The Journal of Membrane Biology

, Volume 246, Issue 2, pp 121–129 | Cite as

Analytical Expressions for the Steady-State Concentrations of Glucose, Oxygen and Gluconic Acid in a Composite Membrane for Closed-Loop Insulin Delivery



The mathematical model of Abdekhodaie and Wu (J Membr Sci 335:21–31, 2009) of glucose-responsive composite membranes for closed-loop insulin delivery is discussed. The glucose composite membrane contains nanoparticles of an anionic polymer, glucose oxidase and catalase embedded in a hydrophobic polymer. The model involves the system of nonlinear steady-state reaction–diffusion equations. Analytical expressions for the concentration of glucose, oxygen and gluconic acid are derived from these equations using the Adomian decomposition method. A comparison of the analytical approximation and numerical simulation is also presented. An agreement between analytical expressions and numerical results is observed.


Glucose-sensitive membrane Insulin delivery Enzymatic reaction Reaction–diffusion equation Adomian decomposition method 



A part of this study was performed during the visit of Dr. L. Rajendran at the Institute of Physical Chemistry of the Polish Academy of Sciences in November 2011, sponsored by the Polish Academy of Sciences and the Indian National Science Academy.

Supplementary material

232_2012_9510_MOESM1_ESM.doc (32 kb)
Supplementary material 1 (DOC 31 kb)


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of MathematicsThe Madura CollegeMaduraiIndia
  2. 2.Department of Complex Systems and Chemical Processing of InformationInstitute of Physical Chemistry of the Polish Academy of SciencesKracówPoland

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