A lung tumour is treated by external-beam radiotherapy

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Nuclear medicine, dosimetry and radiotherapy · Nuclear medicine, dosimetry and radiotherapy

Life at Thermal Energy, Ch Echoes, precession and the therapeutic beam

Problem

A lung tumour is treated by external-beam radiotherapy. Both the tumour and the late-responding healthy lung tissue obey the linear-quadratic survival law ln⁡S=−(αLQD+βLQD2)\ln\mathcal{S} = -(\alpha_{\rm LQ}\mathcal{D} + \beta_{\rm LQ}\mathcal{D}^2) for the dose D\mathcal{D} (in Gy) delivered in a single fraction, and the losses ln⁡S\ln\mathcal{S} from successive fractions simply add (each fraction is separated in time so that surviving cells fully repair their lesser, non-lethal damage before the next one, and neither tissue regrows during the course). The tumour has αLQ=0.35 Gy−1\alpha_{\rm LQ} = 0.35\,\mathrm{Gy^{-1}}, βLQ=0.035 Gy−2\beta_{\rm LQ} = 0.035\,\mathrm{Gy^{-2}}; the late-responding lung tissue has αLQ=0.18 Gy−1\alpha_{\rm LQ} = 0.18\,\mathrm{Gy^{-1}}, βLQ=0.045 Gy−2\beta_{\rm LQ} = 0.045\,\mathrm{Gy^{-2}}. ((a)) A standard schedule delivers 2020 fractions of 3.0 Gy3.0\,\mathrm{Gy} each. Find ln⁡S\ln\mathcal{S} for the tumour and for the late-responding tissue after the full course. ((b)) An oncologist proposes delivering the same total tumour kill in only 55 fractions. Find the dose per fraction this requires. ((c)) Find ln⁡S\ln\mathcal{S} for the late-responding tissue under this 55-fraction schedule, and state whether it is more or less damaging to that tissue than the standard schedule, for the same tumour kill.

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