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Plenary Lecture

Analytical Solutions in Travelling Wave Coordinate of Controlled Drug Release on Planar Structure

Professor Yongwimon Lenbury
co-author: Pailin Chayapham
Department of Mathematics
Faculty of Science
Mahidol University
Bangkok, Thailand
E-mail: scylb@yahoo.com

Abstract: Mathematical modeling and computation play an important role in the design of pharmaceutical products. The United States Food and Drug Administration Critical Path Initiative has recently identified model-based drug development, including drug and disease modeling, as an important goal (www.fda.gov/oc/initiatives/criticalpath). New discoveries and theories generated by model construction have been appearing in many prominent biologically related journals. In the formulation of pharmaceutical products, the use of controlled-release technology is becoming increasingly important. In 2003, Göran Frenning formulated and numerically investigated a mathematical model of the drug dissolution and release processes. The model can be expressed in terms of two coupled nonlinear partial differential equations. Later, Chontita and Lenbury (2012) explained how analytical solutions can be found for a system of reaction diffusion equations in the form of a travelling wave front using the travelling wave coordinate when the wave is assumed to be moving at constant speed. Here, we present certain travelling wave solutions of the model of controlled drug released, in a planar geometry, for different cases in which analytical solutions can be derived exactly.

Brief Biography of the Speaker: After Professor Yongwimon Lenbury obtained her Ph.D. in Mathematics from Vanderbilt University, USA, she returned to the Department of Mathematics, Faculty of Science, Mahidol University to teach, and conduct research in dynamical modeling of nonlinear systems in biology and medicine. She was appointed professor of Mathematics in 1996. Prof. Lenbury has been involved in research work in the field by Mathematical Modelling and Nonlinear Systems in Biology and Medicine. Her work involves dynamical modelling and analysis of nonlinear systems such as food chains coupled by parasitic infections, hormone secretion systems in the human body, and so on. Of particular interest are the pacemaker oscillations and rhythmogenesis in human mechanism which have been proposed as a way to differentiate sickness from health. For example, some of her works involves the construction and analysis of a model for insulin kinetics and the identification of oscillatory behavior subject to various feeding regimens. Her recent interest has been concentrated in the signal transduction system involving GPCR, a major drug target. She received an award from the National Research Council as the Outstanding Researcher in the field of Physical Science in the year 1998. Her continued achievements have resulted in her being granted the prestigious position of Senior Researcher of the Thailand Research Fund in Mathematics, 2000-2002 and a Fellow of the Royal Institute of Thailand. Collaborating with several researchers in various countries such as the United States, Germany, Italy, and New Zealand, Prof. Lenbury has been devoted to the promotion of research and education in the field of Mathematics in Thailand.

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