A Mathematical Treatment of the Fluorescence Capillary-Fill Device
Abstract
A mathematical model in the form of two coupled diffusion equations is provided for a competitive chemical reaction between an antigen and a labeled antigen for antibody sites on a cell wall; boundary conditions are such that the problem is both nonlinear and nonlocal. This is then recharacterized first as a pair of coupled singular integro-differential equations and then as a system of four Volterra integral equations. The latter permits a proof of existence and uniqueness of the solution of the original problem. Small and large time asymptotic solutions are derived and, from the first characterization, a regular perturbation solution is obtained. Numerical schemes are briefly discussed and graphical results are presented for human immunoglobulin.
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© 2012, Society for Industrial and Applied Mathematics.
History
Submitted: 8 July 2011
Accepted: 9 April 2012
Published online: 15 August 2012
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Cited By
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- Modelling a Competitive Antibody/Antigen Chemical Reaction that Occurs in the Fluorescence Capillary-Fill DeviceProgress in Industrial Mathematics at ECMI 2012 | 27 March 2014
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