Computational Simulation and Modelling of Arterial Drug Delivery From Half-Embedded Drug-Eluting Stents in Single-Layered Homogeneous Vessel Wall
DOI:
https://doi.org/10.26713/cma.v15i1.2373Keywords:
Cardiovascular tissue wall, Half-embedded DES, Specific binding, Non-specific binding, Marker and cell (MAC) methodAbstract
The next-generation of drug therapics has started as a consequence of the invention of controlled-dose pharmaceutical delivery tools. More specifically, coronary angioplasty (CA) treatments often involve drug-eluting stents (DESs) that eluting drug molecules. This mechanism decreases the in-stent restenosis with the help of releasing drugs from a thin polymer membrane covering into the coronary vessel tissue around it. Present day DES equipments, as the protective covering, biodurable polymers has been deployed, that, remains there forever until the drug has fully eluted from DES. In this present work, we investigated the aforementioned problems using a numerical simulation of vascular distribution of drugs as well as receptor binding mechanisms. Modelling is done for the intravascular drug delivery of a hydrophobic (like sirolimus or paclitaxel) drug from DES. The content of this paper discusses the effects of drug delivery from half-embedded circular drug-eluting stent struts. We introduce an elaborate mathematical approach based on axi-symmetry 2D layout, incorporates a two non-linear phases of drug binding namely specific and non-specific, and combines the impact of diffusion and advection, within the single-layered homogeneous vessel wall. The pharmaceutical delivery via five stent struts has been significantly strengthened in this framework. The free pharmaceuticals are moved using an unsteady covection-diffusion- reaction mechanism, even though the binding pharmaceuticals are being through an unsteady reaction-diffusion mechanism. The governing equations along with the initial and boundary conditions has been evaluated numerically using a finite-difference technique in staggered grids. The marker and cell (MAC) methodology has been employed to solved the model equations while taking into account the cylindrical system of polar coordinates. In this present assessment, our target is to visually illustrate the impact of the embedment of the stent on the drug release from stent and vessel drug distribution. According to the findings, it is indicate that the drug gradually binds to specific receptors and extracellular matrix sites until binding sites become saturated. Model simulations have improved our understanding of the potential influences of the different factors that may affect the effectiveness of drug administration. The created modelling allows for the modification of the model’s parameters for upcoming research on the development of PLGA-coated drug-eluting stents.
Downloads
References
G. Acharya and K. Park, Mechanisms of controlled drug release from drug-eluting stents, Advanced Drug Delivery Reviews 58(3) (2006), 387 – 401, DOI: 10.1016/j.addr.2006.01.016.
B. Balakrishnan, J. Dooley, G. Kopia and E. R. Edelman, Thrombus causes fluctuations in arterial drug delivery from intravascular stents, Journal of Controlled Release 131(3) (2008), 173 – 180, DOI: 10.1016/j.jconrel.2008.07.027.
B. Balakrishnan, J. F. Dooley, G. Kopia and E. R. Edelman, Intravascular drug release kinetics dictate arterial drug deposition, retention, and distribution, Journal of Controlled Release 123(2) (2007), 100 – 108, DOI: 10.1016/j.jconrel.2007.06.025.
B. Balakrishnan, 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(22) (2005), 2958 – 2965, DOI: 10.1161/CIRCULATIONAHA.104.512475.
B. E. Bierer, P. S. Mattila, R. F. Standaert, L. A. Herzenberg, S. Burakoff, G. Crabtree and S. L. Schreiber, Two distinct signal transmission pathways in T lymphocytes are inhibited by complexes formed between an immunophilin and either FK506 or rapamycin, Proceedings of the National Academy of Sciences 87(23) (1990), 9231 – 9235, DOI: 10.1073/pnas.87.23.9231.
A. Borghi, E. Foa, R. Balossino, F. Migliavacca and G. Dubini, Modelling drug elution from stents: Effects of reversible binding in the vascular wall and degradable polymeric matrix, Computer Methods in Biomechanics and Biomedical Engineering 11(4) (2008), 367 – 377, DOI: 10.1080/10255840801887555.
F. Bozsak, D. Gonzalez-Rodriguez, Z. Sternberger, P. Belitz, T. Bewley, J. M. Chomaz and A. I. Barakat, Optimization of drug delivery by drug-eluting stents, PloS One 10(6) (2015), e0130182, DOI: 10.1371/journal.pone.0130182.
M. A. Costa and D. I. Simon, Molecular basis of restenosis and drug-eluting stents, Circulation 111(17) (2005), 2257 – 2273, DOI: 10.1161/01.CIR.0000163587.36485.A7.
J. Escuer, I. Aznar, C. McCormick, E. Peña, S. McGinty and M. A. Martínez, Influence of vessel curvature and plaque composition on drug transport in the arterial wall following drugeluting stent implantation, Biomechanics and Modeling in Mechanobiology 20 (2021), 767 – 786, DOI: 10.1007/s10237-020-01415-3.
GBD 2017 Causes of Death Collaborators, Global, regional, and national age-sex-specific mortality for 282 causes of death in 195 countries and territories, 1980–2017: A systematic analysis for the Global Burden of Disease Study 2017, The Lancet 392(10159) (2018), 1736 – 1788, DOI: 10.1016/S0140-6736(18)32203-7.
M. Grassi, G. Pontrelli, L. Teresi, G. Grassi, L. Comel, A. Ferluga and L. Galasso, Novel design of drug delivery in stented arteries: A numerical comparative study, Mathematical Biosciences and Engineering 6(3) (2009), 493 – 508, DOI: 10.3934/mbe.2009.6.493.
T. Higuchi, Mechanism of sustained-action medication. Theoretical analysis of rate of release of solid drugs dispersed in solid matrices, Journal of Pharmaceutical Sciences 52(12) (1963), 1145 – 1149, DOI: 10.1002/jps.2600521210.
S. Hossainy and S. Prabhu, A mathematical model for predicting drug release from a biodurable drug-eluting stent coating, Journal of Biomedical Materials Research Part A 87A(2) (2008), 487 – 493, DOI: 10.1002/jbm.a.31787.
Z. J. Huang and J. M. Tarbell, Numerical simulation of mass transfer in porous media of blood vessel walls, American Journal of Physiology-Heart and Circulatory Physiology 273(1) (1997), H464 – H477, DOI: 10.1152/ajpheart.1997.273.1.H464.
C.-W. Hwang, D. Wu and E. R. Edelman, Physiological transport forces govern drug distribution for stent-based delivery, Circulation 104(5) (2001), 600 – 605, DOI: 10.1161/hc3101.092214.
S. McGinty, A decade of modelling drug release from arterial stents, Mathematical Biosciences 257 (2014), 80 – 90, DOI: 10.1016/j.mbs.2014.06.016.
S. McGinty, S. McKee, C. McCormick and M. Wheel, Release mechanism and parameter estimation in drug-eluting stent systems: Analytical solutions of drug release and tissue transport, Mathematical Medicine and Biology: A Journal of the IMA 32(2) (2015), 163 – 186, DOI: 10.1093/imammb/dqt025.
S. McGinty and G. Pontrelli, A general model of coupled drug release and tissue absorption for drug delivery devices, Journal of Controlled Release 217 (2015), 327 – 336, DOI: 10.1016/j.jconrel.2015.09.025.
S. McGinty and G. Pontrelli, On the role of specific drug binding in modelling arterial eluting stents, Journal of Mathematical Chemistry 54 (2016), 967 – 976, DOI: 10.1007/s10910-016-0618-7.
C. M. McKittrick, S. Kennedy, K. G. Oldroyd, S. McGinty and C. McCormick, Modelling the impact of atherosclerosis on drug release and distribution from coronary stents, Annals of Biomedical Engineering 44(2) (2016), 477 – 487, DOI: 10.1007/s10439-015-1456-7.
F. Migliavacca, F. Gervaso, M. Prosi, P. Zunino, S. Minisini, L. Formaggia and G. Dubini, Expansion and drug elution model of a coronary stent, Computer Methods in Biomechanics and Biomedical Engineering 10(1) (2007), 63 – 73, DOI: 10.1080/10255840601071087.
R. Mongrain, I. Faik, R. L. Leask, J. Rodés-Cabau, É. Larose and O. F. Bertrand, Effects of diffusion coefficients and struts apposition using numerical simulations for drug eluting coronary stents, Journal of Biomechanical Engineering 129(5) (2007), 733 – 742, DOI: 10.1115/1.2768381.
K. L. Napoli and P. J. Taylor, From beach to bedside: History of the development of sirolimus, Therapeutic Drug Monitoring 23(5) (2001), 559 – 586, DOI: 10.1097/00007691-200110000-00012.
R. Saha and P. K. Mandal, Modelling time-dependent release kinetics in stent-based delivery, Journal of Exploratory Research in Pharmacology 3(2) (2018), 61 – 70, DOI: 10.14218/JERP.2018.00001.
A. R. Tzafriri, A. Groothuis, G. S. Price and E. R. Edelman, Stent elution rate determines drug deposition and receptor-mediated effects, Journal of Controlled Release 161(3) (2012), 918 – 926, DOI: 10.1016/j.jconrel.2012.05.039.
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 Proliferation 42(3) (2009), 348 – 363, DOI: 10.1111/j.1365-2184.2009.00602.x.
G. Vairo, M. Cioffi, R. Cottone, G. Dubini and F. Migliavacca, Drug release from coronary eluting stents: A multidomain approach, Journal of Biomechanics 43(8) (2010), 1580 – 1589, DOI: 10.1016/j.jbiomech.2010.01.033.
M. A. Wear and M. D. Walkinshaw, Determination of the rate constants for the FK506 binding protein/rapamycin interaction using surface plasmon resonance: An alternative sensor surface for Ni2+-nitrilotriacetic acid immobilization of His-tagged proteins, Analytical Biochemistry 371(2) (2007), 250 – 252, DOI: 10.1016/j.ab.2007.06.034.
X. Zhu, Mathematical Modeling and Simulation of Intravascular Drug Delivery from Drug-Eluting Stents with Biodegradable PLGA Coating, Ph.D. Thesis, Massachusetts Institute of Technology, USA.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
