An explicit spectral collocation method for the drug release coronary stents
Abstract
This research aims to solve a comprehensive one-dimensional model of drug release from cardiovascular stents in which the drug binding is saturable and reversible. We used the Lagrange collocation method for space dimension and the modified Euler method for time discretization. The existence and uniqueness of the solution, are provided. The consistency, stability, and convergence analysis of the proposed scheme are provided, to show that numerical simulations are valid. Numerical results accurate enough and efficient just by using fewer mesh.
Keyword : spectral collocation method, explicit method, modified Euler method, stent, drug release
How to Cite
Fakhri, S., & Momeni-Masuleh, S. H. (2022). An explicit spectral collocation method for the drug release coronary stents. Mathematical Modelling and Analysis, 27(3), 452–470. https://doi.org/10.3846/mma.2022.15066
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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F. Bozsak, J.M. Chomaz and A.I. Barakat. Modeling transport of drugs eluted from stents: physical phenomena driving drug distribution in the arterial wall. Biomech. Model. Mechanobiol., 13:327–347, 2014. https://doi.org/10.1007/s10237-013-0546-4
C. Canuto, M. Hussaini, A. Quarteroni and T. Zang. Spectral Methods: Fundamentals in Single Domains. Springer-Verlag, Berllin, Heidelberg, 3td edition, 2006. ISBN 978-3-540-30725-9.
C. D’Angelo, P. Zunino, A. Porpora, S. Morlacchi and F. Migliavacca. Model reduction strategies enable computational analysis of controlled drug release from cardiovascular stents. SIAM J. Appl. Math., 71(6):2312–2333, 2011. https://doi.org/10.1137/10081695X
J.A. Ferreira, M. Grassi, E. Gudino and P. de Oliveria. A 3D model for mechanistic control of drug release. SIAM J. Appl. Math., 74(3):620–633, 2014. https://doi.org/10.1137/130930674
J.A. Ferreira, J. Naghipoor, and P. de Oliveira. Analytical and numerical study of a coupled cardiovascular drug delivery model. J. Comput. Appl. Math., 275:433– 446, 2015. https://doi.org/10.1016/j.cam.2014.04.021
G. Frenning. Modelling drug release from inert matrix systems: From moving boundary to continuous-field descriptions. Int. J. Pharm., 418(1):88–99, 2011. https://doi.org/10.1016/j.ijpharm.2010.11.030
E. Gudin˜o and A. Sequeira. 3D mathematical model for blood flow and nonFickian mass transport by a coronary drug-eluting stent. Appl. Math. Mod., 46:161–180, 2017. https://doi.org/10.1016/j.apm.2017.01.057
A.W. Hixson and J.H. Crowell. Dependence of reaction velocity upon surface and agitation. Ind. Eng. Chem., 23:923–931, 1931. https://doi.org/10.1021/ie50260a018
M. Livingston and A. Tan. Coating techniques and release kinetics of drug-eluting stents. J. Med. Devices., 10(1):15–23, 2016. https://doi.org/10.1115/1.4031718
X. Lu, J. Yang, J.B. Zhao, H. Gregersen and G.S. Kassab. Shear modulus of porcine coronary artery: contributions of media and adventitia. Am. J. Physiol. Heart Circ. Physiol, 285:H1966–H1975, 2003. https://doi.org/10.1152/ajpheart.00357.2003
S. McGinty. Stents and arterial flows. PhD thesis, University of Strathclyde, Glasgow, UK, March 2010.
S. McGinty, S. McKee, R.M. Wadsworth and C. McCormick. Modeling arterial wall drug concentrations following the insertion of a drug-eluting stent. SIAM J. Appl. Math., 73(6):2004–2028, 2013. https://doi.org/10.1137/12089065X
S. McGinty and G. Pontrelli. A general model of coupled drug release and tissue absorption for drug delivery devices. J. Contr. Release., 217:327–336, 2015. https://doi.org/10.1016/j.jconrel.2015.09.025
A.A. Noyes and W.R. Whitney. The rate of solution of solid substances in their own solutions. J. Am. Chem. Soc., 19(12):930–934, 1897. https://doi.org/10.1021/ja02086a003
H.K. Pathak. An Introduction to Nonlinear Analysis and Fixed Point Theory. Springer, Nature, Singapore, 2018. ISBN 978-981-10-8866-7.
G. Pontrelli and F. de Monte. Mass diffusion through two-layer porous media: an application to the drug-eluting stent. Int. J. Heat Mass Transf., 50(17-18):3658– 3669, 2007. https://doi.org/10.1016/j.ijheatmasstransfer.2006.11.003
A.R. Tzafriri, A.D. Levin and E.R. Edelman. Diffusion-limited binding explains binary dose response for local arterial and tumour drug delivery. Cell Prolif., 42(3):348–363, 2009. https://doi.org/10.1111/j.1365-2184.2009.00602.x
P. Zunino. Multidimensional pharmacokinetic models applied to the design of drug-eluting stents. Int. J. Cardiov. Eng., 4(2):181–191, 2004. https://doi.org/10.1023/B:CARE.0000031547.39178.cb
P. Zunino, C. D’Angelo, L. Petrini, C. Vergara, C. Capelli and F. Migliavacc. Numerical simulation of drug eluting coronary stents: mechanics, fluid dynamics and drug release. Comput. Meth. Appl. Mech. Eng., 198(45-46):3633–3644, 2009. https://doi.org/10.1016/j.cma.2008.07.019