Annals of Biomedical Engineering

, Volume 41, Issue 5, pp 1062–1073 | Cite as

An Analysis of Three Dimensional Diffusion in a Representative Arterial Wall Mass Transport Model

  • William J. Denny
  • Barry M. O’Connell
  • John Milroy
  • Michael T. Walsh


The development and use of drug eluting stents has brought about significant improvements in reducing in-stent restenosis, however, their long term presence in the artery is still under examination due to restenosis reoccurring. Current studies focus mainly on stent design, coatings and deployment techniques but few studies address the issue of the physics of three dimensional mass transport in the artery wall. There is a dearth of adequate validated numerical mass transport models that simulate the physics of diffusion dominated drug transport in the artery wall whilst under compression. A novel experimental setup used in a previous study was adapted and an expansion of that research was carried out to validate the physics of three dimensional diffusive mass transport into a compressed porous media. This study developed a more sensitive method for measuring the concentration of the species of interest. It revalidated mass transport in the radial direction and presented results which highlight the need for an evaluation of the governing equation for transient diffusive mass transport in a porous media, in its current form, to be carried out.


Diffusion Drug transport Porosity Tortuosity Effective diffusivity Species Anisotropic material Radial and longitudinal diffusivities Experimental validation Numerical modelling 



The authors would like to thank the Irish Research Council for Science, Engineering and Technology (IRCSET) and Boston Scientific for funding this research.


  1. 1.
    Balakrishnan, B., J. F. Dooley, G. Kopia, and E. R. Edelman. Intravascular drug release kinetics dictate arterial drug deposition, retention and distribution. J. Controlled Release 123:100–108, 2007.CrossRefGoogle Scholar
  2. 2.
    Balakrishnan, B., J. F. Dooley, G. Kopia, and E. R. Edelman. Thrombus causes fluctuations in arterial drug delivery from intravascular stents. J. Controlled Release 131:173–180, 2008.CrossRefGoogle Scholar
  3. 3.
    Balakrishnan, B., A. R. Tzafriri, P. Seifert, A. Groothuis, C. Rogers, and E. R. Edelman. Strut position, blood flow, and drug deposition: implications for single and overlapping drug-eluting stents. Circulation 111:2958–2965, 2005.PubMedCrossRefGoogle Scholar
  4. 4.
    Barrett, E. P., L. G. Joyner, and P. H. Halenda. The determination of pore volume and area distributions in porous substances. I. Computations from nitrogen isotherms. J. Am. Chem. Soc. 73:373–380, 1951.CrossRefGoogle Scholar
  5. 5.
    Brunauer, S., P. H. Emmet, and E. Teller. Adsorption of gases in multimolecular layers. J. Am. Chem. Soc. 60(2):309–319, 1938.CrossRefGoogle Scholar
  6. 6.
    Creel, C. J., M. A. Lovich, and E. R. Edelman. Arterial paclitaxel distribution and deposition. Circ. Res. 86:879–884, 2000.PubMedCrossRefGoogle Scholar
  7. 7.
    Dogu, G., and J. M. Smith. A dynamic method for catalyst diffusivities. AIChE J. 21(1): 58–61, 1975.Google Scholar
  8. 8.
    Finkelstein, A., D. McClean, S. Kar, K. Takizawa, K. Varghese, N. Baek, K. Park, M. C. Fishbein, R. Makkar, F. Litvack, and N. L. Eigler. Local drug delivery via a coronary stent with programmable release pharmacokinetics. Circulation 107:1–8, 2003.CrossRefGoogle Scholar
  9. 9.
    Fraser, B., C. Murphy, and F. Bunting. Computer and colour: colour by number. In: Real World Color Management. 2nd ed. Berkeley, CA: Peachpit Press, pp. 69–74, 2004.Google Scholar
  10. 10.
    Friedman, M. H. Principles and Models of Biological Transport (2nd ed.). New York: Springer, pp. 282–290, 2008.CrossRefGoogle Scholar
  11. 11.
    Fry, D. L., and R. N. Vaishnav. Basic Hemodynamics and Its Role in Disease Processes. Baltimore: University Park Press, pp. 425–485, 1980.Google Scholar
  12. 12.
    Groen, J. C., L. A. A. Peffer, and J. Perez-Ramirez. Pore size determination in modified micro- and mesoporous materials. Pitfalls and limitations in gas adsorption data analysis. J. Micropor. Mesopor. Mater. 60:1–17, 2003.CrossRefGoogle Scholar
  13. 13.
    Klanchar, M., and J. M. Tarbell. Modelling water flow through arterial tissue. Bull. Math. Biol. 49(6):651–669, 1987.PubMedGoogle Scholar
  14. 14.
    Lovich, M. A., and E. R. Edelman. Computational simulations of local vascular heparin deposition and distribution. Am. J. Physiol. Heart Circ. Physiol. 271(5):2014–2024, 1996.Google Scholar
  15. 15.
    Mather, J. Color Management and Color Transformations in MATLAB (2005). Available: Last Accessed 14th Nov 2011.
  16. 16.
    Moreira, E. A., and J. R. Coury. The influence of structural parameters on the permeability of ceramic forms. Braz. J. Chem. Eng. 21(1):23–33, 2004.CrossRefGoogle Scholar
  17. 17.
    Mota, M., A. Yelshin, M. Fidaleo, and M. C. Flickinger. Modelling diffusivity in porous polymeric membranes with an intermediate layer containing microbial cells. Biochem. Eng. J. 37(1):285–293, 2007.CrossRefGoogle Scholar
  18. 18.
    O’Connell, B. M., and M. T. Walsh. Demonstrating the influence of compression on artery wall mass transport. Ann. Biomed. Eng. 38(4):1354–1366, 2010.PubMedCrossRefGoogle Scholar
  19. 19.
    Serruys, P. W., and A. H. Gershlick. Handbook of Drug-Eluting Stents (2nd ed.). London: Taylor & Francis, pp. 3–11, 2005.Google Scholar
  20. 20.
    Truskey, G. A., C. K. Colton, and K. A. Smith. Structure and Function of the Circulation. New York: Plenum, pp. 287–355, 1981.CrossRefGoogle Scholar
  21. 21.
    Vairo, G., M. Cioffi, R. Cottone, G. Dubini, and F. Migliavacca. Drug release from coronary eluting stents: a multidomain approach. J. Biomech. 43(8):1580–1589, 2010.PubMedCrossRefGoogle Scholar
  22. 22.
    Westermarck, S., A. M. Juppo, L. Kervinen, and J. Yliruusi. Pore structure and surface area of mannitol powder, granules and tablets determined with mercury porosimetry and nitrogen adsorption. Eur. J. Pharm. Biopharm. 46(1):61–68, 1998.PubMedCrossRefGoogle Scholar
  23. 23.
    Yuan, F., S. Chien, and S. Weinbaum. A new view of convective–diffusive transport. J. Biomech. Eng. 133:314–329, 1991.CrossRefGoogle Scholar
  24. 24.
    Zhu, X., D. W. Pack, and R. D. Braatz. Modelling intravascular delivery from drug-eluting stents with biodurable coating: investigation of anisotropic vascular drug diffusivity and arterial drug distribution. Comput. Methods Biomech. Biomed. Eng. iFirst Article (1), 1–12, 2012.Google Scholar

Copyright information

© Biomedical Engineering Society 2012

Authors and Affiliations

  • William J. Denny
    • 1
  • Barry M. O’Connell
    • 1
  • John Milroy
    • 2
  • Michael T. Walsh
    • 1
  1. 1.Centre for Applied Biomedical Engineering Research (CABER), Department of Mechanical, Aeronautical and Biomedical Engineering and Materials and Surface Science InstituteUniversity of LimerickLimerickIreland
  2. 2.Boston ScientificGalwayIreland

Personalised recommendations