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Progress in Industrial Mathematics at ECMI 2012 pp 229–236Cite as

Modelling a Competitive Antibody/Antigen Chemical Reaction that Occurs in the Fluorescence Capillary-Fill Device

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Part of the book series: Mathematics in Industry ((TECMI,volume 19))

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 as a pair of coupled singular integro-differential equations which is solved by a product integration method. Some numerical results based on real data are presented.

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References

  1. Badley, R.A., Drake, R.A.L., Shanks, I.A., Smith, A.M., Stephenson, P.R.: Optical biosensors for immunoassays, the fluorescence capillary-fill device. Philos. Trans. R. Soc. Lond. Ser. B 316, 143–160 (1987)

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  2. Jones, S., Jumarhon, B., McKee, S., Scott, J.A.: A mathematical model of a biosensor. J. Eng. Math. 30, 321–337 (1996)

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  3. Rebelo, M., Diogo, T., McKee, S.: A mathematical treatment of the fluorescence capillary-fill device. SIAM J. Appl. Math. 71(4), 1081–1112 (2012)

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Acknowledgements

The authors acknowledge support from Fundação para a Ciência e a Tecnologia, Portugal, through Project PTDC/MAT/101867/2008.

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Authors and Affiliations

  1. Department of Mathematics, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Monte de Caparica, 2829-516, Caparica, Portugal

    Magda Rebelo

  2. CEMAT-Instituto Superior Técnico, Lisbon, Portugal

    Magda Rebelo

  3. CEMAT-Department of Mathematics, Instituto Superior Técnico, Lisbon, Portugal

    Teresa Diogo

  4. Department of Mathematics and Statistics, University of Strathclyde, Glasgow, Scotland, UK

    Sean McKee

Authors
  1. Magda Rebelo
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  2. Teresa Diogo
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  3. Sean McKee
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Corresponding author

Correspondence to Magda Rebelo .

Editor information

Editors and Affiliations

  1. Lunds Universitet, Centre for Mathematical Sciences, Lund, Sweden

    Magnus Fontes

  2. Bergische Universität Wuppertal, Applied Math. and Numerical Analysis, Wuppertal, Germany

    Michael Günther

  3. Lehrstuhl für Angew.Math. 1, Friedrich-Alexander-Universität Erlangen, Department of Mathematics, Erlangen, Germany

    Nicole Marheineke

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© 2014 Springer International Publishing Switzerland

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Rebelo, M., Diogo, T., McKee, S. (2014). Modelling a Competitive Antibody/Antigen Chemical Reaction that Occurs in the Fluorescence Capillary-Fill Device. In: Fontes, M., Günther, M., Marheineke, N. (eds) Progress in Industrial Mathematics at ECMI 2012. Mathematics in Industry(), vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-05365-3_31

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