Basic mathematical principles in skin permeation

Dermatological and Transdermal Formulations

Volumn , Issue , 2002, Pages 61-88

  Watkinson, Adam C ^a   Brain, Keith R ^a  

^a An eX Analytical Services Ltd   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84966859948     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (46)

1. Crank J. The Mathematics of Diffusion. 2nd ed. London: Oxford University Press, 1975.
2. Daynes HA. The process of diffusion through a rubber membrane. Proc R Soc Lond A 97:286-307, 1920.
3. Barrer RM. Permeation, diffusion and solution of gases. Trans Faraday Soc 35:628-643, 1939.
4. Flynn GL, Carpenter OS, Yalkowsky SH. Total mathematical resolution of diffusion layer control of barrier flux. J Pharm Sci 61:312-314, 1972.
5. Flynn GL. Dermal diffusion and delivery principles. In: Swarbrick J, Boylan JC, eds. Encyclopedia of Pharmaceutical Technology. Vol. 3. New York: Marcel Dekker, pp. 457-503, 1991.
6. Hadgraft J. Calculations of drug release rates from controlled release devices. The slab. Int J Pharm 2:177-194, 1979.
7. Watkinson AC, Bunge AL, Hadgraft J. Computer simulation of penetrant concentration- depth profiles in the stratum corneum. Int J Pharm 87:175-182, 1992.
8. Yamashita F, Koyama Y, Sezaki H, Hashida M. Estimation of a concentration profile of acyclovir in the skin after topical administration. Int J Pharm 89:199-206, 1993.
9. Shah JC. Analysis of permeation data: evaluation of the lag time method. Int J Pharm 90:161-169, 1993.
10. Potts RO, Guy RH. Drug transport across the skin and the attainment of steady-state flux. Proc Int Symp Control Release Bioact Mat 21:162-163, 1994.
11. Lafforgue C, Eynard I, Falson F, Watkinson A, Hadgraft J. Percutaneous absorption of methyl nicotinate. Int J Pharm 121:89-93, 1995.
12. Parry GE, Bunge AL, Silcox GD, Pershing DW, Pershing DW. Percutaneous absorption of benzoic acid across human skin. I. In-vitro experiments and mathematical modelling. Pharm Res 7:230-236, 1990.
13. Rogers WA, Buritz RS, Alpert D. Diffusion coefficient, solubility, and permeability for helium in glass. J Appl Phys 25:868-875, 1954.
14. Short PM, Abbs ET, Rhodes CT. Effect of non-ionic surfactants on the transport of testosterone across a cellulose acetate membrane. J Pharm Sci 59:995-998, 1970.
15. Brandt H. Determination of diffusion specific parameters by means of IR-ATR spectroscopy. Exp Tech Phys 33:423-431, 1985.
16. Brandt H, Hemmelmann K. On the evidence of non-linear sorption at the surface poly- ethylene/ATR-element for the diffusion of ethylacetate in polystyrene films. Exp Tech Phys 35:349-358, 1987.
17. Hemmelmann K, Brandt H. Investigation of diffusion and sorption properties of polyethylene films for different liquids by means of IR-ATR spectroscopy. Exp Tech Phys 34:439-446, 1986.
18. Van Alsten JG, Lustig SR. Polymer mutual diffusion measurements using infrared ATR spectroscopy. Macromolecules 25:5069-5073, 1992.
19. Potts RO, Doh L, Venkatraman, S, Farinas KC. Characterisation of solute diffusion in a polymer using ATR-FTIR spectroscopy. Macromolecules 27:5220-5222, 1994.
20. Wurster DE, Buraphacheep V, Patel JM. The determination of diffusion coefficients in semisolids by Fourier transform infrared (FT-IR) spectroscopy. Pharm Res 10:616-620, 1993.
21. Tralhao AM, Watkinson AC, Brain KR, Hadgraft J, Armstrong NA. Use of ATR-FTIR spectroscopy to study the diffusion of ethanol through glycerogelatine films. Pharm Res 12:572-575, 1995.
22. Harrison JE, Watkinson AC, Green DM, Hadgraft J, Brain KR. The relative effect of Azone and Transcutol on permeant diffusivity and solubility in human stratum corneum. Pharm Res 13:542-546, 1996.
23. Watkinson AC, Brain KR, Hadgraft J. The deconvolution of diffusion and partition coefficients in permeability studies. Proc Int Symp Controlled Release Bioact Mat 21: 160-161, 1994.
24. Flynn GL, Yalkowsky SH, Roseman TJ. Mass transport phenomena and models: theoretical concepts. J Pharm Sci 63:479-510, 1974.
25. Flynn GL, Yalkowsky SH. Correlation and prediction of mass transport across membranes. I. Influence of alkyl chain length on flux determining properties of barrier and diffusant. J Pharm Sci 61:838-852, 1972.
26. Stehle RG, Higuchi WI. Diffusional model for transport rate studies across membranes. J Pharm Sci 56:1367-1368, 1967.
27. Roberts MS, Anderson RA, Swarbrick J. Permeability of human epidermis to phenolic compounds. J Pharm Pharmacol 29:677-683, 1978.
28. Zwolinski BJ, Eyring H, Reese CE. Diffusion and membrane permeability. J Phys Chem 53:1426-1453, 1949.
29. Danielli JF. The theory of penetration of a thin membrane-derivation of a fundamental equation. In: Davson H, Danielli JF. The Permeability of Natural Membranes. 2nd ed. London: Cambridge University Press, pp. 324-335, 1952.
30. Lakshminarayanaiah N. Transport Phenomena in Membranes. New York: Academic Press, pp. 119-126, 1969.
31. Schaefer H, Watts F, Brod J, Illel B. Follicular penetration. In: Scott RC, Guy RH, Hadgraft J, eds. Prediction of Percutaneous Penetration. Vol. 1. London: IBC Technical Services, pp. 163-173, 1989.
32. Lauer AC, Lieb LM, Ramachandran C, Flynn GL, Weiner ND. Transfollicular drug delivery. Pharm Res 12:179-186, 1995.
33. Hueber F, Wepierre J, Schaefer H. Role of transfollicular routes in percutaneous absorption of hydrocortisone and testosterone: in vivo study in the hairless rat. Int J Pharm 5:99-107, 1992.
34. Jadoul A, Hanchard C, Thysman S, Preat V. Quantification and localisation of fentanyl and trh delivered by iontophoresis in the skin. Int J Pharm 120:221-228, 1995.
35. Craane van Hinsberg WHM, Verhoef JC, Bax LJ, Junginger HE, Bodde HE. Role of appendages in skin resistance and iontophoretic peptide flux: human versus snake skin. Pharm Res 12:1506-1512, 1995.
36. Scheuplein RJ, Analysis of solubility data for the case of parallel diffusion pathways. Biophys J 6:1-17, 1966.
37. Scheuplein RJ, Blank IH, Brauner GJ, MacFarlane DJ. Percutaneous absorption of steroids. J Invest Dermatol 52:63-70, 1969.
38. Barrer RM. Diffusion and permeation in heterogeneous media. In: Crank J, Park GS, eds. Diffusion in Polymers. London: Academic Press, pp. 165-217, 1968.
39. Higuchi WI, Higuchi T. Theoretical analysis of diffusional movement through heterogeneous barriers. J Am Pharm Assoc Sci Ed 49:598-606, 1960.
40. Finger KF, Lemberger AP, Higuchi T, Busse LW, Wurster DE. Investigation and development of protective ointment IV. The influence of active fillers on the permeability of semisolids. J Am Pharm Assoc Sci Ed 49:569-573, 1960.
41. Flynn GL, Roseman TJ. Membrane diffusion II. Influence of physical adsorption on molecular flux through heterogeneous dimethypolysiloxane barriers. J Pharm Sci 60: 1788-1796, 1970.
42. Paul DR, Kemp DR. The diffusion time lag in polymer membranes containing adsorptive fillers. J Polymer Sci Polymer Symp 41. Transport Phenomena Through Polymer Films, Kumins CA, ed. pp. 79-93, 1973.
43. Guy RH, Hadgraft J. A theoretical description relating skin penetration to the thickness of the applied medicament. Int J Pharm 6:321-332, 1980.
44. Addicks WJ, Flynn GL, Weiner N, Curl R. A mathematical model to describe drug release from thin topical applications. Int J Pharm 56:243-248, 1989.
45. Crank J, Park GS. Diffusion in Polymers. London: Academic Press, 1968.
46. Potts RO, Francoeur ML. Lipid biophysics of water loss through the skin. Proc Natl Acad Sci USA 87:1-3, 1990.