A three-dimensional mathematical model for drug delivery from drug-eluting stents

Document Type: Full article

Authors

Department of Chemical Engineering, School of Engineering, Yasouj University, Yasouj, Iran

Abstract

Current drug-eluting stent (DES) technology is not optimized with regard to the pharmacokinetics of drug release, more research on the drug-eluting stent design and flux of drug release to the arterial wall is necessary. Considering a three-dimensional (3D) cylindrical mathematical model, a novel free drug mass transfer release has been formulated and applied for better estimation of the drug concentration in the tissue. The transport equations involved both convection and diffusion equations. Besides, a reversible reaction in the arterial wall was considered. The present model was solved by an appropriate numerical simulation method and the predicted results were compared with in vivo data. To find out the rate-limiting step, the time scale analysis was also applied. The obtained results showed that the binding process is more limited by convection and diffusion, where convection is the rate-controlling step. It is also demonstrated that the presented approach has advantages over the prior free drug mass transfer models, including better data prediction and satisfying mass transfer consistency.

Keywords


[1] U.S. Department of Health and Human Services, The National Heart, Lung and Blood Institute, How Are Stents Used? http://www.nhlbi.nih.gov/health/health topics/topics/ stents/used.html.

[2] Balakrishnan, B. Tzafriri, A. R. Seifert, P. Groothuis, A. Rogers, C. and Edelman, E. R., "Strut position, blood flow, and drug deposition-implications for single and overlapping drug-eluting stents", Circulation, 111 (22), 2958 (2005).

[3] LaDisa, J. F., "Stent design properties and deployment ratio influence indexes of wall shear stress: a three-dimensional computational fluid dynamics investigation within a normal artery", J. Appl Physiol., 97 (1), 424 (2004).

[4] Seo, T. Schachter, L. G. and Barakat, A. I., "Computational study of fluid mechanical disturbance induced by endovascular stents", Ann. Biomed Eng., 33 (4), 444 (2005).

[5] Hara, H. Nakamura, M. Palmaz, J. C. and Schwartz, R. S., "Role of stent design and coatings on restenosis and thrombosis", Adv. Drug Deliv. Rev., 58 (3), 377 (2006).

[6] McGinty, S. McKee, S. Wadsworth, R. M. and McCormick, C., "Modelling drug-eluting stents", Math. Med. Biol., 28, 1 (2011).

[7] Pontrelli, G. and De Monte, F., "Mass diffusion through two-layer porous media: an application to the drug-eluting stent", Int. J. Heat and Mass Trans., 50, 3658 (2007).

[8] Pontrelli, G. Mascio, A. D. and De Monte, F., "Local mass non-equilibrium dynamics in multi-layered porous media: application to the drug-eluting stent", Int. J. Heat and Mass Trans., 66 (1), 844 (2013).

[9] Zunino, P., "Multidimensional pharmacokinetic models applied to the design of drug-eluting stents", Cardiovascular Eng., 4 (2), 181 (2004).

[10] Hossainy, S. and Prabhu, S., "A mathematical model for predicting drug release from a biodurable drug-eluting stent coating", J. Biomed. Mater. Res., 87A, 487 (2008).

[11] Siepmann, J. and Siepmann, F., "Modelling of diffusion controlled drug delivery", J. Control. Release, 161, 351 (2012).

[12] McGinty, S. McKee, S. McCormick, C. and Wheel, M., "Release mechanism and parameter estimation in drug-eluting stent systems: analytical solutions of drug release and tissue transport", Math. Med. Biol., 1-24 (2014).

[13] Fredenberg, S. Reslow, M. W. M. and Axelsson, A., "The mechanisms of drug release in poly (lactic-co-glycolic acid)-based drug delivery systems-a review", Int. J. Pharm., 415, 34 (2011).

[14] Prabhu, S. and Hossainy, S., "Modeling of degradation and drug release from a biodegradable stent coating", J. Biomed. Mater. Res., 80A (3), 732 (2007).

[15] Siepmann, J. and Gopferich, A., "Mathematical modeling of bioerodible, polymeric drug delivery systems", Adv. Drug Deliv. Rev., 48 (2-3), 229 (2001).

[16] Joshi, A. and Himmelstein, K. J., "Dynamics of controlled release from bioerodible matrices", J. Membrane Sci., 15, 95 (1991).

[17] Lee, P. I., "Diffusional release of a solute from a polymeric matrix approximate analytical solution", J. Membrane Sci., 7, 255 (1980).

[18] Rossi, F. Casalini, T. Masi, E. R. M. and Perale, G., "Bioresorbable polymer coated drug eluting stent: a model study", Mol. Pharmacol., 9 (7), 1898 (2012).

[19] Rothstein, S. N. Federspiel, W. J. and Little, S. R., "A unified mathematical model for the prediction of controlled release from surface and bulk eroding polymer matrices", Biomaterials, 30 (8), 1657 (2009).

[20] Soares, J. S. and Zunino, P., "A mixture model for water uptake, degradation, erosion and drug release from polydisperse polymeric networks", Biomaterials, 31 (11), 3032 (2010).

[21] Siepmann, J. and Gopferich, A., "Mathematical modeling of bioerodible, polymeric drug delivery systems", Adv. Drug Deliv. Rev., 48 (2-3), 229 (2001).

[22] Horner, M. Joshi, S. Dhruva, V. Sett, S. and Stewart, S. F. C., "A two-species drug delivery model is required to predict deposition from drug-eluting stents", Cardiovasc. Eng. Technol., 1 (3), 225 (2010).

[23] Abraham, J. P. Gorman, J. M. Sparrow, E. M. Stark, J. R. and Kohler, R. E., "A mass transfer model of temporal drug deposition in artery walls", Int. J. Heat Mass Trans., 58, 632 (2013).

[24] Pontrelli, G. and De Monte, F., "Modeling of mass dynamics in arterial drug-eluting stents", J. Porous Media, 12 (1), 19 (2009).

[25] Pontrelli, G. and De Monte, F., "A multi-layer porous wall model for coronary drug-eluting stents", Int. J Heat Mass Transfer., 53 (19-20), 3629 (2010).

[26] McGinty, S., "A decade of modelling drug release from arterial stents", Mathematical Biosciences, 257, 80 (2014).

[27] Sakharov, D. V. Kalachev, L. V. and Rijken, D. C., "Numerical simulation of local pharmacokinetics of a drug after intravascular delivery with an eluting stent", J. Drug Target., 10, 507 (2002).

[28] Tzafriri, A. R. Levin, A. D. and Edelman, E. R., "Diffusion-limited binding explains binary dose response for local arterial and tumor drug delivery", Cell Proliferation, 42 (3), 348 (2009).

[29] Tzafriri, A. R. Groothuis, A., Price, G. S. and Edelman, E. R., "Stent elution rate determines drug deposition and receptor-mediated effects", J. Control Release, 161 (3), 918 (2012).

[30] Bozsak, F. Chomaz, J. and Barakat, A. I., "Modeling transport of drugs eluted from stents: physical phenomena driving drug distribution in the arterial wall", Biomech Model Mechanobiol, 13 (2), 327 (2014).

[31] Kuypers, D. R. J., "Benefit-risk assessment of Sirolimus in renal transplantation", Drug Saf., 28 (2), 153 (2005).

[32] Rapamune® prescribing information. Wyeth Pharmaceuticals Inc., December 2005.

[33] A. C. Hindmarsh, suite of nonlinear and differential/algebraic equation solvers, Brown PN SUNDIALS (2005).

[34] Constantinides, A. and Mostoufi, N., "Numerical Methods for Chemical Engineers with Matlab Applications", Prentice Hall: Upper Saddle River, NJ, 1999.

[35] Bae, H. Mrsny, R. J. and Park, K., "Cancer Targeted Drug Delivery: An Elusive Dream", springer, 593 (2013).