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Optimal design of the vascular stent ring in order to maximise radial stiffness

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Abstract

The therapeutic efficacy of stents strongly depends upon their mechanical properties. An important component of stents is rings, which are usually made of crowns. Such rings can be treated as circular ones, corrugated out of the plane. The deformation of such structure under the action of external pressure is considered in the paper. An asymptotic homogenization method is applied. A formula is obtained for the dependence of the deformation on the external pressure for an arbitrary smooth corrugation profile. The problem is posed to optimise the shape of the corrugation profile in order to maximise radial stiffness. This optimal profile will reduce the cross-sectional area of the fibres of the stent, which will improve its medical performance. The optimal profile found is close to sinusoidal.

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References

  1. Shi, W., Li, H., Zhu, T., et al.: Study on the bending behaviour of biodegradable metal cerebral vascular stents using finite element analysis. J. Biomech. 108, 109843–109856 (2020)

    Article  Google Scholar 

  2. Bonsignore, C.: Open source stent calculator. In: Open Stent Design project, FDA / NHLBI / NSF Workshop on Computer Methods for Cardiovascular Devices, pp. 1–93 (2010)

  3. Tambaca, J., Canic, S., Kosor, M., Fish, R., Paniagua, D.: Mechanical behaviour of fully expanded commercially available endovascular coronary stents. Texas Heart Inst. J. 38(5), 491–501 (2011)

    Google Scholar 

  4. Wei, Y., Wang, M., Zhao, D., Li, H., Jin, Y.: Structural design of mechanical property for biodegradable polymeric stent. Adv. Mater. Sci. Eng. 2019, 1–14 (2019)

    Article  Google Scholar 

  5. Lindholm, D., James, S.: Bioresorbable stents in PCI. Curr. Cardiol. Rep. 18, 1–6 (2016)

    Article  Google Scholar 

  6. Kočka, V., Toušek, P., Widimský, P.: Absorb bioresorbable stents for the treatment of coronary artery disease. Expert Rev. Med. Devices 12, 545–557 (2015)

    Article  Google Scholar 

  7. Alexy, R., Levi, D.: Materials and manufacturing technologies available for production of a paediatric bioabsorbable stent. Biomed Res. Int. 2013, 1–11 (2013)

    Article  Google Scholar 

  8. Ang, H., Huang, Y., Lim, S., Wong, P., Joner, M., Foin, N.: Mechanical behavior of polymer-based vs. metallic-based bioresorbable stents. J. Thorac. Dis. 9, 923–934 (2017)

    Article  Google Scholar 

  9. Ho, M., Chen, C., Wang, C., et al.: The development of coronary artery stents: from bare-metal to bio-resorb able types. Metals 6(7), 168–182 (2016)

    Article  Google Scholar 

  10. Schiavone, A., Zhao, L., Abdel-Wahab, A.: Effects of material, coating, design and plaque composition on stent deployment inside a steno tic artery-finite element simulation. Mater. Sci. Eng. C: Mater. Biol. Appl. 42, 479–488 (2014)

    Article  Google Scholar 

  11. Hsiao, H., Chiu, Y., Lee, K., Lin, C.: Computational modelling of effects of intravascular stent design on key mechanical and hemodynamic behaviour. CAD 44, 757–765 (2012)

    Google Scholar 

  12. Wu, W., Petrini, L., Gastaldi, D., et al.: Finite element shape optimization for biodegradable magnesium alloy stents. Ann. Biomed. Eng. 38, 2829–2840 (2010)

    Article  Google Scholar 

  13. Bobel, A., Petisco, S., Sarasua, W., Mchugh, P.: Computational bench testing to evaluate the short-term mechanical performance of a polymeric stent. CVET 6, 519–532 (2015)

    Google Scholar 

  14. Bae, I., Lim, K., Park, J., et al.: Mechanical behaviour and in vivo properties of newly designed bare metal stent for enhanced flexibility. J. Ind. Eng. Chem. 21, 1295–1300 (2015)

    Article  Google Scholar 

  15. Feng, Q., Jiang, W., Sun, K., et al.: Mechanical properties and in vivo performance of a novel sliding-lock bio absorbable poly-p-dioxin one stent. J. Mater. Sci.: Mater. Med. 22, 2319–2327 (2011)

    Google Scholar 

  16. Wang, X.: Finite element analysis for the stiffness and the buckling of corrugated tubes in heat exchanger. Adv. Mater. Res. 468–471, 1675–1680 (2012)

    Google Scholar 

  17. Wennberg, D., Wennhage, P., Stichel, S.: Orthotropic models of corrugated sheets in finite element analysis. ISRN Mech. Eng. 3, 1–9 (2011)

    Article  Google Scholar 

  18. Wang, K., Zhou, M., Hassanein, M., et al.: Study on elastic global shear buckling of curved girders with corrugated steel webs: theoretical analysis and FE modelling. Appl. Sci. 8, 2457–2471 (2018)

    Article  Google Scholar 

  19. Sowiński, K.: Buckling of shells with special shapes with corrugated middle surfaces – FEM study. Eng. Struct. 179, 310–320 (2019)

    Article  Google Scholar 

  20. Xue, H., Luo, Z., Brown, T., Beier, S.: Design of self-expanding auxetic stents using topology optimization. Front. Bioeng. Biotechnol. 8, 736 (2020)

    Article  Google Scholar 

  21. Andrianov, I.V., Awrejcewicz, J., Manevitch, L.I.: Asymptotical Mechanics of Thin-Walled Structures: A Handbook. Springer, Berlin (2004)

    Book  Google Scholar 

  22. Ye, Z., Berdichevsky, V., Yu, W.: An equivalent classical plate model of corrugated structures. Int. J. Solids Struct. 51, 2073–2083 (2014)

    Article  Google Scholar 

  23. Xia, Y., Friswell, M., Saavedra Flores, E.: Equivalent models of corrugated panels. Int. J. Solids Struct. 49, 1453–1462 (2012)

    Article  Google Scholar 

  24. Nguyen-Minh, N., Tran-Van, N.: Static analysis of corrugated panels using homogenization models and a cell-based smoothed Mindlin plate element. Front. Struct. Civ. Eng. 13, 251–272 (2019)

    Article  Google Scholar 

  25. Kolpakov, A.A., Kolpakov, A.G.: On the effective stiffnesses of corrugated plates of various geometries. Int. J. Eng. Sci. 154(6), 103327 (2020)

    Article  MathSciNet  Google Scholar 

  26. Kolpakov, A., Rakin, I.: Calculation of the effective stiffness of the corrugated plate by solving the problem on the plate cross-section. J. Appl. Mech. Techn. Phys. 57, 757–767 (2016)

    Article  Google Scholar 

  27. Kolpakov, A.A., Kolpakov, A.G.: Discussion of the effective stiffness’s in: Ye, Berdichevsky, and Yu [Int. J. Solids Struct. 51 (2014) 2073–2083]. Int. J. Solids Struct. 174–175, 145–146 (2014)

    Google Scholar 

  28. Syerko, E., Diskovsky, A., Andrianov, I.V., Comas-Cardona, S., Binetruy, Ch.: Corrugated beams mechanical behaviour modelling by the homogenization method. Int. J. Solids Struct. 50, 928–936 (2013)

    Article  Google Scholar 

  29. Andrianov, I.I., Awrejcewicz, J., Diskovsky, A.: Optimal design of a functionally graded corrugated cylindrical shell subjected to axisymmetric loading. Arch. Appl.Mech. 88, 1027–1039 (2018)

    Article  Google Scholar 

  30. Andrianov, I.V., Awrejcewicz, J., Diskovsky, A.: The optimal design of a functionally graded corrugated cylindrical shell under axisymmetric loading. Int. J. Nonlinear Sci. Numer. Simul. 20, 387–398 (2019)

    Article  MathSciNet  Google Scholar 

  31. Andrianov, I.V., Awrejcewicz, J., Diskovsky, A.: Optimal design of a functionally graded corrugated rods subjected to longitudinal deformation. Arch Appl Mech 85, 303–314 (2015)

    Article  Google Scholar 

  32. Andrianov, I.I., Andrianov, I.V., Diskovsky, A., Ryzhkov, E.: Buckling of corrugated ring under uniform external pressure. Symmetry 12, 1250–1260 (2020)

    Article  Google Scholar 

  33. Tap, K.: Differential Geometry of Curves and Surfaces. Springer, New York (2016)

    Book  Google Scholar 

  34. Timoshenko, S., Gere, J.: Theory of Elastic Stability. McGraw-Hill, New York (1961)

    Google Scholar 

  35. Yang, J., Huang, N.: Mechanical formula for the plastic limit pressure of stent during expansion. Acta Mech. Sinica 25, 795–801 (2009)

    Article  MathSciNet  Google Scholar 

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The author(s) received no financial support for the research, authorship, and/or publication of this article.

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Authors and Affiliations

  1. Chair and Institute of General Mechanics, RWTH Aachen University, Eilfschornsteinstraße 18, 52062, Aachen, Germany

    I. V. Andrianov

  2. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90924, Lodz, Poland

    J. Awrejcewicz

  3. Department of Economic and Information Security, Dnipro State University of Foreign Affairs, Gagarina Ave 26, Dnipro, UA-49005, Ukraine

    A. A. Diskovsky

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  1. I. V. Andrianov
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  2. J. Awrejcewicz
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  3. A. A. Diskovsky
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Correspondence to J. Awrejcewicz.

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Andrianov, I.V., Awrejcewicz, J. & Diskovsky, A.A. Optimal design of the vascular stent ring in order to maximise radial stiffness. Arch Appl Mech 92, 667–678 (2022). https://doi.org/10.1007/s00419-022-02118-0

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  • DOI: https://doi.org/10.1007/s00419-022-02118-0

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