Numerical simulation of a glucose sensitive composite membrane closed-loop insulin delivery system
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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.
KeywordsEnzymatic 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.
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Conflict of interest
The authors have no competing interests.
- 5.Wu X, Zhang Q, Arshady R (2003) Stimuli sensitive hydrogels. Polymer structure and phase transition. Polymeric biomaterials Citus Books, London, pp 157–194Google Scholar
- 6.Wu X, Zhang Q, Arshady R (2003) Stimuli sensitive hydrogels. Response and release modulation. Polymeric biomaterials. Citus Books, London, pp 195–231Google Scholar
- 29.Malik M, Bert C, Kukreti A (1970) Differential quadrature solution of uniformly loaded circular plate resting on elastic half-space. WIT Trans Eng Sci 1:385–396Google Scholar
- 30.Chen W (1996) Differential quadrature method and its applications in engineering. Department of Mechanical Engineering, Shanghai Jiao Tong University, ShanghaiGoogle Scholar
- 31.Joy RA, Rajendran L (2012) Mathematical modelling and transient analytical solution of a glucose sensitive composite membrane for closed-loop insulin delivery using he’s variational iteration method. Int Rev Chem Eng 4:516–523Google Scholar