An imaging-physics plot gives against photon energy for fat and for soft tissue

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

An imaging-physics plot gives μ/ρ\mu/\rho against photon energy for fat and for soft tissue. Two readable points 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 fat μ/ρ=0.3063 cm2 g−1\mu/\rho = 0.3063\,\mathrm{cm^2\,g^{-1}}; at 1 MeV1\,\mathrm{MeV}, soft tissue μ/ρ=0.07006 cm2 g−1\mu/\rho = 0.07006\,\mathrm{cm^2\,g^{-1}} and fat μ/ρ=0.07078 cm2 g−1\mu/\rho = 0.07078\,\mathrm{cm^2\,g^{-1}}. ((a)) Compute the ratio (fat attenuation per gram)/(soft-tissue attenuation per gram) at each energy, and explain the trend using the energy dependence of the two photon interactions. ((b)) A survival plot for a second cell line gives S=0.55\mathcal{S}=0.55 at D=2 Gy\mathcal{D}=2\,\mathrm{Gy} and S=0.045\mathcal{S}=0.045 at D=6 Gy\mathcal{D}=6\,\mathrm{Gy}, obeying ln⁡S=−(αLQD+βLQD2)\ln\mathcal{S} = -(\alpha_{\rm LQ}\mathcal{D}+\beta_{\rm LQ}\mathcal{D}^2). Find αLQ\alpha_{\rm LQ} and βLQ\beta_{\rm LQ} from these two points, and predict S\mathcal{S} at 4 Gy4\,\mathrm{Gy}.

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