A radiology teaching plot shows the mass attenuation coefficient against photon…

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

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

Problem

A radiology teaching plot shows the mass attenuation coefficient μ/ρ\mu/\rho against photon energy for cortical bone and for soft tissue. Two points read off the plot are: at 30 keV30\,\mathrm{keV}, soft tissue μ/ρ=0.3790 cm2 g−1\mu/\rho = 0.3790\,\mathrm{cm^2\,g^{-1}} and bone μ/ρ=1.331 cm2 g−1\mu/\rho = 1.331\,\mathrm{cm^2\,g^{-1}}; at 150 keV150\,\mathrm{keV}, soft tissue μ/ρ=0.1492 cm2 g−1\mu/\rho = 0.1492\,\mathrm{cm^2\,g^{-1}} and bone μ/ρ=0.1480 cm2 g−1\mu/\rho = 0.1480\,\mathrm{cm^2\,g^{-1}}. ((a)) Compute the ratio (bone attenuation per gram)/(soft-tissue attenuation per gram) at each energy, and explain in terms of the two photon interactions why the ratio falls as energy rises. ((b)) A second plot, of surviving fraction S\mathcal{S} against dose D\mathcal{D} on a semi-logarithmic axis for a cell line obeying ln⁡S=−(αLQD+βLQD2)\ln\mathcal{S} = -(\alpha_{\rm LQ}\mathcal{D}+\beta_{\rm LQ}\mathcal{D}^2), gives two readable points: S=0.76\mathcal{S}=0.76 at D=1 Gy\mathcal{D}=1\,\mathrm{Gy} and S=0.38\mathcal{S}=0.38 at D=3 Gy\mathcal{D}=3\,\mathrm{Gy}. Use these to find αLQ\alpha_{\rm LQ} and βLQ\beta_{\rm LQ}, and predict S\mathcal{S} at 5 Gy5\,\mathrm{Gy}.

Browse the problem library