In vitro culture increases mechanical stability of human tissue engineered cartilage constructs by prevention of microscale scaffold buckling

Many studies have measured the global compressive properties of tissue engineered (TE) cartilage grown on porous scaffolds. Such scaffolds are known to exhibit strain softening due to local buckling under loading. As matrix is deposited onto these scaffolds, the global compressive properties increase. However the relationship between the amount and distribution of matrix in the scaffold and local buckling is unknown. To address this knowledge gap, we studied how local strain and construct buckling in human TE constructs changes over culture times and GAG content. Confocal elastography techniques and digital image correlation (DIC) were used to measure and record buckling modes and local strains. Receiver operating characteristic (ROC) curves were used to quantify construct buckling. The results from the ROC analysis were placed into Kaplan-Meier survival function curves to establish the probability that any point in a construct buckled. These analysis techniques revealed the presence of buckling at early time points, but bending at later time points. An inverse correlation was observed between the probability of buckling and the total GAG content of each construct. This data suggests that increased GAG content prevents the onset of construct buckling and improves the microscale compressive tissue properties. This increase in GAG deposition leads to enhanced global compressive properties by prevention of microscale buckling.     

The toughness of secondary cell wall and woody tissue

The ''across grain'' toughness of 51 woods has been determined on thin wet sections using scissors. The moisture content of sections and the varying sharpness of the scissor blades had little effect on the results. In thin sections (less than 0.6mm), toughness rose linearly with section thickness. The intercept toughness at zero thickness, estimated from regression analysis, was proportional to relative density, consistent with values reported for non-woody plant tissues. Extrapolation of the intercept toughness of these woods and other plant tissues/materials to a relative density of 1.0 predicted a toughness of 3.45kJ m^-2 , which we identify with the intrinsic toughness of the cell wall. This quantity appears to predict published results from K_IC tests on woods and is related to the propensity for crack deflection. The slope of the relationship between section thickness and toughness, describing the work of plastic buckling of cells, was not proportional to relative density, the lightest (balsa) and heaviest (lignum vitae) woods fracturing with less plastic work than predicted. The size of the plastic zone around the crack tip was estimated to be 0.5mm in size. From this, the hypothetical overall toughness of a thick (greater than 1 mm) block of solid cell wall material was calculated as 39.35 kJ m^-2, due to both cell wall resistance (10 per cent) and the plastic buckling of cells (90 per cent). This value successfully predicts the toughness of most commercial woods (of relative densities between 0.2 and 0.8) from ''work area'' tests in tension and bending. Though density was the most important factor, both fibre width/fibre length (in hardwoods) and lignin/cellulose ratios were negatively correlated with the work of plastic buckling, after correcting for density. At low densities the work of plastic buckling in the longitudinal radial (LR) direction exceeded that in longitudinal tangential (LT), but the reverse was true for relative densities above 0.25. This could be attributed to the direction of rays. Density for density, the toughness of temperate hardwoods tested was about 20 per cent lower than that of tropical hardwoods. This is probably due to the much greater number of vessels in temperate hardwoods. Vessels appear either not to display buckling behaviour during fracture at all or to collapse cheaply. These general results have applications to other plant tissues.     

Twist buckling of veins under torsional loading

Veins are often subjected to torsion and twisted veins can hinder and disrupt normal blood flow but their mechanical behavior under torsion is poorly understood. The objective of this study was to investigate the twist deformation and buckling behavior of veins under torsion. Twist buckling tests were performed on porcine internal jugular veins (IJVs) and human great saphenous veins (GSVs) at various axial stretch ratio and lumen pressure conditions to determine their critical buckling torques and critical buckling twist angles. The mechanical behavior under torsion was characterized using a two-fiber strain energy density function and the buckling behavior was then simulated using finite element analysis. Our results demonstrated that twist buckling occurred in all veins under excessive torque characterized by a sudden kink formation. The critical buckling torque increased significantly with increasing lumen pressure for both porcine IJV and human GSV. But lumen pressure and axial stretch had little effect on the critical twist angle. The human GSVs are stiffer than the porcine IJVs. Finite element simulations captured the buckling behavior for individual veins under simultaneous extension, inflation, and torsion with strong correlation between predicted critical buckling torques and experimental data (R² = 0.96). We conclude that veins can buckle under torsion loading and the lumen pressure significantly affects the critical buckling torque. These results improve our understanding of vein twist behavior and help identify key factors associated in the formation of twisted veins.     

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).     

Torque-induced deformations of charged elastic DNA rods: thin helices,loops, and precursors of DNA supercoiling

We study the deformations of charged elastic rods under applied end forces and torques. For neutral filaments, we analyze the energetics of initial helical deformations and loop formation. We supplement this elastic approach with electrostatic energies of bent filaments and find critical conditions for buckling depending on the ionic strength of the solution. We also study force-induced loop opening, for parameters relevant for DNA. Finally, some applications of this nano-mechanical DNA model to salt-dependent onset of the DNA supercoiling are discussed.     

Biomechanical Modelling of Colorectal Crypt Budding and Fission

This paper presents a biomechanical model for the small pits, called crypts, that line the colon. A continuum approach is adopted, with the crypt epithelium modelled as a growing beam attached to the underlying lamina by cell bonds, which generate tension within the layer. These cell attachments are assumed to be viscoelastic thus allowing for cell progression along the crypt. It is shown that any combination of: an increase in net proliferation (i.e. cell production minus apoptosis), an enlargement of the proliferative compartment, an increase in the strength of the cellular attachment to the underlying lamina, or a change in the rate of cell growth or cell bonding may generate buckling of the tissue. These changes can all be generated by an activating mutation of the Wnt cascade, which is generally accepted to be the first genetic change in colorectal cancer, with subsequent deformation, budding, and crypt fission an observed feature of the adenomatous crypt.     

A biomechanical model of artery buckling

The stability of arteries under blood pressure load is essential to the maintenance of normal arterial function and the loss of stability can lead to tortuosity and kinking that are associated with significant clinical complications. However, mechanical analysis of arterial bent buckling is lacking. To address this issue, this paper presents a biomechanical model of arterial buckling. Using an elastic cylindrical arterial model, the mechanical equations for arterial buckling were developed and the critical buckling pressure was found to be a function of the wall stiffness (Young's modulus), arterial radius, length, wall thickness, and the axial strain. Both the model equations and experimental results demonstrated that the critical pressure is related to the axial strain. Arteries may buckle and become tortuous due to reduced (subphysiological) axial strain, hypertensive pressure, and a weakened wall. These results are in accordance with, and provide a possible explanation to the clinical observations that hypertension and aging are the risk factors for arterial tortuosity and kinking. The current model is also applicable to veins and ureters.     

The behaviour of roots encountering cracks in soil

Summary It is shown that probabilities of root penetration across cracks in soil can be calculated effectively using a mathematical model involving root stress and soil distributions and penetrometer/root stress ratios. Penetration criteria are developed, and it is found that the effective penetrometer/root stress ratios take values of about 4 for crack widths smaller than about 2 mm and about 8 for wider cracks. Root swelling does not appear to contribute significantly to the probability of root penetration through any effect on root buckling stress. Suggestions are made for further work on the effects of soil structure and strength on root behaviour.     

Buckling of inner cell wall layers after manipulations to reduce tensile stress: observations and interpretations for stress transmission

The inner layer of the cell wall in tissues that are under tensile stress in situ, e.g. epidermis and collenchyma of etiolated sunflower hypocotyls, shows a pattern of transverse folds when the tissues are detached and plasmolysed. This can be observed by Nomarski imaging of inner surfaces of the outer cell walls and electron microscopy of longitudinal sections after peeling the epidermis and bathing it in plasmolysing solutions. The folds are apparently caused by buckling of the inner layer due to the longitudinal compressive force exerted on this layer by the outer wall layer, when it shrinks after the removal of the longitudinal tensile stresses. In these stresses, two components can be distinguished: the tissue stress, disappearing on peeling, and that caused directly by turgor pressure, disappearing in hyperosmotic solution. Investigation of the buckling indicates that the outer layer of the cell wall transmits in situ most of the longitudinal tensile stress in the wall. The common concept that the inner layer of the wall is the region bearing most stress and therefore regulating growth can still be valid with respect to the transverse stress component.