Travelling wave solutions of a nonlinear model for drug release: analytical solution in comparison to numerical approximation

  • Authors:

  • Chontita Rattanakul;Yongwimon Lenbury

  • Affiliations:

  • Department of Mathematics, Faculty of Science, Mahidol University, Bangkok, Thailand and Centre of Excellence in Mathematics, Bangkok, Thailand;Department of Mathematics, Faculty of Science, Mahidol University, Bangkok, Thailand and Centre of Excellence in Mathematics, Bangkok, Thailand

  • Venue:
  • ACACOS'12 Proceedings of the 11th WSEAS international conference on Applied Computer and Applied Computational Science
  • Year:
  • 2012

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Abstract

We study a theoretical model of drug release from planar matrix. A mathematical model of the drug dissolution and release processes was formulated and investigated numerically in terms of two coupled nonlinear partial differential equations by Göran Frenning (2003). Disregarding drug adsorption, assuming concentration-independent diffusion coefficients, using perfect sink conditions, and specializing to a planar geometry, The concentration profile of the mobile, or diffusing, the resulting model is rather complex and has been investigated only numerically and only approximate solution have been possible. In this paper it is shown that an analytical solution can be obtained exactly in the form of a travelling wave front. We describe the method for finding the analytical solutions using the travelling wave coordinate when the wave is assumed to be moving at constant speed. We then discuss a comparison between the exact solutions obtained here and the "analytical short-time approximation" as well as the numerical solution obtained from the modified Higuchi formula reported by Frenning (2003).