MECHANICAL BEHAVIOR OF PLANT TISSUES AS INFERRED FROM THE THEORY OF PRESSURIZED CELLULAR SOLIDS

The mechanical behavior of plant tissues and its dependency on tissue geometry and turgor pressure are analytically dealt with in terms of the theory of cellular solids. A cellular solid is any material whose matter is distributed in the form of beamlike struts or complete “cell” walls. Therefore, its relative density is less than one and typically less than 0.3. Relative density is the ratio of the density of the cellular solid to the density of its constitutive (“cell wall”) material. Relative density depends upon cell shape and the density of cell wall material. It largely influences the mechanical behavior of cellular solids. Additional important parameters to mechanical behavior are the elastic modulus of “cell walls” and the magnitude of internal “cell” pressure. Analyses indicate that two “stiffening” agents operate in natural cellular solids (plant tissues): 1) cell wall infrastructure and 2) the hydrostatic influence of the protoplasm within each cellular compartment. The elastic modulus measured from a living tissue sample is the consequence of both agents. Therefore, the mechanical properties of living tissues are dependent upon the magnitude of turgor pressure. High turgor pressure places cell walls into axial tension, reduces the magnitude of cell wall deformations under an applied stress, and hence increases the apparent elastic modulus of the tissue. In the absence of turgid protoplasts or in the case of dead tissues, the cell wall infrastructure will respond as a linear elastic, nonlinear elastic, or “densifying” material (under compression) dependent upon the magnitude of externally applied stress. Accordingly, it is proposed that no single tangent (elastic) modulus from a stress-strain curve of a plant tissue is sufficient to characterize the material properties of a sample. It is also suggested that when a modulus is calculated that it be referred to as the tissue composite modulus to distinguish it from the elastic modulus of a noncellular solid material.     

Determining the mechanical properties of yeast cell walls

The intrinsic cell wall mechanical properties of Baker's yeast (Saccharomyces cerevisiae) cells were determined. Force-deformation data from compression of individual cells up to failure were recorded, and these data were fitted by an analytical model to extract the elastic modulus of the cell wall and the initial stretch ratio of the cell. The cell wall was assumed to be homogeneous, isotropic, and incompressible. A linear elastic constitutive equation was assumed based on Hencky strains to accommodate the large stretches of the cell wall. Because of the high compression speed, water loss during compression could be assumed to be negligible. It was then possible to treat the initial stretch ratio and elastic modulus as adjustable parameters within the analytical model. As the experimental data fitted numerical simulations well up to the point of cell rupture, it was also possible to extract cell wall failure criteria. The mean cell wall properties for resuspended dried Baker's yeast were as follows: elastic modulus 185 ± 15 MPa, initial stretch ratio 1.039 ± 0.006, circumferential stress at failure 115 ± 5 MPa, circumferential strain at failure 0.46 ± 0.03, and strain energy per unit volume at failure 30 ± 3 MPa. Data on yeast cells obtained by this method and model should be useful in the design and optimization of cell disruption equipment for yeast cell processing.     

Loss of stability-a new model for stress relaxation in plant cell walls

This study addresses the mechanism of wall stress relaxation in growing plant cells. The current viscoelastic model of cell wall relaxation, which dates from the work of Preston, Cleland, Lockhart, and others in the 1960s, has serious shortcomings. It has been shown however that the theory of loss of stability (LOS) can be applied to materials in tension, leading to the conclusion that the relaxation of stresses in the walls of any pressure vessel is rigorously modeled using LOS. We propose that LOS also provides a more appropriate and versatile model of stress relaxation in growing plant cells. We argue that when treated as a manifestation of LOS, the regulation of cell turgor has a rigorous and demonstrable basis in the geometrical and physical properties of the cell wall and the cell's ability to import water. Thus plant cell growth can be regarded as an inherently self-limiting process, tunable by biochemical or structural means. Lastly, despite the current limitations of our model, we apply direct measurement of elastic modulus, wall thickness and cell radius obtained from cylindrical Chara corallina cells to generate an initial calculation of critical pressures in a hypothetical spherical cell with the same material properties.     

Cell wall elasticity: I. A critique of the bulk elastic modulus approach and an analysis using polymer elastic principles

The traditional bulk elastic modulus approach to plant cell pressure-volume relations is inconsistent with its definition. The relationship between the bulk modulus and Young's modulus that forms the basis of their usual application to cell pressure-volume properties is demonstrated to be physically meaningless. The bulk modulus describes stress/strain relations of solid, homogeneous bodies undergoing small deformations, whereas the plant cell is best described as a thin-shelled, fluid-filled structure with a polymer base. Because cell walls possess a polymer structure, an alternative method of mechanical analysis is presented using polymer elasticity principles. This initial study presents the groundwork of polymer mechanics as would be applied to cell walls and discusses how the matrix and microfibrillar network induce nonlinear stress/strain relationships in the cell wall in response to turgor pressure. In subsequent studies, these concepts will be expanded to include anisotropic expansion as regulated by the microfibrillar network.     

pH and expansin action on single suspension-cultured tomato (Lycopersicon esculentum) cells

The aim of this study was to measure key material properties of the cell walls of single suspension-cultured plant cells and relate these to cell-wall biochemistry. To this end, micromanipulation was used to compress single tomato cells between two flat surfaces until they ruptured, and force-deformation data were obtained. In addition to measuring the bursting force, we also determined the elastic (Young’s) modulus of the cell walls by matching low strain (≤20% deformation) experimental data with a cell compression model, assuming linear elastic cell walls. The walls were most elastic at pH 4.5, the pH optimum for expansin activity, with an elastic modulus of 2.0 ± 0.1 GPa. Following the addition of exogenous expansins, cell walls became more elastic at all pH values. Western blot analysis of proteins from walls of cultured cells revealed the presence of expansin epitopes, suggesting that the inherent pH dependence of elasticity and other compression phenomena is related to the presence of endogenous expansin proteins and their wall-loosening ability. Although strict application of the linear-elastic model could not be applied to large deformations—for example, up to cell bursting—because of irreversible behaviour, the deviation of the data from the model was generally small enough to allow estimation of the strain in the cell wall at failure. This strain was greater at pH 4.5 and when expansins were added to the suspension. The changes in elasticity are consistent with suggestions about the mode of expansin action. The estimated strains at failure are compatible with data on the failure of Acetobacter-derived cellulose–xyloglucan composites and proposed mechanisms of such failure. Through the measurement of cell-wall material properties using micromanipulation, it may be possible to understand more fully how cell-wall composition, structure and biochemistry lead to cell mechanical behaviour.     

On the sensitivity of wall stresses in diseased arteries to variable material properties

Accurate estimates of stress in an atherosclerotic lesion require knowledge of the material properties of its components (e.g., normal wall, fibrous plaque, calcified regions, lipid pools) that can only be approximated. This leads to considerable uncertainty in these computational predictions. A study was conducted to test the sensitivity of predicted levels of stress and strain to the parameter values of plaque used in finite element analysis. Results show that the stresses within the arterial wall, fibrous plaque, calcified plaque, and lipid pool have low sensitivities for variation in the elastic modulus. Even a +/- 50% variation in elastic modulus leads to less than a 10% change in stress at the site of rupture. Sensitivity to variations in elastic modulus is comparable between isotropic nonlinear, isotropic nonlinear with residual strains, and transversely isotropic linear models. Therefore, stress analysis may be used with confidence that uncertainty in the material properties generates relatively small errors in the prediction of wall stresses. Either isotropic nonlinear or anisotropic linear models provide useful estimates, however the predictions in regions of stress concentration (e.g., the site of rupture) are somewhat more sensitive to the specific model used, increasing by up to 30% from the isotropic nonlinear to orthotropic model in the present example. Changes resulting from the introduction of residual stresses are much smaller.     

Apparent Young's modulus of human radius using inverse finite-element method

The ability to assess the elastic and failure properties of cortical bone at the radial diaphysis has a clinical importance. A new generation of quantitative ultrasound (QUS) devices and peripheral quantitative computed tomography (p-QCT) has been developed to assess non-invasively bone material and structural properties at the distal radius. This anatomical site is characterized by a thin cortical thickness that complicates traditional mechanical testing methods on specimens. Until now, mechanical properties of cortical bone at distal radius (e.g., elastic modulus, yield stress and strain) remain rarely studied probably due to experimental difficulties. The present study introduces an inverse finite-element method strategy to measure the elastic modulus and yield properties of human cortical specimens of the radial diaphysis. Twenty millimeter-thick portions of diaphysis were cut from 40 human radii (ages 45-90) for biomechanical test. Subsequently the same portion was modeled in order to obtain a specimen-specific three dimensional finite-element model (3D-FEM). Longitudinal elastic constants at the apparent level and stress characterizations were performed by coupling mechanical parameters with isotropic linear-elastic simulations. The results indicated that the mean apparent Young's modulus for radial cortical bone was 16 GPa (SD 1.8) and the yield stress was 153 MPa (SD 33). Breaking load was 12,946 N (SD 3644), cortical thickness 2.9 mm (SD 0.6), structural effective strain at the yield (epsilon(y)=0.0097) and failure (epsilon(u)=0.0154) load were also calculated. The 3D-FEM strategy described here may help to investigate bone mechanical properties when some difficulties arise from machining mechanical sample.     

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.     

Measurement of the circumferential mechanical properties of the umbilical vein: experimental and numerical analyses

Coronary artery disease is responsible for almost 30% of all deaths worldwide. The saphenous vein and umbilical vein (UV) are the most common veins using for treatment as a coronary artery bypass graft (CABG). The mechanical properties of UV belonging to its long-term patency for CABG are very important. However, there is a lack of knowledge on the linear elastic and nonlinear hyperelastic mechanical properties of the UV. In this study, three stress definitions (second Piola–Kichhoff stress, engineering stress and true stress) and four strain definitions (Almansi–Hamel strain, Green–St Venant strain, engineering strain and true strain) are used to determine the elastic modulus, maximum stress and strain of eight human UVs under circumferential loading. The nonlinear mechanical behaviour of the UV is computationally investigated using Mooney–Rivlin hyperelastic model. A numerical finite element analysis is also carried out to simulate the constitutive modelling versus its numerical results. The results show that the Almansi–Hamel strain definition overestimates the elastic modulus while Green–St Venant strain definition underestimates the elastic modulus at different stress definitions. The true stress–true strain definition, which gives more accurate measurements of the tissue's response using the instantaneous values, reveals the Young's modulus and maximum stress of 2.18 and 6.01 MPa, respectively. The Mooney–Rivlin material model is well represented by the nonlinear mechanical behaviour of the UV. The findings of this study could have implications not only for understanding the extension and rupture mechanism of UV but also for interventions and surgeries, including balloon angioplasty, bypass and stenting.     

Material properties of the human lumbar facet joint capsule

The human facet joint capsule is one of the structures in the lumbar spine that constrains motions of vertebrae during global spine loading (e.g., physiological flexion). Computational models of the spine have not been able to include accurate nonlinear and viscoelastic material properties, as they have not previously been measured. Capsules were tested using a uniaxial ramp-hold protocol or a haversine displacement protocol using a commercially available materials testing device. Plane strain was measured optically. Capsules were tested both parallel and perpendicular to the dominant orientation of the collagen fibers in the capsules. Viscoelastic material properties were determined. Parallel to the dominant orientation of the collagen fibers, the complex modulus of elasticity was E*=1.63MPa, with a storage modulus of E'=1.25MPa and a loss modulus of: E" =0.39MPa. The mean stress relaxation rates for static and dynamic loading were best fit with first-order polynomials: B(epsilon) = 0.1110epsilon-0.0733 and B(epsilon)= -0.1249epsilon + 0.0190, respectively. Perpendicular to the collagen fiber orientation, the viscous and elastic secant moduli were 1.81 and 1.00 MPa, respectively. The mean stress relaxation rate for static loading was best fit with a first-order polynomial: B (epsilon) = -0.04epsilon - 0.06. Capsule strength parallel and perpendicular to collagen fiber orientation was 1.90 and 0.95 MPa, respectively, and extensibility was 0.65 and 0.60, respectively. Poisson's ratio parallel and perpendicular to fiber orientation was 0.299 and 0.488, respectively. The elasticity moduli were nonlinear and anisotropic, and capsule strength was larger aligned parallel to the collagen fibers. The phase lag between stress and strain increased with haversine frequency, but the storage modulus remained large relative to the complex modulus. The stress relaxation rate was strain dependent parallel to the collagen fibers, but was strain independent perpendicularly.     

Effect of osmolarity on the zero-stress state and mechanical properties of aorta

Some pathological conditions may affect osmolarity, which can impact cell, tissue, and organ volume. The hypothesis of this study is that changes in osmolarity affect the zero-stress state and mechanical properties of the aorta. To test this hypothesis, a segment of mouse abdominal aorta was cannulated in vivo and mechanically distended by perfusion of physiological salt (NaCl) solutions with graded osmolarities from 145 to 562 mosM. The mechanical (circumferential stress, strain, and elastic modulus) and morphological (wall thickness and wall area) parameters in the loaded state were determined. To determine the osmolarity-induced changes of zero-stress state, the opening angle was observed by immersion of the sectors of mouse, rat, and pig thoracic aorta in NaCl solution with different osmolarities. Wall volume and tissue water content of the rings were also recorded at different osmolarities. Our results show that acute aortic swelling due to low osmolarity leads to an increase in wall thickness and area, a change in the stress-strain relationship, and an increase in the elastic modulus (stiffness) in mouse aorta. The opening angle, wall volume, and water content decreased significantly with increase in osmolarity. These findings suggest that acute aortic swelling and shrinking result in immediate mechanical changes in the aorta. Osmotic pressure-induced changes in the zero-stress state may serve to regulate mechanical homeostasis.     

Mechanical Consequences of Cell-Wall Turnover in the Elongation of a Gram-Positive Bacterium

A common feature of walled organisms is their exposure to osmotic forces that challenge the mechanical integrity of cells while driving elongation. Most bacteria rely on their cell wall to bear osmotic stress and determine cell shape. Wall thickness can vary greatly among species, with Gram-positive bacteria having a thicker wall than Gram-negative bacteria. How wall dimensions and mechanical properties are regulated and how they affect growth have not yet been elucidated. To investigate the regulation of wall thickness in the rod-shaped Gram-positive bacterium Bacillus subtilis, we analyzed exponentially growing cells in different media. Using transmission electron and epifluorescence microscopy, we found that wall thickness and strain were maintained even between media that yielded a threefold change in growth rate. To probe mechanisms of elongation, we developed a biophysical model of the Gram-positive wall that balances the mechanical effects of synthesis of new material and removal of old material through hydrolysis. Our results suggest that cells can vary their growth rate without changing wall thickness or strain by maintaining a constant ratio of synthesis and hydrolysis rates. Our model also indicates that steady growth requires wall turnover on the same timescale as elongation, which can be driven primarily by hydrolysis rather than insertion. This perspective of turnover-driven elongation provides mechanistic insight into previous experiments involving mutants whose growth rate was accelerated by the addition of lysozyme or autolysin. Our approach provides a general framework for deconstructing shape maintenance in cells with thick walls by integrating wall mechanics with the kinetics and regulation of synthesis and turnover.     

Non-Linear Elasticity of Extracellular Matrices Enables Contractile Cells to Communicate Local Position and Orientation

Most tissue cells grown in sparse cultures on linearly elastic substrates typically display a small, round phenotype on soft substrates and become increasingly spread as the modulus of the substrate increases until their spread area reaches a maximum value. As cell density increases, individual cells retain the same stiffness-dependent differences unless they are very close or in molecular contact. On nonlinear strain-stiffening fibrin gels, the same cell types become maximally spread even when the low strain elastic modulus would predict a round morphology, and cells are influenced by the presence of neighbors hundreds of microns away. Time lapse microscopy reveals that fibroblasts and human mesenchymal stem cells on fibrin deform the substrate by several microns up to five cell lengths away from their plasma membrane through a force limited mechanism. Atomic force microscopy and rheology confirm that these strains locally and globally stiffen the gel, depending on cell density, and this effect leads to long distance cell-cell communication and alignment. Thus cells are acutely responsive to the nonlinear elasticity of their substrates and can manipulate this rheological property to induce patterning.     

Factors influencing left-ventricular stiffness

The aim of the study was to investigate the relative contributions of geometrical and material factors to overall left-ventricular cavity stiffness. Left-ventricular cavity shapes were reconstructed using a computer and the variation of myocardial elastic modulus was calculated, by the finite element method, through the passive phase of diastole when rising volume coincided with rising pressure. Geometric data were obtained from biplane cineangiography, with micromanometer pressure measurements, for ten patients with left ventricular disease. Dimensional analysis was applied to the initial and derived data from which the influences of myocardial compliance, wall thickness-to-long dimension ratio, and aspect ratio (long-to-short axes) were determined. The ratio between the volume elasticity and the myocardial modulus of elasticity, the normalized stiffness ratio (NSR), is proposed as a useful index of left ventricular mechanical behaviour in diastole. The volume elasticity of the chamber is dependent not only upon the myocardium elastic modulus and the wall thickness ratio, but also on the shape of the chambe. Changes in the thickness/radius ratio of the ventricle have less effect upon its distention than those in the long dimension/radius ratio. The left ventricle becomes more spherical in shpae through diastole and hence becomes stiffer by this geometric mechanism.     

Effects of elastic property of the wall on flow characteristics through arterial stenoses

Hemodynamic characteristics of blood flow through arterial stenoses are numerically investigated in this work. The blood is assumed as a Newtonian fluid and the pulsatile nature of flow is modeled by using measured values of the flowrate and pressure for the canine femoral artery. An isotropic elastic and incompressible material is assumed for the wall at each axial section, but a non-uniform distribution of the shear modulus in axial direction is used to model the high stiffness of the wall at the stenosis location. Full Navier equations for a thick wall are used as the governing equations for the wall displacements. A continuous grid extending over the flow field and the wall is considered and governing equations are transformed for use in the computational domain. Discretized forms of the transformed wall and flow equations, which are coupled through the boundary conditions at their interface, are obtained by control volume method and simultaneously solved using the well-known SIMPLER algorithm. To study the effects of wall deformability, solutions are obtained for both rigid and elastic walls. The results indicate that deformability of the wall causes an increase in the time average of pressure drop, but a decrease in the maximum wall shear stress. Displacement and stress distributions in the wall are presented.     

Effect of age on mechanical properties of rat mesenteric small arteries

With aging, large arteries become stiffer and systolic blood pressure consequently increases. Less is known, however, about the age-related change in mechanics of small resistance arteries. The aim of this study was to determine whether aging plays a role in the stiffening of the small mesenteric arteries of rats. Intra-arterial systolic, diastolic, mean and pulse pressures were measured in male Wistar rats aged 2, 4, 15 and 26 months. The passive mechanical properties of the wall of isolated perfused and pressurized arterial segments of mesenteric small arteries were also investigated. Intra-arterial systolic, diastolic and mean blood pressures tended to decrease with age and were significantly lower in the oldest rats (26-month-old group). Pulse pressure was significantly higher in the 15- and 26-month-old groups than in the two younger groups. Under isobaric conditions, increasing age is associated with an outward hypertrophic remodeling of the mesenteric arteries. Under relaxed conditions, incremental distensibility in response to increasing intravascular pressure did not change with aging. As a function of strain (under isometric conditions), stress shifted to the left as age increased, indicating an age-related vascular stiffening. Under isobaric conditions or in relation to wall stress, the elastic modulus was greater in the adult 15-month-old rats than in the younger rats. These findings suggest that distensibility seems to be preserved with aging, despite stiffness of the wall components, probably by arterial wall geometric adaptation, which limits the pulse pressure damage. It is interesting to note that elastic modulus in mesenteric arteries from the oldest rats (26-month-old), examined in relation to wall stress and intravascular pressure, did not differ from that of the youngest rats, thus suggesting that elasticity of wall components had been restored.     

The role of fabric in the large strain compressive behavior of human trabecular bone

Osteoporosis-related vertebral body fractures involve large compressive strains of trabecular bone. The small strain mechanical properties of the trabecular bone such as the elastic modulus or ultimate strength can be estimated using the volume fraction and a second order fabric tensor, but it remains unclear if similar estimations may be extended to large strain properties. Accordingly, the aim of this work is to identify the role of volume fraction and especially fabric in the large strain compressive behavior of human trabecular bone from various anatomical locations. Trabecular bone biopsies were extracted from human T12 vertebrae (n=31), distal radii (n=43), femoral head (n=44), and calcanei (n=30), scanned using microcomputed tomography to quantify bone volume fraction (BV/TV) and the fabric tensor (M), and tested either in unconfined or confined compression up to very large strains (～70%). The mechanical parameters of the resulting stress-strain curves were analyzed using regression models to examine the respective influence of BV/TV and fabric eigenvalues. The compressive stress-strain curves demonstrated linear elasticity, yielding with hardening up to an ultimate stress, softening toward a minimum stress, and a steady rehardening followed by a rapid densification. For the pooled experiments, the average minimum stress was 1.89 ± 1.77 MPa, while the corresponding mean strain was 7.15 ± 1.84%. The minimum stress showed a weaker dependence with fabric as the elastic modulus or ultimate strength. For the confined experiments, the stress at a logarithmic strain of 1.2 was 8.08 ± 7.91 MPa, and the dissipated energy density was 5.67 ± 4.42 MPa. The latter variable was strongly related to the volume fraction (R(2)=0.83) but the correlation improved only marginally with the inclusion of fabric (R(2)=0.84). The influence of fabric on the mechanical properties of human trabecular bone decreases with increasing strain, while the role of volume fraction remains important. In particular, the ratio of the minimum versus the maximum stress, i.e., the relative amount of softening, decreases strongly with fabric, while the dissipated energy density is dominated by the volume fraction. The collected results will prove to be useful for modeling the softening and densification of the trabecular bone using the finite element method.     

Assessment of the aortic stress-strain relation in uniaxial tension

The passive elastic characteristics of the abdominal aorta were investigated in two experimental animal models, aiming at assessing the stress-strain relation of the aortic wall. Twenty porcine and 15 rabbit healthy abdominal aortas were subjected to uniaxial stress-strain analysis, performed on a tensile-testing device, while immersed in a physiologic saline bath at body temperature. Measured parameters included original length, width and thickness, as well as axial force and extension. Based on these data, Kirchhoff stress and Green-St.Venant strain were computed and one-dimensional constitutive equations were defined, comprising of a power function and two exponential ones, in turn, for the low, physiologic and high-stress regions. The stress-strain curves were plotted as elastic modulus versus stress, displaying nonlinear part I and linear parts II and III. These were regressed, yielding parameters k, q (part I), a, b (part II) and c, d (part III). A detailed comparison of these constitutive parameters was undertaken between the two species, demonstrating variations in d (p<0.05). No statistical differences were found in parameters a, b, c, k and q, implying that the two aortas were equally stiff under low and physiologic stresses, whereas the porcine aorta was stiffer at higher stresses. In conclusion, a bi-exponential in addition to a power law was established, relating stress and strain in the aorta, which is advantageous in comparison with previous constitutive equations. Under passive conditions, the nonlinear nature of this constitutive law may account for the low, part I, physiologic, part II, and high-stress, part III of the stress-strain relationship, supporting the concept of the aortic wall as a biphasic material.     

The bulk elastic modulus and the reversible properties of cell walls in developing Quercus leaves

We examined the relationship between the bulk elastic modulus (epsilon) of an individual leaf obtained by the pressure-volume (P-V) technique and the mechanical properties of cell walls in the leaf. The plants used were Quercus glauca and Q. serrata, an evergreen and a deciduous broad-leaved tree species, respectively. We compared epsilon and Young's modulus of leaf specimens determined by the stretch technique at various stages of their leaf development. The results showed that epsilon increased from approximately 5 to 20 MPa during leaf development, although other potential determinants of epsilon such as the apoplastic water content in the leaf and the diameter of a palisade tissue cells remained almost constant. epsilon in these two species was similar at every developmental stages, although the apparent mechanical strength of the leaf lamina and thickness of mesophyll cell walls were greater in Q. glauca. There were significant linear relationships between Young's modulus and epsilon (P < 0.01; R (2) = 0.78 and 0.84 in Q. glauca and Q. serrata, respectively) with small y-intercepts. From these results, we conclude that epsilon is closely related to the reversible properties of the cell walls. From the estimation of epsilon based on a physical model, we suggest that the effective thickness of cell walls responsible for epsilon is smaller than the observed wall thickness.     

Adaptation of passive rat left ventricle in diastolic dysfunction.

This article deals with providing a theoretical explanation for quantitative changes in the geometry, the opening angle and the deformation parameters of the rat ventricular wall during adaptation of the passive left ventricle in diastolic dysfunction. A large deformation theory is applied to analyse transmural stress and strain distribution in the left ventricular wall considering it to be made of homogeneous, incompressible, transversely isotropic, non-linear elastic material. The basic assumptions made for computing stress distributions are that the average circumferential stress and strain for the adaptive ventricle is equal to the average circumferential stress and strain in the normotensive ventricle, respectively.All the relevant parameters, such as opening angle, twist per unit length, axial extension, internal and external radii and others, in the stress-free, unloaded and loaded states of normotensive, hypertensive and adaptive left ventricle are determined. The circumferential stress and strain distribution through the ventricular wall are also computed. Our analysis predicts that during adaptation, wall thickness and wall mass of the ventricle increase. These results are consistent with experimental findings and are the indications of initiation of congestive heart failure.