Layout design of a bi-stable cardiovascular stent using topology optimization

Abstract

We present a novel design concept for a bi-stable cardiovascular stent in which the device has two fully stable, unloaded configurations: a contracted configuration used for insertion and positioning of the device, and an expanded configuration intended to facilitate blood flow. Once the device is in place, a small trigger force applied in the radial direction induces snap-through, causing the device to snap into its expanded configuration. We model the mechanics of the stent structure using a neo-Hookean hyperelastic formulation, which is discretized using a uniform mesh of solid isoparametric finite elements. Topology optimization is used to obtain the material layout and to tailor the nonlinear response of the baseline structure to achieve bi-stable snap-through behavior. The design domain is defined as a two-dimensional unit cell within the larger mesh pattern that comprises the cylindrical stent structure. We further introduce a novel transverse bracing system, which exerts a containing force that allows snap-through to occur, and that also ensures that the length of the stent does not change due to radial expansion. Optimization results are presented for several two dimensional examples including a benchmark problem based on a bi-stable beam, and a two-dimensional stent patch. Results confirm that topology optimization has been used successfully to achieve bi-stability in both the beam and the stent structures.

Introduction

Cardiovascular stents are meshed tubular devices that are used to prop open diseased arteries to repair and prevent blockages. These devices constitute an indispensable means of treating cardiovascular disease, and offer a minimally invasive alternative to by-pass surgery  [1]. When an obstruction is identified, the mesh is inserted into the artery, and once in place, the stent is expanded in the radial direction to promote blood flow. The expansion process typically involves the use of a balloon, which is inflated to generate the outward radial force that causes the stent structure to deform in a controlled fashion. Stent design is a highly complex engineering task that must take into account a multitude of performance requirements. The various design considerations include but are not limited to stress due to tissue interaction, hemodynamic performance, mechanical behavior, and drug delivery (in the case of drug eluting stents)  [2].

One of the main challenges in the design and implantation of stents is the failure of the mesh to fully expand [1], [3], [4]. This is a commonly occurring phenomenon, which is estimated to account for up to 8% of stent failures  [5]. The inability to fully expand may be due to an insufficiently stiff structure, which collapses under the forced exerted by the walls of the blood vessel [3]. Alternatively, a non-uniform expansion (i.e. varying levels of expansion at different locations along the axis of the stent) due to poor layout design can cause injury to the artery, thus triggering an inflammatory response which can lead to restenosis (i.e. re-closure) of the blood vessel [6], [7]. For these reasons, it has long been understood that the clinical performance of a cardiovascular stent is highly dependent of the stent’s mechanical properties  [8], [9].

To address these challenges, several authors have investigated the use of computational mechanics and design optimization to create stent designs with improved mechanical properties. For example, in a 2012 study by Gundert et al.  [10], the authors used computational fluid dynamics to design the layout of a stent mesh for optimal spatial distribution of the wall shear stress in the blood vessel, which has been linked to a variety of adverse effects including hyperplasia (inflammation) and restenosis. This study primarily addressed hemodynamic performance and fluid–structure interaction, however many others have focused on the elasto-plastic properties of the stent itself. In their 2013 study [4], Li et al. used a Kriging surrogate model to optimize the stent design and reduce the so-called “dogboning” effect in which the ends of the stent expand faster and wider than the interior portion of the structure. To model the structural response, the authors used an elastic–plastic finite element model, which they implemented using the commercial software tool, ANSYS. Prior to this, Pant et al. implemented a multi-objective design optimization framework, which optimized recoil, tissue stresses, hemodynamic disturbance, flexibility and drug delivery [2]. Here the multi-objective optimization was carried out using a genetic algorithm and the finite element analysis was implemented using Abaqus, another commercially available software tool.

In contrast to the above-mentioned studies, Guimarães et al.  [1] used a topology optimization approach in which they optimized the layout of a unitary patch within the stent mesh. The structural response was simulated using an elasto-plastic model implemented in ANSYS. During the expansion process, the stent structure underwent a combination of elastic and plastic strains. The objective of the optimization was to maximize the portion of the expansion, which took place in the plastic regime. In this way, the authors were able to minimize elastic recoil so that the stent would remain in its expanded configuration once deployed. The reliance on plastic expansion is typical among conventional approaches to stent design. However, the imprecision of plastic expansion can contribute to failure of the structure to fully expand, as well as potentially causing non-uniformity in the expanded stent structure.

The current study presents a novel approach, which addresses both of these challenges. The stent structures presented are designed to exhibit snap-though behavior. Each structure will have a default contracted configuration, and once the expansion force is applied, they will snap-through to a larger expanded configuration which is fully stable. In this way, we dispense with the reliance on plastic expansion, and instead rely on the geometric nonlinearity of the design, which will naturally bias the expansion process toward the configuration of the designer’s choosing. In this way, the expansion process will be more controlled and may be less susceptible to anomalies that could lead to failure or diminished performance.

Due to the snap-through functionality of these specialized stent designs, they can be treated as compliant mechanisms from a design standpoint. In recent years there have been several prominent studies highlighting the benefits of harnessing snap-through and buckling instabilities to achieve actuation as opposed to using more traditional pneumatic actuators  [11]. This snap-through approach has been applied successfully in a wide range of applications from actuation of thick-walled electroactive balloons  [12] to actuation of soft machines and robots [13]. Furthermore there have been many examples throughout the literature demonstrating the efficacy of topology optimization in tackling the design of actuated structures and compliant mechanisms,  [14], [15], [16], [17]. Similarly, topology optimization has also been shown to be highly effective in the design of periodic materials with unique mechanical, properties, such as extreme coefficients of thermal expansion  [18] and negative Poisson’s ratio  [19]. Many of these design principles can be leveraged in the layout design of a bi-stable stent, since the stent layout is effectively a repeating pattern of unit cells endowed with snap-through capability.

The large deformations required to achieve snap-through motion require special attention when modeling the structural response. Most topology optimization studies, even those involving compliant mechanisms, limit the structural analysis to linear elastic models. However, to accurately capture the snap-through effect, we require a hyperelastic material model. The combination of hyperelasticity with topology optimization presents some unique challenges. However, a few studies have investigated this topic, including, most recently, a study by Ramos and Paulino that looked at topology optimization of hyperelastic trusses  [20]. Earlier that same year, Wallin and Ristinmaa  [21] published a paper in which they addressed this issue using phase-field regularization. Also, in the previous year, Wang et al. [22] introduced an energy interpolation scheme for topology optimization of structures that undergo large deformations. The number of authors who have investigated topology optimization for structures exhibiting snap-through and bucking instability is even smaller still. Two notable examples are those of Bruns et al. [23] and Lindgaard and Dahl  [24]. In the latter of these studies, the authors used geometrically nonlinear analysis based on the Total Lagrangian approach to design beams with maximal buckling load. In the former study the authors implemented a Kirchoff–St. Venant material model to design beams that intentionally exhibited snap-through instability.

Both of the above-mentioned studies limited their examples to beam problems. In the current study we devise and implement unique boundary conditions necessary to achieve snap-through and bi-stability in a unitary cell within the larger stent mesh, and we address the various numerical and design challenges that arise due to the unique geometry of the problem. The geometrically non-linear finite element analysis is implemented using a Neo-Hookean material model, and solved iteratively using the arc-length method. We present two distinct examples of stent designs, obtained using the proposed optimization algorithm, and provide discussion and analysis of the merits of each design. The remainder of the paper is organized as follows. In Section  2 we present the theoretical framework and methodology used to solve the structural analysis problem, while accounting for large deformations. In the following Section  3 we provide an overview of the topology optimization problem, and give a breakdown of the various components of the optimization algorithm and the role of each in the larger design task. In this section we provide an outline of the gradient-based optimization algorithm, and a description of the adjoint sensitivity analysis calculation. In Section  4 we present the problem specifications and numerical results, along with analysis and discussion of several example problems. Lastly, in Section  5, we summarize and draw conclusions based on our findings.