A 2D Finite Element Model of the Interventricular Septum Under Normal and Abnormal Loading

Abstract

The interventricular septum is the structure that separates the left and right ventricles of the heart. Under normal loading conditions, it is concave to the left ventricle, but under abnormal loading the septum flattens and occasionally inverts. In the past, the septum has frequently been modelled as integral to the left ventricle with the effects of pressure from the right ventricle being ignored. Under abnormal loading, the septum has been described as behaving equivalent to a “flapping sail”. There has been no consideration of structural behaviour under these conditions. A 2-D plane stress FE model of the septum was used to investigate the difference in structural behaviour of the septum during diastole between normal and abnormal loading. The biaxial stress patterns that develop are distinctively disparate. Under normal loading, the septum behaves much like a thick-walled cylinder subject to internal and external pressure, with the resulting stresses being circumferential tension and radial compression, both varying with radius. These stresses are very low throughout most of diastole. However, under abnormal loading, the septum behaves in an arch-like fashion, with high compressive stresses almost circumferential in direction, combined with radial compression. We conclude that right ventricular pressures cause bending effects in the wall of the heart, and that under abnormal loading, the compressive stresses that develop in the septum may lead to an understanding of certain, previously unexplained, pathological conditions.     

A 2D finite element model of the interventricular septum under normal and abnormal loading

The interventricular septum is the structure that separates the left and right ventricles of the heart. Under normal loading conditions, it is concave to the left ventricle, but under abnormal loading the septum flattens and occasionally inverts. In the past, the septum has frequently been modelled as integral to the left ventricle with the effects of pressure from the right ventricle being ignored. Under abnormal loading, the septum has been described as behaving equivalent to a "flapping sail". There has been no consideration of structural behaviour under these conditions. A 2-D plane stress FE model of the septum was used to investigate the difference in structural behaviour of the septum during diastole between normal and abnormal loading. The biaxial stress patterns that develop are distinctively disparate. Under normal loading, the septum behaves much like a thick-walled cylinder subject to internal and external pressure, with the resulting stresses being circumferential tension and radial compression, both varying with radius. These stresses are very low throughout most of diastole. However, under abnormal loading, the septum behaves in an arch-like fashion, with high compressive stresses almost circumferential in direction, combined with radial compression. We conclude that right ventricular pressures cause bending effects in the wall of the heart, and that under abnormal loading, the compressive stresses that develop in the septum may lead to an understanding of certain, previously unexplained, pathological conditions.     

Branching responses in Silphium integrifolium (Asteraceae) following mechanical or gall damage to apical meristems and neighbor removal

Branching in plants increases plant access to light and provides pathways for regrowth following damage or loss of the apical meristem. We conducted two experiments in an eastern Kansas tallgrass prairie to determine how apical meristem loss (by clipping), apical meristem damage (by insect galling), and increased light availability affected growth, reproduction, and branching in Silphium integrifolium (Asteraceae). The first experiment compared clipping with galling. Clipping increased axillary shoot numbers, while galling increased axillary shoot lengths, reflecting different allocation responses among damage types and inhibition of branching by galls. However, total capitulum production was less in all gall/clip treatments than in intact shoots. The second experiment compared clipping with mowing the surrounding vegetation to increase light availability. Mowing increased total leaf, total capitulum, and axillary shoot length and axillary capitulum production in clipped and unclipped plants and in large vs. small shoots. The presence of the neighboring canopy, not of an intact apical meristem, was therefore the stronger limitation on leaf and capitulum production. These experiments suggest that damage and light competition affected both branching frequency and the partitioning of resources among shoots, branches, and leaves. Because Silphium's growth form is widespread, similar responses may occur in other grassland forbs.     

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.     

Putative dual pathway of auxin transport in organogenesis of <Emphasis Type="Italic">Arabidopsis</Emphasis>

In Arabidopsis, damage to the superficial acropetal polar auxin transport (PAT) inhibits generative but not vegetative organ initiation. In order to verify whether in a vegetative phase auxin can be transported to the meristem in a different way, the research on wild-type and plants with defective PAT was performed. Distance from the differentiated vascular elements to the shoot apical meristem (SAM) was measured for Arabidopsis cultured in different experimental systems. The influence of this distance on the ability to induce organogenesis as well as transport of the fluorescent dye to the SAM, and the LEAFY gene expression were analyzed. The youngest protoxylem elements were used as a marker of the vascular tissues. The distance of protoxylem to the SAM and organogenesis were interrelated. Organ initiation occurred only when protoxylem was localized near to the SAM. Experimental elongation of internodes in a vegetative rosette caused an increase in the distance between protoxylem and the SAM organogenic zone. Thus, the inhibition of organ initiation took place already during the vegetative phase. The results suggest the presence of at least two pathways of acropetal transport of auxin inducing organogenesis: one superficial way through PAT, and the second, putative one, internal through the vascular system. Possibly, organogenesis is completely blocked only when both these pathways are dysfunctional.     

Stress gradients in the walls of large arteries

Elastic behavior of vascular wall, assuming the vessels to be ‘thick-walled’ and utilizing finite deformation theory, was investigated. It was found that canine carotid arterial wall is neither isotropic nor transversely isotropic. Previously, stress-strain relations were obtained for carotid arteries on the basis of membrane theory (Doyle and Dobrin, 1971). Since strain gradients across the wall are fairly steep, the applicability of such expressions, for pointwise evaluation of stress, required examination. The study indicated that these relationships between mean circumferential stress and mean extension ratio in the circumferential direction could be used to relate the specific circumferential stress value to the specific extension ratio at any designated point within the wall. From this analysis it was possible to evaluate circumferential and radial wall stresses. Both of these stresses are maximal at the inner surface of the intima. At this point the radial stress is equal to the transmural pressure and is compressive, while the circumferential stress is tensile and is 1·5 to 2 times the value of the mean stress, i.e. the product of transmural pressure and the ratio of internal radius-to-wall thickness. Both stresses are lowest at the outer edge of the adventitia. These stress distributions were considered with respect to the spacing of the elastic lamellae and the absence of discernible vasa vasora in the inner third of the wall.     

Compression or tension? The stress distribution in the proximal femur

Background  

Questions regarding the distribution of stress in the proximal human femur have never been adequately resolved. Traditionally, by considering the femur in isolation, it has been believed that the effect of body weight on the projecting neck and head places the superior aspect of the neck in tension. A minority view has proposed that this region is in compression because of muscular forces pulling the femur into the pelvis. Little has been done to study stress distributions in the proximal femur. We hypothesise that under physiological loading the majority of the proximal femur is in compression and that the internal trabecular structure functions as an arch, transferring compressive stresses to the femoral shaft.     

Trabecular bone microdamage and microstructural stresses under uniaxial compression

The balance between local remodeling and accumulation of trabecular bone microdamage is believed to play an important role in the maintenance of skeletal integrity. However, the local mechanical parameters associated with microdamage initiation are not well understood. Using histological damage labeling, micro-CT imaging, and image-based finite element analysis, regions of trabecular bone microdamage were detected and registered to estimated microstructural von Mises effective stresses and strains, maximum principal stresses and strains, and strain energy density (SED). Bovine tibial trabecular bone cores underwent a stepwise uniaxial compression routine in which specimens were micro-CT imaged following each compression step. The results indicate that the mode of trabecular failure observed by micro-CT imaging agreed well with the polarity and distribution of stresses within an individual trabecula. Analysis of on-axis subsections within specimens provided significant positive relationships between microdamage and each estimated tissue stress, strain and SED parameter. In a more localized analysis, individual microdamaged and undamaged trabeculae were extracted from specimens loaded within the elastic region and to the apparent yield point. As expected, damaged trabeculae in both groups possessed significantly higher local stresses and strains than undamaged trabeculae. The results also indicated that microdamage initiation occurred prior to apparent yield at local principal stresses in the range of 88-121 MPa for compression and 35-43 MPa for tension and local principal strains of 0.46-0.63% in compression and 0.18-0.24% in tension. These data provide an important step towards understanding factors contributing to microdamage initiation and establishing local failure criteria for normal and diseased trabecular bone.     

Buckling Behavior of Individual and Bundled Microtubules

As the major structural constituent of the cytoskeleton, microtubules (MTs) serve a variety of biological functions that range from facilitating organelle transport to maintaining the mechanical integrity of the cell. Neuronal MTs exhibit a distinct configuration, hexagonally packed bundles of MT filaments, interconnected by MT-associated protein (MAP) tau. Building on our previous work on mechanical response of axonal MT bundles under uniaxial tension, this study is focused on exploring the compression scenarios. Intracellular MTs carry a large fraction of the compressive loads sensed by the cell and therefore, like any other column-like structure, are prone to substantial bending and buckling. Various biological activities, e.g., actomyosin contractility and many pathological conditions are driven or followed by bending, looping, and buckling of MT filaments. The coarse-grained model previously developed in our lab has been used to study the mechanical behavior of individual and bundled in vivo MT filaments under uniaxial compression. Both configurations show tip-localized, decaying, and short-wavelength buckling. This behavior highlights the role of the surrounding cytoplasm and MAP tau on MT buckling behavior, which allows MT filaments to bear much larger compressive forces. It is observed that MAP tau interconnections improve this effect by a factor of two. The enhanced ability of MT bundles to damp buckling waves relative to individual MT filaments, may be interpreted as a self-defense mechanism because it helps axonal MTs to endure harsher environments while maintaining their function. The results indicate that MT filaments in a bundle do not buckle simultaneously implying that the applied stress is not equally shared among the MT filaments, that is a consequence of the nonuniform distribution of MAP tau proteins along the bundle length. Furthermore, from a pathological perspective, it is observed that axonal MT bundles are more vulnerable to failure in compression than tension.     

Tissue morphogenesis: a surface buckling mechanism

Surface patterns can emerge during growth of anisotropic tissues because of surface buckling. This morphogenetic scenario is examined in the present paper based on a simple phenomenological theory of tissue growth. In particular, we show that constrained growth can lead to tissue compression, which in turn may result in surface buckling of the tissue. The latter means the appearance of wavy patterns on the surface. These patterns decay away from the surface. It is interesting that the critical magnitude of the parameter of mass supply, which corresponds to surface buckling, is independent of the pattern wavelength and various patterns can generally be generated in growth. Results of theoretical analysis show that the surface buckling scenario is realistic if the growing tissue matches the following two conditions. First, compression should appear during tissue growth. Second, the tissue should exhibit strong anisotropy. The former condition does not necessarily mean geometric constraints: inhomogeneous growth or material inhomogeneity and anisotropy can lead to the appearance of compressive stresses. The latter condition is typical of some tissues with fiber reinforcement in planes parallel to the surface. In the latter case, the tissue material is much softer in the out-of-plane direction than in plane. The creation of patterns by restraining tissue growth and forcing the surface to buckle represents a challenging experimental problem.     

Palaeo-adaptive properties of the xylem of Metasequoia: mechanical/hydraulic compromises

The xylem of Metasequoia glyptostroboides Hu et Cheng is characterized by very low density (average specific gravity = 0.27) and tracheids with relatively large dimensions (length and diameter). The microfibril angle in the S2 layer of tracheid walls is large, even in outer rings, suggesting a cambial response to compressive rather than tensile stresses. In some cases, this compressive stress is converted to irreversible strain (plastic deformation), as evidenced by cell wall corrugations. The heartwood is moderately decay resistant, helping to prevent Brazier buckling. These xylem properties are referenced to the measured bending properties of modulus of rupture and modulus of elasticity, and compared with other low-to-moderate density conifers. The design strategy for Metasequoia is to produce a mechanically weak but hydraulically efficient xylem that permits rapid height growth and crown development to capture and dominate a wet site environment. The adaptability of these features to a high-latitude Eocene palaeoenvironment is discussed.     

Relationship between capitulum size and pre-dispersal seed predation by insect larvae in common Asteraceae

The evolution of a showy floral display as an advertisement to pollinators could simultaneously advertise the availability of resources to pre-dispersal seed-predators. The hypotheses tested here are that the incidence of seed predation by bud-infesting insect larvae in capitula of Asteraceae is positively related to (1) capitulum size among species, (2) capitulum size within species, (3) capitulum lifespan, and (4) the degree of flowering asynchrony on individual plants. Three populations of each of 20 common herbaceous species of Asteraceae from disturbed ground and grassland habitats were monitored for the presence of pre-dispersal, seed-eating insect larvae. Mean capitulum size (receptacle width) of each species was measured. In a sub-set of eight species, individual capitula were tagged to determine their flowering phenology and lifespan (from anthesis to seed shedding). From these data an index of flowering synchrony on individual plants was derived. Among species, the incidence of larval infestation increased with capitulum size. Small-flowered species such as Achillea millefolium were largely free of bud-infesting larvae, whilst large-flowered species such as Arctium minus were heavily infested. In three cases investigated in greater detail, bud infestation was found to increase with capitulum size within species, suggesting a potential for natural selection to favour smaller capitula. No relationship was found between infestation levels and either capitulum lifespan or degree of flowering synchrony, and there was no evidence that the relationship between capitulum size and infestation was confounded by correlations with these other features. The results support hypotheses 1 and 2, but not 3 and 4. It is suggested that the characteristic capitulum size of each species may represent a trade-off between the opposing selection pressures of pollinators and pre-dispersal seed predators.     

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.     

Some unusual considerations about vessel walls and wall stresses

The "zero-stress state" of blood vessels is usually defined with respect to the atmospheric pressure p(a) ( approximately 750 mmHg). As a consequence, circumferential and axial wall stresses due to a positive transmural pressure can only be positive and thus, by definition, only tensile. If the zero-stress state were defined with respect to vacuum pressure (0 mmHg), the compressive stress -p(a) generated by p(a) everywhere in the wall would, however, be included so that negative (=compressive) wall stresses would formally become possible. In order to examine the consequences this alternative definition would have for arteries, we have compared radial, circumferential, and axial stresses calculated "conventionally" to the values they take when the zero-stress state is defined "correctly" by reference to the vacuum pressure. It turns out that, under normal physiologic conditions, axial stress and perhaps also circumferential stress might well be compressive in many elastic and conductance arteries, contrary to the intuitive conviction of many people. Since the type of stresses a vessel wall is submitted to may be highly relevant for its structure and mechanical properties, this unconventional way of considering wall stresses may reveal unsuspected relationships between wall stresses on one side, and wall structure, vessel growth, adaptation and repair processes, atherosclerosis, angioplasty or stenting on the other side. Similar considerations might also prove useful with regard to cardiac hypertrophy.     

Pericardial heterograft valves: An assessment of leaflet stresses and their implications for heart valve design

Bovine pericardium, stabilized with glutaraldehyde, is used widely in the construction of heart valve substitutes, but the design and construction of valve substitutes from this material are empirically based. Collagenous tissue can support tension, but experimental evidence indicates that flexure-induced compressive stresses can lead to fatigue failure. This study uses experimental results obtained from cyclic uniaxial load tests to predict the type and magnitude of operational stresses which occur in pericardial heterograft leaflets. Both Young's modulus and Poisson's ratio varied with uniaxial loading in pericardium, chemically modified free of tension. Leaflet stresses were analysed by using effective incremental representations of these parameters. In leaflets with unrestricted rotation at the point of attachment to the stent, the mid-plane tensions always exceeded the bending stresses, and no zones of leaflet compression were predicted. In contrast, with totally restricted leaflet rotation induced by clamping (possibly between a male and female frame) the bending stresses were greater than the mid-plane tensions at the hinge line and significant compressive stresses were predicted at this site. If elastic boundary conditions were introduced at the stent (possibly by wrapping the stent in pericardium) then the compressive stresses were reduced as the degree of elasticity was increased. Glutaraldehyde fixation of the pericardium under load produced a stiffer material; higher compressive stresses at the stent and significant increases in total stress were predicted for this tissue. The application of elevated pressure loading also increased the compressive and total stresses in the leaflet. Finally, it was shown that bicuspid leaflets were likely to experience higher stresses than tricuspid leaflets. This simple stress analysis should help valve designers of pericardial heterografts to identify those conditions which lead to tissue compression, high total stress, and ultimately material fatigue.     

Value of coining on the improvement of endurance in slotted intramedullary nails

Cracking of intramedullary nails, starting at the proximal end of the partial slot and propagating in a circumferential direction, has been observed. These partial cracks are relatively frequent, although full failures are very rare and do not disturb fracture healing. Coining is a cold-working process used to improve the endurance of structures with residual compressive stresses generated by plastic deformation. The influence of coining was investigated to evaluate its practical value in controlling these fatigue cracks. Bending and torsional tests were performed on high frequency machines. Coined zones of different shapes and depths were examined, comparing the elapsed number of load cycles with crack initiation. The results showed that the endurance of coined nails was improved by factors of approximately 10 and 5 in bending and torsion, respectively. This increase in fatigue life corresponds to a more than 50% larger dynamic load after a million cycles. Variations in coining shape and depth did not yield any significant differences.     

Contributions to the Biomechanics of Plants.; II. Stability Against Local Buckling in Hollow Plant Stems*

Hollow plant stems are, compared to solid ones, endangered by a particular kind of mechanical damage: local buckling. In upright stems centric forces due to the weight of the plant itself are not critical. Bending, however, as caused by wind forces causes transverse stresses that lead to local buckling, long before the critical tension or compression stresses are reached. A new numerical method is proposed to treat local buckling of hollow plant stems caused by bending forces. The results emphasize the importance of transverse reinforcements in the nodes and/or the nodal thickenings for the stability of hollow structures.