Insight into Control Architecture of Skin Pathology and Skin Penetration by Mathematical Modeling: an Introduction for Non-mathematicians


  • Sutapa Biswas Majee NSHM College of Pharmaceutical Technology NSHM Knowledge Campus, Kolkata-Group of Institutions 124 B L Saha Road, Kolkata 700053, West Bengal, India
  • Gopa Roy Biswas


Mathematical modeling, Atopic dermatitis, psoriasis, , transdermal drug delivery


Mathematical modeling involves construction of a set of equations or description of a stochastic process closely mimicking a real phenomenon of practical significance and biological or physiological relevance. This paper reviews some specific pathological conditions of the skin and permeation of drugs across the skin during topical administration and transdermal route of delivery in the light of mathematical modeling. It aims at providing an insight into different variables governing any pathological situation of the skin involving a complex architecture of chemical mediators. The factors controlling skin permeability of a drug molecule have also been studied. The final outcome of the paper is to equip non-mathematicians with simple mathematical tools to conduct real experiments in a more satisfactory manner and explain the physiological phenomena in a robust fashion.

Author Biography

Sutapa Biswas Majee, NSHM College of Pharmaceutical Technology NSHM Knowledge Campus, Kolkata-Group of Institutions 124 B L Saha Road, Kolkata 700053, West Bengal, India

Division of Pharmaceutics

Associate Professor


D. Kirschner, V. DiRita, and J. A. Flynn, “Overcoming math anxiety: Malthus meets Koch,†ASM News vol. 71, pp. 357-362, 2005.

H. Squires, and P. Tappenden,“Mathematical modeling and its application to social care,†Meth. Rev. vol. 7, pp. 1-22, 2011.

N. V. Valeyev, C. Hundhausen, Y. Umezawa, N. V. Kotov, G. Williams, A. Clop, C. Ainali, C. Ouzounis, S. Tsoka, and F. O. Nestle,“A systems model for immune cell interactions unravels the mechanism of inflammation in human skin,†PLoS Comput. Biol., vol. 6, no. 12, e1001024, 2010.

R. J. Tanaka, and M. Ono,“Skin disease modeling from a mathematical perspective,†J. Invest. Dermatol. vol. 133, pp. 1472–1478, 2013.

L. Erikson, A. Wise, S. Fleming, M. Baird, and Z. Lateef, “A preliminary mathematical model of skin dendritic cell trafficking and induction of T cell immunity,†Discr. Cont. Dyn. Syst., Series B, vol. 12, no. 2, pp. 323-336, 2009.

K. H. Hänel, C. Cornelissen, B. Lüscher, and J. M. Baron,“Cytokines and the skin barrier,†Int. J. Mol. Sci. vol. 14, pp. 6720-6745, 2013.

E. Domı´nguez-Hu¨ttinger, M. Ono, M. Barahona, and R. Tanaka,“Risk factor-dependent dynamics of atopic dermatitis: modelling multi-scale regulation of epithelium homeostasis,†Interface Focus, vol. 3, 20120090, 2013.

R. J. Tanaka, M. Ono, and H. A. Harrington,“Skin barrier homeostasis in atopic dermatitis: feedback regulation of kallikrein activity,†PLoSONE, vol. 6, no. 5, e19895, 2011.

J. Witt, S. Barisic, E. Schumann, F. Allgo¨wer, O. Sawodny, T. Sauter, and D. Kulms, “Mechanism of PP2Amediated IKK beta dephosphorylation: a systems biological approach,†BMC Syst. Biol., vol. 3, 71, 2009.

E. A. O’Toole,“Molecular biology,†in Rook’sTextbook of Dermatology, T. Burns, S. Breathnach, N. Cox, et al. Eds. UK: Wiley-Blackwell, Oxford, 2010 , pp. 1–22.

T. Sumi, S. Nukaya, T. Kaburagi, H. Tanaka, K. Watanabe, and Y. Kurihara, “Development of scratching monitoring system based on mathematical model of unconstrained bed sensing method,†Int. J. Med., Health, Pharm. Biomed. Engg., vol. 7, no. 12, pp. 554-561, 2013.

R. O. Bak, and J. G. Mikkelsen,“Regulation of cytokines by small RNAs during skin inflammation,†J. Biomed. Sci., vol. 17, pp. 53, 2010.

H. Blumberg, H. Dinh, C. Dean, Jr., E. S. Trueblood, K. Bailey, D. Shows, N. Bhagavathula, M. N. Aslam, J. Varani, J. E. Towne, and J. E. Sims, “IL-1RL2 and its ligands contribute to the cytokine network in psoriasis,†J. Immunol., vol. 185, pp. 4354–4362, 2010.

W. R. Swindell, X. Xing, P. E. Stuart, C. S. Chen, and A. Aphale et al.,“Heterogeneity of inflammatory and cytokine networks in chronic plaque psoriasis,â€. PLoS ONE, vol. 7, no. 3, e34594, 2012.

P. K. Roy, and A. Datta,“Negative feedback control may regulate cytokines effect during growth of keratinocytes in the chronic plaque of psoriasis: a mathematical study,†Int. J. Appl. Math, vol. 25, no. 2, pp. 233-254, 2012.

B. Chattopadhyay, and N. Hui, “Immunopathogenesis in psoriasis through a density-type mathematical model,â€WSEAS Trans. Math. vol. 11, no. 5, pp. 440-450, 2012.

B. L. Diffey, “Towards optimal regimens for the UV-B phototherapy of psoriasis: A mathematical model,†Acta Derm. Venereol. vol. 84, pp. 259–264, 2004.

S. Gilmore, and K. A. Landman,“Is the skin an excitable medium? Pattern formation wound healing disorders,†J. Theor. Med., vol. 6, no. 1, pp.57-65, 2005.

W. M. Boon, “Mathematical modeling of wound healing and subsequent scarring,†(unpublished Master’s degree thesis). Delft University of Technology, 2013. Available :

L. Olsen, J. A. Sherratt, P. K. Maini, “A mathematical model for fibro-proliferative wound healing disorders,†Bull. Math. Biol., vol. 58, no. 4, pp. 787-808, 1996.

N. Lemo, G. Marignac, E. Reyes-Gomes, T. Lilin, O. Crosaz, and D. H. Dohan Ehrenfast, “Cutaneous re-epithelialisation and wound contraction after skin biopsies in rabbits: a mathematical model for healing and remodeling index,†Vet. Archiv. vol. 80, no. 5, pp.637-652, 2010.

K. Murphy,“Mathematical investigation of the interactions between the inflammatory response and mechanical aspects of dermal wound repair,†(unpublished doctoral dissertation). Queensland University of Technology, Australia, 2011.

M. M. Stolnitz, A. Y. Peshkova, A. N. Bashkatov, E. A. Genina,“Mathematical modeling of changes in the optical properties of epidermis due to UV-induced melanogenesis,†in Controlling Tissue Optical Properties: Applications in Clinical Study, V. V. Tuchin, (Ed.), Proceedings of SPIE 4162, pp. 194-201, 2000.

S. Kang, “Mathematical modeling of collagenase-1 induction Technology #4053 Inventors TECHtransfer ,†University of Michigan.

H. Todo, T. Oshizaka, W. R. Kadhum, and K. Sugibayashi,“Mathematical model to predict skin concentration after topical application of drugs,†Pharmaceutics, vol. 5, pp. 634-651, 2013.

S. Huth, L. Boltze, and R. Neubert,“Mathematical assessment of different penetration mechanisms from vehicles with propylene glycol,†J. Contr. Rel. vol. 49, pp. 141–148, 1997.

N. Coceani, I. Colombo, M. Grassi, “Acyclovir permeation through rat skin: mathematical modelling and in vitro experiments,†Int. J. Pharm., vol. 254, pp.197–210, 2003.

B. Al-Qallaf, D. B. Das, D. Mori, and Z. Cui, “Modelling transdermal delivery of high molecular weight drugs from microneedle systems,†Phil. Trans. R. Soc. A, vol. 365, pp. 2951-2957, 2007.

S. Mitragotri, Y. G. Anissimov, A. L. Bunge, H. F. Frasch, R. H. Guy, J. Hadgraft, G. B. Kasting, M. E. Lane, and M. S. Roberts,“Mathematical models of skin permeability: An overview,â€Int. J. Pharm., vol. 418, no. 1, pp. 115-129, 2011.

V. Gupta, S. S. Pagey, and V. P. Saxena,“Numerical analysis of drug diffusion in human dermal region with linear shape function,†IOSR J. Math. vol. 4, no. 2, pp. 31-36, 2012.

A. L. Weltner,“Mathematical modeling of transient state transdermal drug delivery,†(unpublished Master’s degree thesis). Department of Chemical Engineering, Faculty of New Jersey Institute of Technology, 2004.




How to Cite

Biswas Majee, S., & Biswas, G. R. (2015). Insight into Control Architecture of Skin Pathology and Skin Penetration by Mathematical Modeling: an Introduction for Non-mathematicians. Asian Journal of Applied Sciences, 3(1). Retrieved from