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Radiation carcinogenesis modelling for risk of treatment-related second tumours following radiotherapy

K A Lindsay1, E G Wheldon1, C Deehan2 and T E Wheldon3,4

1Department of Mathematics, University Gardens, University of Glasgow, Glasgow G12 8QW, 2Department of Physics, Royal Marsden Hospital, Fulham Road, London, 3Department of Radiation Oncology, Glasgow University, CRC Beatson Labs, Glasgow G61 1BD, and 4Department of Clinical Physics, Beatson Oncology Centre, Western Infirmary, Glasgow G11 6NT, UK



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  		Figure 1. Two-stage model of carcinogenesis is based on populations P0(t) of non-mutated stem cells and P1(t) of one-mutant stem cells. Cells survive dose D with probability e-{alpha}D-ßD2 and, independently, are not mutated with probability e-{gamma}D-{delta}D2. Dashed lines show pathways that are active as a result of irradiation.

 


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  		Figure 2. Percentage incidence of carcinogenesis 20 years after irradiation is illustrated in (A) for various levels of cell repopulation, in (B) for various values of the intrinsic cellular radiosensitivities {alpha} and ß with ß={alpha}/10, in (C) for various values of the spontaneous mutation rate µ, and in (D) for various values of the mutational radiosensitivities {gamma} and {delta} with {delta}={gamma}/10. In each of (A), (B), (C) and (D) only one parameter changes while the others take their values from Table 1Go.

 


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  		Figure 3. (a), (b) and (c) each illustrate a dose–volume histogram (DVH) on the left with its respective treatment plan on the right. In each case, the DVH for the tumour (T) is shown on the far right of the graph, along with the DVHs for the spinal cord (S, dashed line), left lung (L, solid line on left) and right lung (R, dotted line).

 




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