Distribution of stresses in the left ventricular wall of the intact heart

The left ventricle is modelled as a prolate spheroid of viscoelastic material with an aim to demonstrate the qualitative effects of anistropy and nonhomogeneity in the calculation of intact ventricular wall stresses. The pericardial pressure is accounted for in the analysis and an attempt is made to examine to what extent this influences the ventricular stresses. Numerical results are also obtained by computing the analytical expressions derived through the analysis.     

Effect of bone graft characteristics on the mechanical behavior of the lumbar spine

There is little information about the influence of bone graft size, position and elasticity on the mechanical behavior of the lumbar spine. Intersegmental motion, intradiscal pressure and stresses in the lumbar spine were calculated using a three-dimensional, nonlinear finite element model which included an internal spinal fixation device and a bone graft. Cross-sectional area, position, and elastic modulus of the graft were varied in this study. Bone grafts, especially very stiff ones, increase stresses on adjacent endplates. Though larger grafts lead to less contact pressure, it is difficult to judge the quality of different bone graft positions. In general, ventral flexion results in lower maximum contact pressure than lateral bending. There is always little intersegmental rotation in the bridged region compared with that of an intact spine.A larger graft with low stiffness should be favored from a mechanical point of view. Patients should avoid lateral bending of the upper body shortly after surgery.     

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.     

A Mathematical Model of Spatial Self-Organization in a Mechanically Active Cellular Medium

A general continual model of a medium composed of mechanically active cells is proposed. The medium is considered to be formed by three phases: cells, extracellular fluid, and an additional phase that is responsible for active interaction forces between cells and, for instance, may correspond to a system of protrusions that provide the development of active contractile forces. The deformation of the medium, which is identified with the deformation of the cell phase, consists of two components: elastic deformation of individual cells and cell rearrangements. The elastic deformation is associated with stresses in the cell phase. The spherical component of the stress tensor describes the nonlinear resistance of the cellular medium, which leads to the impossibility of its excessive compression. The constitutive equation for pressure in the cell phase is taken in the form of a nonlinear dependence on the volume cell density. The rearrangement of cells is considered as a flow controlled by stresses in the cell phase, active stresses, and fluid pressure. The tensor of active stresses is assumed to be spherical and nonlocally dependent on the cell density. Assuming that the process of biological tissue deformation is slow, we obtained a reduced model that neglects the elastic deformation of cells, compared to the inelastic deformation. A linear stability analysis of a spatially uniform steady-state solution was performed. The hydrostatic pressure of fluid is present among the parameters that are responsible for the loss of stability of the steady-state solution: an increase in it has a destabilizing effect owing to the action of the component of the interphase interaction force that is determined by the fluid pressure. The model we obtained can be used to describe the process of cavity formation in an initially homogeneous cell spheroid. The role of local and nonlocal mechanisms of active stress generation in the formation of cavity is investigated.     

A novel computational method to determine subject-specific bite force and occlusal loading during mastication

The evaluation of three-dimensional occlusal loading during biting and chewing may assist in development of new dental materials, in designing effective and long-lasting restorations such as crowns and bridges, and for evaluating functional performance of prosthodontic components such as dental and/or maxillofacial implants. At present, little is known about the dynamic force and pressure distributions at the occlusal surface during mastication, as these quantities cannot be measured directly. The aim of this study was to evaluate subject-specific occlusal loading forces during mastication using accurate jaw motion measurements. Motion data was obtained from experiments in which an individual performed maximal effort dynamic chewing cycles on a rubber sample with known mechanical properties. A finite element model simulation of one recorded chewing cycle was then performed to evaluate the deformation of the rubber. This was achieved by imposing the measured jaw motions on a three-dimensional geometric surface model of the subject’s dental impressions. Based on the rubber’s deformation and its material behaviour, the simulation was used to compute the resulting stresses within the rubber as well as the contact pressures and forces on the occlusal surfaces. An advantage of this novel modelling approach is that dynamic occlusal pressure maps and biting forces may be predicted with high accuracy and resolution at each time step throughout the chewing cycle. Depending on the motion capture technique and the speed of simulation, the methodology may be automated in such a way that it can be performed chair-side. The present study demonstrates a novel modelling methodology for evaluating dynamic occlusal loading during biting or chewing.     

Possible role of stresses in inducing spinal stenosis--a long term complication following disk excision

A three-dimensional finite element model of an intact ligamentous lumbar motion segment (L3-4) was used to predict stresses in the pars interarticularis regions of the modeled vertebral bodies. The changes in stresses following disk excision, as compared to the intact model, also were computed. The predicted results show an increase in stresses in the posterior bony elements following disk excision. In some patients over a long period of time this increase in stresses, in association with other clinical factors, may lead to bony hypertrophy of the structures that surround the nerve roots. Ultimately, over a long period of time the increase in pressure on the entrapped nerve root may induce recurrent pain and other complications reported in the literature.     

Uterine peristalsis-induced stresses within the uterine wall may sprout adenomyosis

Adenomyosis is a disease in which ectopic endometrial glands and stromal cells appear in the uterine myometrium. This pathology is common among women of reproductive age, and in addition to chronic pelvic pain and heavy periods it may also cause infertility. The ‘tissue injury and repair’ mechanism in response to increased intrauterine pressures was proposed as the etiology for migration of fragments of basal endometrium into the myometrial wall. In order to investigate this mechanism, a conceptual two-dimensional model of the uterine wall subjected to intrauterine pressures was implemented using ADINA commercial software. The stress field within the uterine wall was examined for a variety of intrauterine sinusoidal pressure waves with varying frequencies. The results revealed that: (1) as the wavelength of the subjected pressure wave decreased, high concentration of stresses developed near the inner uterine cavity; (2) as the pressure wave frequency increased, high gradients of the stresses were obtained; (3) at menstrual phase, the highest stresses obtained at the endometrial–myometrial interface. Therefore, increased uterine activity results in high stresses which may lead to tissue lesions and detachment of endometrial cells.     

Compression of interventricular septum during right ventricular pressure loading

The interventricular septum, which flattens and inverts in conditions such as pulmonary hypertension, is considered by many to be an unstressed membrane, in that its position is assumed to be determined solely by the transseptal pressure gradient. A two-dimensional finite element model was developed to investigate whether compression and bending moments (behavior incompatible with a membrane) exist in the septum during diastole under abnormal loading, i.e., pulmonary artery (PA) constriction. Hemodynamic and echocardiographic data were obtained in six open-chest anesthetized dogs. For both control and PA constriction, the measured left ventricular and right ventricular pressures were applied to a residually stressed mesh. Adjustments were made to the stiffness and end-bending moments until the deformed and loaded residually stressed mesh matched the observed configuration of the septum. During PA constriction, end-bending moments were required to obtain satisfactory matches but not during control. Furthermore, substantial circumferential compressive stresses developed during PA constriction. Such stresses might impede septal blood flow and provoke the unexplained ischemia observed in some conditions characterized by abnormal septal motion.     

Collagen fibers reduce stresses and stabilize motion of aortic valve leaflets during systole

The effect of collagen fibers on the mechanics and hemodynamics of a trileaflet aortic valve contained in a rigid aortic root is investigated in a numerical analysis of the systolic phase. Collagen fibers are known to reduce stresses in the leaflets during diastole, but their role during systole has not been investigated in detail yet. It is demonstrated that also during systole these fibers substantially reduce stresses in the leaflets and provide smoother opening and closing. Compared to isotropic leaflets, collagen reinforcement reduces the fluttering motion of the leaflets. Due to the exponential stress-strain behavior of collagen, the fibers have little influence on the initial phase of the valve opening, which occurs at low strains, and therefore have little impact on the transvalvular pressure drop.     

The Effect of Temperature Gradients on Stress Development During Cryopreservation via Vitrification

This study addresses the problem of thermal stress development in bulky specimens during cryopreservation via vitrification (vitreous means glassy in Latin). While this study is a part of an ongoing effort to associate the developing mechanical stress with the relevant physical properties of the cryopreserved media and to its the thermal history, the current paper focuses exclusively on the role of temperature gradients. Temperature gradients arise due to the high cooling rates necessary to facilitate vitrification; the resulting non-uniform temperature distribution leads to differential thermal strain, possibly resulting in cracking. The cooling rate is assumed constant on the outer surface in this study, and the material properties are assumed constant. It is demonstrated that under these assumptions, mechanical stress develops only when the temperature distribution in the specimen approaches thermal equilibrium at a cryogenic storage temperature. It is shown that the maximum possible stresses for a given cooling rate can be computed with a simple thermo-elastic analysis; these stresses are associated with cooling to sufficiently low temperatures and are independent of the variation of viscosity with temperature. Analytic estimates for these stresses are obtained for several idealized shapes, while finite element analysis is used to determine stresses for geometries used in cryopreservation practice. Stresses that develop under a wider range of storage temperatures are also studied with finite element analysis, and the results are summarized with suitable normalizations. It is found that no stresses arise if cooling ceases above the set-temperature, which defines the transition from viscous-dominated to elastic-dominated behavior; the set-temperature is determined principally by the dependency of viscosity upon temperature. Strategies for rapidly reaching low temperatures and avoiding high stresses are inferred from the results.     

Biphasic finite element simulation of the TMJ disc from in vivo kinematic and geometric measurements

Understanding the biomechanical nature of the degeneration of the temporomandibular joint requires a coupling between experimental measurements and numerical simulation. In this study, geometry measured from MRI, and motion obtained from a specially designed optoelectronic system are fed into a three-dimensional biphasic finite element analysis to generate the spatial and temporal mechanical response of the disc. This study demonstrates how this coupling can effectively predict the biomechanical response of the temporomandibular joint disc to physiological loading. For small jaw opening movements, asymmetries in the load of the disc are found, with especially higher shear stresses in the lateral portion.     

Method for the design and analysis of a non-linear anisotropic lower limb prosthetic socket

A simplified computer-based structural analysis procedure has been developed for evaluating the stresses in a lower limb prosthetic socket when subjected to external loads. This technique has been tested by studying a simple linear axisymmetric shell subjected to uniform loads. It was found that the stress and strain distributions obtained are close to those determined by a finite element technique. The method that has been proposed involves an incremental procedure, which can be used to analyse the behaviour of a prosthetic socket of irregular shape made from non-linear anisotropic materials. By employing the proposed procedure to study an example, in which a simplified lower limb prosthetic socket is subject to internal pressure and frictional forces, the effects of the material non-linearity have been found to be significant.     

Visualizing protein motion in Couette flow by all-atom molecular dynamics

In living cells, biomacromolecules are exposed to a highly crowded environment. The cytoplasm, the nucleus, and other organelles are highly viscous fluids that differ from dilute in vitro conditions. Viscosity, a measure of fluid internal friction, directly affects the forces that act on immersed macromolecules. Although active motion of this viscous fluid – cytoplasmic streaming – occurs in many plant and animal cells, the effect of fluid motion (flow) on biomolecules is rarely discussed. Recently NMR experiments that apply a shearing flow in situ have been used for protein studies. While these NMR experiments have succeeded in spectroscopically tracking protein aggregation in real time, they do not provide a visual picture of protein motion under shear. To fill this gap, here we have used molecular dynamics simulations to study the motion of three proteins of different size and shape in a simple shearing flow. The proteins exhibit a superposition of random diffusion and shear-flow-induced rotational motion. Random rotational diffusion dominates at lower shear stresses, whereas an active “rolling motion” along the axis of the applied flow occurs at higher shear stress. Even larger shear stresses perturb protein secondary structure elements resulting in local and global unfolding. Apart from shear-induced unfolding, our results imply that, in an ideal Couette flow field biomolecules undergo correlated motion, which should enhance the probability of inter-molecular interaction and aggregation. Connecting biomolecular simulation with experiments applying shear flow in situ appears to be a promising strategy to study protein alignment, deformation, and dynamics under shear.     

Load transfer mechanics between trans-tibial prosthetic socket and residual limb--dynamic effects

The effects of inertial loads on the interface stresses between trans-tibial residual limb and prosthetic socket were investigated. The motion of the limb and prosthesis was monitored using a Vicon motion analysis system and the ground reaction force was measured by a force platform. Equivalent loads at the knee joint during walking were calculated in two cases with and without consideration of the material inertia. A 3D nonlinear finite element (FE) model based on the actual geometry of residual limb, internal bones and socket liner was developed to study the mechanical interaction between socket and residual limb during walking. To simulate the friction/slip boundary conditions between the skin and liner, automated surface-to-surface contact was used. The prediction results indicated that interface pressure and shear stress had the similar double-peaked waveform shape in stance phase. The average difference in interface stresses between the two cases with and without consideration of inertial forces was 8.4% in stance phase and 20.1% in swing phase. The maximum difference during stance phase is up to 19%. This suggests that it is preferable to consider the material inertia effect in a fully dynamic FE model.     

An accurate validation of a computational model of a human lumbosacral segment

Clinical studies have recently documented that there is sufficient evidence to suggest that abnormal motion may be an indicator of abnormal mechanics of the spine and, therefore, may be associated with some types of low-back pain. However, designating a motion as abnormal requires knowledge of normal motions. This work hence aims to develop an accurate computational model to simulate the bio-mechanical response of the whole lumbosacral spinal unit (L1–S1) under physiological loadings and constraint conditions. In order to meet this objective, computed tomography (CT) scanning protocols, finite element (FE) analysis and accurate constitutive modelling have been integrated. Then the ranges of motion (ROM) under flexion, extension and lateral bending moment were measured and compared with experimental data, finding an excellent agreement. In particular, the ability of the model to reproduce the relative rotation between each couple of vertebrae was proved. Finally, the shear stresses for the most extreme load cases were reported in order to predict which are the most risky conditions and where the maximum damage would be located. The results indicate that the greater values of the stresses were located at L4–S1 levels just in the interfaces between disc and vertebrae across the posterior and posterolateral zone. This result can be clinically correlated with the existence of damage exactly where the stresses were maximal in the proposed finite element model.     

Simulation of a balloon expandable stent in a realistic coronary artery—Determination of the optimum modelling strategy

Computational models of stent deployment in arteries have been widely used to shed light on various aspects of stent design and optimisation. In this context, modelling of balloon expandable stents has proved challenging due to the complex mechanics of balloon–stent interaction and the difficulties involved in creating folded balloon geometries. In this study, a method to create a folded balloon model is presented and utilised to numerically model the accurate deployment of a stent in a realistic geometry of an atherosclerotic human coronary artery. Stent deployment is, however, commonly modelled by applying an increasing pressure to the stent, thereby neglecting the balloon. This method is compared to the realistic balloon expansion simulation to fully elucidate the limitations of this procedure. The results illustrate that inclusion of a realistic balloon model is essential for accurate modelling of stent deformation and stent stresses. An alternative balloon simulation procedure is presented however, which overcomes many of the limitations of the applied pressure approach by using elements which restrain the stent as the desired diameter is achieved. This study shows that direct application of pressure to the stent inner surface may be used as an optimal modelling strategy to estimate the stresses in the vessel wall using these restraining elements and hence offer a very efficient alternative approach to numerically modelling stent deployment within complex arterial geometries. The method is limited however, in that it can only predict final stresses in the stented vessel and not those occurring during stent expansion, in which case the balloon expansion model is required.     

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.     

Initial stress and nonlinear material behavior in patient-specific AAA wall stress analysis

Rupture risk estimation of abdominal aortic aneurysms (AAA) is currently based on the maximum diameter of the AAA. A more critical approach is based on AAA wall stress analysis. For that, in most cases, the AAA geometry is obtained from CT-data and treated as a stress free geometry. However, during CT imaging, the AAA is subjected to a time-averaged blood pressure and is therefore not stress free. The aim of this study is to evaluate the effect of neglecting these initial stresses (IS) on the patient-specific AAA wall stress as computed by finite element analysis. Additionally, the contribution of the nonlinear material behavior of the AAA wall is evaluated.Thirty patients with maximum AAA diameters below the current surgery criterion were scanned with contrast-enhanced CT and the AAA's were segmented from the image data. The mean arterial blood pressure (MAP) was measured immediately after the CT-scan and used to compute the IS corresponding with the CT geometry and MAP. Comparisons were made between wall stress obtained with and without IS and with linear and nonlinear material properties.On average, AAA wall stresses as computed with IS were higher than without IS. This was also the case for the stresses computed with the nonlinear material model compared to the linear material model. However, omitting initial stress and material nonlinearity in AAA wall stress computations leads to different effects in the resulting wall stress for each AAA. Therefore, provided that other assumptions made are not predominant, IS cannot be discarded and a nonlinear material model should be used in future patient-specific AAA wall stress analyses.     

Numerical investigation of mechanical effects caused by various fixation positions on a new radius intramedullary nail

Fracture of the radius diaphysis is an unusual injury in adults. Open reduction and plate osteosynthesis has been recommended by most of the authors. However, this trend has started to change with the recent introduction of newly designed interlocking intramedullary (IM) nails. New generation of IM nails are developed in order to utilise the advantages of IM nails against plates. Because of its anatomical structure, the radius bone has a complex geometry. Therefore, the callus structure, which forms during the healing period, should not be affected from external effects, such as excessive loads or motion. In this study, effects of radial styloid process (RSP), dorsal side and ulnar notch edge fixations of a new design radius IM nail on the healing period were numerically investigated. A three-dimensional solid model of radius was obtained from computed tomography images of a volunteer and callus structure model, was placed accordingly and different fixations of implants were performed. The models were analysed under axial loads transferring from the wrist to the radius bone using finite element method. As a result of the analysis, fixation of IM nail from RSP was found to be beneficial on healing period in terms of both callus motion and emerging stresses.     

Biomechanical analysis of the three-dimensional foot structure during gait: a basic tool for clinical applications

A novel three-dimensional numerical model of the foot, incorporating, for the first time in the literature, realistic geometric and material properties of both skeletal and soft tissue components of the foot, was developed for biomechanical analysis of its structural behavior during gait. A system of experimental methods, integrating the optical Contact Pressure Display (CPD) method for plantar pressure measurements and a Digital Radiographic Fluoroscopy (DRF) instrument for acquisition of skeletal motion during gait, was also developed in this study and subsequently used to build the foot model and validate its predictions. Using a Finite Element solver, the stress distribution within the foot structure was obtained and regions of elevated stresses for six subphases of the stance (initial-contact, heel-strike, midstance, forefoot-contact, push-off, and toe-off) were located. For each of these subphases, the model was adapted according to the corresponding fluoroscopic data, skeletal dynamics, and active muscle force loading. Validation of the stress state was achieved by comparing model predictions of contact stress distribution with respective CPD measurements. The presently developed measurement and numerical analysis tools open new approaches for clinical applications, from simulation of the development mechanisms of common foot disorders to pre- and post-interventional evaluation of their treatment.