Tissue Radiation Response with Maximum Tsallis Entropy

The expression of survival factors for radiation damaged cells is currently based on probabilistic assumptions and experimentally fitted for each tumor, radiation, and conditions. Here, we show how the simplest of these radiobiological models can be derived from the maximum entropy principle of the classical Boltzmann-Gibbs expression. We extend this derivation using the Tsallis entropy and a cutoff hypothesis, motivated by clinical observations. The obtained expression shows a remarkable agreement with the experimental data found in the literature.

Figure 1

Survival fraction $F_s$ as a function of the rescaled dose $1-D/D_0$ for different tissues: intestinal stem cells, Chinese hamster cells, human melanoma, human kidney cells, and cultured mammalian cells under different irradiation conditions detailed in 17, 18, 19, 20, 21. Various shapes represent tissues whereas each color points out different radiation conditions. Five solids lines represent fitting to experimental data, detailed in 23.

Figure 2

Normalized survival fractions $(F_s{)}^{1/\gamma }$ as a function of the rescaled radiation dose, $1-D/D_0$ for different tissues: intestinal stem cells (■), chinese hamster cells (●), human melanoma (▴), human kidney cells (▾), and cultured mammalian cells (◆) under different irradiation conditions detailed in 17, 18, 19, 20, 21 and grouped in 23. The straight line shown is $y=x$.

Figure 3

Comparison between the LQ model best fit ($\alpha =0.167\pm 0.015{\mathrm{Gy}}^{-1}$ and $\beta =0.0205\pm 0.0015{\mathrm{Gy}}^{-2}$) reported in 24 and our model fitted to $\gamma =5.0\pm 0.4$ and $D_0=19.4\pm 0.4\mathrm{Gy}$ for the cell line CHO AA8 under 250 k-Vp x rays.