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Mandal AP, Mandal PK. Specific and nonspecific binding of drug eluted from a half-embedded stent in presence of atherosclerotic plaque. Comput Methods Biomech Biomed Engin 2021; 25:922-935. [PMID: 34615426 DOI: 10.1080/10255842.2021.1986813] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
This study is dealt with the two-phase binding (specific and nonspecific) of drug eluted from a half- embedded drug-eluting stent in presence of atherosclerotic plaque. The specific binding due to the interaction of drug molecules with specific receptors and nonspecific binding caused by the trapping of drug in the extra-cellular matrix have been paid due attention. An idealised wall consisting of a plaque and a healthy tissue region has been considered. Moreover, a Dirichlet release condition is imposed on the strut surface. In this investigation, a two-dimensional model governing drug transport and its two-phase binding in cylindrical polar coordinate system has been solved numerically by a finite-difference method. Our simulation predicts that plaque behaves like a physical barrier in two types of the binding process and there is an inverse relationship between bound drug concentration and plaque thickness. Simulations show that a single peak profile of drug is noted when the struts are situated one-strut radius apart and as the inter-strut distance increases, the peak concentration falls and distinct peak profiles over each strut are visualised. The model also reveals that in the region downstream of a strut, the concentration of both bound drug forms in the plaque and healthy regions increases, and eventually, the saturation length of binding sites increases. Predicted results show for smaller Damköhler number, the rapid saturation of binding sites takes place and the stent having thinner strut may perform well in terms of effectiveness as well as efficacy in the stent-based delivery.
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Affiliation(s)
- Akash Pradip Mandal
- Department of Mathematics, Ananda Chandra College, North Bengal University, Jalpaiguri, West Bengal, India
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2
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Marino M, Vairo G, Wriggers P. Mechano-chemo-biological Computational Models for Arteries in Health, Disease and Healing: From Tissue Remodelling to Drug-eluting Devices. Curr Pharm Des 2021; 27:1904-1917. [PMID: 32723253 DOI: 10.2174/1381612826666200728145752] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2020] [Accepted: 06/14/2020] [Indexed: 11/22/2022]
Abstract
This review aims to highlight urgent priorities for the computational biomechanics community in the framework of mechano-chemo-biological models. Recent approaches, promising directions and open challenges on the computational modelling of arterial tissues in health and disease are introduced and investigated, together with in silico approaches for the analysis of drug-eluting stents that promote pharmacological-induced healing. The paper addresses a number of chemo-biological phenomena that are generally neglected in biomechanical engineering models but are most likely instrumental for the onset and the progression of arterial diseases. An interdisciplinary effort is thus encouraged for providing the tools for an effective in silico insight into medical problems. An integrated mechano-chemo-biological perspective is believed to be a fundamental missing piece for crossing the bridge between computational engineering and life sciences, and for bringing computational biomechanics into medical research and clinical practice.
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Affiliation(s)
- Michele Marino
- Institute of Continuum Mechanics, Leibniz Universität Hannover, An der Universität 1, 30823 Garbsen, Germany
| | - Giuseppe Vairo
- Department of Civil Engineering and Computer Science, University of Rome "Tor Vergata" via del Politecnico 1, 00133 Rome, Italy
| | - Peter Wriggers
- Institute of Continuum Mechanics, Leibniz Universität Hannover, An der Universität 1, 30823 Garbsen, Germany
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Song J, Kouidri S, Bakir F. Review on the numerical investigations of mass transfer from drug eluting stent. Biocybern Biomed Eng 2021. [DOI: 10.1016/j.bbe.2021.06.010] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Milocco A, Scuor N, Lughi V, Lamberti G, Barba AA, Divittorio R, Grassi G, Perkan A, Grassi M, Abrami M. Thermal gelation modeling of a pluronic‐alginate blend following coronary angioplasty. J Appl Polym Sci 2020. [DOI: 10.1002/app.48539] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Alessio Milocco
- Department of Engineering and ArchitectureTrieste University, via Valerio 6, I‐34127 Trieste Italy
| | - Nicola Scuor
- Department of Engineering and ArchitectureTrieste University, via Valerio 6, I‐34127 Trieste Italy
| | - Vanni Lughi
- Department of Engineering and ArchitectureTrieste University, via Valerio 6, I‐34127 Trieste Italy
| | - Gaetano Lamberti
- Department of Industrial EngineeringUniversity of Salerno, Via Giovanni Paolo II, 132, I‐84084 Fisciano SA Italy
| | - Anna Angela Barba
- Department of PharmacySalerno University, Via Giovanni Paolo II, 132, I‐84084 Fisciano SA Italy
| | - Rosario Divittorio
- Department of Engineering and ArchitectureTrieste University, via Valerio 6, I‐34127 Trieste Italy
| | - Gabriele Grassi
- Department of Life SciencesCattinara University Hospital, Trieste University, Strada di Fiume 447, I‐34149 Trieste Italy
| | - Andrea Perkan
- Struttura Complessa di Cardiologia, Azienda per l'Assistenza Sanitaria n. 1 Triestina, Cattinara Hospital, Strada di Fiume 447, I‐34149 Trieste Italy
| | - Mario Grassi
- Department of Engineering and ArchitectureTrieste University, via Valerio 6, I‐34127 Trieste Italy
| | - Michela Abrami
- Department of Engineering and ArchitectureTrieste University, via Valerio 6, I‐34127 Trieste Italy
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Mandal AP, Mandal PK. Distribution and retention of drug through an idealised atherosclerotic plaque eluted from a half-embedded stent. ACTA ACUST UNITED AC 2017. [DOI: 10.1007/s40435-017-0372-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Mandal AP, Mandal PK. Computational Modelling of Three-phase Stent-based Delivery. JOURNAL OF EXPLORATORY RESEARCH IN PHARMACOLOGY 2017; 2:31-40. [DOI: 10.14218/jerp.2017.00001] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Integrated Stent Models Based on Dimension Reduction: Review and Future Perspectives. Ann Biomed Eng 2015; 44:604-17. [PMID: 26452562 DOI: 10.1007/s10439-015-1459-4] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2015] [Accepted: 09/12/2015] [Indexed: 10/22/2022]
Abstract
Stent modeling represents a challenging task from both the theoretical and numerical viewpoints, due to its multi-physics nature and to the complex geometrical configuration of these devices. In this light, dimensional model reduction enables a comprehensive geometrical and physical description of stenting at affordable computational costs. In this work, we aim at reviewing dimensional model reduction of stent mechanics and drug release. Firstly, we address model reduction techniques for the description of stent mechanics, aiming to illustrate how a three-dimensional stent model can be transformed into a collection of interconnected one-dimensional rods, called a "stent net". Secondly, we review available model reduction methods similarly applied to drug release, in which the "stent net" concept is adopted for modeling of drug elution. As a result, drug eluting stents are described as a distribution of concentrated drug release sources located on a graph that fully represents the stent geometry. Lastly, new results about the extension of these model reduction approaches to biodegradable stents are also discussed.
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d'Errico M, Sammarco P, Vairo G. Analytical modeling of drug dynamics induced by eluting stents in the coronary multi-layered curved domain. Math Biosci 2015; 267:79-96. [PMID: 26162517 DOI: 10.1016/j.mbs.2015.06.016] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2014] [Revised: 06/18/2015] [Accepted: 06/19/2015] [Indexed: 11/16/2022]
Abstract
Pharmacokinetics induced by drug eluting stents (DES) in coronary walls is modeled by means of a one-dimensional multi-layered model, accounting for vessel curvature and non-homogeneous properties of the arterial tissues. The model includes diffusion mechanisms, advection effects related to plasma filtration through the walls, and bio-chemical drug reactions. A non-classical Sturm-Liouville problem with discontinuous coefficients is derived, whose closed-form analytical solution is obtained via an eigenfunction expansion. Soundness and consistency of the proposed approach are shown by numerical computations based on possible clinical treatments involving both hydrophilic and hydrophobic drugs. The influence of the main model parameters on drug delivery mechanisms is analyzed, highlighting the effects induced by vessel curvature and yielding comparative indications and useful insights into the concurring mechanisms governing the pharmacokinetics.
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Affiliation(s)
- Michele d'Errico
- Department of Civil Engineering and Computer Science Engineering (DICII), Università degli Studi di Roma "Tor Vergata", via del Politecnico 1, Rome 00133, Italy.
| | - Paolo Sammarco
- Department of Civil Engineering and Computer Science Engineering (DICII), Università degli Studi di Roma "Tor Vergata", via del Politecnico 1, Rome 00133, Italy.
| | - Giuseppe Vairo
- Department of Civil Engineering and Computer Science Engineering (DICII), Università degli Studi di Roma "Tor Vergata", via del Politecnico 1, Rome 00133, Italy.
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Ferreira JA, Naghipoor J, Oliveira PD. A coupled non-Fickian model of a cardiovascular drug delivery system. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2015; 33:329-57. [DOI: 10.1093/imammb/dqv023] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2014] [Accepted: 06/08/2015] [Indexed: 11/13/2022]
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A decade of modelling drug release from arterial stents. Math Biosci 2014; 257:80-90. [DOI: 10.1016/j.mbs.2014.06.016] [Citation(s) in RCA: 74] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2014] [Revised: 05/16/2014] [Accepted: 06/26/2014] [Indexed: 11/20/2022]
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Morlacchi S, Migliavacca F. Modeling stented coronary arteries: where we are, where to go. Ann Biomed Eng 2012; 41:1428-44. [PMID: 23090621 DOI: 10.1007/s10439-012-0681-6] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2012] [Accepted: 10/16/2012] [Indexed: 01/09/2023]
Abstract
In the last two decades, numerical models have become well-recognized and widely adopted tools to investigate stenting procedures. Due to limited computational resources and modeling capabilities, early numerical studies only involved simplified cases and idealized stented arteries. Nowadays, increased computational power allows for numerical models to meet clinical needs and include more complex cases such as the implantation of multiple stents in bifurcations or curved vessels. Interesting progresses have been made in the numerical modeling of stenting procedures both from a structural and a fluid dynamics points of view. Moreover, in the drug eluting stents era, new insights on drug elution capabilities are becoming essential in the stent development. Lastly, image-based methods able to reconstruct realistic geometries from medical images have been proposed in the recent literature aiming to better describe the peculiar anatomical features of coronary vessels and increase the accuracy of the numerical models. In this light, this review provides a comprehensive analysis of the current state-of-the-art in this research area, discussing the main methodological advances and remarkable results drawn from a number of significant studies.
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Affiliation(s)
- Stefano Morlacchi
- Laboratory of Biological Structure Mechanics, Structural Engineering Department, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milan, Italy.
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Cutrì E, Zunino P, Morlacchi S, Chiastra C, Migliavacca F. Drug delivery patterns for different stenting techniques in coronary bifurcations: a comparative computational study. Biomech Model Mechanobiol 2012; 12:657-69. [DOI: 10.1007/s10237-012-0432-5] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2012] [Accepted: 08/14/2012] [Indexed: 11/29/2022]
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Zhu X, Pack DW, Braatz RD. Modelling intravascular delivery from drug-eluting stents with biodurable coating: investigation of anisotropic vascular drug diffusivity and arterial drug distribution. Comput Methods Biomech Biomed Engin 2012; 17:187-98. [PMID: 22512464 DOI: 10.1080/10255842.2012.672815] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Abstract
In-stent restenosis occurs in coronary arteries after implantation of drug-eluting stents with non-uniform restenosis thickness distribution in the artery cross section. Knowledge of the spatio-temporal drug uptake in the arterial wall is useful for investigating restenosis growth but may often be very expensive/difficult to acquire experimentally. In this study, local delivery of a hydrophobic drug from a drug-eluting stent implanted in a coronary artery is mathematically modelled to investigate the drug release and spatio-temporal drug distribution in the arterial wall. The model integrates drug diffusion in the coating and drug diffusion with reversible binding in the arterial wall. The model is solved by the finite volume method for both high and low drug loadings relative to its solubility in the stent coating with varied isotropic-anisotropic vascular drug diffusivities. Drug release profiles in the coating are observed to depend not only on the coating drug diffusivity but also on the properties of the surrounding arterial wall. Time dependencies of the spatially averaged free- and bound-drug levels in the arterial wall on the coating and vascular drug diffusivities are discussed. Anisotropic vascular drug diffusivities result in slightly different average drug levels in the arterial wall but with very different spatial distributions. Higher circumferential vascular diffusivity results in more uniform drug loading in the upper layers and is potentially beneficial in reducing in-stent restenosis. An analytical expression is derived which can be used to determine regions in the arterial with higher free-drug concentration than bound-drug concentration.
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Affiliation(s)
- Xiaoxiang Zhu
- a Department of Chemical Engineering , Massachusetts Institute of Technology , Cambridge , MA 02139 , USA
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Mathematical modeling of simultaneous drug release and in vivo absorption. Int J Pharm 2011; 418:130-41. [DOI: 10.1016/j.ijpharm.2010.12.044] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2010] [Revised: 12/22/2010] [Accepted: 12/27/2010] [Indexed: 01/17/2023]
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Drug release from coronary eluting stents: A multidomain approach. J Biomech 2010; 43:1580-9. [DOI: 10.1016/j.jbiomech.2010.01.033] [Citation(s) in RCA: 69] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2009] [Revised: 11/17/2009] [Accepted: 01/03/2010] [Indexed: 11/23/2022]
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