Bioprocess and Biosystems Engineering

, Volume 40, Issue 10, pp 1453–1462 | Cite as

Numerical simulation of a glucose sensitive composite membrane closed-loop insulin delivery system

  • Shashi Bajaj Mukherjee
  • Debabrata Datta
  • Soumyendu Raha
  • Debnath PalEmail author
Research Paper


Closed-loop insulin delivery system works on pH modulation by gluconic acid production from glucose, which in turn allows regulation of insulin release across membrane. Typically, the concentration variation of gluconic acid can be numerically modeled by a set of non-linear, non-steady state reaction diffusion equations. Here, we report a simpler numerical approach to time and position dependent diffusivity of species using finite difference and differential quadrature (DQ) method. The results are comparable to that obtained by analytical method. The membrane thickness directly determines the concentrations of the glucose and oxygen in the system, and inversely to the gluconic acid. The advantage with the DQ method is that its parameter values need not be altered throughout the analysis to obtain the concentration profiles of the glucose, oxygen and gluconic acid. Our work would be useful for modeling diabetes and other systems governed by such non-linear and non-steady state reaction diffusion equations.


Enzymatic reaction Boundary value problem Glucose sensitive composite membrane Differential quadrature method Finite difference method 



The work is supported by a research Grant the Science and Engineering Board, Department of Science and Technology (DST) under the DST Centre for Mathematical Biology.

Compliance with ethical standards

Conflict of interest

The authors have no competing interests.

Supplementary material

449_2017_1803_MOESM1_ESM.doc (51 kb)
Supplementary material 1 (DOC 51 kb)


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Computational and Data SciencesIndian Institute of ScienceBangaloreIndia
  2. 2.Radiological Physics and Advisory DivisionBhabha Atomic Research CentreMumbaiIndia

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