Bulletin of Mathematical Biology

, Volume 81, Issue 1, pp 105–130 | Cite as

A Nonlinear Mathematical Model of Drug Delivery from Polymeric Matrix

  • Koyel ChakravartyEmail author
  • D. C. Dalal
Original Article


The objective of the present study is to mathematically model the integrated kinetics of drug release in a polymeric matrix and its ensuing drug transport to the encompassing biological tissue. The model embodies drug diffusion, dissolution, solubilization, polymer degradation and dissociation/recrystallization phenomena in the polymeric matrix accompanied by diffusion, advection, reaction, internalization and specific/nonspecific binding in the biological tissue. The model is formulated through a system of nonlinear partial differential equations which are solved numerically in association with pertinent set of initial, interface and boundary conditions using suitable finite difference scheme. After spatial discretization, the system of nonlinear partial differential equations is reduced to a system of nonlinear ordinary differential equations which is subsequently solved by the fourth-order Runge–Kutta method. The model simulations deal with the comparison between a drug delivery from a biodegradable polymeric matrix and that from a biodurable polymeric matrix. Furthermore, simulated results are compared with corresponding existing experimental data to manifest the efficaciousness of the advocated model. A quantitative analysis is performed through numerical computation relied on model parameter values. The numerical results obtained reveal an estimate of the effects of biodegradable and biodurable polymeric matrices on drug release rates. Furthermore, through graphical representations, the sensitized impact of the model parameters on the drug kinetics is illustrated so as to assess the model parameters of significance.


Local drug delivery Polymer degradation Biodurable Specific/nonspecific drug binding Internalization 



Authors are extremely grateful to all the anonymous reviewers for their fruitful comments and suggestions towards improvement of the present article.


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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology GuwahatiGuwahatiIndia

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