Poisson's ratio of a crossed fibre sheath: the skin of aquatic salamanders

Many animal connective tissues are composite materials formed into sheaths containing regularly organized collagen fibres in a crossed, fabric-like array. From a few simple assumption about the interactions between fibres, we construct a model for the effect of such a fabric-like construction on the Poisson's ratio of connective tissue sheaths. Surprisingly, the model predicts high Poisson's ratios (often greater than 1.0) Mdashespecially high given the value of 0.5 that is usually used for primarily aqueous biological tissues (based on assumptions of incompressibility and anisotropy). However, virtually all empirical attempts to measure Poisson's ratio in animal connective tissue sheaths (including our own experiments on salamander skin) reveal similarly high Poisson's ratios. The model also predicts that Poisson's ratio will increase with increasing strain, at a rate dependent on the initial angle of the crossed fibres relative to the direction of strain. Since the Poisson's ratio of a material is directly correlated with the material's stiffness, such strain-dependent changes in Poisson's ratio have important implications for the stiffness properties of connective tissue sheaths. Given the structural support role of connective tissues, stiffness is assumed to be one of their most important qualities, and several examples of how our model might predict the stiffness qualities within the walls of cylinders formed from helically wound crossed fibre sheaths (such as mammalian annular ligament and nematode cuticle) are given.     

Morphogenesis of the elastic fiber: an immunoelectronmicroscopy investigation

In this study a rabbit antiserum against human aortic elastin, which showed a high degree of species specificity in ELISA tests, was used to examine elastin fiber formation in the human fetal aorta between the ages of 14 and 23 weeks. Elastin was first detected by the antibody in the matrix of the 14-week-old specimen in association with the microfibrillar component. At this stage of development, the sections did not reveal structures morphologically identifiable as elastin. By the 17th week, discrete loci of elastin deposition were observed together with well-defined elastin fibrils. Only by the 23rd week did the aorta show the characteristic layering of elastic fibrils separating the myoblasts of the tunica media. In the latter specimen, the newly synthesized uncrosslinked elastin appeared to be unevenly distributed on the surface of elastin fibrils where it formed continuous strips of variable width arranged mostly in the form of spirals. This observation is discussed with respect to the proposals that the morphogenesis of elastic tissue is a dynamic process involving a close interrelationship between elastic fibrils and elastogenic cells and the morphogenetic movement of elastogenic cells plays an important role not only in the growth of elastic fibrils but also in the ultrastructural organization of the tissue.     

Decrease of elastic moduli of DOPC bilayers induced by a macrolide antibiotic, azithromycin

The elastic properties of membrane bilayers are key parameters that control its deformation and can be affected by pharmacological agents. Our previous atomic force microscopy studies revealed that the macrolide antibiotic, azithromycin, leads to erosion of DPPC domains in a fluid DOPC matrix [A. Berquand, M. P. Mingeot-Leclercq, Y. F. Dufrene, Real-time imaging of drug-membrane interactions by atomic force microscopy, Biochim. Biophys. Acta 1664 (2004) 198-205.]. Since this observation could be due to an effect on DOPC cohesion, we investigated the effect of azithromycin on elastic properties of DOPC giant unilamellar vesicles (GUVs). Microcinematographic and morphometric analyses revealed that azithromycin addition enhanced lipid membranes fluctuations, leading to eventual disruption of the largest GUVs. These effects were related to change of elastic moduli of DOPC, quantified by the micropipette aspiration technique. Azithromycin decreased both the bending modulus (k(c), from 23.1+/-3.5 to 10.6+/-4.5 k(B)T) and the apparent area compressibility modulus (K(app), from 176+/-35 to 113+/-25 mN/m). These data suggested that insertion of azithromycin into the DOPC bilayer reduced the requirement level of both the energy for thermal fluctuations and the stress to stretch the bilayer. Computer modeling of azithromycin interaction with DOPC bilayer, based on minimal energy, independently predicted that azithromycin (i) inserts at the interface of phospholipid bilayers, (ii) decreases the energy of interaction between DOPC molecules, and (iii) increases the mean surface occupied by each phospholipid molecule. We conclude that azithromycin inserts into the DOPC lipid bilayer, so as to decrease its cohesion and to facilitate the merging of DPPC into the DOPC fluid matrix, as observed by atomic force microscopy. These investigations, based on three complementary approaches, provide the first biophysical evidence for the ability of an amphiphilic antibiotic to alter lipid elastic moduli. This may be an important determinant for drug: lipid interactions and cellular pharmacology.     

Decrease of elastic moduli of DOPC bilayers induced by a macrolide antibiotic, azithromycin

The elastic properties of membrane bilayers are key parameters that control its deformation and can be affected by pharmacological agents. Our previous atomic force microscopy studies revealed that the macrolide antibiotic, azithromycin, leads to erosion of DPPC domains in a fluid DOPC matrix [A. Berquand, M. P. Mingeot-Leclercq, Y. F. Dufrene, Real-time imaging of drug-membrane interactions by atomic force microscopy, Biochim. Biophys. Acta 1664 (2004) 198-205.]. Since this observation could be due to an effect on DOPC cohesion, we investigated the effect of azithromycin on elastic properties of DOPC giant unilamellar vesicles (GUVs). Microcinematographic and morphometric analyses revealed that azithromycin addition enhanced lipid membranes fluctuations, leading to eventual disruption of the largest GUVs. These effects were related to change of elastic moduli of DOPC, quantified by the micropipette aspiration technique. Azithromycin decreased both the bending modulus (k_c, from 23.1 ± 3.5 to 10.6 ± 4.5 k_BT) and the apparent area compressibility modulus (K_app, from 176 ± 35 to 113 ± 25 mN/m). These data suggested that insertion of azithromycin into the DOPC bilayer reduced the requirement level of both the energy for thermal fluctuations and the stress to stretch the bilayer. Computer modeling of azithromycin interaction with DOPC bilayer, based on minimal energy, independently predicted that azithromycin (i) inserts at the interface of phospholipid bilayers, (ii) decreases the energy of interaction between DOPC molecules, and (iii) increases the mean surface occupied by each phospholipid molecule. We conclude that azithromycin inserts into the DOPC lipid bilayer, so as to decrease its cohesion and to facilitate the merging of DPPC into the DOPC fluid matrix, as observed by atomic force microscopy. These investigations, based on three complementary approaches, provide the first biophysical evidence for the ability of an amphiphilic antibiotic to alter lipid elastic moduli. This may be an important determinant for drug: lipid interactions and cellular pharmacology.     

Estimation of the effective transversely isotropic elastic constants of a material from known values of the material's orthotropic elastic constants

A method is illustrated for determining the effective transversely isotropic (or isotropic) elastic constants from measured orthotropic elastic constants. This method consists of constructing upper and lower bounds on the effective transversely isotropic (or isotropic) elastic constants using the known orthotropic values. This method is illustrated using three sets of elastic constants for bone. Fortunately, the upper and lower bounds are very close. Thus very good approximations for the effective transversely isotropic (or isotropic) elastic constants for cortical and cancellous bone are obtained from previously published data on the orthotropic elastic constants for those tissue types. This work is undertaken to build a greater database for the transversely isotropic elastic constants of bone with the intention of employing them in a transversely isotropic model of bone poroelasticity. An interesting aspect of the present result is that the Voigt and Reuss bounds are very tight for these anisotropic materials. This is not always the case for these bounds. Received: 14 November 2001 / Accepted: 25 February 2002     

Collagen fibrils and elastic fibers in rat-tail tendon: an electron microscopic investigation

Earlier studies by the authors showed that the collagen fibrils in rat-tail tendon have a bi-modal distribution of fibril diameters from a time shortly after birth through to the onset of maturity at about 3–4 months. Present work has extended those observations for rats up to the age of 2 years. Histograms of the fibril diameter distributions for mature tail tendon and direct electron microscope observations show that the fibrils break down as the tendon ages. Further work on the constant diameter subfibrils of diameter 140 Å described previously, has confirmed that these are part of the elastic fibers present in tendon at all ages. It has been shown that there is relatively little variation in the collagen fibril diameter distribution as a function of the position of the specimen in the tail, and as the measured percentage of the area taken by the collagen fibrils present at any particular point. Estimation of the fibrillar collagen content of rat-tail tendon as a function of age indicates that it increases steadily from birth and reaches a maximum at the onset of maturity, beyond which the fibrillar collagen content appears to remain constant.     

Estimation of diet in extinct raccoon dog species by the molar ratio method

Estimation of the dietary habits of extinct species using morphological traits has been attempted in numerous studies; however, previous methods have encountered several difficulties, such as requiring specialized equipment. In this study, we describe an easy quantitative method for estimating the dietary habits, and apply it to extinct raccoon dogs (Nyctereutes) species (Carnivora, Mammalia). The method is based on the lower molar ratios (M₂/M₁ size) that reflect the species diet (carnivorous and omnivorous tendencies) in Canidae. Among the species statistically compared, Nyctereutes sinensis showed a lower M₂/M₁ score similar to that of Nyctereutes procyonoides albus (Hokkaido, Japan), whereas Nyctereutes tingi had a higher M₂/M₁ score similar to that of Nyctereutes procyonoides viverrinus (Honshu and Kyushu, Japan). These scores suggest that the diets of N. sinensis and N. tingi were similar to those of N. p. albus (relatively carnivorous) and N. p. viverrinus (relatively omnivorous), respectively. Other extinct raccoon dogs also showed varied M₂/M₁ score, suggesting dietary difference. These results suggest that raccoon dogs underwent dietary transitions or exhibited dietary plasticity during evolution, while their range of diets might have remained the same as those of different populations of extant species Nyctereutes procyonoides.     

The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus

The elastic moduli of human subchondral, trabecular, and cortical bone tissue from a proximal tibia were experimentally determined using three-point bending tests on a microstructural level. The mean modulus of subchondral specimens was 1.15 GPa, and those of trabecular and cortical specimens was 4.59 GPa and 5.44 GPa respectively. Significant differences were found in the modulus values between bone tissues, which may have mainly resulted from the differences in the microstructures of each bone tissue rather than in the mineral density. Furthermore, the size-dependency of the modulus was examined using eight different sizes of cortical specimens (heights h = 100-1000 microns). While the modulus values for relatively large specimens (h greater than 500 microns) remained fairly constant (approximately 15 GPa), the values decreased as the specimens became smaller. A significant correlation was found between the modulus and specimen size. The surface area to volume ratio proved to be a key variable to explain the size-dependency.     

Estimation of the size of an open population using local estimating equations II: a partially parametric approach

Kernel smoothing methods are applied to extend a modification of the closed population approach of Lloyd and Yip (1991, in Estimating Equations, 65-88) to open populations with frequent capture occasions. The method complements previous nonparametric methods and, when the parametric assumptions are met, simulations show the new method has a smaller integrated mean squared error than the previous fully nonparametric method. The method is applied to capture-recapture data on short-tailed shearwaters collected annually for 48 years.     

Buckling of adaptive elastic bone-plate: theoretical and numerical investigation

During day-to-day activities, many bones in the axial and appendicular skeleton are subjected to repetitive, cyclic loading that often results directly in an increased risk of bone fracture. In clinical orthopedics, trabecular fatigue fractures are observed as compressive stress fractures in the proximal femur, vertebrae, calcaneus and tibia, that are often preceded by buckling and bending of microstructural elements (Müller et al. in J Biomechanics 31:150 1998; Gibson in J Biomechanics 18:317-328 1985; Gibson and Ashby in Cellular solids 1997; Lotz et al. in Osteoporos Int 5:252-261 1995; Carter and Hayes in Science 194:1174-1176 1976). However, the relative importance of bone density and architecture in the etiology of these fractures are poorly understood and consequently not investigated from a biomechanical point of view. In the present contribution, an attempt is made to formulate a bone-plate buckling theory using Cowin's concepts of adaptive elasticity (Cowin and Hegedus in J Elast 6:313-325 1976; Hegedus and Cowin J Elast 6:337-352 1976). In particular, the buckling problem of a Kirchhoff-Love bone plate is investigated numerically by using the finite difference method and an iterative solving approach (Chen in Comput Methods Appl Mech Eng 167:91-99 1998; Hildebland in Introduction to numerical analysis 1974; Richtmyer and Morton in Difference methods for initial-value problems 1967).     

Myocardial material mechanics: characteristic variation of the circumferential and longitudinal systolic moduli in left ventricular dysfunction

Active systolic moduli for the circumferential (E theta) and longitudinal (E phi) axes of the left ventricle were determined along with circumferential and longitudinal contractile filament stress (sigma theta and sigma phi) and circumferential and longitudinal fiber strain (epsilon theta and epsilon phi). These material property parameters were determined at four points during cardiac systole. Thirty-nine patients comprising five clinical groups were evaluated using pressure and volume data acquired from single-plane cineangiography. The results indicate that the active moduli exponentially decrease during cardiac systole. Characteristic variations from normal differentiated the various pathological groups. With compensated volume overload, E theta was significantly reduced during the latter half of systole (p less than 0.25). With decompensated volume overload, both E theta and E phi were not significantly different from the normal group throughout cardiac systole. With compensated pressure overload, both E theta and E phi were significantly lower than the normal group at end-systole (p less than 0.005; p less than 0.005). With congestive cardiomyopathy, both E theta and E phi were significantly greater during the latter half of systole compared to the normal group (p less than 0.05 and p less than or equal to 0.025).     

A unit-cell-based three-dimensional molecular mechanics analysis for buckling load,effective elasticity and Poisson's ratio determination of the nanosheets

By using a three-dimensional (3D) space-frame-like model, a molecular mechanics (MM) approach is proposed for determination of the buckling loads, effective Young's modulus and Poisson's ratio of the nanosheets, using a proper unit cell. The governing equations are derived based on the 3D kinematics of deformations and the principle of minimum total potential energy. The unit-cell-based results are employed for the space-frame-like finite element model of the nanosheet. The nonlinear MM equations are solved by representing bonds of the boron nitride nanosheet (BNNS) by beam elements to extract the local characteristics. These properties are employed in modelling of the nanosheet, as a space-frame-like finite element structure. The force field constants are chosen according to the Morse, AMBER, UFF and DREIDING models to determine the buckling strength, and effective Poisson's ratio and in-plane rigidity of the whole graphene and BNNSs. Silicon Carbide nanosheets are analysed based on different force constants. These results are concordant with the results available in the literature. The comparisons reveal that the DREIDING force field usually gives the most accurate predictions.     

Comparative analysis of endothelial cell and sub-endothelial cell elastic moduli in young and aged mice: Role of CD36

ObjectiveTo perform comparative analysis of the role of scavenger receptor CD36 on endothelial vs. sub-endothelial elastic modulus (stiffness) in the aortas of young and aged mice.Approaches and ResultsElastic moduli of endothelial and sub-endothelial layers of freshly isolated mouse aortas were quantified using atomic force microscopy. In young mice (4–6 months old), we found that while endothelial stiffness is markedly reduced in aortas of CD36^−/−mice, as compared to WT controls, no difference between CD36^−/− and WT aortas is observed in the stiffness of the sub-endothelial layer in denuded arteries. Additionally, inhibition of myosin phosphorylation also decreases the elastic modulus in the EC, but not the sub-EC layer in WT mice. Moreover, inhibiting CD36 mediated uptake of oxLDL in intact WT aortas abrogated oxLDL-induced endothelial stiffening. Further analysis of aged mice (22–25 months) revealed that aging resulted not only in significant stiffening of the denuded arteries, as was previously known, but also a comparable increase in the elastic modulus of the endothelial layer. Most significantly, this stiffening in the EC layer is dependent on CD36, whereas the denuded layer is not affected.ConclusionsOur results show that the role CD36 in stiffening of cellular components of intact aortas is endothelial-specific and that genetic deficiency of CD36 protects against endothelial stiffening in aged mice. Moreover, these data suggest that endothelial stiffness in intact mouse aortas depends more on the expression of CD36 than on the stiffness of the sub-endothelial layer.     

Parameter estimation and sensitivity analysis of a nonlinearly elastic static lung model

A model for the static pressure-volume behavior of the lung parenchyma based on a pseudo-elastic strain energy function was tested. Values of the model parameters and their variances were estimated by an optimal least-squares fit of the model-predicted pressures to the corresponding data from excised, saline-filled dog lungs. Although the model fit data from twelve lungs very well, the coefficients of variation for parameter values differed greatly. To analyze the sensitivity of the model output to its parameters, we examined an approximate Hessian, H, of the least-squares objective function. Based on the determinant and condition number of H, we were able to set formal criteria for choosing the most reliable estimates of parameter values and their variances. This in turn allowed us to specify a normal range of parameter values for these dog lungs. Thus the model not only describes static pressure-volume data, but also uses the data to estimate parameters from a fundamental constitutive equation. The optimal parameter estimation and sensitivity analysis developed here can be widely applied to other physiologic systems.     

Estimation and inference of R0 of an infectious pathogen by a removal method

The basic reproductive ratio, R0, is a central quantity in the investigation and management of infectious pathogens. The standard model for describing stochastic epidemics is the continuous time epidemic birth-and-death process. The incidence data used to fit this model tend to be collected in discrete units (days, weeks, etc.), which makes model fitting, and estimation of R0 difficult. Discrete time epidemic models better match the time scale of data collection but make simplistic assumptions about the stochastic epidemic process. By investigating the nature of the assumptions of a discrete time epidemic model, we derive a bias corrected maximum likelihood estimate of R0 based on the chain binomial model. The resulting 'removal' estimators provide estimates of R0 and the initial susceptible population size from time series of infectious case counts. We illustrate the performance of the estimators on both simulated data and real epidemics. Lastly, we discuss methods to address data collected with observation error.     

The material properties of the native porcine mitral valve chordae tendineae: an in vitro investigation

The material properties of the mitral valve chordae tendineae are important for the understanding of leaflet coaptation configuration and chordal pathology. There is limited information about the mechanical properties of the chordae during physiologic loading. Dual camera stereo photogrammetry was used to measure strains of the chordae in vitro under physiologic loading conditions. Two high-speed, high-resolution cameras captured the movement of graphite markers attached to the central section of the chordae. A uniaxial test simulating the same loading conditions was conducted on the same chordae using the same markers. The maximum strain experienced during the cardiac cycle was 4.29% +/- 3.43%. The loading rate was higher at 75.3% +/- 48.6% strain per second than the unloading rate at -54.8% +/- -56.6% strain per second. The anterior lateral strut chordae had a higher maximum strain (5.7% +/- 3.8%) and loading rate (80.5% +/- 51.9% strain per second) than the posterior medial strut chordae (5.5% +/- 2.3% strain and 68.1% +/- 48.3% strain per second). The posterior medial strut chordae had a higher unloading rate (-68.5% +/- -59.1% strain per second) than the anterior lateral strut chordae (-44.9% +/- -57.2% strain per second). Although the anterior lateral and posterior medial strut chordae have a significantly different diameter and length, they experience a similar strain, strain rate, and tension. In conclusion, a non-destructive technique was developed to measure in vitro chordal strain in the mitral valve. This technique allows the investigation of the behavior of biological tissues under physiologic loading conditions.     

Computational modeling of healing: an application of the material force method

The basic aim of the present contribution is the qualitative simulation of healing phenomena typically encountered in hard and soft tissue mechanics. The mechanical framework is provided by the theory of open system thermodynamics, which will be formulated in the spatial as well as in the material motion context. While the former typically aims at deriving the density and the spatial motion deformation field in response to given spatial forces, the latter will be applied to determine the material forces in response to a given density and material deformation field. We derive a general computational framework within the finite element context that will serve to evaluate both the spatial and the material motion problem. However, once the spatial motion problem has been solved, the solution of the material motion problem represents a mere post-processing step and is thus extremely cheap from a computational point of view. The underlying algorithm will be elaborated systematically by means of two prototype geometries subjected to three different representative loading scenarios, tension, torsion, and bending. Particular focus will be dedicated to the discussion of the additional information provided by the material force method. Since the discrete material node point forces typically point in the direction of potential material deposition, they can be interpreted as a driving force for the healing mechanism.Blues the healer, John Lee Hooker [1989]     

Estimation of a common odds ratio in case-control studies of familial aggregation

A new estimator of a common odds ratio is proposed for case-control studies of familial aggregation. The proposed estimator is a modification to the usual Mantel-Haenszel estimator that relies on an empirical adjustment for the within-family clustering which is typical of such designs. A simulation study shows that the estimator tends to have smaller mean squared error than the unmodified Mantel-Haenszel estimator under conditions likely to arise in practice. The construction of confidence intervals is also discussed.