Drug release from viscoelastic polymeric matrices - a stable and supraconvergent FDM

Drug release from viscoelastic polymeric matrices is a complex phenomenon where the main actors are the fluid, the polymeric structure and the drug. As the fluid enters into the polymer, the polymeric chains relax inducing a resistance to the fluid entrance. In contact with the fluid, a dissolution processes takes place and the dissolved drug diffuses through the medium. Our main goal in this paper is to propose a stable finite difference method that leads to a supraconvergent approximations for the fluid, solid and dissolved drug concentrations. The analysis proposed is non-standard in the sense that the error estimates have an important role in the stability analysis.

[1]  Andrew B. White,et al.  Sharp fronts due to diffusion and viscoelastic relaxation in polymers , 1991 .

[2]  Lawrence F. Shampine,et al.  The MATLAB ODE Suite , 1997, SIAM J. Sci. Comput..

[3]  Mario Grassi,et al.  Mathematical modelling and controlled drug delivery: matrix systems. , 2005, Current drug delivery.

[4]  Byung Kook Lee,et al.  Controlled Drug Delivery: Historical perspective for the next generation. , 2015, Journal of controlled release : official journal of the Controlled Release Society.

[5]  Luís Pinto,et al.  Non-Fickian convection–diffusion models in porous media , 2018, Numerische Mathematik.

[6]  David A. Edwards,et al.  An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems , 1995, SIAM J. Appl. Math..

[7]  S. Agarwal,et al.  Oral Sustained Release Tablets: An Overview with a special emphasis on Matrix Tablet , 2017 .

[8]  Luís Pinto,et al.  Supraconvergence and supercloseness in quasilinear coupled problems , 2013, J. Comput. Appl. Math..

[9]  H. Fujita.  Diffusion in polymer-diluent systems , 1961 .

[10]  L. Brinson,et al.  Polymer Engineering Science and Viscoelasticity: An Introduction , 2007 .

[11]  Donald S. Cohen,et al.  A mathematical model for a dissolving polymer , 1995 .

[12]  Mario Grassi,et al.  A 3D Model for Mechanistic Control of Drug Release , 2014, SIAM J. Appl. Math..

[13]  David A. Edwards,et al.  Non‐fickian diffusion in thin polymer films , 1996 .

[14]  C. M. Oishi,et al.  Modeling of non‐Fickian diffusion and dissolution from a thin polymeric coating: An application to drug‐eluting stents , 2018 .

[15]  T. Rabczuk,et al.  The effect of plaque eccentricity on blood hemodynamics and drug release in a stented artery. , 2018, Medical engineering & physics.

[16]  J. A. Ferreira,et al.  A NEW LOOK TO NON-FICKIAN DIFFUSION , 2015 .

[17]  J. Dormand,et al.  A family of embedded Runge-Kutta formulae , 1980 .

[18]  Daniel De Kee,et al.  Mass transport through swelling membranes , 2005 .

[19]  J. M. Sanz-Serna,et al.  Nonlinear stability and convergence of finite-difference methods for the “good” Boussinesq equation , 1990 .

[20]  Gorjan Alagic,et al.  #p , 2019, Quantum information & computation.

[21]  Giulio C. Sarti,et al.  Mass transport with relaxation in polymers , 1990 .