Repeated unit cell (RUC) approach for pure bending analysis of coronary stents

Flexibility is one of the key properties of coronary stents. The objective of this paper is to characterize the bending behaviour of stents through finite element analysis with repeated unit cell (RUC) models. General periodic boundary conditions for the RUC under the pure bending condition are formulated. It is found that the proposed RUC approach can provide accurate numerical results of bending behaviour of stents with much less computational costs. Bending stiffness, post-yield bending behaviour and the relationship between moment and bending curvature are investigated for Palmaz–Schatz stents and stents with the V- and S-shaped links. It is found that the effect of link geometry on the bending behaviour of stent is significant. The behaviour of stents subjected to cyclic bending is also investigated.     

General patterns and asymptotic dose in the design of coated stents

Stents are used in interventional cardiology to keep a diseased vessel open. New stents are coated with a medicinal agent to prevent early reclosure due to the proliferation of smooth muscle cells. It is recognised that it is the dose of the agent that effectively controls the growth. This paper focusses on the asymptotic behaviour of the dose for general families of coated stents under a fixed ratio between the coated region of the stent and the targeted region of the vessel and set therapeutic bounds on the dose. It generalises the results of Delfour, Garon and Longo for stents made of a sequence of thin equally spaced rings to stents with an arbitrary pattern. It gives the equation of the asymptotic dose for a normal tiling of the target region using the theory of tilings, patterns and motifs on a cylinder.     

Stresses in peripheral arteries following stent placement: a finite element analysis

The success of stents to restore blood flow in atherosclerotic peripheral arteries is low relative to coronary arteries. It has been shown that joint flexion induces a mechanical environment that makes stent placement in these arteries highly incompatible, and damage and destruction of stents has been recorded. However, the effect of this environment on the stresses in the arteries is unknown. It is hypothesised that the stresses induced in arteries as a result of this mechanical environment could be sufficient to explain the relatively low success rates. To investigate this hypothesis, a finite element model of the stent-artery interaction was developed. Following stent expansion, bending was simulated by applying a displacement boundary condition to the artery. It is found that high stresses occur at the proximal/distal ends of the stent. As high stress and vascular injury are hypothesised to cause restenosis, the results presented here suggest that the mechanical environment of peripheral arteries could be the predominant cause of high restenosis rates.     

Behaviour of implantable coronary stents during magnetic resonance imaging

BACKGROUND: Magnetic resonance imaging (MRI) becomes more and more a routine diagnostic tool in clinical cardiology. In patients undergoing MRI, metallic implants may be harmful by motion or heating under certain circumstances. Many cardiac patients have implanted intracoronary stents. However, the safety of these metallic implants and especially their temperature behaviour during MRI has not been sufficiently tested. METHODS: This study investigated motion and temperature changes of 14 different stents for intracoronary application in two clinical scanners at field strengths of 1.0 and 1.5 T. At 1.5 T these studies were repeated after implantation of the stents into the coronary arteries of excised porcine hearts. Furthermore, the clinical status of 33 patients was assessed after a cardiac MR study and compared with a group of 33 patients matched for age, sex and risk factors for restenosis. RESULTS: No visible motion of the stents was observed. Furthermore, using a highly sensitive infrared camera any significant heating of the stents during MRI could be excluded. The rate of clinical events was not different in patients after MRI as compared with the control group. CONCLUSION: It is concluded that MRI is safe in patients with the currently available intracoronary stents.     

Cardiovascular stent design and vessel stresses: a finite element analysis

Intravascular stents of various designs are currently in use to restore patency in atherosclerotic coronary arteries and it has been found that different stents have different in-stent restenosis rates. It has been hypothesized that the level of vascular injury caused to a vessel by a stent determines the level of restenosis. Computational studies may be used to investigate the mechanical behaviour of stents and to determine the biomechanical interaction between the stent and the artery in a stenting procedure. In this paper, we test the hypothesis that two different stent designs will provoke different levels of stress within an atherosclerotic artery and hence cause different levels of vascular injury. The stents analysed using the finite-element method were the S7 (Medtronic AVE) and the NIR (Boston Scientific) stent designs. An analysis of the arterial wall stresses in the stented arteries indicates that the modular S7 stent design causes lower stress to an atherosclerotic vessel with a localized stenotic lesion compared to the slotted tube NIR design. These results correlate with observed clinical restenosis rates, which have found higher restenosis rates in the NIR compared with the S7 stent design. Therefore, the testing methodology outlined here is proposed as a pre-clinical testing tool, which could be used to compare and contrast existing stent designs and to develop novel stent designs.     

Detection of GDNF secretion in glial cell culture and from transformed cell implants in the brains of live animals

Current ex vivo gene therapy for Parkinson's disease using glial cell line-derived neurotrophic factor (GDNF) is limited by the lack of a monitoring mechanism to determine the expression of GDNF once the cells or other vehicles are transferred into animal models. The purpose of this study was to test whether a Renilla luciferase (RUC)-GDNF fusion protein secreted by the genetically engineered glial cell line RG-1 could be measured photometrically in cerebrospinal fluid (CSF). RG-1 was constructed by permanent transformation with a plasmid DNA construct that contains a GDNF cDNA (gdnf) fused to a RUC cDNA (ruc). The fusion protein secreted by RG-1 was shown to retain both GDNF and RUC activity. The concentration of GDNF determined by enzyme-linked immunoadsorbent assay (ELISA) was correlated with the light emission detected by assaying for RUC bioluminescence in RG-1 culture medium, indicating that RUC can be used as a reporter for GDNF in vitro. The cells were then implanted into rat brain (n=20), and the cisternal CSF was analyzed. Bioluminescence was successfully detected in the CSF samples, and was quantified over a period of 25 days, while Western blotting and ELISA failed to detect GDNF in CSF, presumably because the concentration of the RUC-GDNF fusion was too low. This study demonstrates that the transformed glial cell line RG-1 offers a sensitive self-reporting assay for GDNF expression.     

The role of the shaft in the golf swing.

Current marketing of golf clubs places great emphasis on the importance of the correct choice of shaft in relation to the golfer. The design of shafts is based on a body of received wisdom for which there appears to be little in the way of hard evidence, either of a theoretical or experimental nature. In this paper the behaviour of the shaft in the golf swing is investigated using a suitable dynamic computer simulation and by making direct strain gauge measurements on the shaft during actual golf swings. The conclusion is, contrary to popular belief, that shaft bending flexibility plays a minor dynamic role in the golf swing and that the conventional tests associated with shaft specification are peculiarly inappropriate to the swing dynamics; other tests are proposed. A concomitant conclusion is that it should be difficult for the golfer to actually identify shaft flexibility. It is found that if golfers are asked to hit golf balls with sets of clubs having different shafts but identical swingweights the success rate in identifying the shaft is surprisingly low.     

The resonance frequencies and mode shapes of dental implants: Rigid body behaviour versus bending behaviour. A numerical approach

The purpose of this study was to evaluate the modal behaviour of the bone-implant-transducer (Osstell) system by means of finite element analyses. The influence of different parameters was determined: (1) the type of implant anchorage being trabecular, cortical, uni-cortical, or bi-cortical, (2) the implant diameter, (3) the length of the implant embedded in the bone, and (4) the bone stiffness. The type of anchorage determines the resulting modal behaviour of the implant-transducer system. A rigid body behaviour was found for a uni-cortical anchoring and for a homogeneous anchoring with low bone stiffness (< or =1000 MPa), whereas a bending behaviour was found for a homogeneous anchoring with a high bone stiffness (> or =5000 MPa) and for a bi-cortical anchorage. The implant dimensions influence the values for the resonance frequencies. Generally, an increase in implant diameter or implant length (in bone) results in higher resonance frequencies. This study also showed that resonance frequencies in case of rigid body behaviour of the implant-transducer system are more sensitive to changes in bone stiffness than resonance frequencies in case of bending behaviour. In conclusion, it seems that the Osstell transducer is suited for the follow-up in time of the stability of an implant, but not for the quantitative comparison of the stability of implants.     

Analysis of the bending behaviour of porcine xenograft leaflets and of neutral aortic valve material: bending stiffness, neutral axis and shear measurements

Flexibility of the materials used in the construction of bioprosthetic heart valves is essential for proper valve operation. We therefore examined the bending behaviour of glutaraldehyde treated porcine aortic valve cusps in comparison with fresh aortic valve tissue. We repeatedly bent a total of 35 strips of fresh and treated tissue to curvatures ranging from 0.2 to 2.2 mm-1. We compared the stiffness of the two materials between circumferential and radial bending, natural and reverse curvatures and constant or variable tensile stress (0.8-40 kPa). Our results showed a weak positive relationship between bending stiffness and applied tensile stress and a strong positive dependance of stiffness on tissue thickness (t). For the fresh tissue, the bending stiffness increased in proportion to t1.14 while for the glutaraldehyde treated tissue it increased with t2.18. Fourteen strips of fresh and treated tissue were also histologically processed, sectioned and examined with polarized light microscopy. Collagen fiber wavelengths and shear deformations were measured utilizing the tissue banding patterns produced by polarized light microscopy. The neutral axis of bending was found to lie very close to the outer surface of the tissue, suggesting that aortic leaflets have a very low compressive elastic modulus. The shear strains measured in fresh tissue were 10 +/- 2.7% vs 3 +/- 4.4% for the treated, indicating a stiffening of the tissue following glutaraldehyde fixation. We conclude that both natural and bioprosthetic valve cusps have a complex flexural behaviour that cannot be modeled using simple bending principles, although the bioprosthetic material more closely approximates the simple beam than does the fresh. The non-linear elastic modulus, high compressibility and shearing between fiber layers are likely responsible for the observed behaviour of the fresh tissue, while the cross-linking and dehydrating effects of glutaraldehyde are believed to be responsible for the alteration in bending properties observed in the treated tissue. Our study suggests that bioprosthetic valve material does not adequately mimic the mechanics of the natural valve tissue, and that the current glutaraldehyde fixation process eliminates many of the beneficial, stress-reducing properties of the aortic leaflet.     

Effects of bending stress on taper and growth of stems of youngEucalyptus regnans trees

A glasshouse experiment investigated the effect of bending stress on stem radial and height growth and stem taper ofEucalyptus regnans seedlings. Eighteen-week-old, potted seedlings were bent continuously for 8 weeks with a static bending stress. The bending treatment was then removed and the seedlings grown for another 12 weeks. Other seedlings were stayed vertically throughout the experiment whilst control seedlings were neither bent nor stayed. Seedlings were rotated every 2 days to prevent reaction wood developing asymmetrically in the stems of bent trees. Bent trees had higher radial growth rates, developed more tapered stems and had higher safety factors (the ratio of stem radius to the minimum radius required to prevent the tree toppling over) than unbent seedlings. They produced a band of tension wood in their stems and ceased height growth whilst bent. When bending ceased, they resumed normal radial and height growth. Unbent trees developed more cylindrical stems. There were no differences in growth behaviour between stayed and control trees. Bent and unbent trees all developed a butt swell, the taper of which was not affected by treatment. It was concluded that bending stress has substantial effects on both the size and taper of tree stems. However, the development of butt swell is independent of the bending stress applied. The results were considered in relation to biomechanical theories of tree stem development.     

The influence of humidity on the viscoelastic behaviour of human hair

The possibility of curling hair is attributed to the fact that the mechanical properties of hair fibres depend on time, temperature and humidity. In this study the dependence of the viscoelastic behaviour of human hair fibres on humidity is characterised in a bending deformation. An experimental set-up was used to perform bending relaxation measurements at different humidities. The relaxation data were fitted using a so-called "stretched exponential equation". The humidity dependence was incorporated by applying time-humidity superposition. Also, the influence of humidity on the initial E-modulus was found. The influence of humidity on the behaviour of human hair fibres could be modelled by using a general characterisation of the behaviour of human hair fibres.The general characterisation is used to predict the recovery in a human hair fibre after curling. The predicted recovery appeared to agree reasonably well with experimentally determined values.     

The stress-free shape of the red blood cell membrane.

The two main proposals found in the literature for the stress-free shape of the red cell membrane are (a) the bioconcave shape and (b) the sphere of the same surface area. These possibilities are evaluated in this paper using theoretical modeling of equilibrium membrane shapes according to Zarda et al. (1977. J. Biomech. 10:211-221) and by comparison to experiments on red cells whose membrane shear modulus has been increased by treatment with diamide. Neither proposal is found to be compatible with all the experimental behaviour of native red cells. Neither proposal is found to be compatible with all the experimental behaviour of native red cells. To account for this discrepancy we propose that either the shear modulus of the native membrane is dependent on the membrane strain or that the bending stiffness is higher than estimated by Evans (1980. Biophys. J. 30:265-286). These studies suggest that the bioconcave disk is the more likely possibility for the stress-free shape.     

Intra-aneurysmal flow with helix and mesh stent placement across side-wall aneurysm pore of a straight parent vessel

Pulsatile flow fields in a cerebrovascular side-wall aneurysm model with a wide ostium after stenting are presented in terms of particle tracking velocimetry measurements and flow visualization. Among the stent parameters the shape, helix versus mesh, was selected to study its effect on the changes of intraaneurysmal hemodynamics for the reference of minimally invasive endovascular aneurysm treatment. The blocking ratio of the stents was fixed at 30%. The Womersley number was 3.9 and the mean, peak, and minimal Reynolds numbers based on the bulk average velocity and diameter of the parent vessel were 600, 850, and 300, respectively. Four consecutive flow-rate phases were selected to characterize the intra-aneurysmal flow. The results are characterized in terms of velocity vector field, regional average velocity, and intra-aneurysmal vorticity/circulation/wall shear stress. It is found that the hemodynamic features inside the aneurysm alter markedly with the shape of the stent and the size of the orifice. Both stents investigated induce favorable changes in the intra-aneurysmal flow stasis as well as direction and undulation of wall shear stresses. A comparison of the results of the helix to mesh stent shows that the former is more favorable for endovascular treatment.     

The mechanical behaviour of cell membranes as a possible physical origin of cell polarity

The mechanical behaviour of a closed layered membrane enclosing a structureless interior is considered. The shape of such an object in flaccid conditions is determined theoretically by assuming that it corresponds to the minimum value of the membrane bending energy. The symmetry breaking properties of this system are revealed. It is suggested that a continuous transition from an axisymmetrical shape involving mirror symmetry with regard to the equatorial plane of the object to the shape with polar asymmetry could be the primary event in establishing cell polarity.     

Stable operation of an elastic three-segment leg

Quasi-elastic operation of joints in multi-segmented systems as they occur in the legs of humans, animals, and robots requires a careful tuning of leg properties and geometry if catastrophic counteracting operation of the joints is to be avoided. A simple three-segment model has been used to investigate the segmental organization of the leg during repulsive tasks like human running and jumping. The effective operation of the muscles crossing the knee and ankle joints is described in terms of rotational springs. The following issues were addressed in this study: (1) how can the joint torques be controlled to result in a spring-like leg operation? (2) how can rotational stiffnesses be adjusted to leg-segment geometry? and (3) to what extend can unequal segment lengths and orientations be advantageous? It was found that: (1) the three-segment leg tends to become unstable at a certain amount of bending expressed by a counterrotation of the joints; (2) homogeneous bending requires adaptation of the rotational stiffnesses to the outer segment lengths; (3) nonlinear joint torque-displacement behaviour extends the range of stable leg bending and may result in an almost constant leg stiffness; (4) biarticular structures (like human gastrocnemius muscle) and geometrical constraints (like heel strike) support homogeneous bending in both joints; (5) unequal segment lengths enable homogeneous bending if asymmetric nominal angles meet the asymmetry in leg geometry; and (6) a short foot supports the elastic control of almost stretched knee positions. Furthermore, general leg design strategies for animals and robots are discussed with respect to the range of safe leg operation.     

A three-dimensional mechanical analysis of a stentless fibre-reinforced aortic valve prosthesis

Failure of bioprosthetic and synthetic three-leaflet valves has been shown to occur as a consequence of high tensile and bending stresses, acting on the leaflets during opening and closing. Moreover, in the stented prostheses, whether synthetic or biological, the absence of contraction of the aortic base, due to the rigid stent, causes the leaflets to be subjected to an unphysiological degree of flexure, which is related to calcification. It is shown that the absence of the stent, which gives a flexible aortic base and leaflet attachment, and leaflet fibre-reinforcement result in reduced stresses in the weaker parts of the leaflets in their closed configuration. It is postulated that this leads to a decrease of tears and perforations, which may result in a improved long-term behaviour. The effect of a flexible leaflet attachment and aortic base of a synthetic valve is investigated with a finite element model. Different fibre-reinforced structures are analysed with respect to the stresses that are likely to contribute to the failure of fibre-reinforced prostheses and compared with the results obtained for a stented prosthesis. Results show that for the stentless models a reduction of stresses up to 75% is obtained with respect to stented models with the same type of reinforcement.     

Photoreactivity of 5-iodouracil-containing DNA-Sso7d complex.

X-ray structure of DNA-Sso7d complex indicated that binding of this protein causes sharp DNA bending. In order to examine whether this protein also causes DNA bending in solution, photoreactions of 1U-substituted DNA in the presence and the absence of Sso7d protein were investigated. It was found that the unusual intrastrand hydrogen abstraction at methyl of adjacent thymine occurred efficiently at the observed bending site of crystal structure.     

Stainless and shape memory alloy coronary stents: a computational study on the interaction with the vascular wall

Balloon-expandable and self-expandable stents are the two types of coronary stents available. Basically, they differ in the modality of expansion.The present study analyses the stress state induced on the vascular wall, by the expansion of balloon- and self-expandable stents, using the finite element method. Indeed, modified mechanical stress state is in part responsible in the restenosis process. The balloon-expandable stents herein investigated are assumed to be made of stainless steel, while the self-expandable stents are made of a shape memory alloy. The effects of the severity of the coronary stenosis, the atherosclerotic plaque stiffness and the stent design are investigated. Comparing the self-expandable stent with the balloon-expandable one, the former induces fewer stresses and lower damage to the vessel, but, on the other hand, its lower stiffness induces a lower capability to restore vasal lumen and to contrast arterial elastic recoil.     

Modelling of root growth and bending in two dimensions

A special co-ordinate system is developed for modelling the gravitropic bending of plant roots. It is based on the Local Theory of Curves in differential geometry and describes, in one dimension, growth events that may actually occur in two, or even three, dimensions. With knowledge of the spatial distributions of relative elemental growth rates (RELELs) for the upper and lower flanks of a gravistimulated root, and also their temporal dependencies, it is possible to compute the development of curvature along the root and hence describe the time-course of gravitropic bending. In addition, the RELEL distributions give information about the velocity field and the basipetal displacement of points along the root's surface. According to the Fundamental Theorem of Local Curve Theory, the x and y co-ordinates of the root in its bending plane are then determined from the associated values of local curvature and local velocity. With the aid of this model, possible mathematical growth functions that correspond to biological mechanisms involved in differential growth can be tested. Hence, the model can help not only to distinguish the role of various physiological or biophysical parameters in the bending process, but also to validate hypotheses that make assumptions concerning their relative importance. However, since the model is constructed at the level of the organ and treats the root as a fluid continuum, none of the parameters relate to cellular behaviour; the parameters must instead necessarily apply to properties that impinge on the behaviour of the external boundary of the root.