A radiobiology laboratory describes the surviving fraction of a tumour cell line…

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

Life at Thermal Energy, Ch Radiation in tissue: interaction, dose and risk

Problem

A radiobiology laboratory describes the surviving fraction of a tumour cell line after a single dose using the linear-quadratic model

\ln\mathcal{S} = -(\alpha_{\rm LQ}\mathcal{D} + \beta_{\rm LQ}\mathcal{D}^2)

, with

\alpha_{\rm LQ}=0.25\,\mathrm{Gy^{-1}}

and

\beta_{\rm LQ}=0.025\,\mathrm{Gy^{-2}}

for this cell line. ((a)) Calculate the surviving fraction

\mathcal{S}

after a single dose of

3\,\mathrm{Gy}

. ((b)) Predict the surviving fraction after a single dose of

6\,\mathrm{Gy}

, twice the first dose. ((c)) A technician argues that, because doubling a dose should double the cell killing, the surviving fraction at

6\,\mathrm{Gy}

should equal

[\mathcal{S}(3\,\mathrm{Gy})]^2

. Evaluate this claim numerically and explain why it is wrong.

Browse the problem library