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A Nonlinear Mathematical Model of Drug Delivery from Polymeric Matrix

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, 781039, India

    Koyel Chakravarty & D. C. Dalal

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  1. Koyel Chakravarty
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  2. D. C. Dalal
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Correspondence to Koyel Chakravarty.

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Chakravarty, K., Dalal, D.C. A Nonlinear Mathematical Model of Drug Delivery from Polymeric Matrix. Bull Math Biol 81, 105–130 (2019). https://doi.org/10.1007/s11538-018-0519-y

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