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Mass-Preserving Approximation of a Chemotaxis Multi-Domain Transmission Model for Microfluidic Chips

Author

Listed:
  • Elishan Christian Braun

    (Department Mathematics, University of Rome 3, 00146 Rome, Italy
    These authors contributed equally to this work.)

  • Gabriella Bretti

    (Istituto per le Applicazioni del Calcolo “M.Picone”, 00185 Rome, Italy
    These authors contributed equally to this work.)

  • Roberto Natalini

    (Istituto per le Applicazioni del Calcolo “M.Picone”, 00185 Rome, Italy
    These authors contributed equally to this work.)

Abstract

The present work is inspired by the recent developments in laboratory experiments made on chips, where the culturing of multiple cell species was possible. The model is based on coupled reaction-diffusion-transport equations with chemotaxis and takes into account the interactions among cell populations and the possibility of drug administration for drug testing effects. Our effort is devoted to the development of a simulation tool that is able to reproduce the chemotactic movement and the interactions between different cell species (immune and cancer cells) living in a microfluidic chip environment. The main issues faced in this work are the introduction of mass-preserving and positivity-preserving conditions, involving the balancing of incoming and outgoing fluxes passing through interfaces between 2D and 1D domains of the chip and the development of mass-preserving and positivity preserving numerical conditions at the external boundaries and at the interfaces between 2D and 1D domains.

Suggested Citation

  • Elishan Christian Braun & Gabriella Bretti & Roberto Natalini, 2021. "Mass-Preserving Approximation of a Chemotaxis Multi-Domain Transmission Model for Microfluidic Chips," Mathematics, MDPI, vol. 9(6), pages 1-34, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:688-:d:522393
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    References listed on IDEAS

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    1. Ezio Di Costanzo & Vincenzo Ingangi & Claudia Angelini & Maria Francesca Carfora & Maria Vincenza Carriero & Roberto Natalini, 2016. "A Macroscopic Mathematical Model for Cell Migration Assays Using a Real-Time Cell Analysis," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-20, September.
    2. Casimir Emako & Charlène Gayrard & Axel Buguin & Luís Neves de Almeida & Nicolas Vauchelet, 2016. "Traveling Pulses for a Two-Species Chemotaxis Model," PLOS Computational Biology, Public Library of Science, vol. 12(4), pages 1-22, April.
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    Cited by:

    1. Fasma Diele, 2022. "Differential Equation Models in Applied Mathematics: Theoretical and Numerical Challenges," Mathematics, MDPI, vol. 10(2), pages 1-3, January.

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