A sequential algorithm for the non-linear dual-sorption model of percutaneous drug absorption

Mathematical Biosciences

Volumn 152, Issue 1, 1998, Pages 87-103

  Gumel, A B ^a   Kubota, K ^b   Twizell, E H ^c  

^a MULTIMEDIA UNIVERSITY   (Malaysia)

^b UNIVERSITY OF TOKYO   (Japan)

^c BRUNEL UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DRUG VEHICLE;

ALGORITHM; CONCENTRATION (PARAMETERS); DIFFUSION; DRUG ABSORPTION; MATHEMATICAL ANALYSIS; MODEL; NONLINEAR SYSTEM; PERMEABILITY; REVIEW; SKIN ABSORPTION; STATISTICAL MODEL; STEADY STATE;

EID: 0032529074     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(98)10021-4     Document Type: Article

References (42)

1. Chandarasekaran S.K., Michaels A.S., Campbell P.S., Shaw J.E. Scopolamine permeation through human skin in vitro. Am. Inst. Chem. Eng. J. 21:1975;828.
2. Chandarasekaran S.K., Bayne W., Shaw J.E. Pharmacokinetics of drug permeation through human skin. J. Pharm. Sci. 67:1978;1370.
3. Scheuplein R.J. Mechanism of percutaneous drug absorption. I: routes of penetration and the influence of solubility. J. Invest. Dermatol. 45:1965;334.
4. Scheuplein R.J., Blank I.H. Permeability of the skin. Physiol. Rev. 51:1971;702.
5. Burnette R.R. A Monte-Carlo model for the passive diffusion of drugs through the stratum corneum. Int. J. Pharm. 22:1984;89.
6. Cooper E.R., Berner B. Finite dose pharmacokinetics of skin penetration. J. Pharm. Sci. 74:1985;1100.
7. Guy R.H., Hadgraft J. Physico-chemical interpretation of the pharmacokinetics of percutaneous absorption. J. Pharmacokinet. Biopharm. 2:1983;189.
8. Kubota K., Ishizaki T. A theoretical consideration of percutaneous drug absorption. J. Pharmacokinet. Biopharm. 13:1985;55.
9. Okamoto H., Hashida M., Sezaki H. Effect of 1-akyl- or 1-alkenylazacycloalkanone derivatives on the penetration of drugs with different lipophilicities through guinea-pig skin. J. Pharm. Sci. 80:1991;39.
10. Parry G.E., Bunge A.L., Silcox G.D., Pershing L.K., Pershing D.W. Percutaneous absorption of benzoic acid across human skin. I: in vitro experiments and mathematical modeling. Pharm. Res. 7:1990;230.
11. Shah J.C., Idris K., Tenjarla S., Lau S.W.J., Chow D. Analysis of percutaneous permeation data. II: evaluation of the lag time method. Int. J. Pharm. 109:1994;283.
12. Siddiqi O. Physicochemical, physiological and mathematical considerations in optimizing percutaneous absorption of drugs. Crit. Rev. Ther. Drug Carrier Syst. 6:1989;1.
13. Durrheim H., Flynn G.L., Higuchi W.I., Behl C.R. Permeation of hairless mouse skin. I: experimental methods and comparison with human epidermal permeation by alkanols. J. Pharm. Sci. 69:1980;781.
14. Kurihara-Bergstrom T., Flynn G.L., Higuchi W.I. Physicochemical study of percutaneous absorption enhancement by dimethylsulphoxide: kinetic and thermodynamic determinants of dimethylsulphoxide mediated mass transfer of alkonols. J. Pharm. Sci. 75:1986;479.
15. Paul D.R. Effect of immobilizing absorption on the diffusion time lag. J. Polym. Sci., Part A-2. 7:1969;1811.
16. Albery W.J., Hadgraft J. Percutaneous absorption: in vivo experiments. J. Pharm. Pharmacol. 31:1979;140.
17. Michaels A.S., Chandrasekaran S.K., Shaw J.E. Drug permeation through human skin: theory and in vitro experimental measurement. Am. Inst. Chem. Eng. J. 21:1975;985.
18. Peck K.D., Ghanem A.-H., Higuchi W.I. Hindered diffusion of polar molecules through and effective pore radii estimates of intact and ethanol-treated human epidermal membrane. Pharm. Res. 11:1994;1306.
19. Kubota K., Maibach H.I. Significance of viable skin layers in percutaneous permeation and its implication in mathematical models: theoretical consideration based on parameters for betamethasone 17-valerate. J. Pharm. Sci. 83:1994;1300.
20. Okamoto H., Yamashita F., Saito K., Hashida M. Analysis of drug penetration through the skin by the two-layer skin model. Pharm. Res. 6:1989;931.
21. Potts R.O., Guy R.H. Predicting skin permeability. Pharm. Res. 9:1992;663.
22. Ando H.Y., Schultz T.W., Schnaare R.L., Sugita E.T. Percutaneous absorption: a new physicochemical predictive model for maximum in vivo penetration rates. J. Pharm. Sci. 73:1984;461.
23. Flynn G.L., Yalkowsky S.H., Roseman T.J. Mass transport phenomena and models: theoretical concepts. J. Pharm. Sci. 63:1974;479.
24. Guy R.H., Hadgraft J., Maibach H.I. Percutaneous absorption: multi-dose pharmacokinetics. Int. J. Pharm. 17:1983;23.
25. Guy R.H., Hadgraft J., Maibach H.I. Percutaneous absorption in man: a kinetic approach. Toxicol. Appl. Pharmacol. 78:1985;123.
26. Kubota K., Maibach H.I. A compartment model for percutaneous absorption: compatability of the lag time and steady-state flux with the diffusion model. J. Pharm. Sci. 81:1992;863.
27. Ogiso T., Ito Y., Iwaki M., Atago H. A pharmacokinetic model for the percutaneous absorption of indomethacin and the prediction of drug disposition kinetics. J. Pharm. Sci. 78:1989;319.
28. Pozzo A.D., Donzelli G., Liggeri E., Rodriquez L. Percutaneous absorption of nicotinic acid derivatives in vitro. J. Pharm. Sci. 80:1991;54.
29. Singh P., Roberts M.S. Dermal and underlying tissue pharmacokinetics of lidocaine after topical application. J. Pharm. Sci. 83:1994;774.
30. Takada K., Yoshikawa H., Muranishi S. Pharmacokinetic analysis of plasma drug level data obtained from a transdermal therapeutic system with a complex absorption model. Int. J. Pharm. 65:1990;159.
31. Wallace S.M., Barnett G. Pharmocokinetic analysis of percutaneous absorption: evidence of parallel penetration pathways for methotrexate. J. Pharmacokinet. Biopharm. 6:1978;315.
32. Williams P.L., Riviere J.E. A biophysically based dermato-pharmacokinetic compartment model for quantifying percutaneous penetration and absorption of topically applied agents. I: theory. J. Pharm. Sci. 84:1995;599.
33. Kubota K., Koyama E., Twizell E.H. Dual sorption model for the nonlinear percutaneous permeation kinetics of timolol. J. Pharm. Sci. 82:1993;1205.
34. Kubota K., Yamada T. Finite dose percutaneous drug absorption: theory and its application to an in vitro timotol permeation. J. Pharm. Sci. 79:1990;1015.
35. Wearley L.L., Chien Y.W. Iontophoretic transdermal permeation of verapamil (III): effect of binding and concentration gradient on reversibility of skin permeation rate. Int. J. Pharm. 59:1990;87.
36. Wearley L.L., Tojo K., Chien Y.W. A numerical approach to study the effect of binding on the iontophoretic transport of a series of amino acids. J. Pharm. Sci. 79:1990;992.
37. Frisch H.L. The time lag in diffusion. J. Phys. Chem. 61:1957;93.
38. Kubota K., Twizell E.H. A non-linear numerical model of percutaneous drug absorption. Math. Biosc. 108:1992;157.
39. E.H. Twizell, Numerical Methods, with Applications in the Biomedical Sciences, Ellis Horwood, Chichester, and Wiley, New York, 1988.
40. A.B. Gumel, Parallel and sequential algorithms for second-order parabolic equations with applications, PhD thesis, Brunel University, 1993.
41. Khaliq A.Q.M., Twizell E.H., Voss D.A. On parallel algorithms for semidiscretized parabolic PDE's based on subdiagonal Padé approximation. Numer. Methods Partial Different. Eq. 9(2):1993;107.
42. Zakian V. Comment on rational approximants to the matrix exponential. Electron. Lett. 7:1971;261.