Modeling of stents exhibiting negative Poisson's ratio effect

Intravascular stents are metallic scaffolding structures deployed in the stenotic arteries to restore the lumen for the blood flow to the down stream tissues. Most stents are balloon expandable and are deployed from its crimped state through a balloon catheter. The efficacy of the stenting procedure mainly depends on the way the stent is deployed. Both numerical and experimental evaluations show that almost all the present day stents undergo the most undesirable effects namely: (i) longitudinal foreshortening: the axial contraction in the length, and (ii) dogboning: flaring of the distal edges, during the radial expansion of the stents. Due to the foreshortening effect, clinicians are forced to select stents longer than the plaque. Still, the final length of the stent depends on the amount of radial expansion, which is subjective during the procedure. This paper introduces a new stent model called "Murugan", which exhibits negative Poisson's ratio effect. That is, the stent may have zero axial contraction or can have extension when under radial expansion. The presence of hyperelastic balloon and the stent-balloon friction is also considered to study their effects in mechanical properties of the stents under consideration. Free expansion analysis is done using finite element method (FEM) to compare the new stent model with the present day stent geometries.     

Anisotropic Poisson's ratio and compression modulus of cortical bone determined by speckle interferometry

Young's modulus and Poisson's ratios of 6mm-sized cubes of equine cortical bone were measured in compression using a micro-mechanical loading device. Surface displacements were determined by electronic speckle pattern-correlation interferometry. This method allows for non-destructive testing of very small samples in water. Analyses of standard materials showed that the method is accurate and precise for determining both Young's modulus and Poisson's ratio. Material properties were determined concurrently in three orthogonal anatomic directions (axial, radial and transverse). Young's modulus values were found to be anisotropic and consistent with values of equine cortical bone reported in the literature. Poisson's ratios were also found to be anisotropic, but lower than those previously reported. Poisson's ratios for the radial-transverse and transverse-radial directions were 0.15+/-0.02, for the axial-transverse and axial-radial directions 0.19+/-0.04, and for the transverse-axial and radial-axial direction 0.09+/-0.02 (mean+/-SD). Cubes located only millimetres apart had significantly different elastic properties, showing that significant spatial variation occurs in equine cortical bone.     

Contact stress transients during functional loading of ankle stepoff incongruities

Cartilage deformation demonstrates viscoelastic behavior due to its unique structure. However, nearly all contact studies investigating incongruity-associated changes in cartilage surface stresses have been static tests. These tests have consistently measured only modest increases in contact stresses, even with large incongruities. In this study, an experimental approach measuring real-time contact stresses in human cadaveric ankles during quasi-physiologic motion and loading was used to determine how stepoff incongruities of the distal tibia affected contact stresses and contact stress gradients. Peak instantaneous contact stresses, in ankles with stepoffs between 1.0 and 4.0mm of the anterolateral articular surface, increased by between 2.3 x and 3.0 x compared to the corresponding intact ankle values. Peak instantaneous contact stress gradients in stepoff configurations increased by between 1.9 x and 2.6 x the corresponding intact configuration values. Anatomic reduction of the displaced fragment restored intact contact stresses and contact stress gradients. Intact and anatomic configurations demonstrated a heterogeneous population of low-magnitude, randomly oriented contact stress gradient vectors in contrast to high-magnitude, preferentially oriented gradients in stepoff configurations. Peak instantaneous contact stresses may be important pathomechanical determinants of post-traumatic arthritis. Abnormal contact stress gradients could cause regional pathological disturbances in cartilage stress and interstitial fluid distribution. Measuring contact stresses and contact stress gradients during motion allowed potential incongruity-associated pathologic changes in loading that occur over the complete motion cycle to be investigated.     

Direct measurement of the Poisson's ratio of human patella cartilage in tension

Articular cartilage has been shown to exhibit large transverse contractions when loaded in tension, suggesting the existence of large values for the Poisson's ratio. Previous studies have suggested that this effect is dependent on amplitude of applied strain, so that a single Poisson's ratio may not be sufficient to describe cartilage behavior. In this study, the Poisson's ratio (v), toe region modulus (Eo), and linear region modulus (E) of human patellar articular cartilage were calculated in simple tension tests from optical analysis of the two-dimensional strain fields at equilibrium. The Poisson's ratio was found to be independent of strain due to the absence of viscoelastic effects during testing. The Poisson's ratio was found to be significantly higher in the surface zone (1.87 +/- 1.11, p<0.01) than in the middle zone (0.62 +/- 0.23), with no significant correlation of v with age of the cartilage. In general, values for Poisson's ratio were greater than 0.5, suggesting cartilage behavior in tension deviates from isotropy. Reported values for the Poisson's ratio of cartilage in compression have been much lower than values measured here in tension, reflecting a mechanical contribution of the collagen fibers to anisotropy in tension but not compression. The toe-region modulus (Eo) was significantly higher in the surface zone (4.51 +/- 2.78 MPa, n=8) compared to the middle zone (2.51 +/- 1.93 MPa, n=10). In addition, the linear-region modulus (E) in the surface zone, but not middle zone (3.42 +/- 2.17 MPa, n=10), was found to correlate with age (R=0.97, p<0.02) with values of surface zone E equal to 23.92 +/- 12.29 MPa (n=5) for subjects under 70 yr of age, and 4.27 +/- 2.89 MPa (n=3) for subjects over 70 yr. Moduli values and trends with depth were consistent with previous studies of human and animal cartilage. From direct measures of two independent material properties, v and E, we calculated a shear modulus, G, which had not been previously reported for cartilage from tensile testing. Calculated values for surface zone G were 3.64 +/- 1.80 MPa for subjects under 70 yr old and 0.96 +/- 0.69 MPa for subjects over 70 yr old, and were significantly higher in the surface zone than in the middle zone (1.10 +/- 0.78 MPa). This study provides an intrinsic measure for the Poisson's ratio of articular cartilage and its dependence on depth which will be important in understanding the nonlinear tension-compression and anisotropic behaviors of articular cartilage.     

The role of tenascin-C in adaptation of tendons to compressive loading

Although most tendon regions are subjected primarily to high tensile loads, selected regions, primarily those that directly contact bones that change the direction of the tendon, must withstand high compressive loads as well. Compressed tendon regions differ from regions subjected to primarily tensile loads: they have a fibrocartilaginous structure with spherical cells surrounded by a matrix containing aggrecan and collagen types I and II, in contrast regions not exposed to compression have a fibrous structure with spindle shaped fibroblasts surrounded by a matrix of dense, longitudinally oriented type I collagen fibrils. The spherical shape of cells in fibrocartilagenous regions indicates these cells are more loosely attached to the matrix than their spindle-shaped counterparts in fibrous regions, a feature that may help to minimize cell deformation during tendon compression. We hypothesized that expression of tenascin-C, an anti-adhesive protein, is part of the adaptation of tendon cells to compression that helps establish and maintain fibrocartilaginous regions. To test this hypothesis we compared tenascin-C content and expression in compressed (distal) versus uncompressed (proximal) segments of bovine flexor tendons. Immunohistochemistry and immunoblot analyses showed that tenascin-C content was increased in the distal tendon where it co-distributed with type II collagen and aggrecan. Tendon cells from the distal segments expressed more tenascin-C than did cells from the proximal segments for up to four days in cell culture, indicating that increased tenascin-C expression is a relatively stable feature of the distal cells. These observations support the hypothesis that tenascin-C expression is a cellular adaptation to compression that helps establish and maintain fibrocartilagenous regions of tendons.     

An extended relationship for the characterization of Young's modulus and Poisson's ratio of tunable polyacrylamide gels

Substrates with tunable mechanical properties are crucial for the study of cellular processes, and polyacrylamide gels (PAGs) are frequently used in this context. Several experimental techniques have been proposed to obtain the mechanical properties of PAGs. However, the range of the considered Poisson's ratio values remains quite large and no attempt has been made to propose an analytical relationship allowing the estimation of PAG Young's modulus when both bis-acrylamide and acrylamide concentrations are known. In order to complete the actual knowledge on the mechanical properties of PAGs, we took benefit of our original method based on the micropipette aspiration technique (Boudou et al., J. Biomech. 2006) for characterizing gels made with concentrations in the range 0.02% < or =[Bis]< or =0.20% and 3% < or =[Acry]< or =10%. We found that the PAGs Young's modulus varies nonlinearly with the acrylamide amount. Moreover, our study validates the quasi-incompressibility hypothesis usually made in studies using PAGs (mean Poisson's ratio of 0.480+/-0.012). More generally, and in agreement with data published by other groups, we propose an original nonlinear mathematical relationship allowing the computation of Young's modulus of PAG for any given acrylamide and bis-acrylamide amounts taken in the range of values we considered.     

Actin stress fibres and cell-cell adhesion molecules in tendons: organisation in vivo and response to mechanical loading of tendon cells in vitro.

Tendons consist of parallel longitudinal rows of cells separated by collagen fibres. The cells are in intimate contact longitudinally within rows, and laterally via sheet-like lateral cell processes between rows. At points of contact, they are linked by gap junctions. Since tendons stretch under load, such cell contacts require protection. Here we describe the organisation of the actin cytoskeleton and actin-based cell-cell interactions in vivo and examine the effect of cyclic tensile loading on tendon cells in vitro. Cells within longitudinal rows contained short longitudinally running actin stress fibres. Each fibre was aligned with similar fibres in the cells longitudinally on either side, and fibres appeared to be linked via adherens junctions. Overall, these formed long oriented rows of stress fibres running along the rows of tendon cells. In culture, junctional components n-cadherin and vinculin and the stress fibre component tropomyosin increased in strained cultures, whereas actin levels remained constant. These results suggest that: (1) cells are linked via actin-associated adherens junctions along the line of principal strain; and (2) under load, cells appear to attach themselves more strongly together, and assemble more of their cytoplasmic actin into stress fibres with tropomyosin. Taken together, this suggests that cell-cell contacts are protected during stretch, and also that the stress fibres, which are contractile, may provide an active mechanism for recovery from stretch. In addition, stress fibres are ideally oriented to monitor tensile load and thus may be important in mechanotransduction and the generation of signals passed via the gap junction network.     

The integrated function of muscles and tendons during locomotion

The mechanical roles of tendon and muscle contractile elements during locomotion are often considered independently, but functionally they are tightly integrated. Tendons can enhance muscle performance for a wide range of locomotor activities because muscle-tendon units shorten and lengthen at velocities that would be mechanically unfavorable for muscle fibers functioning alone. During activities that require little net mechanical power output, such as steady-speed running, tendons reduce muscular work by storing and recovering cyclic changes in the mechanical energy of the body. Tendon stretch and recoil not only reduces muscular work, but also allows muscle fibers to operate nearly isometrically, where, due to the force-velocity relation, skeletal muscle fibers develop high forces. Elastic energy storage and recovery in tendons may also provide a key mechanism to enable individual muscles to alter their mechanical function, from isometric force-producers during steady speed running to actively shortening power-producers during high-power activities like acceleration or uphill running. Evidence from studies of muscle contraction and limb dynamics in turkeys suggests that during running accelerations work is transferred directly from muscle to tendon as tendon stretch early in the step is powered by muscle shortening. The energy stored in the tendon is later released to help power the increase in energy of the body. These tendon length changes redistribute muscle power, enabling contractile elements to shorten at relatively constant velocities and power outputs, independent of the pattern of flexion/extension at a joint. Tendon elastic energy storage and recovery extends the functional range of muscles by uncoupling the pattern of muscle fiber shortening from the pattern of movement of the body.     

Tryptophan loading induces oxidative stress

In previous studies tryptophan loads have been administered to human subjects in order to raise central levels of 5-hydroxytryptamine (5HT) and assess the effects of 5HT on behaviour and mood. However, tryptophan is metabolised primarily along the oxidative kynurenine pathway. In this study a 6 g oral tryptophan load was administered to 15 healthy volunteers and the levels of kynurenines and lipid peroxidation products (indicative of oxidative stress) were measured. The results demonstrate that tryptophan loading produces a highly significant increase in lipid peroxidation products in parallel with increased kynurenines. The oxidative stress may result from the generation of quinolinic acid, 3-hydroxykynurenine, and 3-hydroxyanthranilic acid, all of which are known to have the ability to generate free radicals. The results may have implications for the use of tryptophan loading in psychiatric practice, and for the chronic use of diets high in tryptophan.     

Influence of a single loading episode on gene expression in healing rat Achilles tendons

Mechanical loading stimulates tendon healing via mechanisms that are largely unknown. Genes will be differently regulated in loaded healing tendons, compared with unloaded, just because of the fact that healing processes have been changed. To avoid such secondary effects and study the effect of loading per se, we therefore studied the gene expression response shortly after a single loading episode in otherwise unloaded healing tendons. The Achilles tendon was transected in 30 tail-suspended rats. The animals were let down from the suspension to load their tendons on a treadmill for 30 min once, 5 days after tendon transection. Gene expression was studied by Affymetrix microarray before and 3, 12, 24, and 48 h after loading. The strongest response in gene expression was seen 3 h after loading, when 150 genes were up- or downregulated (fold change ≥2, P ≤ 0.05). Twelve hours after loading, only three genes were upregulated, whereas 38 were downregulated. Fewer than seven genes were regulated after 24 and 48 h. Genes involved in the inflammatory response were strongly regulated at 3 and 12 h after loading; this included upregulation of iNOS, PGE synthase, and IL-1β. Also genes involved in wound healing/coagulation, angiogenesis, and production of reactive oxygen species were strongly regulated by loading. Microarray results were confirmed for 16 selected genes in a repeat experiment (N = 30 rats) using real-time PCR. It was also confirmed that a single loading episode on day 5 increased the strength of the healing tendon on day 12. In conclusion, the fact that there were hardly any regulated genes 24 h after loading suggests that optimal stimulation of healing requires a mechanical loading stimulus every day.     

Estimation of material elastic moduli in elastography: a local method, and an investigation of Poisson's ratio sensitivity

The local material stiffness of tissues is a well-known indicator of pathology, with locally stiffer tissue related to the possible presence of an abnormal growth in otherwise compliant tissue. Elastography is a non-invasive technique for measuring displacement distributions in loaded tissues within a medical imaging context. From these measured displacement fields, estimated for local strain have been made using well-studied techniques, but the calculation of elastic modulus has been difficult. In this study we show a method for estimating local tissue elastic modulus that gives numerically stable and robust results in test cases, and that is numerically efficient. The method assumes the tissue is isotropic and it requires an independent estimate of tissue Poisson's ratio, but the method reaches a stable result when the estimated Poisson's ratio is in error, and the resulting estimates are not very sensitive to the assumed value.     

Effects of stress shielding on the transverse mechanical properties of rabbit patellar tendons

With the aim of studying mechanisms of the remodeling of tendons and ligaments, the effects of stress shielding on the rabbit patellar tendon were studied by performing tensile and stress relaxation tests in the transverse direction. The tangent modulus, tensile strength, and strain at failure of non-treated, control patellar tendons in the transverse direction were 1272 kPa, 370 kPa, and 40.5 percent, respectively, whereas those of the tendons stress-shielded for 1 week were 299 kPa, 108 kPa, and 40.4 percent, respectively. Stress shielding markedly decreased tangent modulus and tensile strength in the transverse direction, and the decreases were larger than those in the longitudinal direction, which were determined in our previous study. For example, tensile strength in the transverse and longitudinal direction decreased to 29 and 50 percent of each control value, respectively, after 1 week stress shielding. In addition, the stress relaxation in the transverse direction of stress-shielded patellar tendons was much larger than that of nontreated, control ones. In contrast to longitudinal tensile tests for the behavior of collagen, transverse tests reflect the contributions of ground substances such as proteoglycans and mechanical interactions between collagen fibers. Ground substances provide lubrication and spacing between fibers, and also confer viscoelastic properties. Therefore, the results obtained from the present study suggest that ground substance matrix, and interfiber and fiber-matrix interactions have important roles in the remodeling response of tendons to stress.     

On the independence of time and strain effects in the stress relaxation of ligaments and tendons

The hypothesis of variables separation, namely the time and the strain separation in the relaxation function, is widely used in soft tissue biomechanics. Although this hypothesis is central to several biomechanical models, only few experimental works have tried to verify it. From these studies, contradictory results have been found. Moreover, it has recently been noted that no such experimental verification has been performed for ligament tissues. In this paper, an experimental method is developed to test the hypothesis of variables separation. This method is then used with human cruciate ligaments and patellar tendons. It is shown that the use of the variables separation hypothesis is justified at least for strain values lower than 16% for anterior cruciate ligament, lower than 12% for posterior cruciate ligament and lower than 6% for patellar tendon. The method presented in this paper could be used to verify the validity of variables separation for other tissues.     

Modification of ferritin during iron loading

Recombinant human ferritin loaded with iron via its own ferroxidase activity did not sediment through a sucrose-density gradient as a function of iron content. Analysis of the recombinant ferritin by native PAGE demonstrated an increase in altered migration pattern of the ferritins with increasing sedimentation, indicating an alteration of the overall charge of ferritin. Additionally, analysis of the ferritin by SDS-PAGE under nonreducing conditions demonstrated that the ferritin had formed large aggregates, which suggests disulfide bonds are involved in the aggregation. The hydroxyl radical was detected by electron spin resonance spectroscopy during iron loading into recombinant ferritin by its own ferroxidase activity. However, recombinant human ferritin loaded with iron in the presence of ceruloplasmin sedimented through a sucrose-density gradient similar to native ferritin. This ferritin was shown to sediment as a function of iron content. The addition of ceruloplasmin to the iron loading assay eliminated the detection of the DMPO-*OH adduct observed during loading using the ferroxidase activity of ferritin. The elimination of the DMPO-*OH adduct was determined to be due to the ability of ceruloplasmin to completely reduce oxygen to water during the oxidation of the ferrous iron. The implications of these data for the present models for iron uptake into ferritin are discussed.