Numerical Modeling of Drug Release from Polymer Coated Arterial Stent Abstract: Stenting is a surgical procedure in which a mesh like cage is placed within an artery/vessel when blood flow is obstructed. There are three types of arterial stents, including metallic, biodegradable and polymer coated. The polymer coated stent is the most typically used stent, such that it has a lesser rate of restenosis, a.k.a re-narrowing of a chamber. The coating of the stent is infused with a drug that releases into the artery and diffuses through the arterial wall. This diffusion can be modeled through a second order parabolic differential equation. This phenomenon can be modeled via MATLAB in order to understand the rate in which drug diffuses as it relates to time and distance traveled through the artery.More importantly, quantitative analysis can be applied after obtaining data from the model in order to understand the effects this can have in a postoperative patient. The first plot produced by MATLAB showed the relationship between concentration, time and distance for diffusion of Paclitaxel. The second plot showed localization of the drug at time went on for various distances.  The third plot showed the amount of the drug at different distances for different sets of time.References[1]  Gonzalo, Nieves, and Carlos Macaya. “Absorbable Stent: Focus on Clinical Applications and Benefits.” Vascular Health and Risk Management , Dove Medical Press, 29 Feb. 2012, www.ncbi.nlm.nih.gov/pmc/articles/PMC3295634/ .[2]  “Coronary Artery Disease: Overview.” National Center for Biotechnology Information , U.S. National Library of Medicine, 27 July 2017, www.ncbi.nlm.nih.gov/pubmedhealth/PMH0086334/ .[3]  Byrne, Robert A., et al. “Stent Thrombosis and Restenosis: What Have We Learned and Where Are We Going? The Andreas Grüntzig Lecture ESC 2014.” European Heart Journal , Oxford University Press, 14 Dec. 2015, www.ncbi.nlm.nih.gov/pmc/articles/PMC4677274/ .[4]  Bønaa, Kaare H. “Drug-Eluting or Bare-Metal Stents for Coronary Artery Disease | NEJM.” New England Journal of Medicine, 29 Sept. 2016, www.nejm.org/doi/full/10.1056/NEJMoa1607991 .[5]  Hossainy, Syed, and Santosh Prabhu. “A Mathematical Model for Predicting Drug Release from a Biodurable Drug?Eluting Stent Coating.” Journal of Biomedical Materials Research Part A , Wiley-Blackwell, 9 Jan. 2008, onlinelibrary.wiley.com/doi/full/10.1002/jbm.a.31787.[6]  Sevim, Kevser. “Modelling of Drug Release from Biodegradable Polymers.” University of Leicester , 2017.[7]  Mcginty, Sean. “A Decade of Modelling Drug Release from Arterial Stents.” Mathematical Biosciences , vol. 257, 9 July 2014, pp. 80–90., doi:10.1016/j.mbs.2014.06.016.[8]  Fornberg, Bengt. “Finite Difference Method.” Scholarpedia , vol. 6, no. 10, 2011, p. 9685., doi:10.4249/scholarpedia.9685.[9] “Coronary Bypass Surgery.” Mayo Clinic , Mayo Foundation for Medical Education and Research, 21 Mar. 2018,www.mayoclinic.org/tests-procedures/coronary-bypass-surgery/about/pac-20384589 .[10]  “Coronary Angioplasty and Stents.” Mayo Clinic , Mayo Foundation for Medical Education and Research, 30 Dec. 2017, www.mayoclinic.org/tests-procedures/coronary-angioplasty/about/pac-20384761 .[11] Gersh, B.j. “Aspirin Plus Clopidogrel Versus Aspirin Alone After Coronary Artery Bypass Grafting: The Clopidogrel After Surgery for Coronary Artery Disease (CASCADE) Trial.” Yearbook of Cardiology , vol. 2012,