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PubMed2006

Deformation and nano-rheology of red blood cells: an AFM investigation.

Interaction forces, deformation and nano-rheology of individual red blood cells in physiologically relevant solution conditions have been determined by colloid probe atomic force microscopy (AFM). On approach of the physically immobilised cell and silica glass spherical probe surfaces, deformation of the red blood cell was observed in the force curves. At low levels of deformation, spring constants were determined in the range 3-6 m Nm(-1), whereas for higher levels of deformation, the forces increase non-linearly and on retraction, significant force curve hysteresis is observed (i.e. lower forces upon retraction). The extent of force curve hysteresis was dependent on both the drive velocity and loading force, typical of a viscoelastic system. The response of the red blood cell has been described by viscoelastic theory, where the short and long time scale elastic moduli and relaxation times are determined, i.e. the cell's nano-rheological properties elucidated. In addition to a time independent elastic modulus of 4.0 x 10(3)Nm(-2) at low levels of deformation, time-dependent elastic moduli ranges are observed (3.5 x 10(4) to 5.5 x 10(4)Nm(-2) at intermediate levels of deformation and 1.5 x 10(5) to 3.0 x 10(5)Nm(-2) at higher levels of deformation). That is, one elastic and more than one viscoelastic response to the red blood cell deformation is evident, which is considered to reflect the cellular structure.

Cells, Immobilized↗
PubMed2000

Assembly of type I collagen: fusion of fibril subunits and the influence of fibril diameter on mechanical properties.

Structural stability of the extracellular matrix is primarily a consequence of fibrillar collagen and the extent of cross-linking. The relationship between collagen self-assembly, consequent fibrillar shape and mechanical properties remains unclear. Our laboratory developed a model system for the preparation of self-assembled type I collagen fibers with fibrillar substructure mimicking the hierarchical structures of tendon. The present study evaluates the effects of pH and temperature during self-assembly on fibrillar structure, and relates the structural effects of these treatments on the uniaxial tensile mechanical properties of self-assembled collagen fibers. Results of the analysis of fibril diameter distributions and mechanical properties of the fibers formed under the different incubation conditions indicate that fibril diameters grow via the lateral fusion of discrete approximately 4 nm subunits, and that fibril diameter correlates positively with the low strain modulus. Fibril diameter did not correlate with either the ultimate tensile strength or the high strain elastic modulus, which suggests that lateral aggregation and consequently fibril diameter influences mechanical properties during small strain mechanical deformation. We hypothesize that self-assembly is mediated by the formation of fibrillar subunits that laterally and linearly fuse resulting in fibrillar growth. Lateral fusion appears important in generating resistance to deformation at low strain, while linear fusion leading to longer fibrils appears important in the ultimate mechanical properties at high strain.

Animals↗
PubMed1988

Thixotropy: the effect of stretch size in relaxed frog muscle.

Small forces were applied to isolated frog muscle; the resulting displacements were used to calculate muscle stiffness (elastic modulus, E). Stiffness is much greater for small forces within the range of the Short Range Elastic Component (SREC; Hill, 1968). 'Stirring' the muscle greatly reduces the stiffness, but only when the applied force is small. Stiffness subsequently returns to its original level. This strongly suggests that muscle thixotropy (Lakie, Walsh & Wright, 1984) is a property of the SREC.

Animals↗
PubMed1996

Atomic force microscope measurements of the hardness and elasticity of peritubular and intertubular human dentin.

An atomic force microscope was used to measure the hardness and elasticity of fully-hydrated peritubular and intertubular human dentin. The standard silicon nitride AFM tip and silicon cantilever assembly were replaced with a diamond tip and stainless steel cantilever having significantly higher stiffness. Hardness was measured as the ratio of the applied force to the projected indentation area for indentations with depths from 10-20 nm. The sample stiffness was measured by imaging specimens in a force-modulated mode. Hardness values of 2.3 +/- 0.3 GPa and 0.5 +/- 0.1 GPa were measured for the peritubular and intertubular dentin, respectively. Stiffness imaging revealed that the elastic modulus of the peritubular dentin was spatially homogeneous; whereas, there was considerable spatial variation in the elasticity of the intertubular dentin. The atomic force microscope can be used to measure the mechanical properties of fully hydrated calcified tissues at the submicron level of spatial resolution, thus augmenting more traditional depth sensing probes.

Dentin↗
PubMed2005

Mechanical optimization of an arteriovenous malformation embolization material: a predictive model analysis.

Arteriovenous malformations (AVMs) pose a constant danger of hemorrhages, seizures, and headaches to patients; they also disrupt oxygen-rich blood flow entering capillaries of the brain. We have utilized a linear model to mechanically characterize and optimize a water-borne, reverse emulsion, self-reactive, in situ cross-linking material, which we propose clinical use as an embolization material. The material is formed by cross-linking various acrylate and thiol multifunctional precursors with NaOH supplemented PBS. We compared theoretical elastic modulus values to modulus values observed during compression testing to determine the cross-linking efficiency of the material. Empirically determined elastic moduli for various material compositions ranged from 0.76 to 2.26 MPa, with corresponding cross-link efficiencies averaging 55+/-4%. We predict a reduction in theoretical circumferential stress exerted on AVM vasculature from 4933 to 10.9 Pa after embolization with the optimal material configuration. Theoretical risk of AVM rupture, as defined by Hademenos et al., was reduced below 1.0% for extreme variations of vessel modulus, thickness, and blood pressure after embolization with the optimized material. We will be using this material configuration to embolize swine rete mirabile AVM models and further assess the clinical viability of this potential embolization material.

Acrylates↗
PubMed2003

Modelling primary and secondary growth processes in plants: a summary of the methodology and new data from an early lignophyte.

A mathematical method, based on polar coordinates that allow modelling of primary and secondary growth processes in stems of extant and fossil plants, is summarized and its potential is discussed in comparison with numerical methods using digitizing tablets or electronic image analysing systems. As an example, the modelling of tissue distribution in the internode of an extant sphenopsid (Equisetum hyemale) is presented. In the second half of the paper we present new data of a functional analysis of stem structure and biomechanics of the early lignophyte Tetraxylopteris schmidtii (Middle Devonian) using the polar coordinate method for modelling the tissue distribution in stems of different ontogenetic age. Calculations of the mechanical properties of the stems, based on the modelling of the tissue arrangement, indicate that there is no increase in structural bending modulus throughout the entire development of the plant. The oldest ontogenetic stage has a significantly smaller bending elastic modulus than the intermediate ontogenetic stage, a 'mechanical signal', which is not consistent with a self-supporting growth form. These results, and the ontogenetic variations of the contributions of different stem tissues to the flexural stiffness of the entire stem, are discussed in the evolutionary context of cambial secondary growth.

Biological Evolution↗
PubMed2005

Characterizing the viscoelastic properties of thin hydrogel-based constructs for tissue engineering applications.

We present a novel indentation method for characterizing the viscoelastic properties of alginate and agarose hydrogel based constructs, which are often used as a model system of soft biological tissues. A sensitive long working distance microscope was used for measuring the time-dependent deformation of the thin circular hydrogel membranes under a constant load. The deformation of the constructs was measured laterally. The elastic modulus as a function of time can be determined by a large deformation theory based on Mooney-Rivlin elasticity. A viscoelastic theory, Zener model, was applied to correlate the time-dependent deformation of the constructs with various gel concentrations, and the creep parameters can therefore be quantitatively estimated. The value of Young's modulus was shown to increase in proportion with gel concentration. This finding is consistent with other publications. Our results also showed the great capability of using the technique to measure gels with incorporated corneal stromal cells. This study demonstrates a novel and convenient technique to measure mechanical properties of hydrogel in a non-destructive, online and real-time fashion. Thus this novel technique can become a valuable tool for soft tissue engineering.

Biocompatible Materials↗
PubMed2006

Relationship between bone tissue strain and lattice strain of HAp crystals in bovine cortical bone under tensile loading.

Cortical bone is a composite material composed of hydroxyapatite (HAp) and collagen. As HAp is a crystalline structure, an X-ray diffraction method is available to measure the strain of HAp crystals. However, HAp crystals in bone tissue have been known to have the low degree of crystallization. Authors have proposed an X-ray diffraction method to measure the lattice strain of HAp crystals from the diffusive intensity profile due to low crystallinity. The precision of strain measurement was greatly improved by this method. In order to confirm the possibility of estimating the bone tissue strain with measurements of the strain of HAp crystals, this work investigates the relationship between bone tissue strain on a macroscopic scale and the lattice strain of HAp crystals on a microscopic scale. The X-ray diffraction experiments were performed under tensile loading. Strip bone specimens of 40x6x0.8mm in size were cut from the cortical region of a shaft of bovine femur. A stepwise tensile load was applied in the longitudinal direction of the specimen. By detecting the diffracted X-ray beam transmitted through the specimen, the lattice strain was directly measured in the loading direction. As a result, the lattice strain of HAp crystals showed lower value than the bone tissue strain measured by a strain gage. The bone tissue strain was described with the mean lattice strain of the HAp crystals and the elastic modulus.

Animals↗
PubMed1999

A probabilistic rule of mixtures for elastic moduli.

A novel approach is developed for mathematically modeling the variability observed in experimentally determined elastic moduli of longitudinally oriented fibrous tissues such as ligaments and tendons. The elastic modulus of these tissues is modeled with a rule of mixtures (ROM) where each parameter (fibril and matrix moduli and fibril volume fraction) is assumed to be an independent random variable. A joint density function formed from the independent densities results in a probabilistic ROM (pROM). This pROM is used to generate a distribution of moduli which agrees well with moduli determined from tests of rabbit medial collateral ligaments (Woo and Ohland, 1994, Unpublished experimental data as gift). Minimizing the error between the pROM and experimental distributions resulted in an integrated error of 9% for a constrained set of independent distribution parameters derived from the literature. This pROM thus incorporates microstructural observations (fibril and matrix moduli and fibril volume fraction) to partially explain the experimentally observed variability in a macroscopic property (tissue modulus).

Animals↗
PubMed2006

Metabolic control of elastic properties of the inner mitochondrial membrane.

A possible physical mechanism for inner mitochondrial membrane shape rearrangements is given. This analytical study shows that high transmembrane potential at the inner mitochondrial membrane brings about specific, substantial, and dynamic electrochemical contributions to lateral tension, bending rigidity constant, and elastic modulus of Gaussian curvature of the membrane. Changes in mitochondrial metabolism dramatically affect the magnitude of these elastic parameters but not necessarily that of proton-motive force. Metabolic-driven variation of mechanical properties of the inner mitochondrial membrane can promote the membrane remodeling between its principal geometric shapes and serve as a negative feedback in control of the oxidative phosphorylation.

Algorithms↗
PubMed2005

Opposite changes in carotid versus aortic stiffness during healthy human pregnancy.

Systemic arterial compliance has been known to increase during healthy pregnancy, whereas, recently, the carotid artery has been reported to stiffen. To clarify this controversy, we simultaneously measured aortic PWV (pulse wave velocity) and carotid artery elastic parameters in a cohort of pregnant women. Twelve normotensive pregnant women were studied longitudinally during the three trimesters of pregnancy (T1, T2 and T3 respectively) and 12 weeks PP (postpartum). Carotid artery diastolic diameter and pulsatile distension was measured by an echo-wall tracking method and carotid pulse pressure by applanation tonometry. Carotid strain, compliance, distensibility coefficient, stiffness index beta, Einc (incremental elastic modulus) and augmentation index were calculated. Aortic PWV was determined to estimate aortic distensibility. All carotid artery elastic parameters indicated significant stiffening from T1 to T3 (1.8+/-0.2 versus 2.9+/-0.3 mmHg for Einc), which was reversed after delivery (2.3+/-0.2 mmHg). Aortic PWV decreased during pregnancy (6.2+/-0.2 versus 5.4+/-0.2 m/s) and increased in the PP period (6.7+/-0.2 m/s). No correlation was found between changes in carotid artery elastic parameters and changes in aortic PWV either from T1 to T3 or from T3 to PP. The carotid artery exhibits regionally specific stiffening during pregnancy, which appears to represent a qualitatively different change in arterial elastic behaviour.

Adult↗
PubMed2000

Rigid and differential plasma crystal rotation induced by magnetic fields

Observations show that plasma crystals, suspended in the sheath of a radio-frequency discharge, rotate under the influence of a vertical magnetic field. Depending on the discharge conditions, two different cases are observed: a rigid-body rotation (all the particles move with a constant angular velocity) and sheared rotation (the angular velocity of particles has a radial distribution). When the discharge voltage is increased sufficiently, the particles may even reverse their direction of motion. A simple analytical model is used to explain qualitatively the mechanism of the observed particle motion and its dependence on the confining potential and discharge conditions. The model takes into account electrostatic, ion drag, neutral drag, and effective interparticle interaction forces. For the special case of rigid-body rotation, the confining potential is reconstructed. Using data for the radial dependence of particle rotation velocity, the shear stresses are estimated. The critical shear stress at which shear-induced melting occurs is used to roughly estimate the shear elastic modulus of the plasma crystal. The latter is also used to estimate the viscosity contribution due to elasticity in the plasma liquid. Further development is suggested in order to quantitatively implement these ideas.

Journal Article↗
PubMed2000

Leaf water relations and stomatal behavior of four allopatric Eucalyptus species planted in Mediterranean southwestern Australia.

In 1986, four allopatric Eucalyptus species (E. camaldulensis Dehnh, E. saligna Smith, E. leucoxylon F. Muell and E. platypus Hook.) were planted together in a 480-mm rainfall zone, in 8-m wide contour belts as part of a plan to minimize waterlogging and secondary salinization. Throughout 1997, 1998 and 1999, there was significant inter-specific variation in predawn leaf water potential (Psi(pd)); however, maximum stomatal conductance (g(sm)) only differed significantly between species in mid to late summer. Relationships between g(sm) and Psi(pd) were significant and showed that stomata of E. camaldulensis were significantly more sensitive to Psi(pd), and presumably soil water potential, than stomata of E. leucoxylon or E. platypus. When applied to the Psi(pd) data, these relationships predicted that g(sm), and by inference transpiration, varied much less between species than Psi(pd). Diurnal measurements throughout the season confirmed this prediction, and showed that E. camaldulensis and E. saligna avoided drought by gaining access to deeper water, whereas E. leucoxylon and E. platypus maintained greater g(sm) at a given water stress than E. camaldulensis or E. saligna. Osmotic potentials measured after rehydration and water release curves of the leaves indicated that different mechanisms accounted for the apparent drought tolerance of E. leucoxylon and E. platypus. In summer, E. leucoxylon reduced osmotic potential at full and zero turgor by similar amounts compared with winter. In summer, E. platypus had a significantly lower bulk elastic modulus and relative water content at turgor loss point than E. camaldulensis, E. saligna or E. leucoxylon. This elastic adjustment resulted in a larger difference between osmotic potential at full and zero turgor in summer than in winter. The inherently low osmotic potential in E. leucoxylon and elastic adjustment in E. platypus resulted in turgor loss at a similar and significantly lower water potential than in E. camaldulensis or E. saligna. These results have implications for species selection for planting to manage groundwater recharge in areas prone to waterlogging and secondary salinization.

Journal Article↗
PubMed1998

Increased compliance in diaphragm muscle of the cardiomyopathic Syrian hamster.

We investigated the hypothesis that diaphragm compliance was abnormal in cardiomyopathic Syrian hamsters (CSH), an experimental model of myopathy. The passive elastic properties of isolated diaphragm muscles were analyzed at both the muscle and sarcomere levels. We used the following passive exponential relationship between stress (sigma) and strain (epsilon): sigma = (Eo/beta) (ebetaepsilon - 1), where Eo is the initial elastic modulus and beta is the stiffness constant. Immunocytochemistry procedures were used to analyze the distribution of two key elastic components of muscle, extracellular collagen and intracellular titin elastic components, as well as the extracellular matrix glycoprotein laminin. Muscle and sarcomere values of beta were nearly twofold lower in CSH (8.7 +/- 1.9 and 8.3 +/- 1.4, respectively) than in control animals (19.7 +/- 1.7 and 16.8 +/- 2.1, respectively) (P < 0.01 for each). Compared with controls, Eo was higher in CSH. Sarcomere slack length was significantly longer in CSH than in control animals (2.1 +/- 0.1 vs. 1.9 +/- 0.1 micrometer, P < 0.05). The surface area of collagen I was significantly larger in CSH (17.4 +/- 1.8%) than in control animals (12.4 +/- 0.7%, P < 0.05). There was no change in the distribution of titin or laminin labelings between the groups. These results demonstrate increased diaphragm compliance in cardiomyopathic hamsters. The increase in CSH diaphragm compliance was observed despite an increase in the surface area of collagen and was not associated with an abnormal distribution of titin or laminin.

Animals↗
PubMed1998

Finite-element modeling of trabecular bone: comparison with mechanical testing and determination of tissue modulus.

We combined three techniques--mechanical testing, three-dimensional imaging, and finite-element modeling--to distinguish between the contributions of architecture and tissue modulus to mechanical function in human trabecular bone. The objectives of this study were 2-fold. The first was to assess the accuracy of micromechanical modeling of trabecular bone using high-contrast x-ray images of the trabecular architecture. The second was to combine finite-element calculations with mechanical testing to infer an average tissue modulus for the specimen. Specimens from five human L1 vertebrae were mechanically tested along the three anatomic axes. The specimens were then imaged by synchrotron x-ray tomography, and the elastic moduli of each specimen were calculated from the tomographic image by finite-element modeling. We found that 23-microm tomographic images resolved sufficient structural detail such that the calculated anisotropy in the elastic modulus was within the uncertainties of the experimental measurements in all cases. The tissue modulus of each specimen was then estimated by comparing the calculated mean stiffness of the specimen, averaged over the three anatomical directions, with the experimental measurement. The absolute values of the experimental elastic constants could be fitted, again within the uncertainties of the experimental measurements, by a single tissue modulus of 6.6 GPa, which was the average tissue modulus of the five specimens. These observations suggest that a combination of mechanical testing, three-dimensional imaging, and finite-element modeling might enable the physiological variations in tissue moduli to be determined as a function of age and gender.

Aged↗
PubMed1984

Cell poking. Determination of the elastic area compressibility modulus of the erythrocyte membrane.

Cell poking, a new method for measuring mechanical properties of single cells was used to determine the elastic area compressibility modulus of osmotically swollen human erythrocytes. With this method we determined the force required to indent cells attached to a glass coverslip (Petersen, N.O., W. B. McConnaughey , and E. L. Elson , 1982, Proc. Natl. Acad. Sci. USA, 79:5327. Forces on the order of one millidyne and indentations on the order of one micron were detected. An analysis of these data in terms of a simplified mechanical model yielded the elastic area compressibility modulus. This analysis used a variational approach to minimize the isothermal elastic potential energy density function given by E. A. Evans and R. Skalak (Mechanics and Thermodynamics of Biomembranes, 1980, CRC Press, Boca Raton , FL). Measurements on swollen erythrocytes gave a range of values, depending in part on the osmotic conditions, of 17.9 +/- 8.2 to 34.8 +/- 12.0 mdyn /micron for the elastic area compressibility modulus at 25 degrees C. Fractional area expansion greater than 2.6 +/- 0.8% produced rapid cell lysis. These values were not corrected for the reversible movement of water across the cell membrane in response to hydrostatic pressure gradients. Our results agree reasonably with those obtained by Evans et al. (Evans, E.A., R. Waugh , and L. Melnick , 1976, Biophys. J., 16:585-595.) using micropipette aspiration under similar conditions.

Elasticity↗
PubMed2006

Stress-dependent elasticity of composite actin networks as a model for cell behavior.

Networks of filamentous actin cross-linked with the actin-binding protein filamin A exhibit remarkable strain stiffening leading to an increase in differential elastic modulus by several orders of magnitude over the linear value. The variation of the frequency dependence of the differential elastic and loss moduli as a function of prestress is consistent with that observed in living cells, suggesting that cell elasticity is always measured in the nonlinear regime, and that prestress is an essential control parameter.

Actins↗