Mechanical properties of trabecular bone. Dependency on strain rate.

The effect of strain rate (epsilon) and apparent density (rho) on stiffness (E), strength (sigma u), and ultimate strain (epsilon u) was studied in 60 human trabecular bone specimens from the proximal tibia. Testing was performed by uniaxial compression to 5% specimen strain. Six different strain rates were used: 0.0001, 0.001, 0.01, 0.1, 1, and 10 s-1. Apparent density ranged between 0.23 and 0.59 g cm-3. Linear and non-linear regression analyses using strength, stiffness and ultimate strain as dependent variables (Y) and strain rate and apparent density as independent variables were performed using the following models: Y = a rho b epsilon c, Y = rho b(a + c epsilon; Y = (a + b rho)epsilon c, Y = a rho 2 epsilon c, E = a rho 3 epsilon c. The variations of strength and stiffness were explained equally well by the linear and the power function relationship to strain rate. The exponent was 0.07 in the power function relationship between strength and strain rate and 0.05 between stiffness and strain rate. The variation of ultimate strain was explained best using a power function relationship to strain rate (exponent = 0.03). The variation of strength and stiffness was explained equally well by the linear, power function and quadratic relationship to apparent density. The cubic relationship between stiffness and apparent density showed a less good fit. Ultimate strain varied independently of apparent density.     

Mechanical properties of single hyaluronan molecules

Hyaluronan (HA) is a major component of the extracellular matrix. It plays an important role in the mechanical functions of the extracellular matrix and stabilization of cells. Currently, its mechanical properties have been investigated only at the gross level. In this study, the mechanical properties of single HA molecules were directly measured with an optical tweezer technique, yielding a persistence length of 4.5 +/- 1.2 nm. This information may help us to understand the mechanical roles in the extracellular matrix infrastructure, cell attachment, and to design tissue engineering and drug delivery systems where the mechanical functions of HA are essential.     

High strain rate compressive properties of bovine muscle tissue determined using a split Hopkinson bar apparatus

The polymeric split Hopkinson pressure bar (PSHPB) apparatus is introduced as a means for measuring the high strain rate (1,000-2,500 s(-1)) compressive properties of soft tissues. Issues related to specimen design are discussed, and protocols are presented for specimen preparation. Proposed specimen geometries were validated using high-speed photography. Stress-strain data were obtained for high strain rate compression of bovine muscle tissue to strains as high as 80%. The stress-strain curves were found to be strain rate-sensitive and concave upward, as is typical of soft tissues. Rigor had a significant impact on the material properties between 5 and 24 h post mortem, while at longer times, properties returned essentially to their pre-rigor values. This study presents some of the first published high rate properties of muscle tissue, data that are urgently for advanced modeling of the human body and for evaluation of safety systems for the human body.     

Mechanical properties of human mitral valve chordae tendineae: variation with size and strain rate.

A knowledge of the mechanical properties of valve tissue is a necessary prerequisite for a better understanding of valvular behavior and design of prosthetic heart valves. Elastic response of chordae tendineae under strain rates of 0.05 cm min(-1)(6.25% min(-1)) to 12.7 cm min(-1)(1600% min(-1)) were obtained by the application of an uniaxial tensile stress using an Instron machine. The chordae exhibited viscoelastic properties in that extensibility decreased with increasing strain rates. The approximate maximum physiological strain rate of the chordae was estimated from echocardiographic traces at the instant of valve closure, and a high value of 29 (S.D. equals 9) cm s(-1) (2000% s(-1)) was found. The breaking strain and stress were found to have values of 21.4 plus or minus 0.5% and 3.1 plus or minus 0.1 times 10(8) dyn cm(-2) respectively, and were independent of strain rates (1 dyn equals 10(-5) N). These values are typical of collagen fibers. The final modulus, before the proportional limit, was found to be about 10(9) dyn cm(-2), which is again typical of collagen fibers. In addition, smaller chordae exhibited less extensibility than the larger chordae. This behavior could be due to structural and functional differences and allows the more centrally inserted chordae to maintain an even valve surface during valve closure.     

Mechanical properties of bovine pia-arachnoid complex in shear

Traumatic brain injury (TBI) has become a major public health and socioeconomic problem that affects 1.5 million Americans annually. Finite element methods have been widely used to investigate TBI mechanisms. The pia-arachnoid complex (PAC) covering the brain plays an important role in the mechanical response of the brain during impact or inertial loading. Existing finite element brain models have tended to oversimplify the response of the PAC due to a lack of accurately defined material properties of this structure, possibly resulting in a loss of accuracy in the model predictions. The objectives of this study were to experimentally determine the material properties of the PAC under shear loading. Bovine PAC was selected in the current study in view of its availability and comparability with previous studies. Tangential shear tests were conducted at 0.8, 7.3, and 72 s(-1). The mean shear moduli were 11.73, 20.04, and 22.37 kPa at the three strain rates tested. The ultimate stress, at the three strain rates, was 9.21, 17.01, and 22.26 kPa, while the ultimate strain was 1.52, 1.58, and 1.81. Results from the current study provide essential information to properly model the PAC membrane, an important component in the skull/brain interface, in a computational model of the human/animal head. Such an improved representation of the in vivo skull/brain interface will enhance future studies investigating brain injury mechanisms under various loading conditions.     

Zonal and directional variations in tensile properties of bovine articular cartilage with special reference to strain rate variation

THE AIMS of this study were: (i) to investigate the variation in the tensile properties of articular cartilage with depth through cartilage thickness and fibre orientation; (ii) to determine the effect of strain rate on tensile properties of articular cartilage. MATERIALS AND METHOD: All experimental work was performed on cartilage specimens taken from two bovine knee joints. Osteochondral plugs 12 mm in diameter were harvested with a special reamer from the femur and the tibial plateaux of each knee. Slices (0.2 mm thick), of articular cartilage were cut from the plug with a microtome. The predominant orientation of the collagen fibres on the cartilage surface was determined using the pinpricking technique. Each specimen used for the tensile test was cut, so as to produce a dumbbell shape, with a gauge length of 6 mm. Uniaxial tensile tests were performed on each specimen in order to determine the tensile Young's modulus, and ultimate tensile strength (UTS). In this investigation, these tensile tests were carried out at different strain rate: 1, 20, 50 and 70%/sec. RESULTS: As regards the zonal properties, it was found that tensile stiffness was greater in the superficial layer than in deep layer. However, a few specimens from the deep layer displayed similar or greater stiffness compared to the superficial layer. With respect to the directional properties, the specimens oriented parallel to the predominant alignment of collagen, were stiffer than those, which were perpendicular to it in each layer. However, only the results regarding the deep layer can be considered statistically significant. In regard to the variation of modulus with the strain-rate, the results showed that there is no significant increase of the modulus with increasing strain rate from 20 to 50% per second. However, at 70% per second, articular cartilage stiffness considerably increased by up to one order of magnitude greater than that determined at lower strain rates in both the superficial and deep layer. Moreover, the UTS of cartilage specimens tested at 70% per second showed a significant rise, reaching values of four to five times that of those measured at 1, 20 or 50% per second. CONCLUSION: The steep increases in both the stiffness and ultimate tensile strength of cartilage at high strain rates point to the existence in cartilage of a mechanism for its protection from damage by stresses arising in trauma, which are usually applied at high rates. This mechanism needs to be elucidated. The reduced anisotropy found in the present study pointed out that collagen is likely to be less organized in bovine cartilage than in the human and therefore, a study of its ultra-structure would be appropriate.     

Tensile testing of rodlike trabeculae excised from bovine femoral bone

Individual trabeculae, rodlike in form, were excised from bovine femora and tested in tension to obtain stress-strain plots. Tensile grips were constructed to permit such small specimens to be tested and to avoid slippage during the test. Data were collected for 38 specimens. The results of these tests show that rodlike trabeculae obtained from the femora of young bovine animals have an average Young's modulus in tension of approximately 1 GPa. This value is an order of magnitude lower than the corresponding value for cortical bone in the diaphysis of the femur.     

Microtensile measurements of single trabeculae stiffness in human femur

In this paper, the authors perform microtensile tests of single trabeculae excised from a human femur head. One of the main issues of this work is to establish some experimental procedures for preparing and testing the specimens. The use of a well-characterized microtensile apparatus allows for a low intraspecimen dispersion of the measured stiffness. Tensile/compressive tests were chosen because they appear less sensitive to errors in the cross-sectional area measurements with respect to bending tests. By these considerations, some tensile/compressive tests of plate-like trabecular specimens have been carried out. Typical stiffness values are 74.2+/-0.7Nmm(-1) for tensile tests, and 58.9+/-0.6Nmm(-1) for compressive test. Another compressive test performed on a shorter specimen yielded a stiffness value of 148.3+/-5.3Nmm(-1). The maximum applied load was about 0.5N. Rough measurements of specimens sizes yielded a Young's modulus value ranging from 1.41 to 1.89GPa.     

Viscoelastic behaviour and failure of bovine cancellous bone under constant strain rate

A programme has been established to characterize the long-term behaviour of cancellous bone. Fresh bovine cancellous specimens of dimensions 10 x 10 x 10 mm3 and 10 x 40 x 3.6 mm3 were manufactured and used within the testing programme. Results published in the literature indicate that the long-term behaviour of cancellous bone is well described by a power law, which is a very similar response of typical polymers. So far, dynamic mechanical tests (DMA) in three-point bending, under frequencies between 0.01 and 100 Hz at room temperature, confirmed the published results in a qualitative way. Nevertheless, the measured dimensionless damping, tan delta, was slightly higher than the values reported in the literature for the compact bone. The relaxation curves were obtained from dynamic tests and confirmed that bone relaxation modulus can be described by a power law function of time. Tests under constant compression strain rate were performed at four different strain rates: 0.15/s, 0.015/s, 0.0015/s and 0.00015/s and strain rate dependent behaviour was observed. An average elastic bending modulus of 300 MPa was obtained.     

Strength gains in obese females are unaffected by moderate dietary restriction

This study examined the effects of dietary restriction on strength gains from whole body resistance training. Comparisons were made between diet-restricted (n = 12) and non-diet-restricted (n = 10) obese women (mean +/- SD, 36.7 +/- 7.0% fat) undergoing identical 8-week resistance training regimens. Diet-restricted subjects reduced their dietary intake by 4200 kJ/day and reduced body mass by 3.9 kg over 8 weeks. Ten-repetition maximum masses were compared between the groups on biweekly intervals. Results indicated no differences between the groups with respect to the rate or magnitude of strength gains for any of the eight exercises. Significant pre- to post-test increases in strength (p less than 0.05) were found for all eight exercises. The rate or magnitude of strength gains induced by resistance training does not appear to be affected by moderate dietary restrictions in obese females.     

Vasoconstrictor mechanisms in the cerebral circulation are unaffected by insulin resistance

Insulin-resistance (IR) impairs agonist-induced relaxation in cerebral arteries, but little is known about its effect on constrictor mechanisms. We examined the vascular responses of the basilar artery (BA) and its side branches in anesthetized Zucker lean (ZL) and IR Zucker obese (ZO) rats using a cranial window technique. Endothelin-1 (ET-1) constricted the BAs in both the ZL and ZO rats, but there was no significant difference between the two groups (ZL: 36 +/- 8%; ZO: 33 +/- 3% at 10(-8) M). Inhibition of the ET(A) receptors by BQ-123 slightly increased the diameters of the BAs, with no difference shown between the ZL (6 +/- 1%) and ZO (5 +/- 3%) rats. Expressions of the ET(A) receptors and ET-1 mRNA examined by immunoblot analysis and RT-PCR, respectively, were also similar in the ZL and ZO groups. Phorbol 12,13-dibutyrate (PDBu), an activator of protein kinase C (PKC), and the thromboxane A(2) (TxA(2)) mimetic U-46619 constricted the BAs, but similarly to ET-1, there was no significant difference between the ZL and ZO groups (10(-6) M PDBu: ZL: 33 +/- 2%; ZO: 32 +/- 4%; and 10(-7) M U-46619: ZL: 23 +/- 1%; ZO: 19 +/- 2%). Inhibition of Rho-kinase with Y-27632 induced dilation of the BAs, and these responses were also comparable in the ZL and ZO rats (ZL: 39 +/- 4%; ZO: 38 +/- 2% at 10(-5) M). In contrast, nitric oxide-dependent relaxation to bradykinin was significantly reduced in the ZO rats (10(-6) M: 10 +/- 3%) compared with ZLs (29 +/- 7%, P < 0.01). These findings indicate that vasoconstrictor responses of the BA mediated by ET-1, TxA(2), PKC, and Rho-kinase are not affected by IR.     

Analysis of caffeine action in single trabeculae of the frog heart

Effects of caffeine on contractile tension and on intracellular action and resting potentials were examined in single frog heart trabeculae suspended in a rapid perfusion chamber. Trabeculae from atria responded more readily than those from ventricles and were therefore studied in greater detail. Both the contracture and twitch responses, the one obtained at high (greater than or equal to 10mM), the other at low (less than or equal to 10mM) caffeine concentrations, consisted of a transient tension rise followed by a maintained phase of lower, but still enhanced, tension. The hypothesis was tested that the transient response is due to the release of calcium from the sarcoplasmic reticulum (s.r.) whereas the maintained tension results from enhanced calcium influx through the cell surface. Support for these ideas was obtained by examining the response to step changes of external calcium and caffeine concentrations, applied in various combinations, simultaneously and in sequence. It also emerged tht the effects on twitch tension of calcium derived from (a) s.r. discharge and (b) influx are additive, to a first approximation. A test procedure for monitoring the s.r. store content was evolved to follow the accumulation of s.r. calcium after a preceding depletion. The results obtained, and others, suggest that the s.r. calcium pump can be operative in atrial heart cells and capable, after store depletion, of reabsorbing up to some 40% of calcium activating a twitch, the remainder being, presumably, extruded from the cells.     

Mechanical and failure properties of single attached cells under compression

Eukaryotic cells are continuously subjected to mechanical forces under normal physiological conditions. These forces and associated cellular deformations induce a variety of biological processes. The degree of deformation depends on the mechanical properties of the cell. As most cells are anchorage dependent for normal functioning, it is important to study the mechanical properties of cells in their attached configuration. The goal of the present study was to obtain the mechanical and failure properties of attached cells. Individual, attached C2C12 mouse myoblasts were subjected to unconfined compression experiments using a recently developed loading device. The device allows global compression of the cell until cell rupture and simultaneously measures the associated forces. Cell bursting was characterized by a typical reduction in the force, referred to as the bursting force. Mean bursting forces were calculated as 8.7+/-2.5 microN at an axial strain of 72+/-4%. Visualization of the cell using confocal microscopy revealed that cell bursting was preceded by the formation of bulges at the cell membrane, which eventually led to rupturing of the cell membrane. Finite element calculations were performed to simulate the obtained force-deformation curves. A finite element mesh was built for each cell to account for its specific geometrical features. Using an axisymmetric approximation of the cell geometry, and a Neo-Hookean constitutive model, excellent agreement between predicted and measured force-deformation curves was obtained, yielding an average Young's modulus of 1.14+/-0.32 kPa.     

Mechanical properties of single living cells encapsulated in polyelectrolyte matrixes

We have studied the mechanical properties of encapsulated Saccharomyces cerevisiae yeast cells by performing AFM force measurements. Single living cells have been coated through the alternate deposition of oppositely charged polyelectrolyte layers and mechanically trapped into a porous membrane. Coated and uncoated cells in presence/absence of bud scars, i.e. scars resulting from previous budding events, have been investigated. No significant differences between encapsulated and bare cells could be inferred from AFM topographs. On the other hand, investigation on the system elasticity through the acquisition and analysis of force curves allowed us to put in evidence the differences in the mechanical properties between the hybrid cell/polyelectrolyte system and the uncoated cells. Analysis of the curves contact region indicates that the polyelectrolyte coating increases the system rigidity. Quantitative evaluation of the cell rigidity through the Hertz-Sneddon model showed that coated cells are characterized by a Young's modulus higher than the value obtained for uncoated cells and similar to the value observed on the bud scar region of uncoated cells.     

Mechanical properties of mitral allografts are not reasonably influenced by cryopreservation in sheep model

A mitral allograft is used exceptionally in the mitral, as well as in the tricuspid position, mostly as an experimental surgical procedure. The authors decided to evaluate the possibility of inserting a cryopreserved mitral allograft into the tricuspid position in a sheep experimental model. Within the framework of this experimental project the mechanical properties of the cryopreserved mitral allograft were tested. A novel methodology studying the functional unit composed of mitral annulus, leaflet, chordae tendinaea, and papillary muscle is presented. A five-parameter Maxwell model was applied to characterize the viscoelastic behavior of sheep mitral valves. A control group of 39 fresh mitral specimens and a test group of 13 cryopreserved mitral allografts from tissue bank were tested. The testing protocol consisted of six loading cycles with 1 mm elongation every 5 min. There was no significant difference in the mean values of the determined parameters (p>0.05) which confirms the main hypothesis that cryopreservation does not influence significantly material parameters characterizing the tissue mechanics. Slight discrepancy is observed in variances of viscous parameters suggesting that the values of the test group may be spread over larger interval due to the treatment.     

Myocardial function defined by strain rate and strain during alterations in inotropic states and heart rate

For porcine myocardium, ultrasonic regional deformation parameters, systolic strain (epsilon(sys)) and peak systolic strain rate (SR(sys)), were compared with stroke volume (SV) and contractility [contractility index (CI)] measured as the ratio of end-systolic strain to end-systolic wall stress. Heart rate (HR) and contractility were varied by atrial pacing (AP = 120-180 beats/min, n = 7), incremental dobutamine infusion (DI = 2.5-20 microg. kg(-1). min(-1), n = 7), or continuous esmolol infusion (0.5 mg. kg(-1). min(-1)) + subsequent pacing (120-180 beats/min) (EI group, n = 6). Baseline SR(sys) and epsilon(sys) averaged 5.0 +/- 0.4 s(-1) and 60 +/- 4%. SR(sys) and CI increased linearly with DI (20 microg. kg(-1). min(-1); SR(sys) = 9.9 +/- 0.7 s(-1), P < 0.0001) and decreased with EI (SR(sys) = 3.4 +/- 0.1 s(-1), P < 0.01). During pacing, SR(sys) and CI remained unchanged in the AP and EI groups. During DI, epsilon(sys) and SV initially increased (5 microg. kg(-1). min(-1); epsilon(sys) = 77 +/- 6%, P < 0.01) and then progressively returned to baseline. During EI, SV and epsilon(sys) decreased (epsilon(sys) = 38 +/- 2%, P < 0.001). Pacing also decreased SV and epsilon(sys) in the AP (180 beats/min; epsilon(sys) = 36 +/- 2%, P < 0.001) and EI groups (180 beats/min; epsilon(sys) = 25 +/- 3%, P < 0.001). Thus, for normal myocardium, SR(sys) reflects regional contractile function (being relatively independent of HR), whereas epsilon(sys) reflects changes in SV.