A finite element exploration of cartilage stress near an articular incongruity during unstable motion

Both instability and residual articular incongruity are implicated in the development of post-traumatic osteoarthritis (OA) following intra-articular fracture, but currently no information exists regarding cartilage stresses for unstable residual incongruities. In this study, a transversely isotropic poroelastic cartilage finite element model was implemented and validated within physiologically relevant loading ranges. This material model was then used to simulate the loading of cartilage during stable and unstable motion accompanying a step-off incongruity residual from intra-articular fracture, using load data from previous cadaver tests of ankle instability. Peak solid-phase stresses and fluid pressure were found to increase markedly in the presence of instability. Solid-phase transients of normal stress increased from 2.00 to 13.8 MPa/s for stable compared to unstable motion, and tangential stress transients increased from 17.1 to 118.1 MPa/s. Corresponding fluid pressure transients increased from 15.1 to 117.9 MPa/s for unstable motion. In the most rapidly loaded sections of cartilage, the fluid was found to carry nearly all of the normal load, with the pressurization of the fluid resulting in high solid matrix tangential stresses.     

High pressures and asymmetrical stresses in the scoliotic disc in the absence of muscle loading

Background

Loads acting on scoliotic spines are thought to be asymmetric and involved in progression of the scoliotic deformity; abnormal loading patterns lead to changes in bone and disc cell activity and hence to vertebral body and disc wedging. At present however there are no direct measurements of intradiscal stresses or pressures in scoliotic spines. The aim of this study was to obtain quantitative measurements of the intradiscal stress environment in scoliotic intervertebral discs and to determine if loads acting across the scoliotic spine are asymmetric. We performed in vivo measurements of stresses across the intervertebral disc in patients with scoliosis, both parallel (termed horizontal) and perpendicular (termed vertical) to the end plate, using a side mounted pressure transducer (stress profilometry)

Methods

Stress profilometry was used to measure horizontal and vertical stresses at 5 mm intervals across 25 intervertebral discs of 7 scoliotic patients during anterior reconstructive surgery. A state of hydrostatic pressure was defined by identical horizontal and vertical stresses for at least two consecutive readings. Results were compared with similar stress profiles measured during surgery across 10 discs of 4 spines with no lateral curvature and with data from the literature.

Results

Profiles across scoliotic discs were very different from those of normal, young, healthy discs of equivalent age previously presented in the literature. Hydrostatic pressure regions were only seen in 14/25 discs, extended only over a short distance. Non-scoliotic discs of equivalent age would be expected to show large centrally placed hydrostatic nuclear regions in all discs. Mean pressures were significantly greater (0.25 MPa) than those measured in other anaesthetised patients (<0.07 MPa). A stress peak was seen in the concave annulus in 13/25 discs. Stresses in the concave annulus were greater than in the convex annulus indicating asymmetric loading in these anaesthetised, recumbent patients.

Conclusion

Intradiscal pressures and stresses in scoliotic discs are abnormal, asymmetrical and high in magnitude even in the absence of significant applied muscle loading. The origin of these abnormal stresses is unclear.     

The mechanical environment of chondrocytes in articular cartilage

There is a growing literature concerning chondrocyte responses to mechanical loading, but relatively little is known about the mechanical environment these cells experience in a living joint. Calculations indicate that high forces are applied to limb joints whenever the joints are flexed, because flexion can cause body weight to act on long lever arms compared to the joint centre, whereas the muscles which extend the joint act on much shorter lever arms. As a result, joint reaction forces (which compress the cartilage) can rise to 3-6 times body weight during activities such as stair climbing. Articular cartilage tends to spread this load evenly over the joint surface, but is too thin to do this well, and compressive stresses can rise to 10-20 MPa. Within cartilage, matrix stresses vary locally, possibly as a result of variation in composition or undulations in the subchondral bone, and further modifications of stress occur within each chondron. Articular cartilage is a fibrous solid and cells within it are deformed by mechanical loading rather than subjected to a hydrostatic pressure. The mechanical environment of chondrocytes can best be reproduced in vitro by direct compression of the articular surface of cartilage which is supported naturally by adjacent cartilage and subchondral bone.     

Evaluation of a subject-specific finite-element model of the equine metacarpophalangeal joint under physiological load

The equine metacarpophalangeal (MCP) joint is frequently injured, especially by racehorses in training. Most injuries result from repetitive loading of the subchondral bone and articular cartilage rather than from acute events. The likelihood of injury is multi-factorial but the magnitude of mechanical loading and the number of loading cycles are believed to play an important role. Therefore, an important step in understanding injury is to determine the distribution of load across the articular surface during normal locomotion. A subject-specific finite-element model of the MCP joint was developed (including deformable cartilage, elastic ligaments, muscle forces and rigid representations of bone), evaluated against measurements obtained from cadaver experiments, and then loaded using data from gait experiments. The sensitivity of the model to force inputs, cartilage stiffness, and cartilage geometry was studied. The FE model predicted MCP joint torque and sesamoid bone flexion angles within 5% of experimental measurements. Muscle–tendon forces, joint loads and cartilage stresses all increased as locomotion speed increased from walking to trotting and finally cantering. Perturbations to muscle–tendon forces resulted in small changes in articular cartilage stresses, whereas variations in joint torque, cartilage geometry and stiffness produced much larger effects. Non-subject-specific cartilage geometry changed the magnitude and distribution of pressure and the von Mises stress markedly. The mean and peak cartilage stresses generally increased with an increase in cartilage stiffness. Areas of peak stress correlated qualitatively with sites of common injury, suggesting that further modelling work may elucidate the types of loading that precede joint injury and may assist in the development of techniques for injury mitigation.     

Strain-rate dependent stiffness of articular cartilage in unconfined compression

The stiffness of articular cartilage is a nonlinear function of the strain amplitude and strain rate as well as the loading history, as a consequence of the flow of interstitial water and the stiffening of the collagen fibril network. This paper presents a full investigation of the interplay between the fluid kinetics and fibril stiffening of unconfined cartilage disks by analyzing over 200 cases with diverse material properties. The lower and upper elastic limits of the stress (under a given strain) are uniquely established by the instantaneous and equilibrium stiffness (obtained numerically for finite deformations and analytically for small deformations). These limits could be used to determine safe loading protocols in order that the stress in each solid constituent remains within its own elastic limit. For a given compressive strain applied at a low rate, the loading is close to the lower limit and is mostly borne directly by the solid constituents (with little contribution from the fluid). In contrast, however in case of faster compression, the extra loading is predominantly transported to the fibrillar matrix via rising fluid pressure with little increase of stress in the nonfibrillar matrix. The fibrillar matrix absorbs the loading increment by self-stiffening: the quicker the loading the faster the fibril stiffening until the upper elastic loading limit is reached. This self-protective mechanism prevents cartilage from damage since the fibrils are strong in tension. The present work demonstrates the ability of the fibril reinfored poroelastic models to describe the strain rate dependent behavior of articular cartilage in unconfined compression using a mechanism of fibril stiffening mainly induced by the fluid flow.     

Injurious mechanical compression of bovine articular cartilage induces chondrocyte apoptosis

A bovine cartilage explant system was used to evaluate the effects of injurious compression on chondrocyte apoptosis and matrix biochemical and biomechanical properties within intact cartilage. Disks of newborn bovine articular cartilage were compressed in vitro to various peak stress levels and chondrocyte apoptotic cell death, tissue biomechanical properties, tissue swelling, glycosaminoglycan loss, and nitrite levels were quantified. Chondrocyte apoptosis occurred at peak stresses as low as 4.5 MPa and increased with peak stress in a dose-dependent manner. This increase in apoptosis was maximal by 24 h after the termination of the loading protocol. At high peak stresses (>20 MPa), greater than 50% of cells apoptosed. When measured in uniaxial confined compression, the equilibrium and dynamic stiffness of explants decreased with the severity of injurious load, although this trend was not significant until 24-MPa peak stress. In contrast, the equilibrium and dynamic stiffness measured in radially unconfined compression decreased significantly after injurious stresses of 12 and 7 MPa, respectively. Together, these results suggested that injurious compression caused a degradation of the collagen fibril network in the 7- to 12-MPa range. Consistent with this hypothesis, injurious compression caused a dose-dependent increase in tissue swelling, significant by 13-MPa peak stress. Glycosaminoglycans were also released from the cartilage in a dose-dependent manner, significant by 6- to 13-MPa peak stress. Nitrite levels were significantly increased above controls at 20-MPa peak stress. Together, these data suggest that injurious compression can stimulate cell death as well as a range of biomechanical and biochemical alterations to the matrix and, possibly, chondrocyte nitric oxide expression. Interestingly, chondrocyte programmed cell death appears to take place at stresses lower than those required to stimulate cartilage matrix degradation and biomechanical changes. While chondrocyte apoptosis may therefore be one of the earliest responses to tissue injury, it is currently unclear whether this initial cellular response subsequently drives cartilage matrix degradation and changes in the biomechanical properties of the tissue.     

几种椎间盘退变动物模型的建立和应用

椎间盘退变是一种年龄相关的退行性疾病,是引起下腰痛的主要因素,严重影响病人的生活质量,并显著增加家庭的经济负担。目前,缺少椎间盘退变的有效干预和治疗手段,部分原因是其发病机制尚未阐明。椎间盘退变动物模型的构建对于阐明该疾病的病理机制至关重要。椎间盘退变是一个复杂的过程,受机械应力、结构损伤、生物化学与基因表达等多种因素的影响。本文总结了应用异常机械应力、结构损伤、生物化学或化学诱导和基因敲除等方式构建的椎间盘退变动物模型。生物力学是维持椎间盘稳态的重要因素,异常的机械应力会导致椎间盘退变。同时,椎间盘退变常伴随结构性损伤,椎间盘结构破坏也会导致椎间盘发生退变。此外,生物化学或化学诱导和关键基因敲除也会导致椎间盘退变。本文按照造成异常机械应力的因素将机械应力模型分为加压模型和失稳模型;按照椎间盘结构将结构损伤模型分为髓核与纤维环损伤模型和软骨终板损伤模型。总结了生物化学或化学诱导模型以及新型的基因敲除模型。讨论了不同类型椎间盘退变动物模型的可能应用和局限性。     

力学环境对软骨基质代谢的影响

正常关节软骨所受压力是由动态压力与静态压力交替完成。压力引起软骨一系列生理变化包括细胞及细胞外基质成分变形、组织内液体流动、水流电位和生理生化变化。这些变化直接调控细胞外基质代谢。体外构建有良好功能的组织工程化软骨是目前软骨病变、缺损理想的修复方法。研究力学环境对软骨基质代谢的影响,对构建组织工程化软骨有深远意义。     

Effects of shear stress on articular chondrocyte metabolism

The articular cartilage of diarthrodial joints experiences a variety of stresses, strains and pressures that result from normal activities of daily living. In normal cartilage, the extracellular matrix exists as a highly organized composite of specialized macromolecules that distributes loads at the bony ends. The chondrocyte response to mechanical loading is recognized as an integral component in the maintenance of articular cartilage matrix homeostasis. With inappropriate mechanical loading of the joint, as occurs with traumatic injury, ligament instability, bony malalignment or excessive weight bearing, the cartilage exhibits manifestations characteristic of osteoarthritis. Breakdown of cartilage in osteoarthritis involves degradation of the extracellular matrix macromolecules and decreased expression of chondrocyte proteins necessary for normal joint function. Osteoarthritic cartilage often exhibits increased amounts of type I collagen and synthesis of proteoglycans characteristic of immature cartilage. The shift in cartilage phenotype in response to altered load yields a matrix that fails to support normal joint function. Mathematical modeling and experimental studies in animal models confirm an association between altered loading of diarthrotic joints and arthritic changes. Both types of studies implicate shear forces as a critical component in the destructive profile. The severity of cartilage destruction in response to altered loads appears linked to expression of biological factors influencing matrix integrity and cellular metabolism. Determining how shear stress alters chondrocyte metabolism is fundamental to understanding how to limit matrix destruction and stimulate cartilage repair and regeneration. At present, the precise biochemical and molecular mechanisms by which shear forces alter chondrocyte metabolism from a normal to a degenerative phenotype remain unclear. The results presented here address the hypothesis that articular chondrocyte metabolism is modulated by direct effects of shear forces that act on the cell through mechanotransduction processes. The purpose of this work is to develop critical knowledge regarding the basic mechanisms by which mechanical loading modulates cartilage metabolism in health and disease. This presentation will describe the effects of using fluid induced shear stress as a model system for stimulation of articular chondrocytes in vitro. The fluid induced shear stress was applied using a cone viscometer system to stimulate all the cells uniformly under conditions of minimal turbulence. The experiments were carried using high-density primary monolayer cultures of normal and osteoarthritic human and normal bovine articular chondrocytes. The analysis of the cellular response included quantification of cytokine release, matrix metalloproteinase expression and activation of intracellular signaling pathways. The data presented here show that articular chondrocytes exhibit a dose- and time-dependent response to shear stress that results in the release of soluble mediators and extracellular matrix macromolecules. The data suggest that the chondrocyte response to mechanical stimulation contributes to the maintenance of articular cartilage homeostasis in vivo.     

A Theoretical Analysis of Water Transport Through Chondrocytes

Because of the avascular nature of adult cartilage, nutrients and waste products are transported to and from the chondrocytes by diffusion and convection through the extracellular matrix. The convective interstitial fluid flow within and around chondrocytes is poorly understood. This theoretical study demonstrates that the incorporation of a semi-permeable membrane when modeling the chondrocyte leads to the following findings: under mechanical loading of an isolated chondrocyte the intracellular fluid pressure is on the order of tens of Pascals and the transmembrane fluid outflow, on the order of picometers per second, takes several days to subside; consequently, the chondrocyte behaves practically as an incompressible solid whenever the loading duration is on the order of minutes or hours. When embedded in its extracellular matrix (ECM), the chondrocyte response is substantially different. Mechanical loading of the tissue leads to a fluid pressure difference between intracellular and extracellular compartments on the order of tens of kilopascals and the transmembrane outflow, on the order of a nanometer per second, subsides in about 1 h. The volume of the chondrocyte decreases concomitantly with that of the ECM. The interstitial fluid flow in the extracellular matrix is directed around the cell, with peak values on the order of tens of nanometers per second. The viscous fluid shear stress acting on the cell surface is several orders of magnitude smaller than the solid matrix shear stresses resulting from the ECM deformation. These results provide new insight toward our understanding of water transport in chondrocytes.     

The mechanical environment of the chondrocyte: a biphasic finite element model of cell-matrix interactions in articular cartilage

Mechanical compression of the cartilage extracellular matrix has a significant effect on the metabolic activity of the chondrocytes. However, the relationship between the stress–strain and fluid-flow fields at the macroscopic “tissue” level and those at the microscopic “cellular” level are not fully understood. Based on the existing experimental data on the deformation behavior and biomechanical properties of articular cartilage and chondrocytes, a multi-scale biphasic finite element model was developed of the chondrocyte as a spheroidal inclusion embedded within the extracellular matrix of a cartilage explant. The mechanical environment at the cellular level was found to be time-varying and inhomogeneous, and the large difference (3 orders of magnitude) in the elastic properties of the chondrocyte and those of the extracellular matrix results in stress concentrations at the cell–matrix border and a nearly two-fold increase in strain and dilatation (volume change) at the cellular level, as compared to the macroscopic level. The presence of a narrow “pericellular matrix” with different properties than that of the chondrocyte or extracellular matrix significantly altered the principal stress and strain magnitudes within the chondrocyte, suggesting a functional biomechanical role for the pericellular matrix. These findings suggest that even under simple compressive loading conditions, chondrocytes are subjected to a complex local mechanical environment consisting of tension, compression, shear, and fluid pressure. Knowledge of the local stress and strain fields in the extracellular matrix is an important step in the interpretation of studies of mechanical signal transduction in cartilage explant culture models.     

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.     

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.     

Chondrocyte regulation by mechanical load

The effects of load on articular cartilage are complex. Dynamic loading of cartilage is associated with slight cell and tissue deformation as well as cyclical fluctuations in the hydrostatic pressure of cartilage and in fluid movement. Static loading results in expression of fluid from the tissue, concentrating extracellular matrix macromolecules and consequently increasing the concentrations of cations, reducing extracellular pH and increasing extracellular osmolarity. Each of these alterations is implicated in regulating the synthetic response of chondrocytes to load. However, the mechanisms by which these changes affect matrix turnover are poorly understood. In this review we consider how load may affect chondrocyte behaviour through its influence on membrane transport processes and thus on the intracellular environment.     

Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration

The understanding of load support mechanisms in cartilage has evolved with computational models that better mimic the tissue ultrastructure. Fibril-reinforced poroelastic models can reproduce cartilage behaviour in a variety of test conditions and can be used to model tissue anisotropy as well as assess stress and pressure partitioning to the tissue constituents. The goal of this study was to examine the stress distribution in the fibrillar and non-fibrillar solid phase and pressure in the fluid phase of cartilage in axisymmetric models of a healthy and osteoarthritic hip joint. Material properties, based on values from the literature, were assigned to the fibrillar and poroelastic components of cartilage and cancellous and subchondral compact bone regions. A cyclic load representing walking was applied for 25 cycles. Contact stresses in the fibrillar and non-fibrillar solid phase supported less than 1% of the contact force and increased only minimally with load cycles. Simulated proteoglycan depletion increased stresses in the radial and tangential collagen fibrils, whereas fibrillation of the tangential fibrils resulted in increased compressive stress in the non-fibrillar component and tensile stress in the radial fibrils. However neither had an effect on fluid pressure. Subchondral sclerosis was found to have the largest effect, resulting in increased fluid pressure, non-fibrillar compressive stress, tangential fibril stress and greater cartilage consolidation. Subchondral bone stiffening may play an important role in the degenerative cascade and may adversely affect tissue repair and regeneration treatments.     

The role of fibril reinforcement in the mechanical behavior of cartilage

Collagen fibril reinforcement was incorporated into a nonlinear poroelastic model for articular cartilage in unconfined compression. It was found that the radial fibrils play a predominant role in the transient mechanical behavior but a less important role in the equilibrium response of cartilage. The radial fibrils are in tension and can be highly stressed during compression, in contrast to low compressive stresses in all directions for the proteoglycan matrix after a small initial compression. The strain dependent fibril stiffening produces strong nonlinear transient response; the fibrils provide extra stiffness to balance a rising fluid pressure and to restrain stress increase in the proteoglycans. The fibril reinforcement, induced by the fluid pressure and flow, also accounts for a complex pattern of strain-magnitude and strain-rate dependence of cartilage stiffness.     

Modelling of location- and time-dependent deformation of chondrocytes during cartilage loading.

Experimental evidence suggests that the biosynthetic activity of chondrocytes is regulated primarily by the mechanical environment. In order to study the mechanisms underlying remodeling, adaptation, and degeneration of articular cartilage in a joint subjected to changing loads, it is important to know the time-dependent fluid pressure and stress-strain state in chondrocytes. The purpose of the present study was to develop a theoretical model to simulate the mechanical behaviour of articular cartilage and to describe the time-dependent stress-strain state and fluid pressure distribution in chondrocytes during cartilage deformation. It was assumed that the volume occupied by the chondrocytes is small and that cartilage can be treated as a macroscopically homogenized material with effective material properties which depend on the material properties of the cells and matrix and the volumetric fraction of the cells. Model predictions on the time-dependent distribution of fluid pressure and stress and on the time-dependent cell deformation during confined and unconfined compression tests agree with previous theoretical predictions and experimental observations. The proposed model supplies the tools to study the mechanisms of degeneration, adaptation and remodelling of cartilage associated with cell loading and deformation.     

Dynamic unconfined compression of articular cartilage under a cyclic compressive load

To study the effect of dynamic mechanical force on cartilage metabolism, many investigators have applied a cyclic compressive load to cartilage disc explants in vitro. The most frequently used in vitro testing protocol has been the cyclic unconfined compression of articular cartilage in a bath of culture medium. Cyclic compression has been achieved by applying either a prescribed cyclic displacement or a prescribed cyclic force on a loading platen placed on the top surface of a cylindrical cartilage disc. It was found that the separation of the loading platen from the tissue surface was likely when a prescribed cyclic displacement was applied at a high frequency.The purpose of the present study was to simulate mathematically the dynamic behavior of a cylindrical cartilage disc subjected to cyclic unconfined compression under a dynamic force boundary condition protocol, and to provide a parametric analysis of mechanical deformations within the extracellular matrix. The frequency-dependent dynamic characteristics of dilatation, hydrostatic pressure and interstitial fluid velocity were analyzed over a wide range of loading frequencies without the separation of the loading platen. The result predicted that a cyclic compressive force created an oscillating positive-negative hydrostatic pressure together with a forced circulation of interstitial fluid within the tissue matrix. It was also found that the load partitioning mechanism between the solid and fluid phases was a function of loading frequency. At a relatively high loading frequency, a localized dynamic zone was developed near the peripheral free surface of the cartilage disc, where a large dynamic pressure gradient exists, causing vigorous interstitial fluid flow.     

Variability of a three-dimensional finite element model constructed using magnetic resonance images of a knee for joint contact stress analysis

Magnetic resonance (MR) imaging has been widely used to evaluate the thickness and volume of articular cartilage both in vivo and in vitro. While morphological information on the cartilage can be obtained using MR images, image processing for extracting geometric boundaries of the cartilage may introduce variations in the thickness of the cartilage. To evaluate the variability of using MR images to construct finite element (FE) knee cartilage models, five investigators independently digitized the same set of MR images of a human knee. The topology of cartilage thickness was determined using a minimal distance algorithm. Less than 8 percent variation in cartilage thickness was observed from the digitized data. The effect of changes in cartilage thickness on contact stress analysis was then investigated using five FE models of the knee. One FE model (average FE model) was constructed using the mean values of the digitized contours of the cartilage, and the other four were constructed by varying the thickness of the average FE model by +/- 5 percent and +/- 10 percent, respectively. The results demonstrated that under axial tibial compressive loading (up to 1,400 N), variations of cartilage thickness caused by digitization of MR images may result in a difference of approximately 10 percent in peak contact stresses (surface pressure, von Mises stress, and hydrostatic pressure) in the cartilage. A reduction of cartilage thickness caused increases of contact stresses, while an increase of cartilage thickness reduced contact stresses. Furthermore, the effect of variation of material properties of the cartilage on contact stress analysis was investigated. The peak contact stress increased almost linearly with the Young's modulus of the cartilage. The peak von Mises stress was dramatically reduced when the Poisson,s ratio was increased from 0.05 to 0.49 under an axial compressive load of 1,400 N, while peak hydrostatic pressure was dramatically increased. Peak surface pressure was also increased with the Poisson's ratio, but with a lower magnitude compared to von Mises stress and hydrostatic pressure. In conclusion, the imaging process may cause 10 percent variations in peak contact stress, and the predicted stress distribution is sensitive to the accuracy of the material properties of the cartilage model, especially to the variation of Poisson's ratio.     

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.