A mathematical treatment of the fluorescence capillary-fill device

Magda Rebelo, Teresa Diogo, Sean McKee

Research output: Contribution to journalArticle

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.
LanguageEnglish
Pages1081-1112
Number of pages32
JournalSIAM Journal on Applied Mathematics
Volume72
Issue number4
Early online date15 Aug 2012
DOIs
Publication statusPublished - 2012

Fingerprint

Antigens
Fluorescence
Large Time Asymptotics
Perturbation Solution
Immunoglobulin
Singular Equation
Integrodifferential equations
Volterra Integral Equations
Cell Wall
Asymptotic Solution
Antibody
Chemical Reaction
Antibodies
Diffusion equation
Integro-differential Equation
Numerical Scheme
Integral equations
Chemical reactions
Existence and Uniqueness
Cells

Keywords

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

Cite this

Rebelo, Magda ; Diogo, Teresa ; McKee, Sean. / A mathematical treatment of the fluorescence capillary-fill device. In: SIAM Journal on Applied Mathematics . 2012 ; Vol. 72, No. 4. pp. 1081-1112.
@article{7b2b54a67d60410697b3eec6e6e68380,
title = "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 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.",
keywords = "mathematical model, capillary-fill device, antibody-antigen, Volterra equations, existence and uniqueness, asymptotic results, regular perturbation, numerical approximation",
author = "Magda Rebelo and Teresa Diogo and Sean McKee",
note = "new copy of document added",
year = "2012",
doi = "10.1137/110839965",
language = "English",
volume = "72",
pages = "1081--1112",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
number = "4",

}

A mathematical treatment of the fluorescence capillary-fill device. / Rebelo, Magda; Diogo, Teresa; McKee, Sean.

In: SIAM Journal on Applied Mathematics , Vol. 72, No. 4, 2012, p. 1081-1112.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A mathematical treatment of the fluorescence capillary-fill device

AU - Rebelo, Magda

AU - Diogo, Teresa

AU - McKee, Sean

N1 - new copy of document added

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - mathematical model

KW - capillary-fill device

KW - antibody-antigen

KW - Volterra equations

KW - existence and uniqueness

KW - asymptotic results

KW - regular perturbation

KW - numerical approximation

UR - http://epubs.siam.org/siap/resource/1/smjmap

U2 - 10.1137/110839965

DO - 10.1137/110839965

M3 - Article

VL - 72

SP - 1081

EP - 1112

JO - SIAM Journal on Applied Mathematics

T2 - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 4

ER -