2009, 6(3): 493-508. doi: 10.3934/mbe.2009.6.493

Novel design of drug delivery in stented arteries: A numerical comparative study


Dept. of Chemical Engineering, University of Trieste, Italy


Istituto per le Applicazioni del Calcolo, CNR, Roma, Italy


Dept. of Structures, University of Roma Tre, Roma, Italy


Dept. of Life Science, University of Trieste, Italy


Dept. of Material Engineering, University of Trieste, Italy, Italy, Italy

Received  February 2008 Revised  February 2009 Published  June 2009

Implantation of drug eluting stents following percutaneous transluminal angioplasty has revealed a well established technique for treating occlusions caused by the atherosclerotic plaque. However, due to the risk of vascular re-occlusion, other alternative therapeutic strategies of drug delivery are currently being investigated. Polymeric endoluminal pave stenting is an emerging technology for preventing blood erosion and for optimizing drug release. The classical and novel methodologies are compared through a mathematical model able to predict the evolution of the drug concentration in a cross-section of the wall. Though limited to an idealized configuration, the present model is shown to catch most of the relevant aspects of the drug dynamics in a delivery system. Results of numerical simulations shows that a bi-layer gel paved stenting guarantees a uniform drug elution and a prolonged perfusion of the tissues, and remains a promising and effective technique in drug delivery.
Citation: Mario Grassi, Giuseppe Pontrelli, Luciano Teresi, Gabriele Grassi, Lorenzo Comel, Alessio Ferluga, Luigi Galasso. Novel design of drug delivery in stented arteries: A numerical comparative study. Mathematical Biosciences & Engineering, 2009, 6 (3) : 493-508. doi: 10.3934/mbe.2009.6.493

Shalela Mohd--Mahali, Song Wang, Xia Lou, Sungging Pintowantoro. Numerical methods for estimating effective diffusion coefficients of three-dimensional drug delivery systems. Numerical Algebra, Control and Optimization, 2012, 2 (2) : 377-393. doi: 10.3934/naco.2012.2.377


Alexandre Cornet. Mathematical modelling of cardiac pulse wave reflections due to arterial irregularities. Mathematical Biosciences & Engineering, 2018, 15 (5) : 1055-1076. doi: 10.3934/mbe.2018047


Fredrik Hellman, Patrick Henning, Axel Målqvist. Multiscale mixed finite elements. Discrete and Continuous Dynamical Systems - S, 2016, 9 (5) : 1269-1298. doi: 10.3934/dcdss.2016051


John Boscoh H. Njagarah, Farai Nyabadza. Modelling the role of drug barons on the prevalence of drug epidemics. Mathematical Biosciences & Engineering, 2013, 10 (3) : 843-860. doi: 10.3934/mbe.2013.10.843


Giacomo Albi, Lorenzo Pareschi, Mattia Zanella. Opinion dynamics over complex networks: Kinetic modelling and numerical methods. Kinetic and Related Models, 2017, 10 (1) : 1-32. doi: 10.3934/krm.2017001


Weizhu Bao, Yongyong Cai. Mathematical theory and numerical methods for Bose-Einstein condensation. Kinetic and Related Models, 2013, 6 (1) : 1-135. doi: 10.3934/krm.2013.6.1


Shalela Mohd Mahali, Song Wang, Xia Lou. Determination of effective diffusion coefficients of drug delivery devices by a state observer approach. Discrete and Continuous Dynamical Systems - B, 2011, 16 (4) : 1119-1136. doi: 10.3934/dcdsb.2011.16.1119


Jitraj Saha, Nilima Das, Jitendra Kumar, Andreas Bück. Numerical solutions for multidimensional fragmentation problems using finite volume methods. Kinetic and Related Models, 2019, 12 (1) : 79-103. doi: 10.3934/krm.2019004


Peter Monk, Jiguang Sun. Inverse scattering using finite elements and gap reciprocity. Inverse Problems and Imaging, 2007, 1 (4) : 643-660. doi: 10.3934/ipi.2007.1.643


Juan Pablo Aparicio, Carlos Castillo-Chávez. Mathematical modelling of tuberculosis epidemics. Mathematical Biosciences & Engineering, 2009, 6 (2) : 209-237. doi: 10.3934/mbe.2009.6.209


Tuoi Vo, William Lee, Adam Peddle, Martin Meere. Modelling chemistry and biology after implantation of a drug-eluting stent. Part Ⅰ: Drug transport. Mathematical Biosciences & Engineering, 2017, 14 (2) : 491-509. doi: 10.3934/mbe.2017030


Tianliang Hou, Yanping Chen. Superconvergence for elliptic optimal control problems discretized by RT1 mixed finite elements and linear discontinuous elements. Journal of Industrial and Management Optimization, 2013, 9 (3) : 631-642. doi: 10.3934/jimo.2013.9.631


Geoffrey Beck, Sebastien Imperiale, Patrick Joly. Mathematical modelling of multi conductor cables. Discrete and Continuous Dynamical Systems - S, 2015, 8 (3) : 521-546. doi: 10.3934/dcdss.2015.8.521


Nirav Dalal, David Greenhalgh, Xuerong Mao. Mathematical modelling of internal HIV dynamics. Discrete and Continuous Dynamical Systems - B, 2009, 12 (2) : 305-321. doi: 10.3934/dcdsb.2009.12.305


Oliver Penrose, John W. Cahn. On the mathematical modelling of cellular (discontinuous) precipitation. Discrete and Continuous Dynamical Systems, 2017, 37 (2) : 963-982. doi: 10.3934/dcds.2017040


Xiaozhong Yang, Xinlong Liu. Numerical analysis of two new finite difference methods for time-fractional telegraph equation. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3921-3942. doi: 10.3934/dcdsb.2020269


Z. Jackiewicz, B. Zubik-Kowal, B. Basse. Finite-difference and pseudo-spectral methods for the numerical simulations of in vitro human tumor cell population kinetics. Mathematical Biosciences & Engineering, 2009, 6 (3) : 561-572. doi: 10.3934/mbe.2009.6.561


Fan Chen, Ming Cui, Chenguang Zhou. Numerical analysis of two-dimensional unsaturated soil water flow problems with two-grid finite element methods. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022191


Eugene Kashdan, Dominique Duncan, Andrew Parnell, Heinz Schättler. Mathematical methods in systems biology. Mathematical Biosciences & Engineering, 2016, 13 (6) : i-ii. doi: 10.3934/mbe.201606i


Eric Dubach, Robert Luce, Jean-Marie Thomas. Pseudo-Conform Polynomial Lagrange Finite Elements on Quadrilaterals and Hexahedra. Communications on Pure and Applied Analysis, 2009, 8 (1) : 237-254. doi: 10.3934/cpaa.2009.8.237

[Back to Top]