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Numerical modeling of oxygen diffusion in cells with Michaelis-Menten uptake kinetics

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Abstract

A class of singular boundary value problems is studied, which models the oxygen diffusion in a spherical cell with Michaelis-Menten uptake kinetics. Suitable singular Cauchy problems are considered in order to determine one-parameter families of solutions in the neighborhood of the singularities. These families are then used to construct stable shooting algorithms for the solution of the considered problems and also to propose a variable substitution in order to improve the convergence order of the finite difference methods. Numerical results are presented and discussed.

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Authors and Affiliations

  1. Cemat and Dep. Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

    Pedro M. Lima

  2. Cemat, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

    Luisa Morgado

  3. Departamento de Matemática, Universidade de Trás-os-Montes e Alto Douro, Quinta de Prados, 5001-801, Vila Real, Portugal

    Luisa Morgado

Authors
  1. Pedro M. Lima
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  2. Luisa Morgado
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Correspondence to Pedro M. Lima.

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Lima, P.M., Morgado, L. Numerical modeling of oxygen diffusion in cells with Michaelis-Menten uptake kinetics. J Math Chem 48, 145–158 (2010). https://doi.org/10.1007/s10910-009-9646-x

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  • DOI: https://doi.org/10.1007/s10910-009-9646-x

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