Annals of Biomedical Engineering

, Volume 37, Issue 11, pp 2266–2287 | Cite as

The Use of Finite Element Methods and Genetic Algorithms in Search of an Optimal Fabric Reinforced Porous Graft System

  • M. S. Yeoman
  • B. D. Reddy
  • H. C. Bowles
  • P. Zilla
  • D. Bezuidenhout
  • T. Franz
Article

Abstract

The mechanics of arteries result from the properties of the soft tissue constituents and the interaction of the wall layers, predominantly media and adventitia. This concept was adopted in this study for the design of a tissue regenerative vascular graft. To achieve the desired structural properties of the graft, most importantly a diametric compliance of 6%/100 mmHg, finite element methods and genetic algorithms were used in an integrated approach to identify the mechanical properties of an adventitial fabric layer that were required to optimally complement an intimal/medial polyurethane layer with interconnected porosity of three different size classes. The models predicted a compliance of 16.0, 19.2, and 31.5%/100 mmHg for the non-reinforced grafts and 5.3, 5.5, and 6.0%/100 mmHg for the fabric-reinforced grafts. The latter, featuring fabrics manufactured according to the required non-linear mechanical characteristics numerically predicted, exhibited an in vitro compliance of 2.1 ± 0.8, 3.0 ± 2.4, and 4.0 ± 0.7% /100 mmHg. The combination of finite element methods and genetic algorithms was shown to be able to successfully optimize the mechanical design of the composite graft. The method offers potential for the application to alternative concepts of modular vascular grafts and the incorporation of tissue ingrowth and biodegradation.

Keywords

Adventitial reinforcement Constitutive model Diametric compliance Numerical modeling Optimization Vascular mechanics Vascular prosthesis 

Notes

Acknowledgments

This work was mainly funded through a research collaboration grant by Medtronic Inc. (Minneapolis, MN, USA) to the University of Cape Town. The authors acknowledge the assistance of Richard Steventon with the GA coding.

References

  1. 1.
    Bezuidenhout, D. Porous Polymeric Superstructures as In-Growth Scaffolds for Tissue-Engineered Vascular Prosthesis. PhD Thesis, Stellenbosch University, 2001.Google Scholar
  2. 2.
    Bezuidenhout, D., N. Davies, and P. Zilla. Effect of well defined dodecahedral porosity on inflammation and angiogenesis. ASAIO J. 48:465–471, 2002.PubMedCrossRefGoogle Scholar
  3. 3.
    Burkel, W. E. The challenge of small diameter vascular grafts. Med. Prog. Technol. 14:165–175, 1988.PubMedGoogle Scholar
  4. 4.
    Davies, N., S. Dobner, D. Bezuidenhout, C. Schmidt, M. Beck, A. H. Zisch, and P. Zilla. The dosage dependence of vegf stimulation on scaffold neovascularisation. Biomaterials, 29:3531–3538, 2008.PubMedCrossRefGoogle Scholar
  5. 5.
    Deutsch, M., J. Meinhart, P. Zilla, N. Howanietz, M. Gorlitzer, A. Froeschl, A. Stuempflen, D. Bezuidenhout, and M. Grabenwoeger. Long-term experience in autologous in vitro endothelialization of infrainguinal eptfe grafts. J. Vasc. Surg. 49:352–362, 2009.PubMedCrossRefGoogle Scholar
  6. 6.
    Faires, J. D., and R. L. Burden. Numerical Methods. Boston, MA: PWS Publishing, 1993.Google Scholar
  7. 7.
    Fung, Y. C. Biomechanics: Mechanical Properties of Living Tissue, 2nd ed. New York: Springer-Verlag, 1984.Google Scholar
  8. 8.
    Gamble, J., L. Matthias, G. Meyer, P. Kaur, G. Russ, R. Faull, M. Berndt, and M. Vadas. Regulation of in vitro capillary tube formation by anti-intergrin antibodies. J. Cell Biol. 121:931–943, 1993.PubMedCrossRefGoogle Scholar
  9. 9.
    Hasson, J. E., J. Megerman, and W. A. Abbott. Increased compliance near vascular anastamosis. J. Vasc. Surg. 2:419–423, 1985.PubMedCrossRefGoogle Scholar
  10. 10.
    Hayashi, K. Experimental approaches on measuring the mechanical properties and constitutive laws of arterial walls. J. Biomech. Eng. 115:481–487, 1993.PubMedCrossRefGoogle Scholar
  11. 11.
    Hayashi, K., H. Handa, S. Nagasawa, A. Okumura, and K. Moritake. Stiffness and elastic behavior of human intracranial and extracranial arteries. J. Biomech. 13:175–184, 1980.PubMedCrossRefGoogle Scholar
  12. 12.
    Hess, F., C. Jerusalem, and B. Braun. The endothelialisation of a fibrous polyurethane microvascular prosthesis after implantation in the abdominal aorta of the rat. J. Cardiovasc. Surg. 24:516–524, 1983.Google Scholar
  13. 13.
    How, T. V., R. Guidon, and S. K. Young. Engineering design of vascular prosthesis. Proc. Instn. Mech. Eng. [H] 206:61–71, 1992.CrossRefGoogle Scholar
  14. 14.
    Hsu, C.-C., C.-K. Chao, J.-L. Wang, and J. Lin. Multiobjective optimization of tibial locking screw design using a genetic algorithm: evaluation of mechanical performance. J. Orthop. Res. 24:908–916, 2006.PubMedCrossRefGoogle Scholar
  15. 15.
    Khalil, A. S., B. E. Bouma, and M. R. Kaazempur Mofrad. A combined fem/genetic algorithm for vascular soft tissue elasticity estimation. Cardiovas. Eng. 6:93–103, 2006.CrossRefGoogle Scholar
  16. 16.
    Kim, J. H. Fabric Mechanics Analysis Using Large Deformation Orthotropic Shell Theory. PhD Thesis, North Carolina State University, 1991.Google Scholar
  17. 17.
    NN. Cardiovascular Implants—Vascular Prosthesis. American National Standard Association for the Advancement of Medical Instrumentation, AAMI Standard Edition, 1994.Google Scholar
  18. 18.
    NN. Cardiovascular Implants-Tubular Vascular Prosthesis. ISO International Standard 7198, 1998.Google Scholar
  19. 19.
    Oberkampf, W. L., and M. F. Barone. Measures of agreement between computation and experiment: validation metrics. J. Comput. Phys. 217:5–36, 2006.CrossRefGoogle Scholar
  20. 20.
    Pandit, A., X. Lu, C. Wang, and G. S. Kassab. Biaxial elastic material properties of porcine coronary media and adventitia. Am. J. Physiol. Heart Circ. Physiol. 288:H2581–H2587, 2005.PubMedCrossRefGoogle Scholar
  21. 21.
    Seifert, K. B., D. Albo, H. Knowlton, and D. J. Lyman. Effect of elasticty of prosthetic wall on patency of small-diameter arterial prosthesis. Surg. Forum. 30:206–208, 1979.PubMedGoogle Scholar
  22. 22.
    Siauve, N., L. Nicolas, C. Vollaire, and C. Marchal. Optimization of the sources in local hyperthermia using a combined finite element-genetic algorithm method. Int. J. Hyperthermia 20:815–833, 2004.PubMedCrossRefGoogle Scholar
  23. 23.
    Stewart, S. F. C., and D. J. Lyman. Effects of vascular graft/natural artery compliance mismatch on pulsatile flow. J. Biomech. 25:297–310, 1992.PubMedCrossRefGoogle Scholar
  24. 24.
    Storåkers, B. On material representation and constitutive branching in finite compressible elasticity. J. Mech. Phys. Solids, 34:125–145, 1986.CrossRefGoogle Scholar
  25. 25.
    Tai, N. R., H. J. Salacinski, A. Edwards, G. Hamilton, and A. M. Seifalian. Compliance properties of conduits used in vascular reconstruction. Br. J. Surg. 87:1516–1524, 2000.PubMedCrossRefGoogle Scholar
  26. 26.
    Takahara, A., A. J. Coury, R. W. Hergenrother, and S. L. Cooper. Effect of soft segment chemistry on the biostability of segmented polyurethanes. I. In vitro oxidation. J. Biomed. Mater. Res. 25:341–356, 1991.PubMedCrossRefGoogle Scholar
  27. 27.
    Tong, P., and Y. C. Fung. The stress-strain relationship for the skin. J. Biomech. 9:649–657, 1976.PubMedCrossRefGoogle Scholar
  28. 28.
    Wang, C., M. Garcia, X. Lu, Y. Lanir, and G. S. Kassab. Three-dimensional mechanical properties of porcine coronary arteries: a validated two-layer model. Am. J. Physiol. Heart Circ. Physiol. 291:H1200–H1209, 2006.PubMedCrossRefGoogle Scholar
  29. 29.
    Weston, M. W., K. Rhee, and J. M. Tarbell. Compliance and diameter mismatch affect the wall shear rate distribution near end-to-end anastomosis. J. Biomech. 29:187–198, 1996.PubMedCrossRefGoogle Scholar
  30. 30.
    Yeoman, M. S. The Design and Optimisation of Fabric Reinforced Porous Prosthetic Grafts Using Finite Element Methods and Genetic Algorithms. PhD Thesis, University of Cape Town, 2004.Google Scholar
  31. 31.
    Zilla, P., D. Bezuidenhout, and P. Human. Prosthetic vascular grafts: wrong models, wrong questions and no healing. Biomaterials 28:5009–5027, 2007.PubMedCrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 2009

Authors and Affiliations

  • M. S. Yeoman
    • 1
    • 3
  • B. D. Reddy
    • 1
  • H. C. Bowles
    • 2
  • P. Zilla
    • 3
  • D. Bezuidenhout
    • 3
  • T. Franz
    • 3
  1. 1.Centre for Research in Computational and Applied MechanicsUniversity of Cape TownRondeboschSouth Africa
  2. 2.Finite Element Analysis ServicesCape TownSouth Africa
  3. 3.Cardiovascular Research Unit, Chris Barnard Department of Cardiothoracic Surgery, Faculty of Health SciencesUniversity of Cape TownObservatorySouth Africa

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