Mathematical and pharmacokinetic modelling of epidermal and dermal transport processes

Advanced Drug Delivery Reviews

Volumn 65, Issue 2, 2013, Pages 169-190

  Anissimov, Yuri G ^a   Jepps, Owen G ^a   Dancik, Yuri ^b   Roberts, Michael S ^b,c  

^a GRIFFITH UNIVERSITY   (Australia)

^b UNIVERSITY OF QUEENSLAND   (Australia)

^c UNIVERSITY OF SOUTH AUSTRALIA   (Australia)

Author keywords

Mathematical modelling; Percutaneous drug delivery

Indexed keywords

DERMAL EXPOSURE; ENVIRONMENTAL CHEMICALS; SYSTEMIC CIRCULATION; TOPICAL DELIVERY; TRANSDERMAL DRUG DELIVERY; TRANSPORT PROCESS;

DRUG DELIVERY; HISTOLOGY; TISSUE;

MATHEMATICAL MODELS;

ANALGESIC AGENT; ANESTHETIC AGENT; ANTI ACNE AGENT; ANTIHISTAMINIC AGENT; ANTIINFLAMMATORY AGENT; ANTIPERSPIRANT AGENT; COSMETIC; INSECT REPELLENT; SCOPOLAMINE; SUNSCREEN;

COMPARTMENT MODEL; DERMIS; DESORPTION; DIFFUSION COEFFICIENT; DRUG CLEARANCE; DRUG DELIVERY SYSTEM; DRUG DIFFUSION; DRUG DISTRIBUTION; DRUG ELIMINATION; DRUG METABOLISM; DRUG SOLUBILITY; DRUG TRANSPORT; EPIDERMIS; HUMAN; LIPOPHILICITY; MATHEMATICAL MODEL; PARTITION COEFFICIENT; PRIORITY JOURNAL; REVIEW; SKIN; SKIN PERMEABILITY; STEADY STATE; SUBCUTANEOUS TISSUE; THERMODYNAMICS;

ADMINISTRATION, CUTANEOUS; ANIMALS; BIOLOGICAL TRANSPORT; DRUG DELIVERY SYSTEMS; ENVIRONMENTAL EXPOSURE; HUMANS; MODELS, THEORETICAL; PHARMACEUTICAL PREPARATIONS; SKIN; SKIN ABSORPTION; TISSUE DISTRIBUTION;

EID: 84873526957     PISSN: 0169409X     EISSN: 18728294     Source Type: Journal    
DOI: 10.1016/j.addr.2012.04.009     Document Type: Review

References (131)

1. Wu Y., Anissimov Y.G., Roberts M.S. Introduction to dermatokinetics. Dermatokinetics of Therapeutic Agents 2011, 1-23. CRC Press, Boca Raton. S.N. Murthy (Ed.).
2. Dancik Y., Jepps O.G., Roberts M.S. Physiologically based pharmacokinetics and pharmacodynamics of skin. Dermal Absorption and Toxicity Assessment 2008, 179-207. Informa Healthcare, New York. M.S. Roberts, K.A. Walters (Eds.).
3. Dancik Y., Jepps O.G., Roberts M.S. Beyond stratum corneum. Dermal Absorption and Toxicity Assessment 2008, 209-250. Informa Healthcare, New York. M.S. Roberts, K.A. Walters (Eds.).
4. Masters B., So P. Confocal microscopy and multi-photon excitation microscopy of human skin in vivo. Opt. Express 2001, 8:2-10.
5. Touitou E. Drug delivery across the skin. Expert Opin. Biol. Ther. 2002, 2:723-733.
6. Ya-Xian Z., Suetake T., Tagami H. Number of cell layers of the stratum corneum in normal skin - relationship to the anatomical location on the body, age, sex and physical parameters. Arch. Dermatol. Res. 1999, 291:555-559.
7. Waller J.M., Maibach H.I. Age and skin structure and function, a quantitative approach (I): blood flow, pH, thickness, and ultrasound echogenicity. Skin Res. Technol. 2005, 11:221-235.
8. Egawa M., Hirao T., Takahashi M. In vivo estimation of stratum corneum thickness from water concentration profiles obtained with Raman spectroscopy. Acta Derm. Venereol. 2007, 87:4-8.
9. Anissimov Y.G., Roberts M.S. Diffusion modeling of percutaneous absorption kinetics: 3. Variable diffusion and partition coefficients, consequences for stratum corneum depth profiles and desorption kinetics. J. Pharm. Sci. 2004, 93:470-487.
10. Michaels A.S., Chandrasekaran C., Shaw J.E. Drug permeation through human skin: theory and in vitro experimental measurement. AlChE J. 1975, 21:985-996.
11. Zhang Q., Grice J.E., Li P., Jepps O.G., Wang G.J., Roberts M.S. Skin solubility determines maximum transepidermal flux for similar size molecules. Pharm. Res. 2009, 26:1974-1985.
12. Magnusson B.M., Anissimov Y.G., Cross S.E., Roberts M.S. Molecular size as the main determinant of solute maximum flux across the skin. J. Invest. Dermatol. 2004, 122:993-999.
13. Kalia Y.N., Pirot F., Guy R.H. Homogeneous transport in a heterogeneous membrane: water diffusion across human stratum corneum in vivo. Biophys. J. 1996, 71:2692-2700.
14. Anissimov Y.G., Roberts M.S. Modelling dermal drug distribution after topical application in human. Pharm. Res. 2011, 28:2119-2129.
15. Dancik Y., Anissimov Y.G., Jepps O.G., Roberts M.S. Convective transport of highly plasma protein bound drugs facilitates direct penetration into deep tissues after topical application. Br. J. Clin. Pharmacol. 2012, 73:564-578.
16. Cross S.E., Roberts M.S. Dermal blood flow, lymphatics, and binding as determinates of topical absorption, clearance and distribution. Dermal Absorption Models in Toxicology and Pharmacology 2006, 251-282. CRC Press, Boca Raton. J.E. Riviere (Ed.).
17. O.G. Jepps, Y. Dancik, Y.G. Anissimov, M.S. Roberts, (accepted for publication). Modeling the Human Skin Barrier - Towards a Better Understanding of Dermal Absorption, Adv. Drug Delivery Rev. http://dx.doi.org/10.1016/j.addr.2012.04.003.
18. Bendas B., Schmalfuss U., Neubert R. Influence of propylene-glycol as cosolvent on mechanisms of drug transport from hydrogels. Int. J. Pharm. 1995, 116:19-30.
19. Hoelgaard A., Møllgaard B. Dermal drug delivery - improvement by choice of vehicle or drug derivative. J. Control. Release 1985, 2:111-120.
20. Raykar P.V., Fung M.C., Anderson B.D. The role of protein and lipid domains in the uptake of solutes by human stratum corneum. Pharm. Res. 1988, 5:140-150.
21. Caussin J., Gooris G.S., Janssens M., Bouwstra J.A. Lipid organization in human and porcine stratum corneum differs widely, while lipid mixtures with porcine ceramides model human stratum corneum lipid organization very closely. Biochim. Biophys. Acta 2008, 1778:1472-1482.
22. Hansen S., Selzer D., Schaefer U.F., Kasting G.B. An extended database of keratin binding. J. Pharm. Sci. 2011, 100:1712-1726.
23. Barry B.W. Lipid-protein partitioning theory of skin penetration enhancement. J. Control. Release 1991, 15:237-248.
24. Hilton J., Woollen B.H., Scott R.C., Auton T.R., Trebilcock K.L., Wilks M.F. Vehicle effects on in vitro percutaneous absorption through rat and human skin. Pharm. Res. 1994, 11:1396-1400.
25. Hadgraft J., Lane M.E. Skin: the ultimate interface. Phys. Chem. Chem. Phys. 2011, 13:5215-5222.
26. Scheuplein R.J., Blank I.H. Permeability of the skin. Physiol. Rev. 1971, 51:702-747.
27. Roberts M.S., Anderson R.A., Swarbrick J. Permeability of human epidermis to phenolic compounds. J. Pharm. Pharmacol. 1977, 29:677-683.
28. Pugh W.J., Roberts M.S., Hadgraft J. Epidermal permeability - penetrant structure relationships.3. The effect of hydrogen bonding interactions and molecular size on diffusion across the stratum corneum. Int. J. Pharm. 1996, 138:149-165.
29. Bunge A.L., Cleek R.L. A new method for estimating dermal absorption from chemical exposure: 2. Effect of molecular weight and octanol-water partitioning. Pharm. Res. 1995, 12:88-95.
30. Anderson B.D., Raykar P.V. Solute structure-permeability relationships in human stratum corneum. J. Invest. Dermatol. 1989, 93:280-286.
31. Nitsche J.M., Wang T.F., Kasting G.B. A two-phase analysis of solute partitioning into the stratum corneum. J. Pharm. Sci. 2006, 95:649-666.
32. Vecchia B.E., Bunge A.L. Skin absorption databases and predictive equations. Transdermal drug delivery 2002, 57-141. Marcel Dekker, New York. R.H. Guy, J. Hadgraft (Eds.).
33. Roberts M.S., Walters K.A. The relationship between structure and barrier function of skin. Dermal Absorption And Toxicity Assessment 1998, 91:1-42.
34. Anissimov Y.G., Roberts M.S. Diffusion modeling of percutaneous absorption kinetics: 4. Effects of a slow equilibration process within stratum corneum on absorption and desorption kinetics. J. Pharm. Sci. 2009, 98:772-781.
35. Scheuplein R.J., Blank I.H., Brauner G.J., MacFarlane D.J. Percutaneous absorption of steroids. J. Invest. Dermatol. 1969, 52:63-70.
36. Barry B.W., Harrison S.M., Dugard P.H. Vapour and liquid diffusion of model penetrants through human skin; correlation with thermodynamic activity. J. Pharm. Pharmacol. 1985, 37:226-236.
37. Lippold B.C. How to optimize drug penetration through the skin. Pharm. Acta Helv. 1992, 67:294-300.
38. Jiang R.Y., Roberts M.S., Prankerd R.J., Benson H.A.E. Percutaneous absorption of sunscreen agents from liquid paraffin: self-association of octyl salicylate and effects on skin flux. J. Pharm. Sci. 1997, 86:791-796.
39. Scheuplein R.J. Mechanism of percutaneous adsorption. I. Routes of penetration and the influence of solubility. J. Invest. Dermatol. 1965, 45:334-346.
40. Loden M. The in vitro permeability of human skin to benzene, ethylene glycol, formaldehyde, and n-hexane. Acta Pharmacol. Toxicol. (Copenh) 1986, 58:382-389.
41. Franz T.J., Lehman P.A., Franz S.F., North-Root H., Demetrulias J.L., Kelling C.K., Moloney S.J., Gettings S.D. Percutaneous penetration of N-nitrosodiethanolamine through human skin (in vitro): comparison of finite and infinite dose applications from cosmetic vehicles. Fundam. Appl. Toxicol. 1993, 21:213-221.
42. Zorin S., Kuylenstierna F., Thulin H. In vitro test of nicotine's permeability through human skin. Risk evaluation and safety aspects. Ann. Occup. Hyg. 1999, 43:405-413.
43. Nielsen J.B., Nielsen F., Sorensen J.A. Defense against dermal exposures is only skin deep: significantly increased penetration through slightly damaged skin. Arch. Dermatol. Res. 2007, 299:423-431.
44. Fasano W.J., Ten Berge W.F., Banton M.I., Heneweer M., Moore N.P. Dermal penetration of propylene glycols: measured absorption across human abdominal skin in vitro and comparison with a QSAR model. Toxicol. In Vitro 2011, 25:1664-1670.
45. Roberts M.S., Anissimov Y.G. Mathematical models in percutaneous absorption. Percutaneous Absorption Drugs - Cosmetics, Mechanisms, Methodology 2005, 1-44. Marcel Dekker, New York. R.L. Bronaugh, H.I. Maibach (Eds.).
46. Parry G.E., Bunge A.L., Silcox G.D., Pershing L.K., Pershing D.W. Percutaneous-absorption of benzoic-acid across human skin.1. In vitro experiments and mathematical-modeling. Pharm. Res. 1990, 7:230-236.
47. Anissimov Y.G., Roberts M.S. Diffusion modeling of percutaneous absorption kinetics: 1. Effects of flow rate, receptor sampling rate and viable epidermal resistance for a constant donor concentration. J. Pharm. Sci. 1999, 88:1201-1209.
48. Anissimov Y.G., Roberts M.S. Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids. J. Pharm. Sci. 2001, 90:504-520.
49. Kasting G.B. Kinetics of finite dose absorption through skin 1. Vanillylnonanamide. J. Pharm. Sci. 2001, 90:202-212.
50. Guy R.H., Hadgraft J. A theoretical description relating skin penetration to the thickness of the applied medicament. Int. J. Pharm. 1980, 6:321-332.
51. Hadgraft J. The epidermal reservoir: a theoretical approach. Int. J. Pharm. 1979, 2:265-274.
52. Hadgraft J. Theoretical aspects of metabolism in the epidermis. Int. J. Pharm. 1980, 4:229-239.
53. Crank J. The Mathematics of Diffusion 1975, Clarendon Press, Oxford. second ed.
54. Pirot F., Kalia Y.N., Stinchcomb A.L., Keating G., Bunge A., Guy R.H. Characterization of the permeability barrier of human skin in vivo. Proc. Natl. Acad. Sci. U. S. A. 1997, 94:1562-1567.
55. Hadgraft J. Calculations of drug release from controlled release devices. The slab. Int. J. Pharm. 1979, 2:177-194.
56. Albery W.J., Hadgraft J. Percutaneous absorption: theoretical description. J. Pharm. Pharmacol. 1979, 31:129-139.
57. Guy R.H., Hadgraft J. Percutaneous metabolism with saturable enzyme-kinetics. Int. J. Pharm. 1982, 11:187-197.
58. Guy R.H., Hadgraft J. Physicochemical interpretation of the pharmacokinetics of percutaneous-absorption. J. Pharmacokinet. Biopharm. 1983, 11:189-203.
59. Scheuplein R.J., Ross L.W. Mechanism of percutaneous absorption. V. Percutaneous absorption of solvent deposited solids. J. Invest. Dermatol. 1974, 62:353-360.
60. Kakemi K., Kameda H., Kakemi M., Ueda M., Koizumi T. Model studies on percutaneous absorption and transport in the ointment. I. Theoretical aspects. Chem. Pharm. Bull. (Tokyo) 1975, 23:2109-2113.
61. Cross S.E., Jiang R., Benson H.A., Roberts M.S. Can increasing the viscosity of formulations be used to reduce the human skin penetration of the sunscreen oxybenzone?. J. Invest. Dermatol. 2001, 117:147-150.
62. Scheuplein R.J., Morgan L.J. "Bound water" in keratin membranes measured by a microbalance technique. Nature 1967, 214:456-458.
63. Roberts M.S., Triggs E.J., Anderson R.A. Permeability of solutes through biological membranes measured by a desorption technique. Nature 1975, 275:225-227.
64. Mueller B., Anissimov Y.G., Roberts M.S. Unexpected clobetasol propionate profile in human stratum corneum after topical application in vitro. Pharm. Res. 2003, 20:1835-1837.
65. Stamatas G.N., Nikolovski J., Mack M.C., Kollias N. Infant skin physiology and development during the first years of life: a review of recent findings based on in vivo studies. Int. J. Cosmet. Sci. 2011, 33:17-24.
66. Komatsu N., Suga Y., Saijoh K., Liu A.C., Khan S., Mizuno Y., Ikeda S., Wu H.K., Jayakumar A., Clayman G.L., Shirasaki F., Takehara K., Diamandis E.P. Elevated human tissue kallikrein levels in the stratum corneum and serum of peeling skin syndrome-type B patients suggests an over-desquamation of corneocytes. J. Invest. Dermatol. 2006, 126:2338-2342.
67. Komatsu N., Tsai B., Sidiropoulos M., Saijoh K., Levesque M.A., Takehara K., Diamandis E.P. Quantification of eight tissue kallikreins in the stratum corneum and sweat. J. Invest. Dermatol. 2006, 126:925-929.
68. Reddy M.B., Guy R.H., Bunge A.L. Does epidermal turnover reduce percutaneous penetration?. Pharm. Res. 2000, 17:1414-1419.
69. Simon L., Goyal A. Dynamics and control of percutaneous drug absorption in the presence of epidermal turnover. J. Pharm. Sci. 2009, 98:187-204.
70. Roberts M.S., Cross S.E., Anissimov Y.G. Factors affecting the formation of a skin reservoir for topically applied solutes. Skin Pharmacol. Appl. Skin Physiol. 2004, 17:3-16.
71. Anderson R.A., Triggs E.J., Roberts M.S. The percutaneous absorption of phenolic compounds 3. Evaluation of permeability through human stratum corneum using a desorption technique. Aust. J. Pharm. Sci. 1976, NS5:107-110.
72. Roberts M.S., Cross S.E., Pellett M.A. Skin transport. Dermatological and transdermal formulations 2002, 89-195. Marcel Dekker, New York. K.A. Walters (Ed.).
73. Frasch H.F., Barbero A.M. Steady-state flux and lag time in the stratum corneum lipid pathway: results from finite element models. J. Pharm. Sci. 2003, 92:2196-2207.
74. Barbero A.M., Frasch H.F. Transcellular route of diffusion through stratum corneum: results from finite element models. J. Pharm. Sci. 2006, 95:2186-2194.
75. Kushner J.T., Deen W., Blankschtein D., Langer R. First-principles, structure-based transdermal transport model to evaluate lipid partition and diffusion coefficients of hydrophobic permeants solely from stratum corneum permeation experiments. J. Pharm. Sci. 2007, 96:3236-3251.
76. Heisig M., Lieckfeldt R., Wittum G., Mazurkevich G., Lee G. Non-steady-state descriptions of drug permeation through stratum-corneum.1. The biphasic brick-and-mortar model. Pharm. Res. 1996, 13:421-426.
77. Naegel A., Hansen S., Neumann D., Lehr C.M., Schaefer U.F., Wittum G., Heisig M. In-silico model of skin penetration based on experimentally determined input parameters. Part II: mathematical modelling of in-vitro diffusion experiments. Identification of critical input parameters. Eur. J. Pharm. Biopharm. 2008, 68:368-379.
78. Chen L., Lian G., Han L. Use of "bricks and mortar" model to predict transdermal permeation: model development and initial validation. Ind. Eng. Chem. Res. 2008, 47:6465-6472.
79. Rim J.E., Pinsky P.M., van Osdol W.W. Using the method of homogenization to calculate the effective diffusivity of the stratum corneum. J. Membr. Sci. 2007, 293:174-182.
80. Rim J.E., Pinsky P.M., van Osdol W.W. Using the method of homogenization to calculate the effective diffusivity of the stratum corneum with permeable corneocytes. J. Biomech. 2008, 41:788-796.
81. Rim J.E., Pinsky P.M., van Osdol W.W. Multiscale modeling framework of transdermal drug delivery. Ann. Biomed. Eng. 2009, 37:1217-1229.
82. Wang T.F., Kasting G.B., Nitsche J.M. A multiphase microscopic diffusion model for stratum corneum permeability. I. Formulation, solution, and illustrative results for representative compounds. J. Pharm. Sci. 2006, 95:620-648.
83. Wang T.F., Kasting G.B., Nitsche J.M. A multiphase microscopic diffusion model for stratum corneum permeability. II. Estimation of physicochemical parameters, and application to a large permeability database. J. Pharm. Sci. 2007, 96:3024-3051.
84. Johnson M.E., Blankschtein D., Langer R. Evaluation of solute permeation through the stratum corneum: lateral bilayer diffusion as the primary transport mechanism. J. Pharm. Sci. 1997, 86:1162-1172.
85. Mitragotri S. Modeling skin permeability to hydrophilic and hydrophobic solutes based on four permeation pathways. J. Control. Release 2003, 86:69-92.
86. Cornwell P.A., Barry B.W. The routes of penetration of ions and 5-fluorouracil across human skin and the mechanisms of action of terpene skin penetration enhancers. Int. J. Pharm. 1993, 94:189-194.
87. 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. 1994, 11:1306-1314.
88. Li S.K., Ghanem A.H., Peck K.D., Higuchi W.I. Iontophoretic transport across a synthetic membrane and human epidermal membrane: a study of the effects of permeant charge. J. Pharm. Sci. 1997, 86:680-689.
89. Lai P.M., Roberts M.S. Epidermal iontophoresis: II. Application of the ionic mobility-pore model to the transport of local anesthetics. Pharm. Res. 1998, 15:1579-1588.
90. Meidan V.M., Bonner M.C., Michniak B.B. Transfollicular drug delivery - is it a reality?. Int. J. Pharm. 2005, 306:1-14.
91. Riegelman S. Pharmacokinetics. Pharmacokinetic factors affecting epidermal penetration and percutaneous adsorption. Clin. Pharmacol. Ther. 1974, 16:873-883.
92. Wallace S.M., Barnett G. Pharmacokinetic analysis of percutaneous absorption: evidence of parallel penetration pathways for methotrexate. J. Pharmacokinet. Biopharm. 1978, 6:315-325.
93. McCarley K.D., Bunge A.L. Physiologically relevant one-compartment pharmacokinetic models for skin. 1. Development of models. J. Pharm. Sci. 1998, 87:470-481.
94. McCarley K.D., Bunge A.L. Physiologically relevant two-compartment pharmacokinetic models for skin. J. Pharm. Sci. 2000, 89:1212-1235.
95. Zatz J. Simulation studies of skin permeation. J. Soc. Cosmet. Chem. 1992, 43:37-48.
96. Anissimov Y.G. Mathematical models for different exposure conditions. Dermal Absorption and Toxicity Assessment 2008, 271-286. Informa Healthcare, New York. M.S. Roberts, K.A. Walters (Eds.).
97. Potts R.O., Guy R.H. Predicting skin permeability. Pharm. Res. 1992, 9:663-669.
98. Sloan K.B., Koch S.A., Siver K.G., Flowers F.P. Use of solubility parameters of drug and vehicle to predict flux through skin. J. Invest. Dermatol. 1986, 87:244-252.
99. Roberts M.S., Pugh W.J., Hadgraft J. Epidermal permeability: penetrant structure relationships.2. The effect of H-bonding groups in penetrants on their diffusion through the stratum corneum. Int. J. Pharm. 1996, 132:23-32.
100. Cleek R.L., Bunge A.L. A new method for estimating dermal absorption from chemical exposure.1. General approach. Pharm. Res. 1993, 10:497-506.
101. Seko N., Bando H., Lim C.W., Yamashita F., Hashida M. Theoretical analysis of the effect of cutaneous metabolism on skin permeation of parabens based on a two-layer skin diffusion/metabolism model. Biol. Pharm. Bull. 1999, 22:281-287.
102. Ando H.Y., Ho N.F.H., Higuchi W.I. Skin as an active metabolizing barrier. 1. Theoretical analysis of topical bioavailability. J. Pharm. Sci. 1977, 66:1525-1528.
103. Fox J.L., Yu C.D., Higuchi W.I., Ho N.F.H. General physical model for simultaneous diffusion and metabolism in biological-membranes - computational approach for the steady-state case. Int. J. Pharm. 1979, 2:41-57.
104. Boderke P., Schittkowski K., Wolf M., Merkle H.P. Modeling of diffusion and concurrent metabolism in cutaneous tissue. J. Theor. Biol. 2000, 204:393-407.
105. Jakubovic H.R., Ackermann A.B. Structure and function of skin: development, morphology, and physiology. Dermatology 1992, W.B. Saunders Company, Philadelphia. S.L. Moschella, H.J. Hurley (Eds.).
106. Braverman I.M. The cutaneous microcirculation. J. Investig. Dermatol. Symp. Proc. 2000, 5:3-9.
107. Braverman I.M., Keh A., Goldminz D. Correlation of laser Doppler wave patterns with underlying microvascular anatomy. J. Invest. Dermatol. 1990, 95:283-286.
108. Cevc G., Vierl U. Spatial distribution of cutaneous microvasculature and local drug clearance after drug application on the skin. J. Control. Release 2007, 118:18-26.
109. O'Driscoll C.M. Anatomy and physiology of the lymphatics. Lymphatics Transport of Drugs 1992, CRC Press, Boca Raton. W.N. Charman, V.J. Stella (Eds.).
110. Schaefer H., Stuttgen G. Absolute concentrations of an antimycotic agent, econazole, in the human skin after local application. Arzneimittelforschung 1976, 26:432-435.
111. Schaefer H., Zesch A. Penetration of vitamin A acid into human skin. Acta Derm. Venereol. Suppl. (Stockh) 1975, 74:50-55.
112. Schaefer H., Zesch A., Stuttgen G. Penetration, permeation, and absorption of triamcinolone acetonide in normal and psoriatic skin. Arch. Dermatol. Res. 1977, 258:241-249.
113. Schaefer H., Stuttgen G., Zesch A., Schalla W., Gazith J. Quantitative determination of percutaneous absorption of radiolabeled drugs in vitro and in vivo by human skin. Curr. Probl. Dermatol. 1978, 7:80-94.
114. Zesch A., Schaefer H. Penetration of radioactive hydrocortisone in human skin from various ointment bases. II. In vivo-experiments (author's transl). Arch. Dermatol. Forsch. 1975, 252:245-256.
115. Singh P., Roberts M.S. Blood-flow measurements in skin and underlying tissues by microsphere method - application to dermal pharmacokinetics of polar nonelectrolytes. J. Pharm. Sci. 1993, 82:873-879.
116. Singh P., Roberts M.S. Effects of vasoconstriction on dermal pharmacokinetics and local tissue distribution of compounds. J. Pharm. Sci. 1994, 83:783-791.
117. Singh P., Maibach H.I., Roberts M.S. Site of effects. Dermal Absorption And Toxicity Assessment 1998, 91:353-370.
118. Gupta E., Wientjes M.G., Au J.L. Penetration kinetics of 2?,3?-dideoxyinosine in dermis is described by the distributed model. Pharm. Res. 1995, 12:108-112.
119. Cross S.E., Roberts M.S. Defining a model to predict the distribution of topically applied growth factors and other solutes in excisional full-thickness wounds. J. Invest. Dermatol. 1999, 112:36-41.
120. Kretsos K., Kasting G.B., Nitsche J.M. Distributed diffusion-clearance model for transient drug distribution within the skin. J. Pharm. Sci. 2004, 93:2820.
121. Singh P., Roberts M.S. Iontophoretic transdermal delivery of salicylic acid and lidocaine to local subcutaneous structures. J. Pharm. Sci. 1993, 82:127-131.
122. Dedrick R.L., Flessner M.F., Collins J.M., Schultz J.S. Is the peritoneum a membrane?. ASAIO J. 1982, 1-8.
123. Kretsos K., Miller M.A., Zamora-Estrada G., Kasting G.B. Partitioning, diffusivity and clearance of skin permeants in mammalian dermis. Int. J. Pharm. 2008, 346:64-79.
124. Kretsos K., Kasting G.B. A geometrical model of dermal capillary clearance. Math. Biosci. 2007, 208:430-453.
125. Kasting G., Smith R., Cooper E. Effect of lipid solubility and molecular size on percutaneous absorption. Pharmacology and the Skin 1987, 138-153. Karger, Basel. B. Shroot, H. Schaefer (Eds.).
126. Flynn G.L. Physicochemical determinants of skin absorption. Principles of Route to Route Extrapolation for Risk Assessment 1990, 93-127. Elsevier, New York. T.R. Gerrit, C.I. Henry (Eds.).
127. Sloan K.B., Wasdo S.C., Rautio J. Design for optimized topical delivery: prodrugs and a paradigm change. Pharm. Res. 2006, 23:2729-2747.
128. Yalkowsky S.H., Valvani S.C., Roseman T.J. Solubility and partitioning VI: octanol solubility and octanol-water partition coefficients. J. Pharm. Sci. 1983, 72:866-870.
129. Zhang Q., Li P., Roberts M.S. Maximum transepidermal flux for similar size phenolic compounds is enhanced by solvent uptake into the skin. J. Control. Release 2011, 154:50-57.
130. Fitzpatrick D., Golden D., Corish J. Modeling skin permeability in risk assessment. Dermal Absorption and Toxicity Assessment 2008, 287-297. Informa Healthcare, New York. M.S. Roberts, K.A. Walters (Eds.).
131. Blank I.H. Penetration of low-molecular-weight alcohols into skin. I. Effect of concentration of alcohol and type of vehicle. J. Invest. Dermatol. 1964, 43:415-420.