Range versus density dependence of proton-therapy beams in human tissues

Range versus density dependence of proton-therapy beams in human tissues is discussed in the paper. The main attention is paid to energy-scaling of simple fitting functions that fit the range-to-density dependence for single proton-beam energies. These functions have been found by fitting ranges obtained with the aid of the Monte Carlo module of SRIM2013. The simulations have been run for 28 human tissues at 8 energies from 60 MeV to 220 MeV. It has been shown that a fitting function that depends solely on the target density can be found at each proton-beam energy. After the energy-scaling, the fitted ranges have been compared with the Monte Carlo ranges. We conclude that the final energy-scaled fitting function provides ranges within 0.4% of the Monte Carlo range (on average), which is less than 30% of the natural range-straggling (1.4% of the Monte Carlo range on average). The worst data-point has an off-set from the fitting function less than 1.7% of the Monte Carlo range.