Modeling stented coronary arteries: where we are, where to go

Patient-specific coronary angioplasty simulations - A mixed-dimensional finite element modeling approach

Coronary angioplasty with stent implantation is the most frequently used interventional treatment for coronary artery disease. However, reocclusion within the stent, referred to as in-stent restenosis, occurs in up to 10% of lesions. It is widely accepted that mechanical loads on the vessel wall strongly affect adaptive and maladaptive mechanisms. Yet, the role of procedural and lesion-specific influence on restenosis risk remains understudied. Computational modeling of the stenting procedure can provide new mechanistic insights, such as local stresses, that play a significant role in tissue growth and remodeling. Previous simulation studies often featured simplified artery and stent geometries and cannot be applied to real-world examples. Realistic simulations were computationally expensive since they featured fully resolved stenting device models. The aim of this work is to develop and present a mixed-dimensional formulation to simulate the patient-specific stenting procedure with a reduced-dimensional beam model for the stent and 3D models for the artery. In addition to presenting the numerical approach, we apply it to realistic cases to study the intervention's mechanical effect on the artery and correlate the findings with potential high-risk locations for in-stent restenosis. We found that high artery wall stresses develop during the coronary intervention in severely stenosed areas and at the stent boundaries. Herewith, we lay the groundwork for further studies towards preventing in-stent restenosis after coronary angioplasty.

In vivo chronic scaffolding force of a resorbable magnesium scaffold

The aim of this study is to qualitatively characterize the in vivo chronic scaffolding force of the Magmaris® Resorbable Magnesium Scaffold (RMS). This important parameter of scaffolds must be balanced between sufficient radial support during the healing period of the vessel and avoidance of long-term vessel caging. A finite element model was established using preclinical animal data and used to predict the device diameter and scaffolding force up to 90 days after implantation. To account for scaffold resorption, it included backbone degradation as well as formation of discontinuities as observed in vivo. The predictions of the model regarding acute recoil and chronic development of the device diameter were in good agreement with the preclinical data, supporting the validity of the model. It was found that after 28 and 90 days, the Magmaris® RMS retained 90 % and 47 % of its initial scaffolding force, respectively. The reduction in scaffolding force was mainly driven by discontinuities in the meandering segments. Finite element analysis combined with preclinical data is a reliable method to characterize the chronic scaffolding force.

Computational Analysis of Balloon Catheter Behaviour at Variable Inflation Levels

Aortic valvuloplasty is a minimally invasive procedure for the dilatation of stenotic aortic valves. Rapid ventricular pacing is an established technique for balloon stabilization during this procedure. However, low cardiac output due to the pacing is one of the inherent risks, which is also associated with several potential complications. This paper proposes a numerical modelling approach to understand the effect of different inflation levels of a valvuloplasty balloon catheter on the positional instability caused by a pulsating blood flow. An unstretched balloon catheter model was crimped into a tri-folded configuration and inflated to several levels. Ten different inflation levels were then tested, and a Fluid-Structure Interaction model was built to solve interactions between the balloon and the blood flow modelled in an idealised aortic arch. Our computational results show that the maximum displacement of the balloon catheter increases with the inflation level, with a small step at around 50% inflation and a sharp increase after reaching 85% inflation. This work represents a substantial progress towards the use of simulations to solve the interactions between a balloon catheter and pulsating blood flow.

Review of the Development of Hemodynamic Modeling Techniques to Capture Flow Behavior in Arteries Affected by Aneurysm, Atherosclerosis, and Stenting

Cardiovascular diseases (CVDs) are the leading cause of death in the developed world. CVD can include atherosclerosis, aneurysm, dissection, or occlusion of the main arteries. Many CVDs are caused by unhealthy hemodynamics. Some CVDs can be treated with the implantation of stents and stent grafts. Investigations have been carried out to understand the effects of stents and stent grafts have on arteries and the hemodynamic changes post-treatment. Numerous studies on stent hemodynamics have been carried out using computational fluid dynamics (CFD) which has yielded significant insight into the effect of stent mesh design on near-wall blood flow and improving hemodynamics. Particle image velocimetry (PIV) has also been used to capture behavior of fluids that mimic physiological hemodynamics. However, PIV studies have largely been restricted to unstented models or intra-aneurysmal flow rather than peri or distal stent flow behaviors. PIV has been used both as a standalone measurement method and as a comparison to validate the CFD studies. This article reviews the successes and limitations of CFD and PIV-based modeling methods used to investigate the hemodynamic effects of stents. The review includes an overview of physiology and relevant mechanics of arteries as well as consideration of boundary conditions and the working fluids used to simulate blood for each modeling method along with the benefits and limitations introduced.

Numerical modeling of bare and polymer-covered braided stents using torsional and tensile springs connectors

Computational modeling of braided stents using the finite element (FE) method has become an essential tool in the design and development of these medical devices. One of the most challenging issues in such a task is representing in an accurate manner the interaction between the interlacing wires. With the goal of achieving a compromise between accuracy and computational affordability, we propose a new approach consisting in using 1D FE formulations equipped with torsional springs at the crossover points of the wires. In the case of covered braided stents, the model is enriched with a set of tensile springs (defined in the longitudinal direction), aimed at capturing the stiffening effect of the polymeric membrane. The predictive capabilities of the proposed model are evaluated using data of our own experimental tests, as well as data from other tests in the literature. The simulations demonstrate that the proposed model is able to predict the (markedly nonlinear) behavior of stents when subjected to radial and axial cycle loads, with errors at the end of the compression stage ranging from 0.5% to 10% in all cases.

Analytical methods for braided stents design and comparison with FEA

Braiding technology is nowadays commonly adopted to build stent-like devices. Indeed, these endoprostheses, thanks to their typical great flexibility and kinking resistance, find several applications in mini-invasive treatments, involving but not limiting to the cardiovascular field. The design process usually involves many efforts and long trial and error processes before identifying the best combination of manufacturing parameters. This paper aims to provide analytical tools to support the design and optimization phases: the developed equations, based on few geometrical parameters commonly used for describing braided stents and material stiffness, are easily implementable in a worksheet and allow predicting the radial rigidity of braided stents, also involving complex features such as multiple twists and looped ends, and the diameter variation range. Finite element simulations, previously validated with respect to experimental tests, were used as a comparator to prove the reliability of the analytical results. The illustrated tools can assess the impact of each selected parameter modification and are intended to guide the optimal selection of geometrical and mechanical stent proprieties to obtain the desired radial rigidity, deliverability (minimum diameter), and, if forming processes are planned to modify the shape of the stent, the required diameter variations (maximum and minimum diameters).

Deformation mechanics of self-expanding venous stents: Modelling and experiments

Deformation properties of venous stents based on braided design, chevron design, Z design, and diamond design are compared using in vitro experiments coupled with analytical and finite element modelling. Their suitability for deployment in different clinical contexts is assessed based on their deformation characteristics. Self-expanding stainless steel stents possess superior collapse resistance compared to Nitinol stents. Consequently, they may be more reliable to treat diseases like May-Thurner syndrome in which resistance against a concentrated (pinching) force applied on the stent is needed to prevent collapse. Braided design applies a larger radial pressure particularly for vessels of diameter smaller than 75% of its nominal diameter, making it suitable for a long lesion with high recoil. Z design has the least foreshortening, which aids in accurate deployment. Nitinol stents are more compliant than their stainless steel counterparts, which indicates their suitability in veins. The semi-analytical method presented can aid in rapid assessment of topology governed deformation characteristics of stents and their design optimization.

Finite Element Simulations of the ID Venous System to Treat Venous Compression Disorders: From Model Validation to Realistic Implant Prediction

The ID Venous System is an innovative device proposed by ID NEST MEDICAL to treat venous compression disorders that involve bifurcations, such as the May-Thurner syndrome. The system consists of two components, ID Cav and ID Branch, combined through a specific connection that prevents the migration acting locally on the pathological region, thereby preserving the surrounding healthy tissues. Preliminary trials are required to ensure the safety and efficacy of the device, including numerical simulations. In-silico models are intended to corroborate experimental data, providing additional local information not acquirable by other means. The present work outlines the finite element model implementation and illustrates a sequential validation process, involving seven tests of increasing complexity to assess the impact of each numerical uncertainty separately. Following the standard ASME V&V40, the computational results were compared with experimental data in terms of force-displacement curves and deformed configurations, testing the model reliability for the intended context of use (differences < 10%). The deployment in a realistic geometry confirmed the feasibility of the implant procedure, without risk of rupture or plasticity of the components, highlighting the potential of the present technology.

Biomechanical Evaluation of Different Balloon Positions for Proximal Optimization Technique in Left Main Bifurcation Stenting

BACKGROUND

Proximal optimization technique (POT) is a key step during left main (LM) bifurcation stenting. However, after crossover stenting, the ideal position of POT balloon is unclear. We sought to evaluate the biomechanical impact of different POT balloon positions during LM cross-over stenting procedure.

METHODS

We reconstructed the patient-specific LM bifurcation anatomy, using coronary computed tomography angiography data of 5 consecutive patients (3 males, mean age 66.3 ± 21.6 years) with complex LM bifurcation disease, defined as Medina 1,1,1, evaluated between 1st January 2018 to 1st June 2018 at our center. Finite element analyses were carried out to virtually perform the stenting procedure. POT was virtually performed in a mid (marker just at the carina cut plane), proximal (distal marker 1 mm before the carina) and distal (distal marker 1 mm after the carina) position in each investigated case. Final left circumflex obstruction (SBO%), strut malapposition, elliptical ratio and stent malapposition were evaluated.

RESULTS

The use of both proximal and distal POT resulted in a smaller LM diameter compared to the mid POT. SBO was significantly higher in both proximal and distal configurations compared to mid POT: 38.3 ± 5.1 and 29.3 ± 3.1 versus 18.3 ± 3.6%, respectively. Similarly stent malapposition was higher in both proximal and distal configurations compared to mid POT: 1.3 ± 0.4 and 0.82 ± 1.8 versus 0.78 ± 1.2, respectively.

CONCLUSIONS

Mid POT offers the best results in terms of LCx opening maintaining slightly smaller but still acceptable LM and LAD diameters compared to alternative POT configuration.

Interaction of different cell types with magnesium modified by plasma electrolytic oxidation

Magnesium (Mg) is a material widely used in industrial applications due to its low weight, ductility, and excellent mechanical properties. For non-permanent implants, Mg is particularly well-suited because of its biodegradability, while its degradation products are not harmful. However, Mg is chemically reactive, and cytotoxic hydrogen gas is released as part of the degradation. This adverse degradation can be tuned using plasma electrolytic oxidation (PEO). With PEO, a surface layer of MgO/Mg(OH)₂ is deposited on the surface of Mg in a controlled way. The electrolytes used during PEO influence the surface's chemistry and topography and thus expectedly the biological response of adhered cells. In this study, thin samples of commercial pure of Mg (c.p Mg) were modified by PEO guided by different electrolytes, and the biological activity was assessed on vascular cells, immune cells, and repair cells (adipose tissue-derived stromal cells, ASCs). Vascular cells were more vulnerable than ASCs for compounds released by surface-coated Mg. All surface coatings supported the proliferation of adhered ASC. Released compounds from surface-coated Mg delayed but did not block in vitro wound closure of fibroblasts monolayers. Preformed endothelial tubes were vulnerable for released compounds, while their supporting ASC was not. We conclude that PEO-based surface-coating of Mg supports adhesion and future delivery of therapeutic vascular repair cells such as ASC, but that the observed vulnerability of vascular cells for coated Mg components warrants investigations in vivo.

The effects of stenting on hemorheological parameters: An in vitro investigation under various blood flow conditions

 Despite their wide clinical usage, stent functionality may be compromised by complications at the site of implantation, including early/late stent thrombosis and occlusion. Although several studies have described the effect of fluid-structure interaction on local haemodynamics, there is yet limited information on the effect of the stent presence on specific hemorheological parameters. The current work investigates the red blood cell (RBC) mechanical behavior and physiological changes as a result of flow through stented vessels. Blood samples from healthy volunteers were prepared as RBC suspensions in plasma and in phosphate buffer saline at 45% haematocrit. Self-expanding nitinol stents were inserted in clear perfluoroalkoxy alkane tubing which was connected to a syringe, and integrated in a syringe pump. The samples were tested at flow rates of 17.5, 35 and 70 ml/min, and control tests were performed in non-stented vessels. For each flow rate, the sample viscosity, RBC aggregation and deformability, and RBC lysis were estimated. The results indicate that the presence of a stent in a vessel has an influence on the hemorheological characteristics of blood. The viscosity of all samples increases slightly with the increase of the flow rate and exposure. RBC aggregation and elongation index (EI) decrease as the flow rate and exposure increases. RBC lysis for the extreme cases is evident. The results indicate that the stresses developed in the stent area for the extreme conditions could be sufficiently high to influence the integrity of the RBC membrane.

A Mechanical Approach for Smooth Surface Fitting to Delineate Vessel Walls in Optical Coherence Tomography Images

Automated analysis of vascular imaging techniques is limited by the inability to precisely determine arterial borders. Intravascular optical coherence tomography (OCT) offers unprecedented detail of artery wall structure and composition, but does not provide consistent visibility of the outer border of the vessel due to the limited penetration depth. Existing interpolation and surface fitting methods prove insufficient to accurately fill the gaps between the irregularly spaced and sometimes unreliably identified visible segments of the vessel outer border. This paper describes an intuitive, efficient, and flexible new method of 3D surface fitting and smoothing suitable for this task. An anisotropic linear-elastic mesh is fit to irregularly spaced and uncertain data points corresponding to visible segments of vessel borders, enabling the fully automated delineation of the entire inner and outer borders of diseased vessels in OCT images for the first time. In a clinical dataset, the proposed smooth surface fitting approach had great agreement when compared with human annotations: areas differed by just 11 ± 11% (0.93 ± 0.84 mm²), with a coefficient of determination of 0.89. Overlapping and non-overlapping area ratios were 0.91 and 0.18, respectively, with a sensitivity of 90.8 and specificity of 99.0. This spring mesh method of contour fitting significantly outperformed all alternative surface fitting and interpolation approaches tested. The application of this promising proposed method is expected to enhance clinical intervention and translational research using OCT.

PALMAZ–SCHATZ STENT-OPENING MECHANICS USING A SIMPLE APPROACH INVOLVING THE BALLOON–STENT AND STENT–ARTERY CONTACT PROBLEM: APPLICATION TO BIOPOLYMER STENTS

We used the finite element method-based toolbox COMSOL Multiphysics to address the important question of biopolymer coronary stent mechanics. We evaluated the diameter of the stent, the immediate elastic recoil, the dogboning and the foreshortening during deployment while using an idealized model that took into account the presence of the balloon and the coronary artery wall (equivalent pressure hypothesis). We validated our model using the well-known mechanics of the Palmaz–Schatz metal stent and acquired new data concerning a poly-L-lactic acid (PLLA) stent and some other biodegradable co-polymer-based stents. The elastic recoil was relatively high (26.1% to 31.1% depending on the biopolymer used) when taking into account the presence of both the balloon and artery. The dogboning varied from 31% to 46% for the polymer stents and was 62% for the metal stent, suggesting that less arterial damage could be expected with biopolymer stents. Various strut thicknesses were tested for the PLLA stent (114, 180 and 250[Formula: see text][Formula: see text]m) and no significant improvement in elastic recoil was observed. We concluded that the stent geometry has a greater impact on the scaffolding role of the structure than the strut thickness, or even the mechanical properties of the stent.

Numerical study of incomplete stent apposition caused by deploying undersized stent in arteries with elliptical cross-sections

Incomplete stent apposition (ISA) is one of the causes leading to post-stent complications, which can be found when an undersized or under-expanded stent is deployed at lesions. Previous research efforts have focused on ISA in idealized coronary arterial geometry with circular cross-sections. However, arterial cross-section eccentricity plays an important role in both location and severity of ISA. Computational fluid dynamics (CFD) simulations are carried out to systematically study the effects of ISA in arteries with elliptical cross-sections, as such stents are partially embedded on the minor axis sides of the ellipse and malapposed elsewhere. Overall, ISA leads to high time-averaged WSS (TAWSS) at the proximal end of the stent and low TAWSS at the ISA transition region and the distal end. Shear rate depends on both malapposition distance and blood stream locations, which is found to be significantly higher at the inner stent surface than the outer surface. The proximal high shear rate signifies increasing possibility in platelet activation, when coupled with low TAWSS at the transition and distal region which may indicate a nidus for in-stent thrombosis.

Endovascular Metal Devices for the Treatment of Cerebrovascular Diseases

Cerebrovascular disease involves various medical disorders that obstruct brain blood vessels or deteriorate cerebral circulation, resulting in ischemic or hemorrhagic stroke. Nowadays, platinum coils with or without biological modification have become routine embolization devices to reduce the risk of cerebral aneurysm bleeding. Additionally, many intracranial stents, flow diverters, and stent retrievers have been invented with uniquely designed structures. To accelerate the translation of these devices into clinical usage, an in-depth understanding of the mechanical and material performance of these metal-based devices is critical. However, considering the more distal location and tortuous anatomic characteristics of cerebral arteries, present devices still risk failing to arrive at target lesions. Consequently, more flexible endovascular devices and novel designs are under urgent demand to overcome the deficiencies of existing devices. Herein, the pros and cons of the current structural designs are discussed when these devices are applied to the treatment of diseases ranging broadly from hemorrhages to ischemic strokes, in order to encourage further development of such kind of devices and investigation of their use in the clinic. Moreover, novel biodegradable materials and drug elution techniques, and the design, safety, and efficacy of personalized devices for further clinical applications in cerebral vasculature are discussed.

Numerical methods for polyline-to-point-cloud registration with applications to patient-specific stent reconstruction

We present novel numerical methods for polyline-to-point-cloud registration and their application to patient-specific modeling of deployed coronary artery stents from image data. Patient-specific coronary stent reconstruction is an important challenge in computational hemodynamics and relevant to the design and improvement of the prostheses. It is an invaluable tool in large-scale clinical trials that computationally investigate the effect of new generations of stents on hemodynamics and eventually tissue remodeling. Given a point cloud of strut positions, which can be extracted from images, our stent reconstruction method aims at finding a geometrical transformation that aligns a model of the undeployed stent to the point cloud. Mathematically, we describe the undeployed stent as a polyline, which is a piecewise linear object defined by its vertices and edges. We formulate the nonlinear registration as an optimization problem whose objective function consists of a similarity measure, quantifying the distance between the polyline and the point cloud, and a regularization functional, penalizing undesired transformations. Using projections of points onto the polyline structure, we derive novel distance measures. Our formulation supports most commonly used transformation models including very flexible nonlinear deformations. We also propose 2 regularization approaches ensuring the smoothness of the estimated nonlinear transformation. We demonstrate the potential of our methods using an academic 2D example and a real-life 3D bioabsorbable stent reconstruction problem. Our results show that the registration problem can be solved to sufficient accuracy within seconds using only a few number of Gauss-Newton iterations.

Hemodynamics analysis of the serial stenotic coronary arteries

Coronary arterial stenoses, particularly serial stenoses in a single branch, are responsible for complex hemodynamic properties of the coronary arterial trees, and the uncertain prognosis of invasive intervention. Critical information of the blood flow redistribution in the stenotic arterial segments is required for the adequate treatment planning. Therefore, in this study, an image based non-invasive functional assessment is performed to investigate the hemodynamic significances of serial stenoses. Twenty patient-specific coronary arterial trees with different combinations of stenoses were reconstructed from the computer tomography angiography for the evaluation of the hemodynamics. Our results showed that the computed FFR based on CTA images (FFRCT) pullback curves with wall shear stress (WSS) distribution could provide more effectively examine the physiological significance of the locations of the segmental narrowing and the curvature of the coronary arterial segments. The paper thus provides the diagnostic efficacy of FFRCT pullback curve for noninvasive quantification of the hemodynamics of stenotic coronary arteries with serial lesions, compared to the gold standard invasive FFR, to provide a reliable physiological assessment of significant amount of coronary artery stenosis. Further, we were also able to demonstrate the potential of carrying out virtual revascularization, to enable more precise PCI procedures and improve their outcomes.

Numerical Simulation of Stent Angioplasty with Predilation: An Investigation into Lesion Constitutive Representation and Calcification Influence

It is acceptable clinical practice to predilate a severely occluded vessel to allow better positioning of endovascular stents, and while the impact of this intervention has been examined for aggregate response in animals there has been no means to examine whether there are specific vessels that might benefit. Finite element methods offer the singular ability to explore the mechanical response of arteries with specific pathologic alterations in mechanics to stenting and predilation. We examined varying representations of atherosclerotic tissue including homogeneous and heterogeneous dispersion of calcified particles, and elastic, pseudo-elastic, and elastic-plastic constitutive representations of bulk atherosclerotic tissue. The constitutive representations of the bulk atherosclerotic tissue were derived from experimental test data and highlight the importance of accounting for testing mode of loading. The impact of arterial predilation is presented and, in particular, its effect on intimal predicted damage, atherosclerotic tissue von Mises and maximum principal stresses, and luminal deformation was dependent on the type of constitutive representation of diseased tissue, particularly in the presence of calcifications.

Computational Modeling of the Mechanical Performance of a Magnesium Stent Undergoing Uniform and Pitting Corrosion in a Remodeling Artery

Coronary stents made from degradable biomaterials such as magnesium alloy are an emerging technology in the treatment of coronary artery disease. Biodegradable stents provide mechanical support to the artery during the initial scaffolding period after which the artery will have remodeled. The subsequent resorption of the stent biomaterial by the body has potential to reduce the risk associated with long-term placement of these devices, such as in-stent restenosis, late stent thrombosis, and fatigue fracture. Computational modeling such as finite-element analysis has proven to be an extremely useful tool in the continued design and development of these medical devices. What is lacking in computational modeling literature is the representation of the active response of the arterial tissue in the weeks and months following stent implantation, i.e., neointimal remodeling. The phenomenon of neointimal remodeling is particularly interesting and significant in the case of biodegradable stents, when both stent degradation and neointimal remodeling can occur simultaneously, presenting the possibility of a mechanical interaction and transfer of load between the degrading stent and the remodeling artery. In this paper, a computational modeling framework is developed that combines magnesium alloy degradation and neointimal remodeling, which is capable of simulating both uniform (best case) and localized pitting (realistic) stent corrosion in a remodeling artery. The framework is used to evaluate the effects of the neointima on the mechanics of the stent, when the stent is undergoing uniform or pitting corrosion, and to assess the effects of the neointimal formation rate relative to the overall stent degradation rate (for both uniform and pitting conditions).

Stents: Biomechanics, Biomaterials, and Insights from Computational Modeling

Coronary stents have revolutionized the treatment of coronary artery disease. Improvement in clinical outcomes requires detailed evaluation of the performance of stent biomechanics and the effectiveness as well as safety of biomaterials aiming at optimization of endovascular devices. Stents need to harmonize the hemodynamic environment and promote beneficial vessel healing processes with decreased thrombogenicity. Stent design variables and expansion properties are critical for vessel scaffolding. Drug-elution from stents, can help inhibit in-stent restenosis, but adds further complexity as drug release kinetics and coating formulations can dominate tissue responses. Biodegradable and bioabsorbable stents go one step further providing complete absorption over time governed by corrosion and erosion mechanisms. The advances in computing power and computational methods have enabled the application of numerical simulations and the in silico evaluation of the performance of stent devices made up of complex alloys and bioerodible materials in a range of dimensions and designs and with the capacity to retain and elute bioactive agents. This review presents the current knowledge on stent biomechanics, stent fatigue as well as drug release and mechanisms governing biodegradability focusing on the insights from computational modeling approaches.

Electromagnetic computation and modeling in MRI

Electromagnetic (EM) computational modeling is used extensively during the development of a Magnetic Resonance Imaging (MRI) scanner, its installation, and use. MRI, which relies on interactions between nuclear magnetic moments and the applied magnetic fields, uses a range of EM tools to optimize all of the magnetic fields required to produce the image. The main field magnet is designed to exacting specifications but challenges in manufacturing, installation, and use require additional tools to maintain target operational performance. The gradient magnetic fields, which provide the primary signal localization mechanism, are designed under another set of complex design trade-offs which include conflicting imaging performance specifications and patient physiology. Gradients are largely impervious to external influences, but are also used to enhance main field operational performance. The radiofrequency (RF) magnetic fields, which are used to elicit the signals fundamental to the MR image, are a challenge to optimize for a host of reasons that include patient safety, image quality, cost optimization, and secondary signal localization capabilities. This review outlines these issues and the EM modeling used to optimize MRI system performance.

Numerical simulation on the effects of drug-eluting stents with different bending angles on hemodynamics and drug distribution

Implantation of drug-eluting stents in curved blood vessels may cause changes in hemodynamics and drug distribution, and even provoke in-stent restenosis. Due to the complexity of building three-dimensional (3-D) curved stent model, few studies have gone through such numerical simulations. In this study, three virtual stent models with different bending angles (0°, 30° and 90°) were developed to numerically investigate the distribution of wall shear stress (WSS) and drug concentration. The results showed that (1) the low-WSS regions in the inner bend of the stent models increased with the bending angles; (2) the drug concentration differed between the inner and outer bends of the stents but irrespective to the changes of bending angle; (3) the pattern of drug concentration for the curved stents found similar to that of the straight stents, and the phenomenon, 'proximal part low and distal part high' in the drug concentration showed in both the straight and curved stents. The increase in bending angles from 30° to 90° had little effect on the WSS and drug concentration; however, the largest effect of the curved stents was the remarkable difference of drug concentration between the inner and outer bends of the stents-about 20 %. Hence, it is feasible that quick analysis focused on the straight stents instead of the curved stents.

Dynamically scaled phantom phase contrast MRI compared to true-scale computational modeling of coronary artery flow

PURPOSE

To examine the feasibility of combining computational fluid dynamics (CFD) and dynamically scaled phantom phase-contrast magnetic resonance imaging (PC-MRI) for coronary flow assessment.

MATERIALS AND METHODS

Left main coronary bifurcations segmented from computed tomography with bifurcation angles of 33°, 68°, and 117° were scaled-up ∼7× and 3D printed. Steady coronary flow was reproduced in these phantoms using the principle of dynamic similarity to preserve the true-scale Reynolds number, using blood analog fluid and a pump circuit in a 3T MRI scanner. After PC-MRI acquisition, the data were segmented and coregistered to CFD simulations of identical, but true-scale geometries. Velocities at the inlet region were extracted from the PC-MRI to define the CFD inlet boundary condition.

RESULTS

The PC-MRI and CFD flow data agreed well, and comparison showed: 1) small velocity magnitude discrepancies (2-8%); 2) with a Spearman's rank correlation ≥0.72; and 3) a velocity vector correlation (including direction) of r(2) ≥ 0.82. The highest agreement was achieved for high velocity regions with discrepancies being located in slow or recirculating zones with low MRI signal-to-noise ratio (SNRv ) in tortuous segments and large bifurcating vessels.

CONCLUSION

Characterization of coronary flow using a dynamically scaled PC-MRI phantom flow is feasible and provides higher resolution than current in vivo or true-scale in vitro methods, and may be used to provide boundary conditions for true-scale CFD simulations. J. MAGN. RESON. IMAGING 2016;44:983-992.

Impact of bifurcation angle and other anatomical characteristics on blood flow - A computational study of non-stented and stented coronary arteries

The hemodynamic influence of vessel shape such as bifurcation angle is not fully understood with clinical and quantitative observations being equivocal. The aim of this study is to use computational modeling to study the hemodynamic effect of shape characteristics, in particular bifurcation angle (BA), for non-stented and stented coronary arteries. Nine bifurcations with angles of 40°, 60° and 80°, representative of ±1 SD of 101 asymptomatic computed tomography angiogram cases (average age 54±8 years; 57 females), were generated for (1) a non-stented idealized, (2) stented idealized, and (3) non-stented patient-specific geometry. Only the bifurcation angle was changed while the geometries were constant to eliminate flow effects induced by other vessel shape characteristics. The commercially available Biomatrix stent was used as a template and virtually inserted into each branch, simulating the T-stenting technique. Three patient-specific geometries with additional shape variation and ±2 SD BA variation (33°, 42° and 117°) were also computed. Computational fluid dynamics (CFD) analysis was performed for all 12 geometries to simulate physiological conditions, enabling the quantification of the hemodynamic stress distributions, including a threshold analysis of adversely low and high wall shear stress (WSS), low time-averaged WSS (TAWSS), high spatial WSS gradient (WSSG) and high Oscillatory Shear Index (OSI) area. The bifurcation angle had a minor impact on the areas of adverse hemodynamics in the idealized non-stented geometries, which fully disappeared once stented and was not apparent for patient geometries. High WSS regions were located close to the carina around peak-flow, and WSSG increased significantly after stenting for the idealized bifurcations. Additional shape variations affected the hemodynamic profiles, suggesting that BA alone has little effect on a patient׳s hemodynamic profile. Incoming flow angle, diameter and tortuosity appear to have stronger effects. This suggests that other bifurcation shape characteristics and stent placement/strategy may be more important than bifurcation angle in atherosclerotic disease development, progression, and stent outcome.

Experimental and computational study of mechanical and transport properties of a polymer coating for drug-eluting stents

Background: Experimental and computational characterizations in the preclinical development of biomedical devices are complementary and can significantly help in a thorough analysis of the performances before clinical evaluation. Methodology: Here mechanical and drug delivery properties of a polymer platform, ad hoc prepared to obtain coatings for drug-eluting stents, is reported; polymer formulation and starting drug loading were varied to study the behavior of the platform; a finite element model was constructed starting from experimental data. Results: Different platform formulations affected mechanical and drug transport properties; these properties can be fine tuned by varying the starting platform formulation. Finite element analysis allowed visualizing drug distribution maps over time in biological tissues for different commercial stents and polymer platform formulations.

Computational fluid dynamics modelling in cardiovascular medicine

This paper reviews the methods, benefits and challenges associated with the adoption and translation of computational fluid dynamics (CFD) modelling within cardiovascular medicine. CFD, a specialist area of mathematics and a branch of fluid mechanics, is used routinely in a diverse range of safety-critical engineering systems, which increasingly is being applied to the cardiovascular system. By facilitating rapid, economical, low-risk prototyping, CFD modelling has already revolutionised research and development of devices such as stents, valve prostheses, and ventricular assist devices. Combined with cardiovascular imaging, CFD simulation enables detailed characterisation of complex physiological pressure and flow fields and the computation of metrics which cannot be directly measured, for example, wall shear stress. CFD models are now being translated into clinical tools for physicians to use across the spectrum of coronary, valvular, congenital, myocardial and peripheral vascular diseases. CFD modelling is apposite for minimally-invasive patient assessment. Patient-specific (incorporating data unique to the individual) and multi-scale (combining models of different length- and time-scales) modelling enables individualised risk prediction and virtual treatment planning. This represents a significant departure from traditional dependence upon registry-based, population-averaged data. Model integration is progressively moving towards ‘digital patient’ or ‘virtual physiological human’ representations. When combined with population-scale numerical models, these models have the potential to reduce the cost, time and risk associated with clinical trials. The adoption of CFD modelling signals a new era in cardiovascular medicine. While potentially highly beneficial, a number of academic and commercial groups are addressing the associated methodological, regulatory, education- and service-related challenges.

Integrated Stent Models Based on Dimension Reduction: Review and Future Perspectives

Stent modeling represents a challenging task from both the theoretical and numerical viewpoints, due to its multi-physics nature and to the complex geometrical configuration of these devices. In this light, dimensional model reduction enables a comprehensive geometrical and physical description of stenting at affordable computational costs. In this work, we aim at reviewing dimensional model reduction of stent mechanics and drug release. Firstly, we address model reduction techniques for the description of stent mechanics, aiming to illustrate how a three-dimensional stent model can be transformed into a collection of interconnected one-dimensional rods, called a "stent net". Secondly, we review available model reduction methods similarly applied to drug release, in which the "stent net" concept is adopted for modeling of drug elution. As a result, drug eluting stents are described as a distribution of concentrated drug release sources located on a graph that fully represents the stent geometry. Lastly, new results about the extension of these model reduction approaches to biodegradable stents are also discussed.

Hemodynamics in Idealized Stented Coronary Arteries: Important Stent Design Considerations

Stent induced hemodynamic changes in the coronary arteries are associated with higher risk of adverse clinical outcome. The purpose of this study was to evaluate the impact of stent design on wall shear stress (WSS), time average WSS, and WSS gradient (WSSG), in idealized stent geometries using computational fluid dynamics. Strut spacing, thickness, luminal protrusion, and malapposition were systematically investigated and a comparison made between two commercially available stents (Omega and Biomatrix). Narrower strut spacing led to larger areas of adverse low WSS and high WSSG but these effects were mitigated when strut size was reduced, particularly for WSSG. Local hemodynamics worsened with luminal protrusion of the stent and with stent malapposition, adverse high WSS and WSSG were identified around peak flow and throughout the cardiac cycle respectively. For the Biomatrix stent, the adverse effect of thicker struts was mitigated by greater strut spacing, radial cell offset and flow-aligned struts. In conclusion, adverse hemodynamic effects of specific design features (such as strut size and narrow spacing) can be mitigated when combined with other hemodynamically beneficial design features but increased luminal protrusion can worsen the stent’s hemodynamic profile significantly.

Local blood flow patterns in stented coronary bifurcations: an experimental and numerical study

PURPOSE

Despite the atheroprone environment of blood flow in coronary bifurcations, limited quantitative information is available on the hemodynamics occurring in these geometries, both before and after their treatment with endovascular stents. Previous studies have focused on computational fluid dynamics (CFD) analyses and have bypassed the challenges associated with experimentally representing the flow environment, providing no means for validation. This study analyzed steady flow conditions in 3 bifurcation angles and 4 different single- and double-stenting procedures, which are used clinically in coronary bifurcations.

METHODS

The numerical aspect of this study utilized geometries derived from CAD models (nonstented cases) and finite element simulations (stented cases). Digital particle image velocimetry (DPIV) testing was conducted within compliant bifurcating models for which an uncertainty analysis was performed at each measurement location for CFD validation purposes. Results were analyzed in terms of velocity magnitude contour maps and axial velocity profiles at several locations in the bifurcated vessels.

RESULTS AND CONCLUSIONS

Qualitatively, the 2 approaches showed agreement in the bulk flow patterns. However, the velocity computed with CFD was outside the DPIV uncertainty estimates, which can be attributed to the intrinsic difference and modeling assumptions of the 2 approaches. The findings reveal that wider bifurcation angles and double-stenting procedures are both characterized by increased areas of low flow and recirculation. Additionally, inferior performance in terms of viscous and wall shear stresses was observed in double-stented cases.

Computational Modelling of Multi-folded Balloon Delivery Systems for Coronary Artery Stenting: Insights into Patient-Specific Stent Malapposition

Despite the clinical effectiveness of coronary artery stenting, percutaneous coronary intervention or "stenting" is not free of complications. Stent malapposition (SM) is a common feature of "stenting" particularly in challenging anatomy, such as that characterized by long, tortuous and bifurcated segments. SM is an important risk factor for stent thrombosis and recently it has been associated with longitudinal stent deformation. SM is the result of many factors including reference diameter, vessel tapering, the deployment pressure and the eccentric anatomy of the vessel. For the purpose of the present paper, virtual multi-folded balloon models have been developed for simulated deployment in both constant and varying diameter vessels under uniform pressure. The virtual balloons have been compared to available compliance charts to ensure realistic inflation response at nominal pressures. Thereafter, patient-specific simulations of stenting have been conducted aiming to reduce SM. Different scalar indicators, which allow a more global quantitative judgement of the mechanical performance of each delivery system, have been implemented. The results indicate that at constant pressure, the proposed balloon models can increase the minimum stent lumen area and thereby significantly decrease SM.

Deployment of stent grafts in curved aneurysmal arteries: toward a predictive numerical tool

The mechanical behavior of aortic stent grafts plays an important role in the success of endovascular surgery for aneurysms. In this study, finite element analysis was carried out to simulate the expansion of five marketed stent graft iliac limbs and to evaluate quantitatively their mechanical performances. The deployment was modeled in a simplified manner according to the following steps: (i) stent graft crimping and insertion in the delivery sheath, (ii) removal of the sheath and stent graft deployment in the aneurysm, and (iii) application of arterial pressure. In the most curved aneurysm and for some devices, a decrease of stent graft cross-sectional area up to 57% was found at the location of some kinks. Apposition defects onto the arterial wall were also clearly evidenced and quantified. Aneurysm inner curve presented significantly more apposition defects than outer curve. The feasibility of finite element analysis to simulate deployment of marketed stent grafts in curved aneurysm models was demonstrated. The study of the influence of aneurysm tortuosity on stent graft mechanical behavior shows that increasing vessel curvature leads to stent graft kinks and inadequate apposition against the arterial wall. Such simulation approach opens a very promising way toward surgical planning tools able to predict intra and/or post-operative short-term stent graft complications.

Numerical investigations of the haemodynamic changes associated with stent malapposition in an idealised coronary artery

The deployment of a coronary stent near complex lesions can sometimes lead to incomplete stent apposition (ISA), an undesirable side effect of coronary stent implantation. Three-dimensional computational fluid dynamics (CFD) calculations are performed on simplified stent models (with either square or circular cross-section struts) inside an idealised coronary artery to analyse the effect of different levels of ISA to the change in haemodynamics inside the artery. The clinical significance of ISA is reported using haemodynamic metrics like wall shear stress (WSS) and wall shear stress gradient (WSSG). A coronary stent with square cross-sectional strut shows different levels of reverse flow for malapposition distance (MD) between 0mm and 0.12 mm. Chaotic blood flow is usually observed at late diastole and early systole for MD=0mm and 0.12 mm but are suppressed for MD=0.06 mm. The struts with circular cross section delay the flow chaotic process as compared to square cross-sectional struts at the same MD and also reduce the level of fluctuations found in the flow field. However, further increase in MD can lead to chaotic flow not only at late diastole and early systole, but it also leads to chaotic flow at the end of systole. In all cases, WSS increases above the threshold value (0.5 Pa) as MD increases due to the diminishing reverse flow near the artery wall. Increasing MD also results in an elevated WSSG as flow becomes more chaotic, except for square struts at MD=0.06 mm.

From Histology and Imaging Data to Models for In-Stent Restenosis

The implantation of stents has been used to treat coronary artery stenosis for several decades. Although stenting is successful in restoring the vessel lumen and is a minimally invasive approach, the long-term outcomes are often compromised by in-stent restenosis (ISR). Animal models have provided insights into the pathophysiology of ISR and are widely used to evaluate candidate drug inhibitors of ISR. Such biological models allow the response of the vessel to stent implantation to be studied without the variation of lesion characteristics encountered in patient studies.

This paper describes the development of complementary in silico models employed to improve the understanding of the biological response to stenting using a porcine model of restenosis. This includes experimental quantification using microCT imaging and histology and the use of this data to establish numerical models of restenosis. Comparison of in silico results with histology is used to examine the relationship between spatial localization of fluid and solid mechanics stimuli immediately post-stenting. Multi-scale simulation methods are employed to study the evolution of neointimal growth over time and the variation in the extent of neointimal hyperplasia within the stented region. Interpretation of model results through direct comparison with the biological response contributes to more detailed understanding of the pathophysiology of ISR, and suggests the focus for follow-up studies.

In conclusion we outline the challenges which remain to both complete our understanding of the mechanisms responsible for restenosis and translate these models to applications in stent design and treatment planning at both population-based and patient-specific levels.

Influence of plaque calcifications on coronary stent fracture: a numerical fatigue life analysis including cardiac wall movement

Coronary stent fracture is still an unresolved issue in the field of minimally invasive cardiovascular interventions due to its high rate of incidence and uncertain clinical consequences. Recent studies, based on clinical data, proved that there are several factors which can be identified as independently responsible of coronary stent fracture. Among these, calcifications, which increase the local stiffness and heterogeneity of atherosclerotic plaques, seem to play a major role. From a mechanical point of view, stent fracture in coronary arteries is triggered by the cyclic loading of pulsatile blood pressure combined with the movement of cardiac wall. In this context, this study aims at simulating the stent expansion in a model of epicardial atherosclerotic coronary artery and correlating the effects of cyclic blood pressure and cardiac wall movement on the stent fatigue resistance. Two ideal cases of atherosclerotic plaques were modelled: the first one included a localised plaque calcification; the latter one did not include such calcification. Results of stress/strain and fatigue analyses confirmed the influence of the plaque calcification on potential fracture of the devices. In addition, the effects of cardiac wall movement were quantified as more dangerous causes of the stent fatigue fracture with respect to the internal blood pressure oscillations. In conclusion, this study demonstrates the increased risk of coronary stent fracture associated to the presence of localised plaque calcifications. This work also suggests the necessity of more realistic biomechanical models which takes into account the heterogeneity of atherosclerotic plaques in order to assess the mechanical performances of coronary stents.

Simulation of oxygen transfer in stented arteries and correlation with in-stent restenosis

Computational models are used to study the combined effect of biomechanical and biochemical factors on coronary in-stent restenosis, which is a postoperative remodeling and regrowth pathology of the stented arteries. More precisely, we address numerical simulations, on the basis of Navier-Stokes and mass transport equations, to study the role of perturbed wall shear stresses and reduced oxygen concentration in a geometrical model reconstructed from a real porcine artery treated with a stent. Joining in vivo and in silico tools of investigation has multiple benefits in this case. On one hand, the geometry of the arterial wall and of the stent closely correspond to a real implanted configuration. On the other hand, the inspection of histological tissue samples informs us on the location and intensity of in-stent restenosis. As a result, we are able to correlate geometrical factors, such as the axial variation of the artery diameter and its curvature; the numerical quantification of biochemical stimuli, such as wall shear stresses; and the availability of oxygen to the inner layers of the artery, with the appearance of in-stent restenosis. This study shows that the perturbation of the vessel curvature could induce hemodynamic conditions that stimulate undesired arterial remodeling.