A mathematical treatment of the fluorescence capillary-fill device

Magda Rebelo, Teresa Diogo, Sean McKee

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Abstract

A mathematical model in the form of two coupled diffusion equations is provided
for a competitive chemical reaction between an antigen and a labelled antigen for antibody sites on a cell wall; boundary conditions are such that the problem is both nonlinear and nonlocal. This is then re-characterized 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.
Original languageEnglish
Pages (from-to)1081-1112
Number of pages32
JournalSIAM Journal on Applied Mathematics
Volume72
Issue number4
Early online date15 Aug 2012
DOIs
Publication statusPublished - 2012

Keywords

  • mathematical model
  • capillary-fill device
  • antibody-antigen
  • Volterra equations
  • existence and uniqueness
  • asymptotic results
  • regular perturbation
  • numerical approximation

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