A new mathematical model for avascular tumour growth

Jonathan A. Sherratt, Mark A. J. Chaplain

    Research output: Contribution to journalArticle

    168 Citations (Scopus)

    Abstract

    The early development of solid tumours has been extensively studied, both experimentally via the multicellular spheroid assay, and theoretically using mathematical modelling. The vast majority of previous models apply specifically to multicell spheroids, which have a characteristic structure of a proliferating rim and a necrotic core, separated by a band of quiescent cells. Many previous models represent these as discrete layers, separated by moving boundaries. Here, the authors develop a new model, formulated in terms of continuum densities of proliferating, quiescent and necrotic cells, together with a generic nutrient/growth factor. The model is oriented towards an in vivo rather than in vitro setting, and crucially allows for nutrient supply from underlying tissue, which will arise in the two-dimensional setting of a tumour growing within an epithelium. In addition, the model involves a new representation of cell movement, which reflects contact inhibition of migration. Model solutions are able to reproduce the classic three layer structure familiar from multicellular spheroids, but also show that new behaviour can occur as a result of the nutrient supply from underlying tissue. The authors analyse these different solution types by approximate solution of the travelling wave equations, enabling a detailed classification of wave front solutions.
    Original languageEnglish
    Pages (from-to)291-312
    Number of pages22
    JournalJournal of Mathematical Biology
    Volume43
    Issue number4
    DOIs
    Publication statusPublished - 2001

    Fingerprint

    Tumor Growth
    Cellular Spheroids
    Tumors
    Theoretical Models
    mathematical models
    Mathematical Model
    Mathematical models
    Food
    neoplasms
    Growth
    Nutrients
    Contact Inhibition
    Neoplasms
    Cell Movement
    Tumor
    Intercellular Signaling Peptides and Proteins
    Cell
    nutrients
    Epithelium
    Model

    Keywords

    • Mathematical modelling
    • Avascular tumour
    • Reaction-diffusion
    • Travelling waves
    • Cancer

    Cite this

    Sherratt, Jonathan A. ; Chaplain, Mark A. J. / A new mathematical model for avascular tumour growth. In: Journal of Mathematical Biology. 2001 ; Vol. 43, No. 4. pp. 291-312.
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    A new mathematical model for avascular tumour growth. / Sherratt, Jonathan A.; Chaplain, Mark A. J.

    In: Journal of Mathematical Biology, Vol. 43, No. 4, 2001, p. 291-312.

    Research output: Contribution to journalArticle

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