Repeated applications of a transdermal patch: Analytical solution and optimal control of the delivery rate

Mathematical Biosciences

Volumn 209, Issue 2, 2007, Pages 593-607

  Simon, L ^a  

^a NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Integral transform technique; Optimal control; Partial differential equations; Percutaneous absorption

Indexed keywords

ABSORPTION; ALGORITHMS; DIFFUSION; DYNAMIC PROGRAMMING; EIGENVALUES AND EIGENFUNCTIONS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; SKIN;

INTEGRAL TRANSFORM TECHNIQUE; MEDICINAL AGENTS; PERCUTANEOUS ABSORPTION; THERAPEUTIC DRUG MONITORING;

DRUG DELIVERY;

DRUG VEHICLE;

ABSORPTION; DIFFUSION; DRUG; EIGENVALUE; ESTIMATION METHOD; NUMERICAL MODEL; OPTIMIZATION; SKIN;

ALGORITHM; ANALYTIC METHOD; ARTICLE; AUTOMATION; DRUG ABSORPTION; DRUG DELIVERY SYSTEM; DRUG DIFFUSION; DRUG TRANSPORT; MATHEMATICAL MODEL; SKIN ABSORPTION; TRANSDERMAL PATCH;

ADMINISTRATION, CUTANEOUS; ALGORITHMS; DRUG DELIVERY SYSTEMS; HUMANS; MATHEMATICS; MODELS, BIOLOGICAL; SKIN ABSORPTION;

EID: 34548591509     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2007.03.009     Document Type: Article

References (29)

1. Crank J. The Mathematics of Diffusion. second ed. (1975), Clarendon, Oxford
2. Chen S.X., and Lostritto R.T. Diffusion of benzocaine in poly(ethylene-vinyl acetate) membranes: effects of vehicle ethanol concentration and membrane vinyl acetate content. J. Control. Release 38 (1996) 185
3. Degim I.T. Understanding skin penetration: computer aided modeling and data interpretation. Curr. Comput.-Aided Drug Des. 1 (2005) 11
4. Scheuplein R.J. Mechanisms of percutaneous absorption I. Routes of penetration and the influence of solubility. J. Invest. Dermatol. 45 (1965) 334
5. Williams A.C., and Barry B.W. Skin absorption enhancers. Crit. Rev. Ther. Drug Carrier Syst. 9 (1992) 305
6. Hadgraft J. The epidermal reservoir: a theoretical approach. Int. J. Pharm. 2 (1979) 265
7. Kubota K., and Ishizaki T.A. A theoretical consideration of percutaneous drug absorption. J. Pharmacokinet. Biopharm. 13 (1985) 55
8. Berner B., and Cooper E.R. Models of skin permeability. In: Kydonieus A.F., and Berner B. (Eds). Transdermal Delivery of Drugs Vol. II (1987), CRC, Boca Raton, FL
9. Lee A.J., King J.R., and Rogers T.G. A multiple-pathway model for the diffusion of drugs in the skin. J. Math. Appl. Med. Biol. 13 (1996) 127
10. Lee A.J., King J.R., and Barrett D.A. Percutaneous absorption: a multiple pathway model. J. Control. Release 45 (1997) 141
11. Manitz R., Lucht W., Strehmel K., Weiner R., and Neubert R. On mathematical modeling of dermal and transdermal drug delivery. J. Pharm. Sci. 87 (1998) 873
12. Simon L., and Fernandes M. Neural network-based prediction and optimization of estradiol release from ethylene-vinyl acetate membranes. Comput. Chem. Eng. 28 (2004) 2407
13. Bunge A.L. Release rates from topical formulations containing drugs in suspension. J. Control. Release 52 (1998) 141
14. Roberts M.S., Anissimov Y.G., and Gonsalvez R.A. Mathematical models in percutaneous absorption. In: Bronaugh R.L., and Maibach H.I. (Eds). Percutaneous Absorption: Drugs, Cosmetics, Mechanisms, Methodology vol. 97 (1999), Marcel Decker Inc., New York 3
15. Ramraj R., Farrell S., and Loney N.W. Mathematical modeling of a flat-membrane-controlled release device. Sep. Sci. Technol. 34 (1999) 2251
16. Kalia Y.N., and Guy R.H. Modeling transdermal drug release. Adv. Drug Deliv. Rev. 48 (2001) 159
17. Fernandes M., Simon L., and Loney N. Mathematical modeling of drug delivery systems: analysis and applications. J. Membr. Sci. 256 (2005) 184
18. Lu X., Ramirez F., and Anseth K. Modeling and optimization of drug release from laminated polymer matrix devices. AIChE J. 44 (1998) 1689
19. Blatt M., and Schittkowski K. Optimal control of one-dimensional partial differential algebraic equations with applications. Ann. Oper. Res. 98 (2000) 45
20. Simon L., and Loney N.W. An analytical solution for percutaneous drug absorption: application and removal of the vehicle. Math. Biosci. 197 (2005) 119
21. Kubota K., Dey F., Matar S.A., and Twizell E.H. A repeated-dose model of percutaneous drug absorption. Appl. Math. Model. 26 (2002) 529
22. Mikhailov M.D., and Özişik M.N. Unified Analysis and Solutions of Heat and Mass Diffusion (1984), John Wiley and Sons, New York
23. Bryson A.E. Dynamic Optimization (1999), Addison Wesley Longman Inc., Menlo Park
24. Ruggeri A., and Martinelli M. A program for the optimization of cyclosporine therapy using population kinetics modeling. Comput. Methods Programs Biomed. 61 (2000) 61
25. Rohr U.D., and Saeger-Lorenz K. 17Beta-estradiol matrixpatch removal and reapplication in postmenopausal women: theoretical predictions with an oscillating diffusion coefficient model. J. Pharm. Sci. 91 (2002) 822
26. Rohr U.D., and Saeger-Lorenz K. 17Beta-extradiol matrixpatch removal and reapplication in postmenopausal women: experimental results. J. Pharm. Sci. 91 (2002) 810
27. Buell J., Jelliffe R., Kalaba R., and Sridhar R. Modern control theory and optimal drug regimens. II: Combination therapy. Math. Biosci. 6 (1970) 67
28. Bellman R. Topics in pharmacokinetics. Math. Biosci. 12 (1971) 1
29. Kubota K., Koyama E., and Yasuda K. A random walk method for percutaneous drug absorption pharmacokinetics: Application to repeated administration of a therapeutic timolol patch. J. Pharm. Sci. 80 (1991) 752