IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i12p1376-d574620.html
   My bibliography  Save this article

Modeling Interactions among Migration, Growth and Pressure in Tumor Dynamics

Author

Listed:
  • Beatriz Blanco

    (Department of Structural Mechanics, University of Granada, 18071 Granada, Spain
    Instituto de Investigación Biosanitaria, ibs.GRANADA, 18012 Granada, Spain)

  • Juan Campos

    (Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
    Research Unit “Modelling Nature” (MNat), Universidad de Granada, 18071 Granada, Spain)

  • Juan Melchor

    (Instituto de Investigación Biosanitaria, ibs.GRANADA, 18012 Granada, Spain
    Research Unit “Modelling Nature” (MNat), Universidad de Granada, 18071 Granada, Spain
    Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain)

  • Juan Soler

    (Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
    Research Unit “Modelling Nature” (MNat), Universidad de Granada, 18071 Granada, Spain)

Abstract

What are the biomechanical implications in the dynamics and evolution of a growing solid tumor? Although the analysis of some of the biochemical aspects related to the signaling pathways involved in the spread of tumors has advanced notably in recent times, their feedback with the mechanical aspects is a crucial challenge for a global understanding of the problem. The aim of this paper is to try to illustrate the role and the interaction between some evolutionary processes (growth, pressure, homeostasis, elasticity, or dispersion by flux-saturated and porous media) that lead to collective cell dynamics and defines a propagation front that is in agreement with the experimental data. The treatment of these topics is approached mainly from the point of view of the modeling and the numerical approach of the resulting system of partial differential equations, which can be placed in the context of the Hele-Shaw-type models. This study proves that local growth terms related to homeostatic pressure give rise to retrograde diffusion phenomena, which compete against migration through flux-saturated dispersion terms.

Suggested Citation

  • Beatriz Blanco & Juan Campos & Juan Melchor & Juan Soler, 2021. "Modeling Interactions among Migration, Growth and Pressure in Tumor Dynamics," Mathematics, MDPI, vol. 9(12), pages 1-19, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1376-:d:574620
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/12/1376/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/12/1376/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Thomas B. Kornberg & Lilach Gilboa, 2015. "Nanotubes in the niche," Nature, Nature, vol. 523(7560), pages 292-293, July.
    2. Martina Conte & Sergio Casas-Tintò & Juan Soler, 2021. "Modeling invasion patterns in the glioblastoma battlefield," PLOS Computational Biology, Public Library of Science, vol. 17(1), pages 1-20, January.
    3. Marcos Julián Cardozo & Luisa Sánchez-Arrones & África Sandonis & Cristina Sánchez-Camacho & Gaia Gestri & Stephen W. Wilson & Isabel Guerrero & Paola Bovolenta, 2014. "Cdon acts as a Hedgehog decoy receptor during proximal-distal patterning of the optic vesicle," Nature Communications, Nature, vol. 5(1), pages 1-13, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1376-:d:574620. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.