Advertisement

# Mathematical Modelling of Drug Elution from Drug-Filled Stents

• Tuoi T. N. Vo
• Amy M. M. Collins
• William T. Lee
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)

## Abstract

In this paper, we outline the first model to describe drug elution from a drug-filled stent. This novel polymer-free drug-eluting stent stores the therapeutic drug in the inner layer of a tri-layer wire. This inner layer acts a reservoir releasing the drug through laser-drilled holes on the outer surface of the stent struts. We simplify the general model using the assumption of low drug solubility and consider a special case where the dissolution occurs in a uniform downward direction. The main advantage of our simplified model is the ability to achieve analytical solutions. These solutions allow for calculating the drug release profile rapidly and for identifying the dependence of the various parameters of the system. We find that the duration of drug elution is prolonged when the solubility or diffusivity of the drug decreases.

## Notes

### Acknowledgements

The authors acknowledge the support of MACSI, the Mathematics Applications Consortium for Science and Industry (http://ulsites.ul.ie/macsi/), funded by the Science Foundation Ireland Investigator Award 12/IA/1683.

## References

1. 1.
Abdul Hadi, M.S., Mustapa, M.Z., Saad, S.: Complete derivation of 2D shallow-water model from the primitive equations governing geophysical flows. In: 8th International Conference on Marine Technology, 20–22 October 2012, Terengganu, Malaysia (2012)Google Scholar
2. 2.
Abizaid, A., Costa, J.R.: New drug-eluting stents an overview on biodegradable and polymer-free next-generation stent systems. Circ. Cardiovasc. Interv. 3, 384–393 (2010)
3. 3.
Cea, L., Puertas, J., Vázquez-Cendón, M.E.: Depth averaged modelling of turbulent shallow water flow with wet-dry fronts. Arch. Comput. Meth. Eng. 14(3), 303–341 (2007)
4. 4.
McGinty, S., Vo, T.T.N., Meere, M.G., McKee, S., McCormick, C.: Some design considerations for polymer-free drug-eluting stents: a mathematical approach. Acta Biomater. 18, 213–225 (2015)
5. 5.
Medtronic plc: Medtronic drug-filled stent shows promising initial results following first implants. Medtronic Press Release. Available via DIALOG. http://newsroom.medtronic.com/phoenix.zhtml?c=251324&p=irol-newsArticle&ID=2096128 (2015). Cited 3 Oct 2016
6. 6.
Wilcox, J.N.: Progress with a zotarolimus-filled stent technology and preclinical results. Medtronic Press Release. Available via DIALOG. http://www.tctmd.com/privateAssets/0/114/709599/725792/8ad0f2dd-6ad5-41f5-821c-3c0304461300.pdf (2015). Cited 3 Oct 2016

## Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

## Authors and Affiliations

• Tuoi T. N. Vo
• 1
• Amy M. M. Collins
• 1
• William T. Lee
• 2
1. 1.MACSIUniversity of LimerickLimerickIreland
2. 2.University of PortsmouthPortsmouthUK