The Mathematical Model for Drug Delivery Through Skin


  • Nourelhoda Medhat Mahmoud Biomedical Engineering Department Faculty of Engineering Minia University Minia, Egypt
  • Ziad Tarek Alshafee Biomedical Engineering Department Faculty of Engineering Minia University Minia, Egypt



Biomedical Applications, Medications, Mathematical model, Skin


Delivery of the medications is one of the important biomedical applications. It has significant importance for patients. There are a lot of methods for delivery of drugs such as oral, topical, sublingual, inhalation, and nasal and injection routes. Patients are suffering from needles every time they want to take their medications. The oral route is suitable and has the lowest cost, but some drugs can cause gastrointestinal tract irritation and has low bioavailability. Delivery of the medications through skin is the most suitable for patient because it is needleless without any pain for patients. Some medications have large size. Mathematical model for transportation of large molecules of medications and drugs through the skin is described. This model provides a significant reduction of medical complications and improvement in patient compliance. One of the most important parameter is the optimization of the response time of this model. The model shows good stability and response.

Author Biographies

Nourelhoda Medhat Mahmoud, Biomedical Engineering Department Faculty of Engineering Minia University Minia, Egypt

Assistant Professor

Biomedical Engineering Department
Faculty of Engineering
Minia University
Minia, Egypt

Ziad Tarek Alshafee, Biomedical Engineering Department Faculty of Engineering Minia University Minia, Egypt

Undergraduate Student

Biomedical Engineering Department
Faculty of Engineering
Minia University
Minia, Egypt


(1) Torin, J.; Sivaloganathan, S.; Kohandel M.; Marianna, F., Drug delivery through the skin: molecular simulations of barrier lipids to design more effective noninvasive dermal and transdermal delivery systems for small molecules, biologics, and cosmetics. John Wiley & Sons, Inc. WIREs Nanomedicine and Nanobiotechnology, 2011. 3: p. 449-462.

(2) Ahlam, Z.; Maelíosa, T.; Ryan, F., Transdermal Drug Delivery: Innovative Pharmaceutical Developments Based on Disruption of the Barrier Properties of the stratum corneum. Pharmaceutics, 2015. 7: p. 438-470.

(3) Marc, B.; Gary, P.; Stuart, A.; Franklin, K., Dermal and Transdermal Drug Delivery Systems: Current and Future Prospects. Drug Delivery, 2006. 13: p. 175-187.

(4) Adam, C.; Heather, A., Transdermal and Topical Drug Delivery Principles and Practice.ed 2012, John Wiley & Sons, Inc.

(5) Arora, A.; Prausnitz, M.; Mitragotri, S., Micro-Scale Devices for Transdermal Drug Delivery. International Journal of Pharmaceutics, 2008. 364: p. 227-236.

(6) Donnelly, R.; Singh, T.; Garland, M.; Migalska, K.; Majithiya, R.; McCrudden, C.; Kole, P.; Mahmood, T.; McCarthy, H; Woolfson, A., Hydrogel - Forming Microneedle Arrays for Enhanced Transdermal Drug Delivery. Adv. Funct. Mater, 2012. 22: p. 4879-4890.

(7) Torrisi, B.; Tuan, T.; McCrudden, M.; McAlister, E.; Garland, M.; Singh, T.; Donnelly, R., Microneedles for Intradermal and Transdermal Drug Delivery. European Journal of Pharmaceutical Sciences, 2013. 50: p. 623-637.

(8) Anselmo, A.; Mitragotri, S., An Overview of Clinical and Commercial Impact of Drug Delivery Systems. J. Control. Release, 2014. 190: p. 15-28.

(9) Brambilla, D.; Luciani, P.; Leroux, J., Breakthrough Discoveries in Drug Delivery Technologies: The Next 30 years. J. Control. Release, 2014. 190: p. 9-14.

(10) Charman, S.; McLennan, D.; Porter, C, Subcutaneous Drug Delivery and the Role of the Lymphatics. Drug Discov. Today Technol., 2005. 2: p. 89-96.

(11) Park, E.; Dodds, J.; Smith, N., Dose comparison of ultrasonic transdermal insulin delivery to subcutaneous insulin injection. Int J Nanomedicine, 2008. 3: p. 335-341.

(12) Schoellhammer, C.; Blankschtein, D.; Langer, R., Skin Permeabilization for Transdermal Drug Delivery: Recent Advances and Future Prospects. Expert Opin. Drug Deliv., 2014. 11: p. 393-407.

(13) Pillai, O.; Nair, V.; Panchagnula, R., Transdermal Iontophoresis of Insulin: IV. Influence of Chemical Enhancers. Int. J. Pharm., 2004. 269: p. 109-120.

(14) Ajay, K.; Kalluri, H., Transdermal Delivery of Proteins. American Association of Pharmaceutical Scientists, PharmSciTech, 2011. 12: p. 431- 441.

(15) Yunus, A.; John, M., Fluid Mechanics: Fundamentals and Applications. ed 2006, McGraw-Hill.

(16) Prausnitz, M.; Langer, R., Transdermal drug delivery. Nature Biotechnology, 2008. 26: p. 1261-1268.

(17) Schumm, P.; Scoglio, C.; VanderMerwe, D., A network model of successive partitioning-limited solute diffusion through the stratum corneum. Journal of Theoretical Biology, 2010. 262: p. 471-477.

(18) Barry, B.; Harrison, S.; Dugard, P., Vapour and liquid diffusion of model penetrants through human skin; correlation with thermodynamic activity. J Pharm Pharmacol, 1985. 37: p. 226-236.

(19) Kalluri, H.; Banga, A., Microneedles and transdermal drug delivery. Journal of Drug Delivery Science and Technology, 2009. 19: p. 303-310.

(20) Devraj, D.; Mohd, A., A Review: Different Generation Approaches of

Transdermal drug delivery System. J.Chem. Pharm. Res., 2010. 2: p. 184-193.

(21) Shinkai, N.; Korenaga, K.; Takizawa, H., Percutaneous penetration of felbinac after application of transdermal patches: Relationship with pharmacological effects in rats. J Pharm Pharmacol, 2008. 60: p. 71-76.

(22) Rje, H.; Jenny, N.; William, M., Properties of the Glomerular Barrier and Mechanisms of Proteinuria. Physiol Rev, 2008. 88: p. 451-487.

(23) Martin, G.; Moss, M.; Wheeler, A.; Mealer, M.; Morris, J.; Bernard, G., A randomized, controlled trial of furosemide with or without albumin in hypoproteinemic patients with acute lung injury. Critical Care Medicine, 2005. 33: p. 1681-1687.

(24) Martin, R.; Susan, E.; Melanie, P.; and Lance, D., The Glomerulus: The Sphere of Influence. Clinical Journal of the American Society of Nephrology, 2014. 9: p. 1461-1469.




How to Cite

Mahmoud, N. M., & Alshafee, Z. T. (2018). The Mathematical Model for Drug Delivery Through Skin. Journal of Biomedical Engineering and Medical Imaging, 5(2), 01.