Multi-objective optimization of nitinol stent design

Easy-to-use formulations based on the homogenization theory for vascular stent design and mechanical characterization

BACKGROUND AND OBJECTIVES

Vascular stents are scaffolding structures implanted in the vessels of patients with obstructive disease. Stents are typically designed as cylindrical lattice structures characterized by the periodic repetition of unit cells. Their design, including geometry and material characteristics, influences their mechanical performance and, consequently, the clinical outcomes. Computational optimization frameworks have proven to be effective in assisting the design phase of vascular stents, facilitating the achievement of enhanced mechanical performances. However, the reliance on time-consuming simulations and the challenge of automating the design process limit the number of design evaluations and reduce optimization efficiency. In this context, a rapid and automated method for the mechanical characterization of vascular stents is presented, taking the stent geometry, conceived as the periodic repetition of a unit cell, and material as input and providing the mechanical response of the stent as output.

METHODS

Vascular stents were assumed to be thin-walled hollow cylinders sharing the same macroscopic geometrical characteristics as the cylindrical lattice structure but composed of an anisotropic homogenized material. Homogenization theory was applied to average the microscopic inhomogeneities at the stent unit cell level into a homogenized material at the macro-scale, enabling the calculation of the associated homogenized material tensor. Analytical formulations were derived to relate the stent mechanical behavior to the homogenized stiffness tensor, considering linear elastic theory for thin-walled hollow cylinders and three loading scenarios of relevance for vascular stents: radial crimping; axial traction; torsion. Validation was conducted by comparing the derived analytical formulations with results obtained from finite element analyses on typical stent designs.

RESULTS

Homogenized stiffness tensors were computed for the unit cells of three stent designs, revealing insights into their mechanical performance, including whether they exhibit auxetic behavior. The derived analytical formulations were successfully validated with finite element analyses, yielding low relative differences in the computed values of foreshortening, radial, axial and torsional stiffnesses for all three stents.

CONCLUSIONS

The proposed method offers a rapid, fully automated procedure that facilitates the assessment of the mechanical behavior of vascular stents and is suitable for effective integration into computational optimization frameworks.

Designing the mechanical behavior of NiTi self-expandable vascular stents by tuning the heat treatment parameters

The remarkable mechanical properties of nickel-titanium (NiTi) shape memory alloy, particularly its super-elasticity, establish it as the material of choice for fabricating self-expanding vascular stents, including the metallic backbone of peripheral stents and the metallic frame of stent-grafts. The super-elastic nature of NiTi substantially influences the mechanical performance of vascular stents, thereby affecting their clinical effectiveness and safety. This property shows marked sensitivity to the primary parameters of the heat treatment process used in device fabrication, specifically temperature and processing time. In this context, this study integrates experimental and computational analyses to explore the potential of designing the mechanical characteristics of NiTi vascular stents by adjusting heat treatment parameters. To reach this aim, differently heat-treated NiTi wire samples were experimentally characterized using calorimetric and uniaxial tensile testing. Subsequently, the mechanical response of a stent-graft model featuring a metallic frame made of NiTi wire was assessed in terms of radial forces generated at various implantation diameters through finite element analysis. The stent-graft served as an illustrative case of NiTi vascular stent to investigate the impact of the heat treatment parameters on its mechanical response. From the study a strong linear relationship emerged between NiTi super-elastic parameters (i.e., austenite finish temperature, martensite elastic modulus, upper plateau stress, lower plateau stress and transformation strain) and heat treatment parameters (R2 > 0.79, p-value < 0.001) for the adopted ranges of temperature and processing time. Additionally, a strong linear relationship was observed between: (i) the radial force generated by the stent-graft during expansion and the heat treatment parameters (R2 > 0.82, p-value < 0.001); (ii) the radial force generated by the stent-graft during expansion and the lower plateau stress of NiTi (R2 > 0.93, p-value < 0.001). In conclusion, the findings of this study suggest that designing and optimizing the mechanical properties of NiTi vascular stents by finely tuning temperature and processing time of the heat treatment process is feasible.

Computational Analysis of Polymeric Biodegradable and Customizable Airway Stent Designs

The placement of endotracheal prostheses is a procedure used to treat tracheal lesions when no other surgical options are available. Unfortunately, this technique remains controversial. Both silicon and metallic stents are used with unpredictable success rates, as they have advantages but also disadvantages. Typical side effects include restenosis due to epithelial hyperplasia, obstruction and granuloma formation. Repeat interventions are often required. Biodegradable stents are promising in the field of cardiovascular biomechanics but are not yet approved for use in the respiratory system. The aim of the present study is to summarize important information and to evaluate the role of different geometrical features for the fabrication of a new tracheo-bronchial prosthesis prototype, which should be biodegradable, adaptable to the patient's lesion and producible by 3D printing. A parametric design and subsequent computational analysis using the finite element method is carried out. Two different stent designs are parameterized and analyzed. The biodegradable material chosen for simulations is polylactic acid. Experimental tests are conducted for assessing its mechanical properties. The role of the key design parameters on the radial force of the biodegradable prosthesis is investigated. The computational results allow us to elucidate the role of the pitch angle, the wire thickness and the number of cells or units, among other parameters, on the radial force. This work may be useful for the design of ad hoc airway stents according to the patient and type of lesion.

Multi-objective design optimization of bioresorbable braided stents

BACKGROUND AND OBJECTIVES

Bioresorbable braided stents, typically made of bioresorbable polymers such as poly-l-lactide (PLLA), have great potential in the treatment of critical limb ischemia, particularly in cases of long-segment occlusions and lesions with high angulation. However, the successful adoption of these devices is limited by their low radial stiffness and reduced elastic modulus of bioresorbable polymers. This study proposes a computational optimization procedure to enhance the mechanical performance of bioresorbable braided stents and consequently improve the treatment of critical limb ischemia.

METHODS

Finite element analyses were performed to replicate the radial crimping test and investigate the implantation procedure of PLLA braided stents. The stent geometry was characterized by four design parameters: number of wires, wire diameter, initial stent diameter, and braiding angle. Manufacturing constraints were considered to establish the design space. The mechanical performance of the stent was evaluated by defining the radial force, foreshortening, and peak maximum principal stress of the stent as objectives and constraint functions in the optimization problem. An approximate relationship between the objectives, constraint, and the design parameters was defined using design of experiment coupled with surrogate modelling. Surrogate models were then interrogated within the design space, and a multi-objective design optimization was conducted.

RESULTS

The simulation of radial crimping was successfully validated against experimental data. The radial force was found to be primarily influenced by the number of wires, wire diameter, and braiding angle, with the wire diameter having the most significant impact. Foreshortening was predominantly affected by the braiding angle. The peak maximum principal stress exhibited contrasting behaviour compared to the radial force for all parameters, with the exception of the number of wires. Among the Pareto-optimal design candidates, feasible peak maximum principal stress values were observed, with the braiding angle identified as the differentiating factor among these candidates.

CONCLUSIONS

The exploration of the design space enabled both the understanding of the impact of design parameters on the mechanical performance of bioresorbable braided stents and the successful identification of optimal design candidates. The optimization framework contributes to the advancement of innovative bioresorbable braided stents for the effective treatment of critical limb ischemia.

Effects of Tapered-Strut Design on Fatigue Life Enhancement of Peripheral Stents

Peripheral stent could fracture from cyclic loadings as a result of our blood pressures or daily activities. Fatigue performance has therefore become a key issue for peripheral stent design. A simple yet powerful tapered-strut design concept for fatigue life enhancement was investigated. This concept is to move the stress concentration away from the crown and re-distribute the stresses along the strut by narrowing the strut geometry. Finite element analysis was performed to evaluate the stent fatigue performance under various conditions consistent with the current clinical practice. Thirty stent prototypes were manufactured in-house by laser with a series of post-laser treatments, followed by the validation of bench fatigue tests for proof of concept. FEA simulation results show that the fatigue safety factor of the 40% tapered-strut design increased by 4.2 times that of a standard counterpart, which was validated by bench tests with 6.6-times and 5.9-times fatigue enhancement at room temperature and body temperature, respectively. Bench fatigue test results agreed very well with the increasing trend predicted by FEA simulation. The effects of the tapered-strut design were significant and could be considered as an option for fatigue optimization of future stent designs.

Numerical modeling for efficiency and endurance assessment of an indirect mitral annuloplasty device

In recent years, several transcatheter systems have been introduced for treatment of common mitral regurgitation (MR). Such a system that is based on indirect mitral annuloplasty (IMA) is currently indicated for functional MR. Very few clinical studies have been performed to assess the efficiency and durability of such devices, despite their high risk of fracture resulting from ongoing exposure to large cyclic deformations. In this study, numerical models of moderate primary MR were created to test the implantation procedure of a customized IMA device and its sealing efficiency. The ability of the implanted device to reduce systolic leakage was evaluated and affirmed with a model of a more generic device. The long-term durability of the device was tested using a range of Nickel Titanium material properties. Our results demonstrated a considerable reduction in leakage for both the simplified generic device and the more detailed customized device models. The device met different fatigue criteria, confirming its resiliency and safety even after 10 years, even under the harsher conditions of primary MR. This is the first study to assess the performance and fatigue risk of IMA devices for the treatment of more complicated MR conditions. These findings may pave the way for further research to ultimately consider the device in selective cases of PMR.

Multi-Objective Optimization of Bioresorbable Magnesium Alloy Stent by Kriging Surrogate Model

PURPOSE

The study proposed a multi-objective optimization method based on Kriging surrogate model and finite element analysis to mitigate the redial recoil and foreshortening ratio of bioresorbable magnesium alloy stent, and investigate the impact of strut thickness on stent expansion behavior.

METHODS

Finite element analysis have been carried out to compare the expansion behavior of stents with various strut thickness. Latin hypercube sampling (LHS) was adopted to generate train sample points in the design space, and the Kriging surrogate model was constructed between strut parameters and stent behavior. The genetic algorithm (GA) was employed to find the optimal solution in the global design space.

RESULTS

Stents with thinner struts experience lower stress but suffer from severe radial recoil and foreshortening effects. The radial recoil is decreased by 66%, and foreshortening ratio is reduced by 60% for the optimized stent with U-bend width 90.7 [Formula: see text] and link width 77.9 [Formula: see text]. The errors between Kriging surrogate model and finite element simulation are 6% and 9% for the radial recoil and foreshortening ratio.

CONCLUSION

Stent expansion behavior are highly dependent on design parameters, i.e. thickness, U-bend and link strut width. The purposed Multi-objective optimization approach based on Kriging surrogate model and finite element analysis is efficient in stent design optimization problem.

A review on femoropopliteal arterial deformation during daily lives and nickel-titanium stent properties

The increasing number of studies on the behaviour of stent placement in recent decades provides a clear understanding of peripheral artery disease (PAD). The severe mechanical loads (axial tension and compression, bending, radial compression and torsion) deformation of the femoropopliteal artery (FPA) is responsible for the highest failure rate of permanent nickel-titanium (Nitinol) stents. Therefore, the purpose of this article is to review research papers that examined the deformation of the natural load environment of FPA, the properties of Nitinol and mechanical considerations. In conclusion, a better understanding of mechanical behaviour for FPA Nitinol stents contributes to increased mechanical performance and fatigue-life.

Personalised nitinol stent for focal plaques: Design and evaluation

The purpose of this study is to develop personalised nitinol stents for arteries with one and two opposite focal plaques. Novel designs are evaluated through comparison with a commercial stent design, in terms of lumen gain and shape as well as stress levels in the media layer after stenting.

METHODS

Personalised stents are developed for arteries with one and two opposite focal plaques, based on medical imaging of patients and computer simulations. In silico analysis is then carried out for assessment of stent performance in the diseased arteries.

RESULTS

Personalised designs significantly increase the lumen gain, reduce the stresses in the media layer, and improve the lumen shape compared to the commercial nitinol stent.

CONCLUSION

The personalised designs show outstanding performance compared to the commercial stent.

SIGNIFICANCE

This pilot study proves that personalised nitinol stents are able to deliver desirable treatment outcomes.

Pioneering personalised design of femoropopliteal nitinol stents

BACKGROUND/MOTIVATION

Percutaneous femoropopliteal artery intervention moves towards personalised therapy, which requires design of unique lesion-specific stents. However, to date, not much progress has been made in the development of personalised stents.

OBJECTIVE

This paper aims to design personalised nitinol stents for femoropopliteal arteries based on medical imaging of patients and advanced computational mechanics, which is the first attempt to the authors' best knowledge.

METHODS

The design process is based on three objectives: (i) achieving the healthy lumen area; (ii) reducing the stress in the media layer; (iii) improving the lumen shape after stenting. The design parameters include the strut width and thickness, the crown length, the nominal radius and the number of strut units per crown. Using representative unit-cell models, the effects of the five geometric parameters on the stent performance are investigated thoroughly with numerical simulations. Then, design protocols, especially for the circumferentially varying strut size and the oval stent shape, are developed and fully evaluated for an asymmetric stenosis.

RESULTS

Using the design protocols, full personalised stents are designed for arteries with diffuse and focal plaques, based on medical imaging of patients. The personalised stent designs provide a double lumen gain, a reduced stress in the media layer and an improved lumen shape compared to a commercial stent.

CONCLUSIONS

The suggested protocols prove their high effectiveness in design of personalised stents, and the suggested approach can be applied to development of personalised therapies involving the use of stent technology including percutaneous coronary artery intervention, transcatheter aortic valve implantation, endovascular aneurysm repair and ureteric stenting.

A computational optimization study of a self-expandable transcatheter aortic valve

Developing an efficient stent frame for transcatheter aortic valves (TAV) needs thorough investigation in different design and functional aspects. In recent years, most TAV studies have focused on their clinical performance, leaflet design, and durability. Although several optimization studies on peripheral stents exist, the TAV stents have different functional requirements and need to be explicitly studied. The aim of this study is to develop a cost-effective optimization framework to find the optimal TAV stent design made of Ni-Ti alloy. The proposed framework focuses on minimizing the maximum strain occurring in the stent during crimping, making use of a simplified model of the stent to reduce computational cost. The effect of the strut cross-section of the stent, i.e., width and thickness, and the number and geometry of the repeating units of the stent (both influencing the cell size) on the maximum strain is investigated. Three-dimensional simulations of the crimping process are used to verify the validity of the simplified representation of the stent, and the radial force has been calculated for further evaluation. The results suggest the key role of the number of cells (repeating units) and strut width on the maximum strain and, consequently, on the stent design. The difference in terms of the maximum strain between the simplified and the 3D model was less than 5%, confirming the validity of the adopted modeling strategy and the robustness of the framework to improve the TAV stent designs through a simple, cost-effective, and reliable procedure.

Surrogate-based multi-objective design optimization of a coronary stent: Altering geometry toward improved biomechanical performance

The main objective of this study was to solve a multi-objective optimization on a representative coronary stent platform with the goal of finding new geometric designs with improved biomechanical performance. The following set of metrics, calculated via finite element models, was used to quantify stent performance: vessel injury, radial recoil, bending resistance, longitudinal resistance, radial strength and prolapse index. The multi-objective optimization problem was solved with the aid of surrogate-based algorithms; for comparison and validation purposes, four surrogate-based multi-objective optimization algorithms (EI_hv -EGO, P_hv -EGO, ParEGO and SMS-EGO) with a limited sample budget were employed and their results compared. The quality of the non-dominated solution sets outputted by each algorithm was assessed against four quality indicators: hypervolume, R2, epsilon and generational distance. Results showed that P_hv -EGO was the algorithm that exhibited the best performance in overall terms. Afterwards, the highest quality Pareto front was chosen for an in-depth analysis of the optimization results. The amount of correlation and conflict was quantified for each pair of objective functions. Next, through cluster analysis, one was able to identify families of solutions with similar performance behavior and to discuss the nature of the existent trade-offs between objectives, and the trends between design parameters and solutions in a biomechanical perspective. In the end, a constrained-based design selection was performed with the goal of finding solutions in the Pareto front with equal or better performance in all objectives against a baseline design.

Design of Self-Expanding Auxetic Stents Using Topology Optimization

Implanting stents is the most efficient and minimally invasive technique for treating coronary artery diseases, but the risks of stent thrombosis (ST) and in-stent restenosis (IRS) hamper the healing process. There have been a variety of stents in market but dominated by ad hoc design motifs. A systematic design method that can enhance deliverability, safety and efficacy is still in demand. Most existing designs are focused on patient and biological factors, while the mechanical failures related to stenting architectures, e.g., inadequate stent expansion, stent fracture, stent malapposition and foreshortening, are often underestimated. With regard to these issues, the self-expanding (SE) stents may perform better than balloon-expandable (BE) stents, but the SE stents are not popular in clinic practice due to poor deliverability, placement accuracy, and precise match of the stent size and shape to the vessel. This paper addresses the importance between stent structures and clinic outcomes in the treatment of coronary artery disease. First, a concurrent topological optimization method will be developed to systematically find the best material distribution within the design domain. An extended parametric level set method with shell elements is proposed in the topology optimization to ensure the accuracy and efficiency of computations. Second, the auxetic metamaterial with negative Poisson’s ratio is introduced into the self-expanding stents. Auxetics can enhance mechanical properties of structures, e.g., fracture toughness, indentation and shear resistance and vibration energy absorption, which will help resolve the drawbacks due to the mechanical failures. Final, the optimized SE stent is numerically validated with the commercial software ANSYS and then prototyped using additive manufacturing techniques. Topological optimization gives a rare opportunity to exploiting the unique advantages of additive manufacturing. Hence, the topologically optimized auxetic architectures will provide a new solution for developing novel stenting structures, especially conductive to self-expanding SE stents. The new design will overcome the limitations of conventional SE stents associated with mechanical structures while maintain their valuable features, to help reduce the occurrence of ST and ISR and benefit the clinic practice in treating coronary heart disease.

Cross-sectional pinching in human femoropopliteal arteries due to limb flexion, and stent design optimization for maximum cross-sectional opening and minimum intramural stresses

High failure rates of femoropopliteal artery (FPA) interventions are often attributed to severe mechanical deformations that occur with limb flexion. One of these deformations, cross-sectional pinching, has a direct effect on blood flow, but is poorly characterized. Intra-arterial markers were deployed into n = 50 in situ cadaveric FPAs (80 ± 12 years old, 14F/11M), and limbs were imaged in standing, walking, sitting and gardening postures. Image analysis was used to measure marker openings and calculate FPA pinching. Parametric finite element analysis on a stent section was used to determine the optimal combination of stent strut amplitude, thickness and the number of struts per section to maximize cross-sectional opening and minimize intramural mechanical stress and low wall shear stress. Pinching was higher distally and increased with increasing limb flexion. In the walking, sitting and gardening postures, it was 1.16-1.24, 1.17-1.26 and 1.19-1.35, respectively. Stent strut amplitude and thickness had strong effects on both intramural stresses and pinching. Stents with a strut amplitude of 3 mm, thickness of 175 µm and 20 struts per section produced pinching and intramural stresses typical for a non-stented FPA, while also minimizing low wall shear stress areas, and ensuring a stent lifespan of at least 10⁷ cycles. These results can help guide the development of improved devices and materials to treat peripheral arterial disease.

Optimization of a Transcatheter Heart Valve Frame Using Patient-Specific Computer Simulation

PURPOSE

This study proposes a new framework to optimize the design of a transcatheter aortic valve through patient-specific finite element and fluid dynamics simulation.

METHODS

Two geometrical parameters of the frame, the diameter at ventricular inflow and the height of the first row of cells, were examined using the central composite design. The effect of those parameters on postoperative complications was investigated by response surface methodology, and a Nonlinear Programming by Quadratic Lagrangian algorithm was used in the optimization. Optimal and initial devices were then compared in 12 patients. The comparison was made in terms of device performance [i.e., reduced contact pressure on the atrioventricular conduction system and paravalvular aortic regurgitation (AR)].

RESULTS

Results suggest that large diameters and high cells favor higher anchoring of the device within the aortic root reducing the contact pressure and favor a better apposition of the device to the aortic root preventing AR. Compared to the initial device, the optimal device resulted in almost threefold lower predicted contact pressure and limited AR in all patients.

CONCLUSIONS

In conclusion, patient-specific modelling and simulation could help to evaluate device performance prior to the actual first-in-human clinical study and, combined with device optimization, could help to develop better devices in a shorter period.