Realistic finite element-based stent design: the impact of balloon folding

At present, the deployment of an intravascular stent has become a common and widely used minimally invasive treatment for coronary heart disease. To improve these coronary revascularization procedures (e.g. reduce in-stent restenosis rates) the optimal strategy lies in the further development of stent design, material and coatings. In the context of optimizing the stent design, computational models can provide an excellent research tool. In this study, the hypothesis that the free expansion of a stent is determined by the unfolding and expansion of the balloon is examined. Different expansion modeling strategies are studied and compared for a new generation balloon-expandable coronary stent. The trifolded balloon methodology presented in this paper shows very good qualitative and quantitative agreement with both manufacturer's data and experiments. Therefore, the proposed numerical expansion strategy appears to be a very promising optimization methodology in stent design.     

Self-expanding stent modelling and radial force accuracy

Computational simulations using finite element analysis are a tool commonly used to analyse stent designs, deployment geometries and interactions between stent struts and arterial tissue. Such studies require large computational models and efforts are often made to simplify models in order to reduce computational time while maintaining reasonable accuracy. The objective of the study is focused on computational modelling and specifically aims to investigate how different methods of modelling stent–artery interactions can affect the results, computational time taken and computational size of the model. Various different models, each with increasing levels of complexity, are used to simulate this analysis, representing the many assumptions and simplifications used in other similar studies in order to determine what level of simplification will still allow for an accurate representation of stent radial force and resulting stress concentrations on the inner lining of the vessel during self-expanding stent deployment. The main conclusions of the study are that methods used in stent crimping impact on the resulting predicted radial force of the stent; that accurate representation of stent–artery interactions can only be made when modelling the full length of the stent due to the incorporation of end effects; and that modelling self-contact of the stent struts greatly impacts on the resulting stress concentrations within the stent, but that the effect of this on the unloading behaviour and resulting radial force of the stent is negligible.     

Automatically Generated Algorithms for the Vertex Coloring Problem

The vertex coloring problem is a classical problem in combinatorial optimization that consists of assigning a color to each vertex of a graph such that no adjacent vertices share the same color, minimizing the number of colors used. Despite the various practical applications that exist for this problem, its NP-hardness still represents a computational challenge. Some of the best computational results obtained for this problem are consequences of hybridizing the various known heuristics. Automatically revising the space constituted by combining these techniques to find the most adequate combination has received less attention. In this paper, we propose exploring the heuristics space for the vertex coloring problem using evolutionary algorithms. We automatically generate three new algorithms by combining elementary heuristics. To evaluate the new algorithms, a computational experiment was performed that allowed comparing them numerically with existing heuristics. The obtained algorithms present an average 29.97% relative error, while four other heuristics selected from the literature present a 59.73% error, considering 29 of the more difficult instances in the DIMACS benchmark.     

On the effects of different strategies in modelling balloon-expandable stenting by means of finite element method

In recent years, computational structural analyses have emerged as important tools to investigate the mechanical response of stent placement into arterial walls. Although most coronary stents are expanded by inflating a polymeric balloon, realistic computational balloon models have been introduced only recently. In the present study, the finite element method is applied to simulate three different approaches to evaluate stent-free expansion and stent expansion inside an artery. Three different stent expansion modelling techniques were analysed by: (i) imposing a uniform pressure on the stent internal surface, (ii) a rigid cylindrical surface expanded with displacement control and (iii) modelling a polymeric deformable balloon. The computational results showed differences in the free and confined-stent expansions due to different expansion techniques. The modelling technique of the balloon seems essential to estimate the level of injury caused on arterial walls during stent expansion.     

Deployment of self-expandable stents in aneurysmatic cerebral vessels: comparison of different computational approaches for interventional planning

In the last few years, there has been a growing focus on faster computational methods to support clinicians in planning stenting procedures. This study investigates the possibility of introducing computational approximations in modelling stent deployment in aneurysmatic cerebral vessels to achieve simulations compatible with the constraints of real clinical workflows. The release of a self-expandable stent in a simplified aneurysmatic vessel was modelled in four different initial positions. Six progressively simplified modelling approaches (based on Finite Element method and Fast Virtual Stenting--FVS) have been used. Comparing accuracy of the results, the final configuration of the stent is more affected by neglecting mechanical properties of materials (FVS) than by adopting 1D instead of 3D stent models. Nevertheless, the differences showed are acceptable compared to those achieved by considering different stent initial positions. Regarding computational costs, simulations involving 1D stent features are the only ones feasible in clinical context.     

Deployment of self-expandable stents in aneurysmatic cerebral vessels: comparison of different computational approaches for interventional planning

In the last few years, there has been a growing focus on faster computational methods to support clinicians in planning stenting procedures. This study investigates the possibility of introducing computational approximations in modelling stent deployment in aneurysmatic cerebral vessels to achieve simulations compatible with the constraints of real clinical workflows. The release of a self-expandable stent in a simplified aneurysmatic vessel was modelled in four different initial positions. Six progressively simplified modelling approaches (based on Finite Element method and Fast Virtual Stenting – FVS) have been used. Comparing accuracy of the results, the final configuration of the stent is more affected by neglecting mechanical properties of materials (FVS) than by adopting 1D instead of 3D stent models. Nevertheless, the differences showed are acceptable compared to those achieved by considering different stent initial positions. Regarding computational costs, simulations involving 1D stent features are the only ones feasible in clinical context.     

Mechanical and hydrodynamic effects of stent expansion in tapered coronary vessels

Percutaneous coronary intervention (PCI) has become the primary treatment for patients with coronary heart disease because of its minimally invasive nature and high efficiency. Anatomical studies have shown that most coronary vessels gradually shrink, and the vessels gradually become thinner from the proximal to the distal end. In this paper, the effects of different stent expansion methods on the mechanical and hemodynamic behaviors of coronary vessels and stents were studied. To perform a structural-mechanical analysis of stent implantation, the coronary vessels with branching vessels and the coronary vessels with large bending curvature are selected. The two characteristic structures are implanted in equal diameter expansion mode and conical expansion mode, and the stress and mechanical behaviors of the coronary vessels and stents are analyzed. The results of the structural-mechanical analysis showed that the mechanical behaviors and fatigue performance of the cobalt-chromium alloy stent were good, and the different expansion modes of the stent had little effect on the fatigue performance of the stent. However, the equal diameter expansion mode increased distal coronary artery stress and the risk of vascular injury. The computational fluid dynamics analysis results showed that different stent expansion methods had varied effects on coronary vessel hemodynamics and that the wall shear stress distribution of conical stent expansion is more uniform compared with equal diameter expansion. Additionally, the vortex phenomenon is not apparent, the blood flow velocity is slightly increased, the hydrodynamic environment is more reasonable, and the risk of coronary artery injury is reduced.

     

An ovine in vivo framework for tracheobronchial stent analysis

Tracheobronchial stents are most commonly used to restore patency to airways stenosed by tumour growth. Currently all tracheobronchial stents are associated with complications such as stent migration, granulation tissue formation, mucous plugging and stent strut fracture. The present work develops a computational framework to evaluate tracheobronchial stent designs in vivo. Pressurised computed tomography is used to create a biomechanical lung model which takes into account the in vivo stress state, global lung deformation and local loading from pressure variation. Stent interaction with the airway is then evaluated for a number of loading conditions including normal breathing, coughing and ventilation. Results of the analysis indicate that three of the major complications associated with tracheobronchial stents can potentially be analysed with this framework, which can be readily applied to the human case. Airway deformation caused by lung motion is shown to have a significant effect on stent mechanical performance, including implications for stent migration, granulation formation and stent fracture.     

Numerical simulation of aneurysmal haemodynamics with calibrated porous-medium models of flow-diverting stents

Modelling flow-diverting (FD) stents as porous media (PM) markedly improves the efficiency of computational fluid dynamics (CFD) simulations in the study of intracranial aneurysm treatment. Nonetheless, the parameters of PM models adopted for simulations up until now were rarely calibrated to match the represented FD structure. We therefore sought to evaluate the PM parameters for a representative variety of commercially available stents, so characterising the flow-diversion behaviours of different FD devices on the market.We generated fully-resolved geometries for treatments using PED, Silk+, FRED, and dual PED stents. We then correspondingly derived the calibrated PM parameters—permeability (k) and inertial resistance factor (C₂)—for each stent design from CFD simulations, to ensure the calibrated PM model has identical flow resistance to the FD stent it represents. With each of the calibrated PM models respectively deployed in two aneurysms, we studied the flow-diversion effects of these stent configurations.This work for the first time reported several sets of parameters for PM models, which is vital to address the current knowledge gap and rectify the errors in PM model simulations, thereby setting right the modelling protocol for future studies using PM models. The flow resistance parameters were strongly affected by porosity and effective thickness of the commercial stents, and thus accounted for in the PM models. Flow simulations using the PM stent models revealed differences in aneurysmal mass flowrate (MFR) and energy loss (EL) between various stent designs.This study improves the practicability of FD simulation by using calibrated PM models, providing an individualised method with improved simulation efficiency and accuracy.     

The Cardiocoil stent-artery interaction

An analytical approach for the mechanical interaction of the self-expanding Cardiocoil stent with the stenosed artery is presented. The damage factor as the contact stress at the stent-artery interface is determined. The stent is considered as an elastic helical rod having a nonlinear pressure-displacement dependence, while the artery is modeled by an elastic cylindrical shell. An influence of a moderate relative thickness of the shell is estimated. The equations for both the stent and the artery are presented in the stent-associated helical coordinates. The computational efficiency of the model enabled to carry out a parametric study of the damage factor. Comparative examinations are conducted for the stents made of the helical rods with circular and rectangular cross sections. It was found, in particular, that, under same other conditions, the damage factor for the stent with a circular cross section may be two times larger than that for a rectangular one.     

Finite-element Analysis of a Stenotic Artery Revascularization Through a Stent Insertion

Short-term and long-term clinical follow-up data clearly indicate the superiority of stenting techniques within the family of mechanical treatments for percutaneous coronary revascularizations. However, restenosis phenomena are in general still present, representing the major drawback for this innovative non-invasive approach.

Experimental evidence indicates the mechanical interaction between the stent and the artery as a significant cause for the activation of stent-related restenosis. At the same time, the literature shows a significant lack of computational investigations within this field, possibly as consequence of the complexity of the problem.

According to these considerations, the aim of the present work is to study the bio-mechanical interaction between a balloon-expandable stent and a stenotic artery, highlighting considerations able to improve the general understanding of the problem.

In particular, given an initial stent design (J&J Palmaz-Schatz like), we show the presence of possible areas of artery injury during the stent deployment and areas of non-uniform contact pressure after the stent apposition, due to a non-uniform stent expansion. Since these concentrated mechanical actions can play an important role in the activation of restenosis mechanisms, we propose a modified stent design, which shows a more uniform expansion and for which typical stenting parameters (i.e., residual stenosis, elastic recoil, foreshortening) are computed and presented.     

Monitoring the wall mechanics during stent deployment in a vessel

Clinical trials have reported different restenosis rates for various stent designs. It is speculated that stent-induced strain concentrations on the arterial wall lead to tissue injury, which initiates restenosis. This hypothesis needs further investigations including better quantifications of non-uniform strain distribution on the artery following stent implantation. A non-contact surface strain measurement method for the stented artery is presented in this work. ARAMIS stereo optical surface strain measurement system uses two optical high speed cameras to capture the motion of each reference point, and resolve three dimensional strains over the deforming surface. As a mesh stent is deployed into a latex vessel with a random contrasting pattern sprayed or drawn on its outer surface, the surface strain is recorded at every instant of the deformation. The calculated strain distributions can then be used to understand the local lesion response, validate the computational models, and formulate hypotheses for further in vivo study.     

Optimization of cardiovascular stent design using computational fluid dynamics

Coronary stent design affects the spatial distribution of wall shear stress (WSS), which can influence the progression of endothelialization, neointimal hyperplasia, and restenosis. Previous computational fluid dynamics (CFD) studies have only examined a small number of possible geometries to identify stent designs that reduce alterations in near-wall hemodynamics. Based on a previously described framework for optimizing cardiovascular geometries, we developed a methodology that couples CFD and three-dimensional shape-optimization for use in stent design. The optimization procedure was fully-automated, such that solid model construction, anisotropic mesh generation, CFD simulation, and WSS quantification did not require user intervention. We applied the method to determine the optimal number of circumferentially repeating stent cells (N(C)) for slotted-tube stents with various diameters and intrastrut areas. Optimal stent designs were defined as those minimizing the area of low intrastrut time-averaged WSS. Interestingly, we determined that the optimal value of N(C) was dependent on the intrastrut angle with respect to the primary flow direction. Further investigation indicated that stent designs with an intrastrut angle of approximately 40 deg minimized the area of low time-averaged WSS regardless of vessel size or intrastrut area. Future application of this optimization method to commercially available stent designs may lead to stents with superior hemodynamic performance and the potential for improved clinical outcomes.     

Methods to improve dose uniformity for radioactive stents in endovascular brachytherapy

Intravascular brachytherapy (IVBT) has rapidly gained acceptance as a new treatment modality for reducing restenosis and improving the success rate of percutaneous transluminal coronary angioplasty (PTCA). Recent clinical results on patients treated with beta-emitting 32P stents suggest that radiation reduces in-stent restenosis but may exacerbate neointimal growth at the edges of the stents. This has been referred to as the "candy wrapper effect." It is well known that radioactive stents yield extremely inhomogeneous dose distributions, with low doses delivered to tissues in between stent struts, at the ends of the stent, and also at depth. Some animal model studies suggest that low doses of radiation may stimulate rather than inhibit neointimal growth in an injured vessel, and it is hypothesized that dose inhomogeneity at the ends of a stent may contribute to the candy wrapper effect. We present here a theoretical study comparing dose distributions for beta stents vs. gamma stents; "dumbbell" radioactive loaded stents vs. uniformly loaded stents; and stents with alternate strut design. Calculations demonstrate that dose inhomogenieties between stent struts, at the ends of stents, and at depth can be reduced by better stent design and isotope selection. Prior to the introduction of radioactive stents, criteria for stent design included factors such as trackability, flexibility, strength, etc. We show here that if stent design also includes criteria for strut shape and spacing that improved dose distributions are possible, which in turn could reduce the candy wrapper effect.     

Haemodynamic impact of stent–vessel (mal)apposition following carotid artery stenting: mind the gaps!

Carotid artery stenting (CAS) has emerged as a minimally invasive alternative to endarterectomy but its use in clinical treatment is limited due to the post-stenting complications. Haemodynamic actors, related to blood flow in the stented vessel, have been suggested to play a role in the endothelium response to stenting, including adverse reactions such as in-stent restenosis and late thrombosis. Accessing the flow-related shear forces acting on the endothelium in vivo requires space and time resolutions which are currently not achievable with non-invasive clinical imaging techniques but can be obtained from image-based computational analysis. In this study, we present a framework for accurate determination of the wall shear stress (WSS) in a mildly stenosed carotid artery after the implantation of a stent, resembling the commercially available Acculink (Abbott Laboratories, Abbott Park, Illinois, USA). Starting from angiographic CT images of the vessel lumen and a micro-CT scan of the stent, a finite element analysis is carried out in order to deploy the stent in the vessel, reproducing CAS in silico. Then, based on the post-stenting anatomy, the vessel is perfused using a set of boundary conditions: total pressure is applied at the inlet, and impedances that are assumed to be insensitive to the presence of the stent are imposed at the outlets. Evaluation of the CAS outcome from a geometrical and haemodynamic perspective shows the presence of atheroprone regions (low time-average WSS, high relative residence time) colocalised with stent malapposition and stent strut interconnections. Stent struts remain unapposed in the ostium of the external carotid artery disturbing the flow and generating abnormal shear forces, which could trigger thromboembolic events.     

An Agent-Based Model of the Response to Angioplasty and Bare-Metal Stent Deployment in an Atherosclerotic Blood Vessel

Purpose

While animal models are widely used to investigate the development of restenosis in blood vessels following an intervention, computational models offer another means for investigating this phenomenon. A computational model of the response of a treated vessel would allow investigators to assess the effects of altering certain vessel- and stent-related variables. The authors aimed to develop a novel computational model of restenosis development following an angioplasty and bare-metal stent implantation in an atherosclerotic vessel using agent-based modeling techniques. The presented model is intended to demonstrate the body’s response to the intervention and to explore how different vessel geometries or stent arrangements may affect restenosis development.

Methods

The model was created on a two-dimensional grid space. It utilizes the post-procedural vessel lumen diameter and stent information as its input parameters. The simulation starting point of the model is an atherosclerotic vessel after an angioplasty and stent implantation procedure. The model subsequently generates the final lumen diameter, percent change in lumen cross-sectional area, time to lumen diameter stabilization, and local concentrations of inflammatory cytokines upon simulation completion. Simulation results were directly compared with the results from serial imaging studies and cytokine levels studies in atherosclerotic patients from the relevant literature.

Results

The final lumen diameter results were all within one standard deviation of the mean lumen diameters reported in the comparison studies. The overlapping-stent simulations yielded results that matched published trends. The cytokine levels remained within the range of physiological levels throughout the simulations.

Conclusion

We developed a novel computational model that successfully simulated the development of restenosis in a blood vessel following an angioplasty and bare-metal stent deployment based on the characteristics of the vessel cross-section and stent. A further development of this model could ultimately be used as a predictive tool to depict patient outcomes and inform treatment options.     

Evaluating the interaction of a tracheobronchial stent in an ovine in-vivo model

Tracheobronchial stents are used to restore patency to stenosed airways. However, these devices are associated with many complications such as stent migration, granulation tissue formation, mucous plugging and stent strut fracture. Of these, granulation tissue formation is the complication that most frequently requires costly secondary interventions. In this study a biomechanical lung modelling framework recently developed by the authors to capture the lung in-vivo stress state under physiological loading is employed in conjunction with ovine pre-clinical stenting results and device experimental data to evaluate the effect of stent interaction on granulation tissue formation. Stenting is simulated using a validated model of a prototype covered laser-cut tracheobronchial stent in a semi-specific biomechanical lung model, and physiological loading is performed. Two computational methods are then used to predict possible granulation tissue formation: the standard method which utilises the increase in maximum principal stress change, and a newly proposed method which compares the change in contact pressure over a respiratory cycle. These computational predictions of granulation tissue formation are then compared to pre-clinical stenting observations after a 6-week implantation period. Experimental results of the pre-clinical stent implantation showed signs of granulation tissue formation both proximally and distally, with a greater proximal reaction. The standard method failed to show a correlation with the experimental results. However, the contact change method showed an apparent correlation with granulation tissue formation. These results suggest that this new method could be used as a tool to improve future device designs.     

Anomalous hemodynamic effects of a self-expanding intracranial stent: Comparing in-vitro and ex-vivo models using ultra-high resolution MicroCT based CFD

Previous research on the effects of intracranial stents on arterial hemodynamics has involved computational hemodynamics (CHD) simulations applied to artificially generated stent models. In this study, accurate geometric reconstructions of in-vitro (PTFE tube) and ex-vivo (canine artery) deployed stents based on ultra-high resolution MicroCT imaging were used. The primary goal was to compare the hemodynamic effects of deployment in these two different models and to identify flow perturbations due to deployment anomalies such as stent malapposition and strut prolapse, important adverse mechanics occurring in clinical practice, but not considered in studies using idealized stent models.Ultra-high resolution MicroCT data provided detailed visualization of deployment characteristics allowing for accurate in-stent flow simulation. For stent cells that are regularly and symmetrically deployed, the near wall flow velocities and wall shear stresses were similar to previously published results derived from idealized models. In-stent hemodynamics were significantly altered by misaligned or malapposed stent cells, important effects not realistically captured in previous models. This research shows the feasibility and value of an ex-vivo stent model for MicroCT based CHD studies. It validates previous in-vitro studies and further contributes to the understanding of in-stent hemodynamics associated with adverse mechanics of self-expanding intracranial stents.     

An in silico biomechanical analysis of the stent–esophagus interaction

Despite all technological innovations in esophageal stent design over the past 20 years, the association between the stent design’s mechanical behavior and its effect on the clinical outcome has not yet been thoroughly explored. A parametric numerical model of a commercially available esophageal bioresorbable polymeric braided wire stent is set up, accounting for stent design aspects such as braiding angle, strut material, wire thickness, degradation and friction between the wires comprising a predictive tool on the device’s mechanical behavior. Combining this tool with complex multilayered numerical models of the pathological in vivo stressed, actively contracting and buckling esophagus could provide clinicians and engineers with a patient-specific window into the mechanical aspects of stent-based esophageal intervention. This study integrates device and soft tissue mechanics in one computational framework to potentially aid in the understanding of the occurrence of specific symptoms and complications after stent placement.     

Monte Carlo Investigations for Relative Efficiency of Stratified Random Sampling Scheme for Estimation of Relative Risk in Case-Control Studies

Monte Carlo Investigations have been widely used in Sample Surveys in Comparing the efficiency of various methods when exact mathematical comparisons are not possible. In this paper the same has been used for comparing the efficiency of Stratified Random Sampling with respect to Simple Random Sampling for estimation of Relative Risk in Case-Control Studies. The data used relate to a Case Control study on peptic ulcer. On the basis of Monte Carlo Investigations on 50 samples of size 10–20 (Cases and Controls), it has been observed that there is considerable gain in efficiency in using Stratified Random Sampling over Simple Random Sampling. The sensitivity of the results with the change in Sample Size has also been investigated.