Multiobjective design optimization of stent geometry with wall deformation for triangular and rectangular struts

The influence of blood velocity and vessel geometric parameters on wall shear stress

Vascular geometry was proposed to be one risk factor of atherosclerosis (AS). When developing this hypothesis, the discussion of geometry-wall shear stress (WSS) has often been included. However, further exploration on how various geometric parameters were affecting WSS was needed. The purpose of this study was to investigate the influence degree of vessel geometric parameters and blood velocity on WSS. A computational fluid dynamics (CFD) analyses of the vertebral and basilar arteries (VA and BA, respectively) was used. Twenty patients with no plaques or vessel wall thickening at the VA and BA were included. CFD analyses using both specific vessel models and flow conditions measured by ultrasound Doppler were performed. Subsequently, CFD results were post-processed with multiple linear regression to investigate numerical correlations between geometrical and flow parameters and WSS. The results of the multiple linear regression analysis further demonstrated that the BA proximal velocity was the most influential factor positively influencing BA WSS. The lower the WSS was, the stronger the influence brought by BA average diameter would be. The regression demonstrated that the contributions brought by average diameter and proximal velocity in lower WSS regions were lower than that in higher WSS regions. Tortuosity was only positively correlated with 97.5th WSS percentile, and vessel length and curvature showed no correlation with WSS. This study quantified the influence degree of BA morphology and flow velocity on WSS, which may have practical implications for predicting hemodynamic risks.

A Parametric Study of Flushing Conditions for Improvement of Angioscopy Visibility

During an angioscopy operation, a transparent liquid called dextran is sprayed out from a catheter to flush the blood away from the space between the camera and target. Medical doctors usually inject dextran at a constant flow rate. However, they often cannot obtain clear angioscopy visibility because the flushing out of the blood is insufficient. Good flushing conditions producing clear angioscopy visibility will increase the rate of success of angioscopy operations. This study aimed to determine a way to improve the clarity for angioscopy under different values for the parameters of the injection waveform, endoscope position, and catheter angle. We also determined the effect of a stepwise waveform for injecting the dextran only during systole while synchronizing the waveform to the cardiac cycle. To evaluate the visibility of the blood-vessel walls, we performed a computational fluid dynamics (CFD) simulation and calculated the visible area ratio (VAR), representing the ratio of the visible wall area to the total area of the wall at each point in time. Additionally, the normalized integration of the VAR called the area ratio (ARVAR) represents the ratio of the visible wall area as a function of the dextran injection period. The results demonstrate that the ARVAR with a stepped waveform, bottom endoscope, and three-degree-angle catheter results in the highest visibility, around 25 times larger than that under the control conditions: a constant waveform, a center endoscope, and 0 degrees. This set of conditions can improve angioscopy visibility.

A biodegradable magnesium alloy vascular stent structure: Design, optimisation and evaluation

The existing biodegradable magnesium alloy stent (BMgS) structure is prone to problems, such as insufficient support capacity and early fracture at areas of concentrated stress. Herein, a stent structural design, which reduced the cross section of the traditional sin-wave stent by nearly 30% and introduces a regular arc structure in the middle of the support ring. The influence of the dual-parameter design of bending radius (r) and ring length (L) on plastic deformation, expansion and compression resistance performances are discussed. The non-dominated sorting genetic algorithm II (NSGA-II) was used to search for the optimal solution. It was found that the introduction of parameter r effectively improved the plastic deformation and expansion performance, and the reduction of L improved stent compression resistance. Finally, an optimized stent configuration was obtained. In vitro mechanical tests, including balloon inflation, radial strength and flexibility, verified the simulation results. The radial strength for the optimised stent increases by approximately 40% compared with that for the sinusoidal stent. Microarea X-ray diffraction result shows that the circumferential residual stress for the optimised stent decreases by half compared with that for the sinusoidal stent, thus effectively reducing the stress concentration phenomenon. STATEMENT OF SIGNIFICANCE: Despite current progress in BMgS research, the optimal design of the structure is limited. We present a new type of structurally designed stent. The performance of this stent was analysed by a finite element method and experimentally verified. The structural design positively influenced stent performance.

Endothelial Cell Distribution After Flow Exposure With Two Stent Struts Placed in Different Angles

Stent implantation has been a primary treatment for stenosis and other intravascular diseases. However, the struts expansion procedure might cause endothelium lesion and the structure of the struts could disturb the blood flow environment near the wall of the blood vessel. These changes could damage the vascular innermost endothelial cell (EC) layer and pose risks of restenosis and post-deployment thrombosis. This research aims to investigate the effect of flow alterations on EC distribution in the presence of gap between two struts within the parallel flow chamber. To study how the gap presence impacts EC migration and the endothelialization effect on the surface of the struts, two struts were placed with specific orientations and positions on the EC layer in the flow chamber. After a 24-h exposure under wall shear stress (WSS), we observed the EC distribution conditons especially in the gap area. We also conducted computational fluid dynamics (CFD) simulations to calculate the WSS distribution. High EC-concentration areas on the bottom plate corresponded to the high WSS by the presence of gap between the two struts. To find the relation between the WSS and EC distributions on the fluorescence images, WSS condition by CFD simulation could be helpful for the EC distribution. The endothelialization rate, represented by EC density, on the downstream sides of both struts was higher than that on the upstream sides. These observations were made in the flow recirculation at the gap area between two struts. On two side surfaces between the gaps, meaning the downstream at the first and the upstream at the second struts, EC density differences on the downstream surfaces of the first strut were higher than on the upstream surfaces of the second strut. Finally, EC density varied along the struts when the struts were placed at tilted angles. These results indicate that, by the presence of gap between the struts, ECs distribution could be predicted in both perpendicular and tiled positions. And tiled placement affect ECs distribution on the strut side surfaces.

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.

Topological Optimization of Auxetic Coronary Stents Considering Hemodynamics

This paper is to design a new type of auxetic metamaterial-inspired structural architectures to innovate coronary stents under hemodynamics via a topological optimization method. The new architectures will low the occurrence of stent thrombosis (ST) and in-stent restenosis (ISR) associated with the mechanical factors and the adverse hemodynamics. A multiscale level-set approach with the numerical homogenization method and computational fluid dynamics is applied to implement auxetic microarchitectures and stenting structure. A homogenized effective modified fluid permeability (MFP) is proposed to efficiently connect design variables with motions of blood flow around the stent, and a Darcy-Stokes system is used to describe the coupling behavior of the stent structure and fluid. The optimization is formulated to include three objectives from different scales: MFP and auxetic property in the microscale and stenting stiffness in the macroscale. The design is numerically validated in the commercial software MATLAB and ANSYS, respectively. The simulation results show that the new design can not only supply desired auxetic behavior to benefit the deliverability and reduce incidence of the mechanical failure but also improve wall shear stress distribution to low the induced adverse hemodynamic changes. Hence, the proposed stenting architectures can help improve safety in stent implantation, to facilitate design of new generation of stents.

A multi-objective optimization of stent geometries

Stents are scaffolding cardiovascular implants used to restore blood flow in narrowed arteries. However, the presence of the stent alters local blood flow and shear stresses on the surrounding arterial wall, which can cause adverse tissue responses and increase the risk of adverse outcomes. There is a need for optimization of stent designs for hemodynamic performance. We used multi-objective optimization to identify ideal combinations of design variables by assessing potential trade-offs based on common hemodynamic indices associated with clinical risk and mechanical performance of the stents. We studied seven design variables including strut cross-section, strut dimension, strut angle, cell alignment, cell height, connector type and connector arrangement. Optimization objectives were the percentage of vessel area exposed to adversely low time averaged WSS (TAWSS) and adversely high Wall Shear Stress (WSS) assessed using computational fluid dynamics modeling, as well as radial stiffness of the stent using FEA simulation. Two multi-objective optimization algorithms were used and compared to iteratively predict ideal designs. Out of 50 designs, three best designs with respect to each of the three objectives, and two designs in regard to overall performance were identified.

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.

Updated Kriging-Assisted Shape Optimization of a Gravity Dam

The numerical simulation of the optimal design of gravity dams is computationally expensive. Therefore, a new optimization procedure is presented in this study to reduce the computational cost for determining the optimal shape of a gravity dam. Optimization was performed using a combination of the genetic algorithm (GA) and an updated Kriging surrogate model (UKSM). First, a Kriging surrogate model (KSM) was constructed with a small sample set. Second, the minimizing the predictor strategy was used to add samples in the region of interest to update the KSM in each updating cycle until the optimization process converged. Third, an existing gravity dam was used to demonstrate the effectiveness of the GA–UKSM. The solution obtained with the GA–UKSM was compared with that obtained using the GA–KSM. The results revealed that the GA–UKSM required only 7.53% of the total number of numerical simulations required by the GA–KSM to achieve similar optimization results. Thus, the GA–UKSM can significantly improve the computational efficiency. The method adopted in this study can be used as a reference for the optimization of the design of gravity dams.

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.

Shape Optimization of Single-Curvature Arch Dam Based on Sequential Kriging-Genetic Algorithm

Shape optimization of single-curvature arch dams using the finite element method (FEM) is often computationally expensive. To reduce the computational burden, this study introduces a new optimization method, combining a genetic algorithm with a sequential Kriging surrogate model (GA-SKSM), for determining the optimal shape of a single-curvature arch dam. At the start of genetic optimization, a KSM was constructed using a small sample set. In each iteration of optimization, the minimizing predictor criterion and low confidence bound criterion were used to collect samples from the domain of interest and accumulate them into a small sample set to update the KSM until the optimization process converged. A practical problem involving the optimization of a single-curvature arch dam was solved using the introduced GA-SKSM, and the performance of the method was compared with that of GA-KSM and GA-FEM methods. The results revealed that the GA-SKSM method required only 5.40% and 12.40% of the number of simulations required by the GA-FEM and GA-KSM methods, respectively. The GA-SKSM method can significantly improve computational efficiency and can serve as a reference for effective optimization of the design of single-curvature arch dams.

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.