Skip to main content
SpringerLink
Log in

Geometry parameterization and multidisciplinary constrained optimization of coronary stents

  • Original Paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

Abstract

Coronary stents are tubular type scaffolds that are deployed, using an inflatable balloon on a catheter, most commonly to recover the lumen size of narrowed (diseased) arterial segments. A common differentiating factor between the numerous stents used in clinical practice today is their geometric design. An ideal stent should have high radial strength to provide good arterial support post-expansion, have high flexibility for easy manoeuvrability during deployment, cause minimal injury to the artery when being expanded and, for drug eluting stents, should provide adequate drug in the arterial tissue. Often, with any stent design, these objectives are in competition such that improvement in one objective is a result of trade-off in others. This study proposes a technique to parameterize stent geometry, by varying the shape of circumferential rings and the links, and assess performance by modelling the processes of balloon expansion and drug diffusion. Finite element analysis is used to expand each stent (through balloon inflation) into contact with a representative diseased coronary artery model, followed by a drug release simulation. Also, a separate model is constructed to measure stent flexibility. Since the computational simulation time for each design is very high (approximately 24 h), a Gaussian process modelling approach is used to analyse the design space corresponding to the proposed parameterization. Four objectives to assess recoil, stress distribution, drug distribution and flexibility are set up to perform optimization studies. In particular, single objective constrained optimization problems are set up to improve the design relative to the baseline geometry—i.e. to improve one objective without compromising the others. Improvements of 8, 6 and 15% are obtained individually for stress, drug and flexibility metrics, respectively. The relative influence of the design features on each objective is quantified in terms of main effects, thereby suggesting the design features which could be altered to improve stent performance. In particular, it is shown that large values of strut width combined with smaller axial lengths of circumferential rings are optimal in terms of minimizing average stresses and maximizing drug delivery. Furthermore, it is shown that a larger amplitude of the links with minimum curved regions is desirable for improved flexibility, average stresses and drug delivery.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Atherton M, Bates R (2006) Searching for improvement. In: Bryant JA, Atherton MA, Collins MW (eds) Information transfer in biological systems, design in nature series, vol 2. WIT Press, Southampton, pp 345–379. ISBN 1853128538

  • Bedoya J, Meyer C, Timmins L, Moreno M, Moore J Jr (2006) Effects of stent design parameters on normal artery wall mechanics. J Biomech Eng 128: 757–765

    Article  Google Scholar 

  • Blouza A, Dumas L, M’Baye I (2008) Multiobjective optimization of a stent in a fluid-structure context. In: Proceedings of the 2008 GECCO conference companion on Genetic and evolutionary computation, pp 2055–2060

  • Carter AJ, Laird JR, Farb A, Kufs W, Wortham DC, Virmani R (1994) Morphologic characteristics of lesion formation and time course of smooth muscle cell proliferation in a porcine proliferative restenosis model. J Am Coll Cardiol 24: 1398–1405

    Article  Google Scholar 

  • Contiliano J, Zhang Q (2009) Method of manufacturing a polymeric stent having a circumferential ring configuration. WO Patent WO/2009/121048

  • Cordis Corporation (2010) Insrtuctions for use: CYPHER sirolimus-eluting coronary stent on RAPTOR over-the-wire delivery system. Johnson & Johnson company, Warren/Bridgewater Campus, 12th edn, http://www.cordislabeling.com , last accessed 20th May, 2010, 1913 hrs

  • Crank J (1979) The mathematics of diffusion. Oxford University Press, USA

    MATH  Google Scholar 

  • Dassault Syst́emes (2009) Abaqus 6.9.1 user manual. Dassault Systèmes Simulia Corp

  • De Beule M (2008) Finite element stent design. PhD thesis, University of Gent

  • De Beule M, Van Impe R, Verhegghe B, Segers P, Verdonck P (2006) Finite element analysis and stent design: reduction of dogboning. Technol Health Care 14(4): 233–241

    Google Scholar 

  • De Beule M, Mortier P, Carlier S, Verhegghe B, Van Impe R, Verdonck P (2008) Realistic finite element-based stent design: the impact of balloon folding. J Biomech 41(2): 383–389

    Article  Google Scholar 

  • Engineers Hand Book (2010) http://www.engineershandbook.com; last accessed 02 May, 2010

  • Farb A, Sangiorgi G, Carter AJ, Walley VM, Edwards WD, Schwartz RS, Virmani R (1999) Pathology of acute and chronic coronary stenting in humans. Circulation 99: 44–52

    Google Scholar 

  • Feenstra P, Taylor C (2009) Drug transport in artery walls: a sequential porohyperelastic-transport approach. Comput Meth Biomech Biomed Eng 12(3): 263–276

    Article  Google Scholar 

  • Forrester AIJ, Sóbester A, Keane AJ (2008) Engineering design via surrogate modelling: a practical guide. Wiley, Chichester, p 240. ISBN 978-0-470-06068-1

    Book  Google Scholar 

  • Gervaso F, Capelli C, Petrini L, Lattanzio S, Di Virgilio L, Migliavacca F (2008) On the effects of different strategies in modelling balloon-expandable stenting by means of finite element method. J Biomech 41(6): 1206–1212

    Article  Google Scholar 

  • Hara H, Nakamura M, Schwartz R (2006) Role of stent design and coatings on restenosis and thrombosis. Adv Drug Deliv Rev 58: 377–386

    Article  Google Scholar 

  • Hicks R, Henne P (1978) Wing design by numerical optimization. J Aircr 15(7): 407–412

    Article  Google Scholar 

  • Hoffmann R, Mintz GS, Mehran R, Kent KM, Pichard AD, Satler LF, Leon MB (1999) Tissue proliferation within and surrounding palmaz-schatz stents is dependent on the aggressiveness of stent implanation technique. Am J Cardiol 83: 1170–1174

    Article  Google Scholar 

  • Holzapfel G, Sommer G, Regitnig P (2004) Anisotropic mechanical properties of tissue components in human atherosclerotic plaques. J Biomech Eng 126(5): 657–665

    Article  Google Scholar 

  • Holzapfel G, Sommer G, Gasser C, Regitnig P (2005a) Determination of layer-specific mechanical properties of human coronary arteries with nonatherosclerotic intimal thickening and related constitutive modeling. Am J Physiol Heart Circ Physiol 289(5): H2048– H2058

    Article  Google Scholar 

  • Holzapfel GA, Stadler M, Gasser T (2005) Changes in the mechanical environment of stenotic arteries during interaction with stents: computational assessment of parametric stent designs. J Biomech Eng 127: 166–180

    Article  Google Scholar 

  • Hose D, Narracott A, Griffiths B, Mahmood S, Gunn J, Sweeney D, Lawford P (2004) A thermal analogy for modelling drug elution from cardiovascular stents. Comput Meth Biomech Biomed Eng 7(5): 257–264

    Article  Google Scholar 

  • Jones D, Schonlau M, Welch W (1998) Efficient global optimization of expensive black-box functions. J Global Optim 13(4): 455– 492

    Article  MATH  MathSciNet  Google Scholar 

  • Jua F, Xiaa Z, Zhoub C (2008) Repeated unit cell (RUC) approach for pure bending analysis of coronary stents. Comput Meth Biomech Biomed Eng 11(4): 419–431

    Article  Google Scholar 

  • Kastrati A, Mehilli J, Dirschinger J, Dotzer F, Schuhlen H, Neumann F, Fleckenstein M, Pfafferott C, Seyfarth M, Schomig A (2001) Intracoronary stenting and angiographic results: strut thickness effect on restenosis outcome (isar-stereo) trial. Circulation 103: 2816–2821

    Google Scholar 

  • Keane A, Nair P (2005) Computational approaches for aerospace design. The pursuit of excellence. Wiley, Chichester

    Book  Google Scholar 

  • Kiousis D, Gasser T, Holzapfel G (2007) A numerical model to study the interaction of vascular stents with human atherosclerotic lesions. Ann Biomed Eng 35(11): 1857–1869

    Article  Google Scholar 

  • Knig A, Schiele TM, Rieber J, Theisen K, Mudra H, Klauss V (2002) Influence of stent design and deployment technique on neointima formation and vascular remodeling. Z Kardiol 91: 98–102

    Article  Google Scholar 

  • Kock S, Nygaard J, Eldrup N, Frund E, Klærke A, Paaske W, Falk E, Yong Kim W (2008) Mechanical stresses in carotid plaques using MRI-based fluid–structure interaction models. J Biomech 41(8): 1651–1658

    Article  Google Scholar 

  • Kolachalama V, Bressloff N, Nair P (2007a) Mining data from hemodynamic simulations via Bayesian emulation. Biomed Eng Online 6(1): 47

    Article  Google Scholar 

  • Kolachalama V, Bressloff N, Nair P, Shearman C (2007b) Predictive haemodynamics in a one-dimensional human carotid artery bifurcation. Part I: application to stent design. IEEE Trans Biomed Eng 54(5): 802–812

    Article  Google Scholar 

  • Kolachalama V, Tzafriri A, Arifin D, Edelman E (2009) Luminal flow patterns dictate arterial drug deposition in stent-based delivery. J Controlled Release 133(1): 24–30

    Article  Google Scholar 

  • Kornowski R, Hong MK, Tio FO, Bramwell O, Wu H, Leon MB (1998) In-stent restenosis: contributions of inflammatory responses and arterial injury to neointimal hyperplasia. J Am Coll Cardiol 31: 224–230

    Article  Google Scholar 

  • Ku D (1997) Blood flow in arteries. Annu Rev Fluid Mech 29: 399–434

    Article  MathSciNet  Google Scholar 

  • Ku D, Zarins C, Giddens D, Glagov S (1985) Pulsatile flow and atherosclerosis in the human carotid bifurcation: positve correlation between plaque localization and low and oscillating shear stress. Arteriosclerosis 5: 292–302

    Google Scholar 

  • Li N, Gu Y (2005) Parametric design analysis and shape optimization of coronary arteries stent structure. In: Proceedings of 6th world congresses of structural and multidisciplinary optimization, Rio de Janeiro, 30 May–03 June, 2005, Brazil

  • Li N, Zhanga H, Ouyang H (2009) Shape optimization of coronary artery stent based on a parametric model. Finite Elem Anal Des 45: 468–475

    Article  Google Scholar 

  • McGarry J, O’Donnell B, McHugh P, McGarry J (2004) Analysis of the mechanical performance of a cardiovascular stent design based on micromechanical modelling. Comput Mater Sci 31(3–4): 421–438

    Google Scholar 

  • Moore J Jr, Xu C, Glagov S, Zarins C, Ku D (1994) Fluid wall shear stress measurements in a model of the human abdominal aorta: oscillatory behavior and relationship to atherosclerosis. Atherosclerosis 110(2): 225–240

    Article  Google Scholar 

  • Mori K, Saito T (2005) Effects of stent structure on stent flexibility measurements. Ann Biomed Eng 33(6): 733–742

    Article  Google Scholar 

  • Morton AC, Crossman D, Gunn J (2004) The influence of physical stent parameters upon restenosis. Pathol Biol 52: 196–205

    Article  Google Scholar 

  • Murphy B, Savage P, McHugh P, Quinn D (2003) The stress–strain behavior of coronary stent struts is size dependent. Ann Biomed Eng 31(6): 686–691

    Article  Google Scholar 

  • Pache J, Kastrati A, Mehilli J, Schuhlen H, Dotzer F, Hausleiter J, Fleckenstein M, Neumann F, Sattelberger U, Schmitt C, Muller M, Dirschinger J, Schomig A (2003) Intracoronary stenting and angiographic results: strut thickness effect on restenosis outcome (isar-stereo-2) trial. J Am Coll Cardiol 41(8): 1283–1288

    Article  Google Scholar 

  • Pericevic I, Lally C, Toner D, Kelly D (2009) The influence of plaque composition on underlying arterial wall stress during stent expansion: the case for lesion-specific stents. Med Eng Phys 31(4): 428–433

    Article  Google Scholar 

  • Petrini L, Migliavacca F, Auricchio F, Dubini G (2004) Numerical investigation of the intravascular coronary stent flexibility. J Biomech 37(4): 495–501

    Article  Google Scholar 

  • Schwartz RS, Huber KC, Murphy JG, Edwards WD, Camrud AR, Vlietstra RE, Holmes DR (1992) Restenosis and the proportional neointimal response to coronary artery injury: results in a porcine model. J Am Coll Cardiol 19: 267–274

    Article  Google Scholar 

  • Serruys P (1997) Handbook of coronary stents, 4th edn. Martin Dunitz Publishers, London

    Google Scholar 

  • Sobol I (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55(1–3): 271–280

    Article  MATH  MathSciNet  Google Scholar 

  • Statnikov R, Matusov J (2002) Multicriteria analysis in engineering: using the PSI method with MOVI 1.0. Kluwer, Dordrecht

    MATH  Google Scholar 

  • Timmins L, Moreno M, Meyer C, Criscione J, Rachev A, Moore J (2007) Stented artery biomechanics and device design optimization. Med Biol Eng Comput 45(5): 505–513

    Article  Google Scholar 

  • Wang W, Liang D, Yang D, Qi M (2006) Analysis of the transient expansion behavior and design optimization of coronary stents by finite element method. J Biomech 39(1): 21–32

    Article  Google Scholar 

  • Wentzel J, Krams R, Schuurbiers J, Oomen J, Kloet J, Giessen W, Serruys P, Slager C (2001) Relationship between neointimal thickness and shear stress after wallstent implantation in human coronary arteries. Circulation 103: 1740–1745

    Google Scholar 

  • Wong H, Cho K, Tang W (2009) Bending of a stented atherosclerotic artery. In: Proceedings of the COMSOL conference 2009 Boston

  • Wu W, Yang D, Qi M, Wang W (2007) An FEA method to study flexibility of expanded coronary stents. J Mater Process Technol 184(1–3): 447–450

    Article  Google Scholar 

  • Wu W, Petrini L, Gastaldi D, Villa T, Vedani M, Lesma E, Previtali B, Migliavacca F (2010) Finite element shape optimization for biodegradable magnesium alloy stents. Ann Biomed Eng 38(9): 2829–2840

    Article  Google Scholar 

  • Zhou J, Tits A, Lawrence C (1998) User’s guide for FFSQP version 3.7: A FORTRAN code for solving constrained nonlinear (minimax) optimization problems, generating iterates satisfying all inequality and linear constraints. Institute for Systems Research, University of Maryland, College Park, MD

  • Zunino P, D’Angelo C, Petrini L, Vergara C, Capelli C, Migliavacca F (2009) Numerical simulation of drug eluting coronary stents: mechanics, fluid dynamics and drug release. Comput Meth Appl Mech Eng 198(45–46): 3633–3644

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering Sciences, Computational Engineering Design Group, University of Southampton, SO17 1BJ, Southampton, UK

    Sanjay Pant & Neil W. Bressloff

  2. School of Engineering Sciences, National Centre for Advanced Tribology at Southampton (nCATS), University of Southampton, SO17 1BJ, Southampton, UK

    Georges Limbert

  3. School of Engineering Sciences, Bioengineering Sciences Research Group, University of Southampton, SO17 1BJ, Southampton, UK

    Georges Limbert

Authors
  1. Sanjay Pant
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Neil W. Bressloff
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Georges Limbert
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Neil W. Bressloff.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pant, S., Bressloff, N.W. & Limbert, G. Geometry parameterization and multidisciplinary constrained optimization of coronary stents. Biomech Model Mechanobiol 11, 61–82 (2012). https://doi.org/10.1007/s10237-011-0293-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-011-0293-3

Keywords

Search

Navigation