Skip to content

Research at St Andrews

Mathematical modelling of radiotherapy strategies for early breast cancer

Research output: Contribution to journalArticle


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

School/Research organisations


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
Issue number1
Publication statusPublished - Jul 2006

    Research areas

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

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. Learning-induced switching costs in a parasitoid can maintain diversity of host aphid phenotypes although biocontrol is destabilized under abiotic stress

    Preedy, K., Chaplain, M. A. J., Leybourne, D., Marion, G. & Karley, A., 30 Mar 2020, In : Journal of Animal Ecology. Early View

    Research output: Contribution to journalArticle

  2. Bridging the gap between individual-based and continuum models of growing cell populations

    Chaplain, M. A. J., Lorenzi, T. & Macfarlane, F. R., Jan 2020, In : Journal of Mathematical Biology. 80, 1-2, p. 343-371

    Research output: Contribution to journalArticle

  3. Discrete and continuum phenotype-structured models for the evolution of cancer cell populations under chemotherapy

    Stace, R. E. A., Stiehl, T., Chaplain, M. A. J., Marciniak-Czochra, A. & Lorenzi, T., 2020, In : Mathematical Modelling of Natural Phenomena. 15, 22 p., 14.

    Research output: Contribution to journalArticle

Related by journal

  1. Journal of Theoretical Biology (Journal)

    Mark Andrew Joseph Chaplain (Editor)
    10 Apr 2017 → …

    Activity: Publication peer-review and editorial work typesEditor of research journal

Related by journal

  1. Consistency and identifiability of the polymorphism-aware phylogenetic models

    Borges, R. & Kosiol, C., 7 Feb 2020, In : Journal of Theoretical Biology. 486, p. 1-6 6 p., 110074.

    Research output: Contribution to journalArticle

  2. A theory for investment across defences triggered at different stages of a predator-prey encounter

    Wang, L., Ruxton, G. D., Cornell, S. J., Speed, M. P. & Broom, M., 21 Jul 2019, In : Journal of Theoretical Biology. 473, p. 9-19 11 p.

    Research output: Contribution to journalArticle

  3. Spatial-stochastic modelling of synthetic gene regulatory networks

    Macnamara, C. K., Mitchell, E. & Chaplain, M. A. J., 10 Feb 2019, In : Journal of Theoretical Biology. In press

    Research output: Contribution to journalArticle

  4. Approximate Bayesian computation reveals the importance of repeated measurements for parameterising cell-based models of growing tissues

    Kursawe, J., Baker, R. E. & Fletcher, A. G., 14 Apr 2018, In : Journal of Theoretical Biology. 443, p. 66-81 16 p.

    Research output: Contribution to journalArticle

ID: 206434049