Models of tumour cell lines and effects of anticancer drugs

  • Britta Basse (University of Canterbury Christchurch, Biomathematics Research Centre, New Zealand)
A3 01 (Sophus-Lie room)


We have a system of non-linear partial differential equations, each equation representing a different phase of the cell cycle (G1, S, G2, M). Our independent variables are x, relative DNA content, and t, time in hours. In the equation for G1-phase, a non-local term represents newly divided cells from M-phase and gives rise to steady DNA distributions as seen experimentally in cell lines unperturbed by cancer treatment.

We can use this system as a starting point for modelling cancer treatment by changing appropriate model parameters. In particular we consider paclitaxel, an anticancer drug that halts cell division and induces cell death in tumor cell populations. The model enables us to quantify the rate of cell death and the subsequent rate of DNA degradation. These rates are currently unable to be obtained experimentally.