Medical & Biological Engineering & Computing

, Volume 57, Issue 1, pp 15–26 | Cite as

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

  • Narendra Kurnia PutraEmail author
  • Pramudita Satria Palar
  • Hitomi Anzai
  • Koji Shimoyama
  • Makoto Ohta
Original Article


The stent geometrical design (e.g., inter-strut gap, length, and strut cross-section) is responsible for stent–vessel contact problems and changes in the blood flow. These changes are crucial for causing some intravascular abnormalities such as vessel wall injury and restenosis. Therefore, structural optimization of stent design is necessary to find the optimal stent geometry design. In this study, we performed a multiobjective stent optimization for minimization of average stress and low wall shear stress ratio while considering the wall deformation in 3D flow simulations of triangular and rectangular struts. Surrogate-based optimization with Kriging method and expected hypervolume improvement (EHVI) are performed to construct the surrogate model map and find the best configuration of inter-strut gap (G) and side length (SL). In light of the results, G-SL configurations of 2.81–0.39 and 3.00–0.43 mm are suggested as the best configuration for rectangular and triangular struts, respectively. Moreover, considering the surrogate model and flow pattern conditions, we concluded that triangular struts work better to improve the intravascular hemodynamics.

Graphical abstract


Restenosis Stent Computational simulation Multiobjective optimization Kriging surrogate method 



We would like to thank Dr. Yasutomo Shimizu for his help and suggestions during the preparation of this manuscript.

Funding information

This research is supported by Indonesia Endowment for Education Fund (LPDP), Ministry of Finance, Republic of Indonesia through Beasiswa Pendidikan Indonesia Scholarship Program for Doctorate Students and the ImPACT program of Council for Science, Technology and Innovation (Cabinet Office, Government of Japan).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Elmore JB, Mehanna E, Parikh SA, Zidar DA (2016) Restenosis of the coronary arteries: past, present, future directions. Interv Cardiol Clin 5:281–293. CrossRefPubMedGoogle Scholar
  2. 2.
    Giacoppo D, Gargiulo G, Aruta P, Capranzano P, Tamburino C, Capodanno D (2015) Treatment strategies for coronary in-stent restenosis: systematic review and hierarchical Bayesian network meta-analysis of 24 randomised trials and 4880 patients. BMJ:h5392.
  3. 3.
    Chen HY, Hermiller J, Sinha AK, Sturek M, Zhu L, Kassab GS (2009) Effects of stent sizing on endothelial and vessel wall stress: potential mechanisms for in-stent restenosis. J Appl Physiol 106:1686–1691. CrossRefPubMedPubMedCentralGoogle Scholar
  4. 4.
    Patel SM, Li J, Parikh SA (2016) Design and comparison of large vessel stents. Interv Cardiol Clin 5:365–380. CrossRefPubMedGoogle Scholar
  5. 5.
    Freeman JW, Snowhill PB, Nosher JL (2010) A link between stent radial forces and vascular wall remodeling: the discovery of an optimal stent radial force for minimal vessel restenosis. Connect Tissue Res 51:314–326. CrossRefPubMedGoogle Scholar
  6. 6.
    Otsuka F, Nakano M, Ladich E, Kolodgie FD, Virmani R (2012) Pathologic etiologies of late and very late stent thrombosis following first-generation drug-eluting stent placement. Thrombosis 2012:1–16. CrossRefGoogle Scholar
  7. 7.
    Lewis G (2008) Materials, fluid dynamics, and solid mechanics aspects of coronary artery stents: a state-of-the-art review. J Biomed Mater Res Part B Appl Biomater 86B:569–590. CrossRefGoogle Scholar
  8. 8.
    Beier S, Ormiston J, Webster M, Cater J, Norris S, Medrano-Gracia P, Young A, Cowan B (2015) Hemodynamics in idealized stented coronary arteries: important stent design considerations. Ann Biomed Eng 44:315–329. CrossRefPubMedPubMedCentralGoogle Scholar
  9. 9.
    Westerhof N, Stergiopulos N, Noble MIM (2010) Snapshots of hemodynamicsGoogle Scholar
  10. 10.
    Putra NK, Anzai H, Ohta M (2016) Hemodynamic behaviours under blood vessel deformation by stent struts: two dimensional study. In: Thirteenth International Conference on Flow Dynamics pp 294–295Google Scholar
  11. 11.
    Mejia J, Ruzzeh B, Mongrain R, Leask R, Bertrand OF (2009) Evaluation of the effect of stent strut profile on shear stress distribution using statistical moments. Biomed Eng Online 8:8. CrossRefPubMedPubMedCentralGoogle Scholar
  12. 12.
    Chen Z, Zhan F, Ding J, Zhang X, Deng X (2016) A new stent with streamlined cross-section can suppress monocyte cell adhesion in the flow disturbance zones of the endovascular stent. Comput Methods Biomech Biomed Eng 19:60–66. CrossRefGoogle Scholar
  13. 13.
    Srinivas K, Nakayama T, Ohta M, Obayashi S, Yamaguchi T (2008) Studies on design optimization of coronary stents. J Med Device 2:11004-1–11004-7CrossRefGoogle Scholar
  14. 14.
    Srinivas K, Townsend S, Lee C-J, Nakayama T, Ohta M, Obayashi S, Yamaguchi T (2010) Two-dimensional optimization of a stent for an aneurysm. J Med Device 4:21003-1–21003-7CrossRefGoogle Scholar
  15. 15.
    Anzai H, Falcone JL, Chopard B, Hayase T, Ohta M (2014) Optimization of strut placement in flow diverter stents for four different aneurysm configurations. J Biomech Eng 136:61006-1–61006-7CrossRefGoogle Scholar
  16. 16.
    Bressloff NW, Ragkousis G, Curzen N (2015) Design optimisation of coronary artery stent systems. Ann Biomed Eng 44:1–11. CrossRefGoogle Scholar
  17. 17.
    Zhang M, Anzai H, Chopard B, Ohta M (2016) Towards the patient-specific design of flow diverters made from helix-like wires: an optimization study. Biomed Eng Online 15(Suppl):371–382Google Scholar
  18. 18.
    Li H, Gu J, Wang M, Zhao D, Li Z, Qiao A, Zhu B (2016) Multi-objective optimization of coronary stent using kriging surrogate model. Biomed Eng Online 15:148. CrossRefPubMedPubMedCentralGoogle Scholar
  19. 19.
    Janiga G, Daróczy L, Berg P, Thévenin D, Skalej M, Beuing O (2015) An automatic CFD-based flow diverter optimization principle for patient-specific intracranial aneurysms. J Biomech 48:3846–3852. CrossRefPubMedGoogle Scholar
  20. 20.
    Kim YH, Xu X, Lee JS (2010) The effect of stent porosity and strut shape on saccular aneurysm and its numerical analysis with lattice Boltzmann method. Ann Biomed Eng 38:2274–2292. CrossRefPubMedGoogle Scholar
  21. 21.
    Li H, Liu T, Wang M, Zhao D, Qiao A, Wang X, Gu J, Li Z, Zhu B (2017) Design optimization of stent and its dilatation balloon using kriging surrogate model. Biomed Eng Online 16(13):13. CrossRefPubMedPubMedCentralGoogle Scholar
  22. 22.
    Putra NK, Palar PS, Anzai H, et al (2017) Variation of strut parameter effects with wall deformation on stent deployment via surrogate model. In: 5th International Conference on Computational and Mathematical Biomed Eng pp 1007–1010Google Scholar
  23. 23.
    Putra NK, Palar PS, Anzai H, et al (2018) Comparative Study Between Different Strut’s Cross Section Shape on Minimizing Low Wall Shear Stress Along Stent Vicinity via Surrogate-Based Optimization. In: Schumacher A, Vietor T, Fiebig S, et al (eds) Advances in Structural and Multidisciplinary Optimization: Proceedings of the 12th World Congress of Structural and Multidisciplinary Optimization (WCSMO12). Springer International Publishing, Cham, pp 2097–2109 Google Scholar
  24. 24.
    Yang XS, Koziel S, Leifsson L (2012) Computational optimization, modelling and simulation: smart algorithms and better models. In: Procedia Computer Science. Elsevier Masson SAS, pp 852–856Google Scholar
  25. 25.
    AIJ F, Sobester A, Keane AJ (2008) Engineering design via surrogate modelling. Wiley., West-SussexGoogle Scholar
  26. 26.
    Kolar M, OS F (1993) Fast, portable and reliable algorithm for the calculation of Halton numbers. Comput Math Appl 25:3–13CrossRefGoogle Scholar
  27. 27.
    Otsuka F, Finn AV, Yazdani SK, Nakano M, Kolodgie FD, Virmani R (2012) The importance of the endothelium in atherothrombosis and coronary stenting. Nat Rev Cardiol 9:439–453. CrossRefPubMedGoogle Scholar
  28. 28.
    Mori F, Ohta M, Matsuzawa T (2015) Changes in blood flow due to stented parent artery expansion in an intracranial aneurysm. Technol Health Care 23:9–21. CrossRefPubMedGoogle Scholar
  29. 29.
    Kono K, Shintani A, Terada T (2014) Hemodynamic effects of stent struts versus straightening of vessels in stent-assisted coil embolization for sidewall cerebral aneurysms. PLoS One 9:e108033. CrossRefPubMedPubMedCentralGoogle Scholar
  30. 30.
    Putra NK, Palar PS, Anzai H, et al (2017) Stent design optimization based on Kriging surrogate model under deformed vessel wall: pulsatile inlet flow. In: ICA 2017 Proceedings. IEEEGoogle Scholar
  31. 31.
    Components JMM (2015) Nitinol technical properties. Accessed 9 Sept 2015
  32. 32.
    Fung YC (1996) Blood flow in arteries. In: Biomechanics: circulation, second. Springer-Verlag, New York, pp 108–205Google Scholar
  33. 33.
    COMSOL Multiphysics (2014) Fluid structure interaction in a network of blood vessels. In: Structural mechanics module model library manual, vol 1, p 20Google Scholar
  34. 34.
    Li Y, Anzai H, Nakayama T et al (2014) Simulation of hemodynamics in artery with aneurysm and stenosis with different geometric configuration. J Biomech Sci Eng 9:1–11. CrossRefGoogle Scholar
  35. 35.
    Han X, Sakamoto N, Tomita N et al (2017) Influence of shear stress on phenotype and MMP production of smooth muscle cells in a co-culture model. J Biorheol 31:50–56.
  36. 36.
    Chiastra C, Migliavacca F, Martínez MÁ, Malvè M (2014) On the necessity of modelling fluid-structure interaction for stented coronary arteries. J Mech Behav Biomed Mater 34:217–230. CrossRefPubMedGoogle Scholar
  37. 37.
    Shimoyama K, Yoshimizu S, Jeong S et al (2011) Multi-objective design optimization for a steam turbine stator blade using LES and GA. J Comput Sci Technol 5:134–147. CrossRefGoogle Scholar
  38. 38.
    Luo C, Shimoyama K, Obayashi S (2015) A study on many-objective optimization using the Kriging-surrogate-based evolutionary algorithm maximizing expected hypervolume improvement. Math Probl Eng 2015:1–15. CrossRefGoogle Scholar
  39. 39.
    Emmerich MTM, Deutz AH, Klinkenberg JW (2011) Hypervolume-based expected improvement: monotonicity properties and exact computation. In: 2011 IEEE Congress of Evolutionary Computation, CEC 2011. pp 2147–2154Google Scholar
  40. 40.
    Jimenez JM, Prasad V, Yu MD, Kampmeyer CP, Kaakour AH, Wang PJ, Maloney SF, Wright N, Johnston I, Jiang YZ, Davies PF (2014) Macro- and microscale variables regulate stent haemodynamics, fibrin deposition and thrombomodulin expression. J R Soc Interface 11:20131079–20131079. CrossRefPubMedPubMedCentralGoogle Scholar
  41. 41.
    Yeh HH, Rabkin SW, Grecov D (2017) Hemodynamic assessments of the ascending thoracic aortic aneurysm using fluid-structure interaction approach. Med Biol Eng Comput 56:1–17. CrossRefGoogle Scholar

Copyright information

© International Federation for Medical and Biological Engineering 2018

Authors and Affiliations

  1. 1.Department of Bioengineering and Robotics, Graduate School of EngineeringTohoku UniversitySendaiJapan
  2. 2.Institute of Fluid ScienceTohoku UniversitySendaiJapan

Personalised recommendations