Skip to main content
Log in

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

  • Original Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

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

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  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. https://doi.org/10.1016/j.iccl.2016.03.002

    Article  PubMed  Google Scholar 

  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. https://doi.org/10.1136/bmj.h5392

  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. https://doi.org/10.1152/japplphysiol.91519.2008

    Article  PubMed  PubMed Central  Google Scholar 

  4. Patel SM, Li J, Parikh SA (2016) Design and comparison of large vessel stents. Interv Cardiol Clin 5:365–380. https://doi.org/10.1016/j.iccl.2016.03.005

    Article  PubMed  Google Scholar 

  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. https://doi.org/10.3109/03008200903329771

    Article  PubMed  Google Scholar 

  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. https://doi.org/10.1155/2012/608593

    Article  Google Scholar 

  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. https://doi.org/10.1002/jbm.b.31028

    Article  CAS  Google Scholar 

  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. https://doi.org/10.1007/s10439-015-1387-3

    Article  PubMed  PubMed Central  Google Scholar 

  9. Westerhof N, Stergiopulos N, Noble MIM (2010) Snapshots of hemodynamics

  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 294–295

  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. https://doi.org/10.1186/1475-925X-8-8

    Article  PubMed  PubMed Central  Google Scholar 

  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. https://doi.org/10.1080/10255842.2014.984701

    Article  Google Scholar 

  13. Srinivas K, Nakayama T, Ohta M, Obayashi S, Yamaguchi T (2008) Studies on design optimization of coronary stents. J Med Device 2:11004-1–11004-7

    Article  Google Scholar 

  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 4:21003-1–21003-7

    Article  Google Scholar 

  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 136:61006-1–61006-7

    Article  Google Scholar 

  16. Bressloff NW, Ragkousis G, Curzen N (2015) Design optimisation of coronary artery stent systems. Ann Biomed Eng 44:1–11. https://doi.org/10.1007/s10439-015-1373-9

    Article  Google Scholar 

  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):371–382

    Google Scholar 

  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. https://doi.org/10.1186/s12938-016-0268-9

    Article  PubMed  PubMed Central  Google Scholar 

  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. https://doi.org/10.1016/j.jbiomech.2015.09.039

    Article  PubMed  Google Scholar 

  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. https://doi.org/10.1007/s10439-010-9994-5

    Article  PubMed  Google Scholar 

  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. https://doi.org/10.1186/s12938-016-0307-6

    Article  PubMed  PubMed Central  Google Scholar 

  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 1007–1010

  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 

  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 852–856

  25. AIJ F, Sobester A, Keane AJ (2008) Engineering design via surrogate modelling. Wiley., West-Sussex

    Google Scholar 

  26. Kolar M, OS F (1993) Fast, portable and reliable algorithm for the calculation of Halton numbers. Comput Math Appl 25:3–13

    Article  Google Scholar 

  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. https://doi.org/10.1038/nrcardio.2012.64

    Article  CAS  PubMed  Google Scholar 

  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. https://doi.org/10.3233/THC-140871

    Article  PubMed  Google Scholar 

  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. https://doi.org/10.1371/journal.pone.0108033

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  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. IEEE

  31. Components JMM (2015) Nitinol technical properties. http://jmmedical.com/resources/221/Nitinol-Technical-Properties.html. Accessed 9 Sept 2015

  32. Fung YC (1996) Blood flow in arteries. In: Biomechanics: circulation, second. Springer-Verlag, New York, pp 108–205

    Google Scholar 

  33. COMSOL Multiphysics (2014) Fluid structure interaction in a network of blood vessels. In: Structural mechanics module model library manual, vol 1, p 20

    Google Scholar 

  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. https://doi.org/10.1299/jbse.2014jbse0003

    Article  Google Scholar 

  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. https://doi.org/10.17106/jbr.31.50

  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. https://doi.org/10.1016/j.jmbbm.2014.02.009

    Article  CAS  PubMed  Google Scholar 

  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. https://doi.org/10.1299/jcst.5.134

    Article  Google Scholar 

  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. https://doi.org/10.1155/2015/162712

    Article  Google Scholar 

  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 2147–2154

  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. https://doi.org/10.1098/rsif.2013.1079

    Article  PubMed  PubMed Central  Google Scholar 

  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. https://doi.org/10.1007/s11517-017-1693-z

    Article  Google Scholar 

Download references

Acknowledgments

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

Funding

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).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Narendra Kurnia Putra.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Putra, N.K., Palar, P.S., Anzai, H. et al. Multiobjective design optimization of stent geometry with wall deformation for triangular and rectangular struts. Med Biol Eng Comput 57, 15–26 (2019). https://doi.org/10.1007/s11517-018-1864-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-018-1864-6

Keywords

Navigation