title: Part-2: Analytical Expressions of Concentrations of Glucose, Oxygen, and Gluconic Acid in a Composite Membrane for Closed-Loop Insulin Delivery for the Non-steady State Conditions.
abstract: A mathematical model developed by Abdekhodaie and Wu (J Membr Sci 335:21-31, 2009), which describes a dynamic process involving an enzymatic reaction and diffusion of reactants and product inside glucose-sensitive composite membrane has been discussed. This theoretical model depicts a system of non-linear non-steady state reaction diffusion equations. These equations have been solved using new approach of homotopy perturbation method and analytical solutions pertaining to the concentrations of glucose, oxygen, and gluconic acid are derived. These analytical results are compared with the numerical results, and limiting case results for steady state conditions and a good agreement is observed. The influence of various kinetic parameters involved in the model has been presented graphically. Theoretical evaluation of the kinetic parameters like the maximal reaction velocity (Vmax) and Michaelis-Menten constants for glucose and oxygen (Kgand Kox) is also reported. This predicted model is very much useful for designing the glucose-responsive composite membranes for closed-loop insulin delivery.
authors.affiliation: Department of Mathematics, Kamaraj College of Engineering & Technology, Virudhunagar, Tamil Nadu, 626 001, India.
authors.forename: N
authors.initials: N
authors.lastname: Mehala
authors.affiliation: Department of Mathematics, Kamaraj College of Engineering & Technology, Virudhunagar, Tamil Nadu, 626 001, India. raj_sms@rediffmail.com.|Department of Mathematics, Sethu Institute Technology, Kariapatti, Pulloor, Tamilnadu, 626 115, India. raj_sms@rediffmail.com.
authors.forename: L
authors.initials: L
authors.lastname: Rajendran
authors.affiliation: Department of Mathematics, Mangayarkarasi College of Engineering, Madurai, Tamilnadu, 625 402, India.
authors.forename: V
authors.initials: V
authors.lastname: Meena
mesh_terms: D000465:Algorithms; D004058:Diffusion; D005942:Gluconates / Q000737:chemistry* / Q000378:metabolism; D005947:Glucose / Q000737:chemistry* / Q000378:metabolism; D007328:Insulin / Q000008:administration & dosage*; D007700:Kinetics; D008962:Models, Theoretical; D010100:Oxygen / Q000737:chemistry* / Q000378:metabolism; D012996:Solutions
chemical_list: D005942:Gluconates; D007328:Insulin; D012996:Solutions; D005947:Glucose; C030691:gluconic acid; D010100:Oxygen
keywords: Enzymatic reaction; Gluconic acid; Glucose-sensitive membrane; Homotopy perturbation method; Insulin delivery; Oxygen; Reaction diffusion equation