, the P concentration in the chlorotic leaves was more than twice as high as the P concentration in green leaves grown on the same soil. It is thus assumed that the high P content frequently found in chlorotic leaves is the result and not the cause for Fe chlorosis.     

Translocation of aquaporin-containing vesicles to the plasma membrane is facilitated by actomyosin relaxation

Docking and fusion of vesicles to the plasma membrane is a fundamental process in living cells. An established model for the trafficking of vesicles is based on primary epithelial cells from the collecting duct of the nephron. Upon stimulation with the signaling peptide arginine-vasopressin (AVP), aquaporin-containing vesicles are directed to the plasma membrane. Since aquaporin selectively enhances the water permeability of plasma membranes, this process helps to balance the water content of the organism. A mechanism has been suggested involving local depolymerization of F-actin to facilitate the movement of vesicles to the membrane. Since F-actin is the major component of cytoskeletal restoring forces, AVP-stimulated cells can be expected to lose rigidity. Here, we used atomic force microscopy force mapping to test whether AVP alters cell stiffness. The Young's modulus of living epithelial cells at 37°C was continuously monitored, yielding a 51% decrease of Young's modulus after the addition of AVP. The data demonstrate that not the depolymerization of actin but a relaxation of actomyosin interaction facilitates vesicle translocation.     

Influence of 90-day simulated microgravity on human tendon mechanical properties and the effect of resistive countermeasures.

While microgravity exposure is known to cause deterioration of skeletal muscle performance, little is known regarding its effect on tendon structure and function. Hence, the aims of this study were to investigate the effects of simulated microgravity on the mechanical properties of human tendon and to assess the effectiveness of resistive countermeasures in preventing any detrimental effects. Eighteen men (aged 25-45 yr) underwent 90 days of bed rest: nine performed resistive exercise during this period (BREx group), and nine underwent bed rest only (BR group). Calf-raise and leg-press exercises were performed every third day using a gravity-independent flywheel device. Isometric plantar flexion contractions were performed by using a custom-built dynamometer, and ultrasound imaging was used to determine the tensile deformation of the gastrocnemius tendon during contraction. In the BR group, tendon stiffness estimated from the gradient of the tendon force-deformation relation decreased by 58% (preintervention: 124 +/- 67 N/mm; postintervention: 52 +/- 28 N/mm; P < 0.01), and the tendon Young's modulus decreased by 57% postintervention (P < 0.01). In the BREx group, tendon stiffness decreased by 37% (preintervention: 136 +/- 66 N/mm; postintervention: 86 +/- 47 N/mm; P < 0.01), and the tendon Young's modulus decreased by 38% postintervention (P < 0.01). The relative decline in tendon stiffness and Young's modulus was significantly (P < 0.01) greater in the BR group compared with the BREx group. Unloading decreased gastrocnemius tendon stiffness due to a change in tendon material properties, and, although the exercise countermeasures did attenuate these effects, they did not completely prevent them. It is suggested that the total loading volume was not sufficient to completely prevent alterations in tendon mechanical properties.     

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.     

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.     

Modelling the mechanical properties of single suspension-cultured tomato cells

BACKGROUND AND AIMS: The relationship between composition and structure of plant primary cell walls, and cell mechanical properties is not fully understood, partly because intrinsic properties of walls such as Young's modulus cannot be obtained readily. The aim of this work is to show that Young's modulus of walls of single suspension-cultured tomato cells can be determined by modelling force-deformation data. METHODS: The model simulates the compression of a cell between two flat surfaces, with the cell treated as a liquid-filled sphere with thin compressible walls. The cell wall and membrane were taken to be permeable, but the compression was so fast that water loss could be neglected in the simulations. Force-deformation data were obtained by compressing the cells in micromanipulation experiments. RESULTS:Good fits were obtained between the model and low-strain experimental data, using the modulus and initial inflation of the cell as adjustable parameters. The mean Young's modulus for 2-week-old cells was found to be 2.3 +/- 0.2 GPa at pH 5. This corresponds to an instantaneous bulk modulus of elasticity of approx. 7 MPa, similar to a value found by the pressure probe method. However, Young's modulus is a better parameter, as it should depend only on the composition and structure of the cell wall, not on bulk cell behaviour. This new method has been used to show that Young's modulus of cultured tomato cell walls is at its lowest at pH 4.5, the pH optimum for expansin activity. CONCLUSIONS:The linear elastic model is very suitable for estimating wall Young's modulus from micromanipulation experiments on single tomato cells. This is a powerful method for determining cell wall material properties.     

Synthesis, characterization, and in vitro degradation of a biodegradable photo-cross-linked film from liquid poly(epsilon-caprolactone-co-lactide-co-glycolide) diacrylate

There has been little study on the effect of composition or molecular weight on the biodegradation rate of photo-cross-linked biodegradable aliphatic polyesters though such information is important for tissue engineering scaffolds. We have synthesized a new series of photopolymerizable linear poly(epsilon-caprolactone-co-lactide-co-glycolide) diacrylates with different molecular weights (Mn = 1800, 4800, and 9300 Da) and compositions (20%, 40%, and 60% epsilon-CL) and studied their biodegradation rates. The resultant oligomers were amorphous and appeared as viscous liquids at room temperature. Liquid-to-solid polymerization was carried out by UV irradiation in the presence of a photoinitiator. The photocuring yield was high (greater than 95%), and the photo-cross-linked polymers were amorphous and rubbery. Mechanical measurements showed that the polymers can be stretchable or rigid; the high molecular weight/low epsilon-CL network has a strain of 176% and a modulus of 1.66 MPa while the low molecular weight/high epsilon-CL network has a strain of 21% and a modulus of 12.3 MPa. In a 10 week in vitro biodegradation study, the polymers exhibited a two-stage degradation behavior. In the first stage, the polymer weight and strain remained almost constant, but a linear decrease in the Young's modulus (E) and ultimate stress (sigma) were observed. Lower oligomer molecular weight or epsilon-CL content correlated with a faster decrease in Young's modulus. In the second stage, which began when the Young's modulus dropped below 1 MPa, there was rapid weight loss and strain increase. The lower the epsilon-CL content, the earlier the second stage happened. Low molecular weight and high epsilon-CL content correlated with a longer modulus half-life (time for the modulus to degrade to 50% of its initial value). The degradation results suggest principles that may be helpful in predicting the biodegradation behavior of similar polymeric cross-linked networks. Films formed from these new polymers have excellent biocompatibility with smooth muscle cells.     

An AFM study on mechanical properties of native and dimethyl suberimidate cross-linked pericardium tissue

Changes in the stiffness of hog pericardium tissue, native and treated with dimethyl suberimidate (DMS), are investigated by atomic force microscopy (AFM). Young's modulus is calculated on the basis of the Hertz-Sneddon model. The cross-linking process increases the stiffness of the tissue. The values of Young's modulus are higher for the DMS stabilized pericardium than for the native one. We also observe that the Young's modulus of native tissue increases when the time between getting the biological material and performing the measurements is longer. This process is probably connected with natural degradation of the biological samples.     

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.