  Cancer is a heterogeneous disease and tumours of the same type can differ
greatly at the genetic and phenotypic levels. Understanding how these
differences impact sensitivity to treatment is an essential step towards
patient-specific treatment design. In this paper, we investigate how two
different mechanisms for growth control may affect tumour cell responses to
fractionated radiotherapy (RT) by extending an existing ordinary differential
equation model of tumour growth. In the absence of treatment, this model
distinguishes between growth arrest due to nutrient insufficiency and
competition for space and exhibits three growth regimes: nutrient-limited (NL),
space limited (SL) and bistable (BS), where both mechanisms for growth arrest
coexist. We study the effect of RT for tumours in each regime, finding that
tumours in the SL regime typically respond best to RT, while tumours in the BS
regime typically respond worst to RT. For tumours in each regime, we also
identify the biological processes that may explain positive and negative
treatment outcomes and the dosing regimen which maximises the reduction in
tumour burden.
