title: Design optimization of stent and its dilatation balloon using kriging surrogate model.
abstract: BACKGROUND
  Although stents have great success of treating cardiovascular disease, it actually undermined by the in-stent restenosis and their long-term fatigue failure. The geometry of stent affects its service performance and ultimately affects its fatigue life. Besides, improper length of balloon leads to transient mechanical injury to the vessel wall and in-stent restenosis. Conventional optimization method of stent and its dilatation balloon by comparing several designs and choosing the best one as the optimal design cannot find the global optimal design in the design space. In this study, an adaptive optimization method based on Kriging surrogate model was proposed to optimize the structure of stent and the length of stent dilatation balloon so as to prolong stent service life and improve the performance of stent.
  
  
  METHODS
  A finite element simulation based optimization method combing with Kriging surrogate model is proposed to optimize geometries of stent and length of stent dilatation balloon step by step. Kriging surrogate model coupled with design of experiment method is employed to construct the approximate functional relationship between optimization objectives and design variables. Modified rectangular grid is used to select initial training samples in the design space. Expected improvement function is used to balance the local and global searches to find the global optimal result. Finite element method is adopted to simulate the free expansion of balloon-expandable stent and the expansion of stent in stenotic artery. The well-known Goodman diagram was used for the fatigue life prediction of stent, while dogboning effect was used for stent expansion performance measurement. As the real design cases, diamond-shaped stent and sv-shaped stent were studied to demonstrate how the proposed method can be harnessed to design and refine stent fatigue life and expansion performance computationally.
  
  
  RESULTS
  The fatigue life and expansion performance of both the diamond-shaped stent and sv-shaped stent are designed and refined, respectively. (a) diamond-shaped stent: The shortest distance from the data points to the failure line in the Goodman diagram was increased by 22.39%, which indicated a safer service performance of the optimal stent. The dogboning effect was almost completely eliminated, which implies more uniform expansion of stent along its length. Simultaneously, radial elastic recoil (RR) at the proximal and distal ends was reduced by 40.98 and 35% respectively and foreshortening (FS) was also decreased by 1.75%. (b) sv-shaped stent: The shortest distance from the data point to the failure line in the Goodman diagram was increased by 15.91%. The dogboning effect was also completely eliminated, RR at the proximal and distal ends was reduced by 82.70 and 97.13%, respectively, and the FS was decreased by 16.81%. Numerical results showed that the fatigue life of both stents was refined and the comprehensive expansion performance of them was improved.
  
  
  CONCLUSIONS
  This article presents an adaptive optimization method based on the Kriging surrogate model to optimize the structure of stents and the length of their dilatation balloon to prolong stents fatigue life and decreases the dogboning effect of stents during expansion process. Numerical results show that the adaptive optimization method based on Kriging surrogate model can effectively optimize the design of stents and the dilatation balloon. Further investigations containing more design goals and more effective multidisciplinary design optimization method are warranted.
authors.affiliation: School of Mechanical Engineering, Dalian University of Technology, Dalian, 116023, Liaoning, China.
authors.forename: Hongxia
authors.initials: H
authors.lastname: Li
authors.affiliation: School of Mechanical Engineering, Dalian University of Technology, Dalian, 116023, Liaoning, China.
authors.forename: Tao
authors.initials: T
authors.lastname: Liu
authors.affiliation: School of Mechanical Engineering, Dalian University of Technology, Dalian, 116023, Liaoning, China.
authors.forename: Minjie
authors.initials: M
authors.lastname: Wang
authors.affiliation: School of Mechanical Engineering, Dalian University of Technology, Dalian, 116023, Liaoning, China.
authors.forename: Danyang
authors.initials: D
authors.lastname: Zhao
authors.affiliation: College of Life Science and Bioengineering, Beijing University of Technology, Beijing, 100124, China.
authors.forename: Aike
authors.initials: A
authors.lastname: Qiao
authors.affiliation: Mechanical Engineering and Material Science Department, University of Pittsburgh, 4200 Fifth Avenue, Pittsburgh, PA, 15260, USA.
authors.forename: Xue
authors.initials: X
authors.lastname: Wang
authors.affiliation: Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116023, Liaoning, China.
authors.forename: Junfeng
authors.initials: J
authors.lastname: Gu
authors.affiliation: Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116023, Liaoning, China.
authors.forename: Zheng
authors.initials: Z
authors.lastname: Li
authors.affiliation: School of Materials Science and Engineering, Dalian University of Technology, No. 2, Linggong Road, Dalian, 116024, Liaoning, China. bzhu@dlut.edu.cn.
authors.forename: Bao
authors.initials: B
authors.lastname: Zhu
mesh_terms: D000465:Algorithms; D004106:Dilatation / Q000295:instrumentation*; D019544:Equipment Failure Analysis; D020342:Finite Element Analysis; D011474:Prosthesis Design / Q000379:methods*; D015607:Stents; D013314:Stress, Mechanical
keywords: Design optimization; Dogboning effect; Fatigue life; Finite element method; Kriging surrogate model; Stent