Mathematical modelling of radiotherapy strategies for early breast cancer

Heiko Enderling, Alexander R. A. Anderson, Mark A. J. Chaplain, Alastair J. Munro, Jayant S. Vaidya

    Research output: Contribution to journalArticle

    56 Citations (Scopus)

    Abstract

    Targeted intraoperative radiotherapy (Targit) is a new concept of partial breast irradiation where single fraction radiotherapy is delivered directly to the tumour bed. Apart from logistic advantages, this strategy minimizes the risk of missing the tumour bed and avoids delay between surgery and radiotherapy. It is presently being compared with the standard fractionated external beam radiotherapy (EBRT) in randomized trials. In this paper we present a mathematical model for the growth and invasion of a solid tumour into a domain of tissue (in this case breast tissue), and then a model for surgery and radiation treatment of this tumour. We use the established linear-quadratic (LQ) model to compute the survival probabilities for both tumour cells and irradiated breast tissue and then simulate the effects of conventional EBRT and Targit. True local recurrence of the tumour could arise either from stray tumour cells, or the tumour bed that harbours morphologically normal cells having a predisposition to genetic changes, such as a loss of heterozygosity (LOH) in genes that are crucial for tumourigenesis, e.g. tumour suppressor genes (TSGs). Our mathematical model predicts that the single high dose of radiotherapy delivered by Targit would result in eliminating all these sources of recurrence, whereas the fractionated EBRT would eliminate stray tumour cells, but allow (by virtue of its very schedule) the cells with LOH in TSGs or cell-cycle checkpoint genes to pass on low-dose radiation-induced DNA damage and consequently mutations that may favour the development of a new tumour. The mathematical model presented here is an initial attempt to model a biologically complex phenomenon that has until now received little attention in the literature and provides a ‘proof of principle’ that it is possible to produce clinically testable hypotheses on the effects of different approaches of radiotherapy for breast cancer.
    Original languageEnglish
    Pages (from-to)158-171
    Number of pages14
    JournalJournal of Theoretical Biology
    Volume241
    Issue number1
    DOIs
    Publication statusPublished - Jul 2006

    Fingerprint

    Radiotherapy
    radiotherapy
    Breast Cancer
    Mathematical Modeling
    breast neoplasms
    Tumors
    Tumor
    mathematical models
    Breast Neoplasms
    neoplasms
    Neoplasms
    breasts
    Genes
    Cells
    Breast
    tumor suppressor genes
    Theoretical Models
    Cell
    Loss of Heterozygosity
    Gene

    Keywords

    • Mathematical modelling
    • Breast cancer
    • Radiotherapy
    • Targit
    • Intraoperative radiotherapy
    • Targeted intraoperative radiotherapy (Targit)

    Cite this

    Enderling, H., Anderson, A. R. A., Chaplain, M. A. J., Munro, A. J., & Vaidya, J. S. (2006). Mathematical modelling of radiotherapy strategies for early breast cancer. Journal of Theoretical Biology, 241(1), 158-171. https://doi.org/10.1016/j.jtbi.2005.11.015
    Enderling, Heiko ; Anderson, Alexander R. A. ; Chaplain, Mark A. J. ; Munro, Alastair J. ; Vaidya, Jayant S. / Mathematical modelling of radiotherapy strategies for early breast cancer. In: Journal of Theoretical Biology. 2006 ; Vol. 241, No. 1. pp. 158-171.
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    Enderling, H, Anderson, ARA, Chaplain, MAJ, Munro, AJ & Vaidya, JS 2006, 'Mathematical modelling of radiotherapy strategies for early breast cancer', Journal of Theoretical Biology, vol. 241, no. 1, pp. 158-171. https://doi.org/10.1016/j.jtbi.2005.11.015

    Mathematical modelling of radiotherapy strategies for early breast cancer. / Enderling, Heiko; Anderson, Alexander R. A.; Chaplain, Mark A. J.; Munro, Alastair J.; Vaidya, Jayant S.

    In: Journal of Theoretical Biology, Vol. 241, No. 1, 07.2006, p. 158-171.

    Research output: Contribution to journalArticle

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